Daily Papers

Large language models (LLM) have been attracting much attention from the community recently, due to their remarkable performance in all kinds of downstream tasks. According to the well-known scaling law, scaling up a dense LLM enhances its capabilities, but also significantly increases the computational complexity. Mixture-of-Experts (MoE) models address that by allowing the model size to grow without substantially raising training or inference costs. Yet MoE models face challenges regarding knowledge sharing among experts, making their performance somehow sensitive to routing accuracy. To tackle that, previous works introduced shared experts and combined their outputs with those of the top K routed experts in an ``addition'' manner. In this paper, inspired by collective matrix factorization to learn shared knowledge among data, we propose CartesianMoE, which implements more effective knowledge sharing among experts in more like a ``multiplication'' manner. Extensive experimental results indicate that CartesianMoE outperforms previous MoE models for building LLMs, in terms of both perplexity and downstream task performance. And we also find that CartesianMoE achieves better expert routing robustness.

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this task; however, these methods often struggle with scalability and can be time-consuming when applied to large-scale dynamic graphs. Moreover, they tend to lack robustness and are vulnerable to real-world noisy data. To address these issues, we make three key contributions. First, to improve scalability, we propose temporal separated matrix factorization, where a single matrix is divided into multiple smaller matrices for independent factorization, resulting in faster computation. Second, to improve robustness, we introduce bi-clustering regularization, which jointly optimizes graph embedding and clustering, thereby filtering out noisy features from the graph embeddings. Third, to further enhance effectiveness and efficiency, we propose selective embedding updating, where we update only the embeddings of dynamic nodes while the embeddings of static nodes are fixed among different timestamps. Experimental results on six synthetic and five real-world benchmarks demonstrate the scalability, robustness and effectiveness of our proposed method. Source code is available at https://github.com/Clearloveyuan/DyG-MF.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

Learning vector representations (aka. embeddings) of users and items lies at the core of modern recommender systems. Ranging from early matrix factorization to recently emerged deep learning based methods, existing efforts typically obtain a user's (or an item's) embedding by mapping from pre-existing features that describe the user (or the item), such as ID and attributes. We argue that an inherent drawback of such methods is that, the collaborative signal, which is latent in user-item interactions, is not encoded in the embedding process. As such, the resultant embeddings may not be sufficient to capture the collaborative filtering effect. In this work, we propose to integrate the user-item interactions -- more specifically the bipartite graph structure -- into the embedding process. We develop a new recommendation framework Neural Graph Collaborative Filtering (NGCF), which exploits the user-item graph structure by propagating embeddings on it. This leads to the expressive modeling of high-order connectivity in user-item graph, effectively injecting the collaborative signal into the embedding process in an explicit manner. We conduct extensive experiments on three public benchmarks, demonstrating significant improvements over several state-of-the-art models like HOP-Rec and Collaborative Memory Network. Further analysis verifies the importance of embedding propagation for learning better user and item representations, justifying the rationality and effectiveness of NGCF. Codes are available at https://github.com/xiangwang1223/neural_graph_collaborative_filtering.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nystr\"{o}m method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

Collaborative filtering (CF) plays a critical role in the development of recommender systems. Most CF methods utilize an encoder to embed users and items into the same representation space, and the Bayesian personalized ranking (BPR) loss is usually adopted as the objective function to learn informative encoders. Existing studies mainly focus on designing more powerful encoders (e.g., graph neural network) to learn better representations. However, few efforts have been devoted to investigating the desired properties of representations in CF, which is important to understand the rationale of existing CF methods and design new learning objectives. In this paper, we measure the representation quality in CF from the perspective of alignment and uniformity on the hypersphere. We first theoretically reveal the connection between the BPR loss and these two properties. Then, we empirically analyze the learning dynamics of typical CF methods in terms of quantified alignment and uniformity, which shows that better alignment or uniformity both contribute to higher recommendation performance. Based on the analyses results, a learning objective that directly optimizes these two properties is proposed, named DirectAU. We conduct extensive experiments on three public datasets, and the proposed learning framework with a simple matrix factorization model leads to significant performance improvements compared to state-of-the-art CF methods. Our implementations are publicly available at https://github.com/THUwangcy/DirectAU.

Sparse matrix factorization is the problem of approximating a matrix Z by a product of J sparse factors X^{(J)} X^{(J-1)} ldots X^{(1)}. This paper focuses on identifiability issues that appear in this problem, in view of better understanding under which sparsity constraints the problem is well-posed. We give conditions under which the problem of factorizing a matrix into two sparse factors admits a unique solution, up to unavoidable permutation and scaling equivalences. Our general framework considers an arbitrary family of prescribed sparsity patterns, allowing us to capture more structured notions of sparsity than simply the count of nonzero entries. These conditions are shown to be related to essential uniqueness of exact matrix decomposition into a sum of rank-one matrices, with structured sparsity constraints. In particular, in the case of fixed-support sparse matrix factorization, we give a general sufficient condition for identifiability based on rank-one matrix completability, and we derive from it a completion algorithm that can verify if this sufficient condition is satisfied, and recover the entries in the two sparse factors if this is the case. A companion paper further exploits these conditions to derive identifiability properties and theoretically sound factorization methods for multi-layer sparse matrix factorization with support constraints associated to some well-known fast transforms such as the Hadamard or the Discrete Fourier Transforms.

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

Synthetic data has become increasingly important for training large language models, especially when real data is scarce, expensive, or privacy-sensitive. Many such generation tasks require coordinated multi-agent workflows, where specialized agents collaborate to produce data that is higher quality, more diverse, and structurally richer. However, existing frameworks for multi-agent synthesis often depend on a centralized orchestrator, creating scalability bottlenecks, or are hardcoded for specific domains, limiting flexibility. We present Matrix, a decentralized framework that represents both control and data flow as serialized messages passed through distributed queues. This peer-to-peer design eliminates the central orchestrator. Each task progresses independently through lightweight agents, while compute-intensive operations, such as LLM inference or containerized environments, are handled by distributed services. Built on Ray, Matrix scales to tens of thousands of concurrent agentic workflows and provides a modular, configurable design that enables easy adaptation to a wide range of data generation workflows. We evaluate Matrix across diverse synthesis scenarios, such as multi-agent collaborative dialogue, web-based reasoning data extraction, and tool-use trajectory generation in customer service environments. In all cases, Matrix achieves 2--15times higher data generation throughput under identical hardware resources, without compromising output quality.

Since the invention of word2vec, the skip-gram model has significantly advanced the research of network embedding, such as the recent emergence of the DeepWalk, LINE, PTE, and node2vec approaches. In this work, we show that all of the aforementioned models with negative sampling can be unified into the matrix factorization framework with closed forms. Our analysis and proofs reveal that: (1) DeepWalk empirically produces a low-rank transformation of a network's normalized Laplacian matrix; (2) LINE, in theory, is a special case of DeepWalk when the size of vertices' context is set to one; (3) As an extension of LINE, PTE can be viewed as the joint factorization of multiple networks' Laplacians; (4) node2vec is factorizing a matrix related to the stationary distribution and transition probability tensor of a 2nd-order random walk. We further provide the theoretical connections between skip-gram based network embedding algorithms and the theory of graph Laplacian. Finally, we present the NetMF method as well as its approximation algorithm for computing network embedding. Our method offers significant improvements over DeepWalk and LINE for conventional network mining tasks. This work lays the theoretical foundation for skip-gram based network embedding methods, leading to a better understanding of latent network representation learning.

Recently, generative recommendation has emerged as a promising paradigm, attracting significant research attention. The basic framework involves an item tokenizer, which represents each item as a sequence of codes serving as its identifier, and a generative recommender that predicts the next item by autoregressively generating the target item identifier. However, in existing methods, both the tokenizer and the recommender are typically domain-specific, limiting their ability for effective transfer or adaptation to new domains. To this end, we propose UTGRec, a Universal item Tokenization approach for transferable Generative Recommendation. Specifically, we design a universal item tokenizer for encoding rich item semantics by adapting a multimodal large language model (MLLM). By devising tree-structured codebooks, we discretize content representations into corresponding codes for item tokenization. To effectively learn the universal item tokenizer on multiple domains, we introduce two key techniques in our approach. For raw content reconstruction, we employ dual lightweight decoders to reconstruct item text and images from discrete representations to capture general knowledge embedded in the content. For collaborative knowledge integration, we assume that co-occurring items are similar and integrate collaborative signals through co-occurrence alignment and reconstruction. Finally, we present a joint learning framework to pre-train and adapt the transferable generative recommender across multiple domains. Extensive experiments on four public datasets demonstrate the superiority of UTGRec compared to both traditional and generative recommendation baselines.

In recent years, deep neural networks have yielded immense success on speech recognition, computer vision and natural language processing. However, the exploration of deep neural networks on recommender systems has received relatively less scrutiny. In this work, we strive to develop techniques based on neural networks to tackle the key problem in recommendation -- collaborative filtering -- on the basis of implicit feedback. Although some recent work has employed deep learning for recommendation, they primarily used it to model auxiliary information, such as textual descriptions of items and acoustic features of musics. When it comes to model the key factor in collaborative filtering -- the interaction between user and item features, they still resorted to matrix factorization and applied an inner product on the latent features of users and items. By replacing the inner product with a neural architecture that can learn an arbitrary function from data, we present a general framework named NCF, short for Neural network-based Collaborative Filtering. NCF is generic and can express and generalize matrix factorization under its framework. To supercharge NCF modelling with non-linearities, we propose to leverage a multi-layer perceptron to learn the user-item interaction function. Extensive experiments on two real-world datasets show significant improvements of our proposed NCF framework over the state-of-the-art methods. Empirical evidence shows that using deeper layers of neural networks offers better recommendation performance.

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables multiple autonomous agents to collaboratively estimate the smallest eigenvalue of large matrices. Each agent employs a localized neural network, refining its estimates through communication with neighboring agents. Our empirical results confirm the algorithm's convergence towards the true eigenvalue, with estimates clustered closely around the true value. Even in the presence of communication delays or network disruptions, the method demonstrates strong robustness and scalability. Theoretical analysis further validates the accuracy and stability of the proposed approach, while empirical tests highlight its efficiency and precision, surpassing traditional centralized algorithms in large-scale eigenvalue computations.

In this paper, we introduce a novel method of neural network weight compression. In our method, we store weight tensors as sparse, quantized matrix factors, whose product is computed on the fly during inference to generate the target model's weights. We use projected gradient descent methods to find quantized and sparse factorization of the weight tensors. We show that this approach can be seen as a unification of weight SVD, vector quantization, and sparse PCA. Combined with end-to-end fine-tuning our method exceeds or is on par with previous state-of-the-art methods in terms of the trade-off between accuracy and model size. Our method is applicable to both moderate compression regimes, unlike vector quantization, and extreme compression regimes.

Large language model (LLM)-enhanced recommendation models inject LLM representations into backbone recommenders to exploit rich item text without inference-time LLM cost. However, we find that existing LLM-enhanced methods significantly hinder the optimization of backbone models, resulting in high training losses that are difficult to reduce. To address it, we establish a comprehensive theoretical analysis of local optimization curvature and identify two key causes: 1) large norm disparity and 2) semantic-collaboration misaligned angular clustering of LLM representations. Guided by these insights, we propose Training-Friendly LLM-Enhanced Recommender (TF-LLMER), a lightweight framework with two key components. First, we highlight the necessity of item embedding normalization to eliminate norm-driven instability and achieve provable control over optimization conditioning. Second, we introduce Rec-PCA, a recommendation-aware dimensionality reduction method that injects collaborative structure into the representation transformation to resolve semantic-collaboration misaligned angular clustering. It jointly optimizes semantic information retention and alignment with an item-item co-occurrence graph constructed from interaction histories. The graph captures collaborative structure, and alignment is promoted by penalizing total variation over the graph. Both theory and extensive experiments demonstrate that TF-LLMER significantly outperforms state-of-the-art methods. Our code is available at https://github.com/woriazzc/TF-LLMER.

We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can theoretically blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights.

Scaling laws play an instrumental role in the sustainable improvement in model quality. Unfortunately, recommendation models to date do not exhibit such laws similar to those observed in the domain of large language models, due to the inefficiencies of their upscaling mechanisms. This limitation poses significant challenges in adapting these models to increasingly more complex real-world datasets. In this paper, we propose an effective network architecture based purely on stacked factorization machines, and a synergistic upscaling strategy, collectively dubbed Wukong, to establish a scaling law in the domain of recommendation. Wukong's unique design makes it possible to capture diverse, any-order of interactions simply through taller and wider layers. We conducted extensive evaluations on six public datasets, and our results demonstrate that Wukong consistently outperforms state-of-the-art models quality-wise. Further, we assessed Wukong's scalability on an internal, large-scale dataset. The results show that Wukong retains its superiority in quality over state-of-the-art models, while holding the scaling law across two orders of magnitude in model complexity, extending beyond 100 Gflop or equivalently up to GPT-3/LLaMa-2 scale of total training compute, where prior arts fall short.

Network embedding has been widely used in social recommendation and network analysis, such as recommendation systems and anomaly detection with graphs. However, most of previous approaches cannot handle large graphs efficiently, due to that (i) computation on graphs is often costly and (ii) the size of graph or the intermediate results of vectors could be prohibitively large, rendering it difficult to be processed on a single machine. In this paper, we propose an efficient and effective distributed algorithm for network embedding on large graphs using Apache Spark, which recursively partitions a graph into several small-sized subgraphs to capture the internal and external structural information of nodes, and then computes the network embedding for each subgraph in parallel. Finally, by aggregating the outputs on all subgraphs, we obtain the embeddings of nodes in a linear cost. After that, we demonstrate in various experiments that our proposed approach is able to handle graphs with billions of edges within a few hours and is at least 4 times faster than the state-of-the-art approaches. Besides, it achieves up to 4.25% and 4.27% improvements on link prediction and node classification tasks respectively. In the end, we deploy the proposed algorithms in two online games of Tencent with the applications of friend recommendation and item recommendation, which improve the competitors by up to 91.11% in running time and up to 12.80% in the corresponding evaluation metrics.

Developing a single foundation model with the capability to excel across diverse tasks has been a long-standing objective in the field of artificial intelligence. As the wave of general-purpose foundation models sweeps across various domains, their influence has significantly extended to the field of recommendation systems. While recent efforts have explored recommendation foundation models for various generative tasks, they often overlook crucial embedding tasks and struggle with the complexities of multi-task learning, including knowledge sharing & conflict resolution, and convergence speed inconsistencies. To address these limitations, we introduce RecFound, a generative representational learning framework for recommendation foundation models. We construct the first comprehensive dataset for recommendation foundation models covering both generative and embedding tasks across diverse scenarios. Based on this dataset, we propose a novel multi-task training scheme featuring a Task-wise Mixture of Low-rank Experts (TMoLE) to handle knowledge sharing & conflict, a Step-wise Convergence-oriented Sample Scheduler (S2Sched) to address inconsistent convergence, and a Model Merge module to balance the performance across tasks. Experiments demonstrate that RecFound achieves state-of-the-art performance across various recommendation tasks, outperforming existing baselines.

In practical scenarios, the effectiveness of sequential recommendation systems is hindered by the user cold-start problem, which arises due to limited interactions for accurately determining user preferences. Previous studies have attempted to address this issue by combining meta-learning with user and item-side information. However, these approaches face inherent challenges in modeling user preference dynamics, particularly for "minor users" who exhibit distinct preferences compared to more common or "major users." To overcome these limitations, we present a novel approach called ClusterSeq, a Meta-Learning Clustering-Based Sequential Recommender System. ClusterSeq leverages dynamic information in the user sequence to enhance item prediction accuracy, even in the absence of side information. This model preserves the preferences of minor users without being overshadowed by major users, and it capitalizes on the collective knowledge of users within the same cluster. Extensive experiments conducted on various benchmark datasets validate the effectiveness of ClusterSeq. Empirical results consistently demonstrate that ClusterSeq outperforms several state-of-the-art meta-learning recommenders. Notably, compared to existing meta-learning methods, our proposed approach achieves a substantial improvement of 16-39% in Mean Reciprocal Rank (MRR).

In an era of information explosion, recommender systems are vital tools to deliver personalized recommendations for users. The key of recommender systems is to forecast users' future behaviors based on previous user-item interactions. Due to their strong expressive power of capturing high-order connectivities in user-item interaction data, recent years have witnessed a rising interest in leveraging Graph Neural Networks (GNNs) to boost the prediction performance of recommender systems. Nonetheless, classic Matrix Factorization (MF) and Deep Neural Network (DNN) approaches still play an important role in real-world large-scale recommender systems due to their scalability advantages. Despite the existence of GNN-acceleration solutions, it remains an open question whether GNN-based recommender systems can scale as efficiently as classic MF and DNN methods. In this paper, we propose a Linear-Time Graph Neural Network (LTGNN) to scale up GNN-based recommender systems to achieve comparable scalability as classic MF approaches while maintaining GNNs' powerful expressiveness for superior prediction accuracy. Extensive experiments and ablation studies are presented to validate the effectiveness and scalability of the proposed algorithm. Our implementation based on PyTorch is available.

Nonnegative matrix factorization (NMF) is an effective data representation tool with numerous applications in signal processing and machine learning. However, deploying NMF in a decentralized manner over ad-hoc networks introduces privacy concerns due to the conventional approach of sharing raw data among network agents. To address this, we propose a privacy-preserving algorithm for fully-distributed NMF that decomposes a distributed large data matrix into left and right matrix factors while safeguarding each agent's local data privacy. It facilitates collaborative estimation of the left matrix factor among agents and enables them to estimate their respective right factors without exposing raw data. To ensure data privacy, we secure information exchanges between neighboring agents utilizing the Paillier cryptosystem, a probabilistic asymmetric algorithm for public-key cryptography that allows computations on encrypted data without decryption. Simulation results conducted on synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm in achieving privacy-preserving distributed NMF over ad-hoc networks.

Session-based recommender systems (SBRSs) have shown superior performance over conventional methods. However, they show limited scalability on large-scale industrial datasets since most models learn one embedding per item. This leads to a large memory requirement (of storing one vector per item) and poor performance on sparse sessions with cold-start or unpopular items. Using one public and one large industrial dataset, we experimentally show that state-of-the-art SBRSs have low performance on sparse sessions with sparse items. We propose M2TRec, a Metadata-aware Multi-task Transformer model for session-based recommendations. Our proposed method learns a transformation function from item metadata to embeddings, and is thus, item-ID free (i.e., does not need to learn one embedding per item). It integrates item metadata to learn shared representations of diverse item attributes. During inference, new or unpopular items will be assigned identical representations for the attributes they share with items previously observed during training, and thus will have similar representations with those items, enabling recommendations of even cold-start and sparse items. Additionally, M2TRec is trained in a multi-task setting to predict the next item in the session along with its primary category and subcategories. Our multi-task strategy makes the model converge faster and significantly improves the overall performance. Experimental results show significant performance gains using our proposed approach on sparse items on the two datasets.

We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.

Recommendation is the task of ranking items (e.g. movies or products) according to individual user needs. Current systems rely on collaborative filtering and content-based techniques, which both require structured training data. We propose a framework for recommendation with off-the-shelf pretrained language models (LM) that only used unstructured text corpora as training data. If a user u liked Matrix and Inception, we construct a textual prompt, e.g. "Movies like Matrix, Inception, {<m{>}"} to estimate the affinity between u and m with LM likelihood. We motivate our idea with a corpus analysis, evaluate several prompt structures, and we compare LM-based recommendation with standard matrix factorization trained on different data regimes. The code for our experiments is publicly available (https://colab.research.google.com/drive/1f1mlZ-FGaLGdo5rPzxf3vemKllbh2esT?usp=sharing).

Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph structure so that it can be easily exploited by machine learning models. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about a graph (e.g., degree statistics or kernel functions). However, recent years have seen a surge in approaches that automatically learn to encode graph structure into low-dimensional embeddings, using techniques based on deep learning and nonlinear dimensionality reduction. Here we provide a conceptual review of key advancements in this area of representation learning on graphs, including matrix factorization-based methods, random-walk based algorithms, and graph neural networks. We review methods to embed individual nodes as well as approaches to embed entire (sub)graphs. In doing so, we develop a unified framework to describe these recent approaches, and we highlight a number of important applications and directions for future work.

Recently, nonnegative matrix factorization (NMF) has been widely adopted for community detection, because of its better interpretability. However, the existing NMF-based methods have the following three problems: 1) they directly transform the original network into community membership space, so it is difficult for them to capture the hierarchical information; 2) they often only pay attention to the topology of the network and ignore its node attributes; 3) it is hard for them to learn the global structure information necessary for community detection. Therefore, we propose a new community detection algorithm, named Contrastive Deep Nonnegative Matrix Factorization (CDNMF). Firstly, we deepen NMF to strengthen its capacity for information extraction. Subsequently, inspired by contrastive learning, our algorithm creatively constructs network topology and node attributes as two contrasting views. Furthermore, we utilize a debiased negative sampling layer and learn node similarity at the community level, thereby enhancing the suitability of our model for community detection. We conduct experiments on three public real graph datasets and the proposed model has achieved better results than state-of-the-art methods. Code available at https://github.com/6lyc/CDNMF.git.

Clustering has been a major research topic in the field of machine learning, one to which Deep Learning has recently been applied with significant success. However, an aspect of clustering that is not addressed by existing deep clustering methods, is that of efficiently producing multiple, diverse partitionings for a given dataset. This is particularly important, as a diverse set of base clusterings are necessary for consensus clustering, which has been found to produce better and more robust results than relying on a single clustering. To address this gap, we propose DivClust, a diversity controlling loss that can be incorporated into existing deep clustering frameworks to produce multiple clusterings with the desired degree of diversity. We conduct experiments with multiple datasets and deep clustering frameworks and show that: a) our method effectively controls diversity across frameworks and datasets with very small additional computational cost, b) the sets of clusterings learned by DivClust include solutions that significantly outperform single-clustering baselines, and c) using an off-the-shelf consensus clustering algorithm, DivClust produces consensus clustering solutions that consistently outperform single-clustering baselines, effectively improving the performance of the base deep clustering framework.

Most conventional recommendation methods (e.g., matrix factorization) represent user profiles as high-dimensional vectors. Unfortunately, these vectors lack interpretability and steerability, and often perform poorly in cold-start settings. To address these shortcomings, we explore the use of user profiles that are represented as human-readable text. We propose the Language-based Factorization Model (LFM), which is essentially an encoder/decoder model where both the encoder and the decoder are large language models (LLMs). The encoder LLM generates a compact natural-language profile of the user's interests from the user's rating history. The decoder LLM uses this summary profile to complete predictive downstream tasks. We evaluate our LFM approach on the MovieLens dataset, comparing it against matrix factorization and an LLM model that directly predicts from the user's rating history. In cold-start settings, we find that our method can have higher accuracy than matrix factorization. Furthermore, we find that generating a compact and human-readable summary often performs comparably with or better than direct LLM prediction, while enjoying better interpretability and shorter model input length. Our results motivate a number of future research directions and potential improvements.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

Generative models have recently gained attention in recommendation systems by directly predicting item identifiers from user interaction sequences. However, existing methods suffer from significant information loss due to the separation of stages such as quantization and sequence modeling, hindering their ability to achieve the modeling precision and accuracy of sequential dense retrieval techniques. Integrating generative and dense retrieval methods remains a critical challenge. To address this, we introduce the Cascaded Organized Bi-Represented generAtive retrieval (COBRA) framework, which innovatively integrates sparse semantic IDs and dense vectors through a cascading process. Our method alternates between generating these representations by first generating sparse IDs, which serve as conditions to aid in the generation of dense vectors. End-to-end training enables dynamic refinement of dense representations, capturing both semantic insights and collaborative signals from user-item interactions. During inference, COBRA employs a coarse-to-fine strategy, starting with sparse ID generation and refining them into dense vectors via the generative model. We further propose BeamFusion, an innovative approach combining beam search with nearest neighbor scores to enhance inference flexibility and recommendation diversity. Extensive experiments on public datasets and offline tests validate our method's robustness. Online A/B tests on a real-world advertising platform with over 200 million daily users demonstrate substantial improvements in key metrics, highlighting COBRA's practical advantages.

Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by k-means), limiting trade-off control, interpretability, and scalability. We introduce DFNMF, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter lambda tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.

This paper provides an overview of the approach we used as team ISISTANITOS for the ACM RecSys Challenge 2023. The competition was organized by ShareChat, and involved predicting the probability of a user clicking an app ad and/or installing an app, to improve deep funnel optimization and a special focus on user privacy. Our proposed method inferring the probabilities of clicking and installing as two different, but related tasks. Hence, the model engineers a specific set of features for each task and a set of shared features. Our model is called Weighted Multi-Level Feature Factorization because it considers the interaction of different order features, where the order is associated to the depth in a neural network. The prediction for a given task is generated by combining the task specific and shared features on the different levels. Our submission achieved the 11 rank and overall score of 55 in the competition academia-track final results. We release our source code at: https://github.com/knife982000/RecSys2023Challenge

Generative recommendation is emerging as a powerful paradigm that directly generates item predictions, moving beyond traditional matching-based approaches. However, current methods face two key challenges: token-item misalignment, where uniform token-level modeling ignores item-level granularity that is critical for collaborative signal learning, and semantic-collaborative signal entanglement, where collaborative and semantic signals exhibit distinct distributions yet are fused in a unified embedding space, leading to conflicting optimization objectives that limit the recommendation performance. To address these issues, we propose DiscRec, a novel framework that enables Disentangled Semantic-Collaborative signal modeling with flexible fusion for generative Recommendation.First, DiscRec introduces item-level position embeddings, assigned based on indices within each semantic ID, enabling explicit modeling of item structure in input token sequences.Second, DiscRec employs a dual-branch module to disentangle the two signals at the embedding layer: a semantic branch encodes semantic signals using original token embeddings, while a collaborative branch applies localized attention restricted to tokens within the same item to effectively capture collaborative signals. A gating mechanism subsequently fuses both branches while preserving the model's ability to model sequential dependencies. Extensive experiments on four real-world datasets demonstrate that DiscRec effectively decouples these signals and consistently outperforms state-of-the-art baselines. Our codes are available on https://github.com/Ten-Mao/DiscRec.

Recommender systems typically operate on high-dimensional sparse user-item matrices. Matrix completion is a very challenging task to predict one's interest based on millions of other users having each seen a small subset of thousands of items. We propose a Global-Local Kernel-based matrix completion framework, named GLocal-K, that aims to generalise and represent a high-dimensional sparse user-item matrix entry into a low dimensional space with a small number of important features. Our GLocal-K can be divided into two major stages. First, we pre-train an auto encoder with the local kernelised weight matrix, which transforms the data from one space into the feature space by using a 2d-RBF kernel. Then, the pre-trained auto encoder is fine-tuned with the rating matrix, produced by a convolution-based global kernel, which captures the characteristics of each item. We apply our GLocal-K model under the extreme low-resource setting, which includes only a user-item rating matrix, with no side information. Our model outperforms the state-of-the-art baselines on three collaborative filtering benchmarks: ML-100K, ML-1M, and Douban.

Factorization machine (FM) variants are widely used in recommendation systems that operate under strict throughput and latency requirements, such as online advertising systems. FMs are known both due to their ability to model pairwise feature interactions while being resilient to data sparsity, and their computational graphs that facilitate fast inference and training. Moreover, when items are ranked as a part of a query for each incoming user, these graphs facilitate computing the portion stemming from the user and context fields only once per query. Consequently, in terms of inference cost, the number of user or context fields is practically unlimited. More advanced FM variants, such as FwFM, provide better accuracy by learning a representation of field-wise interactions, but require computing all pairwise interaction terms explicitly. The computational cost during inference is proportional to the square of the number of fields, including user, context, and item. When the number of fields is large, this is prohibitive in systems with strict latency constraints. To mitigate this caveat, heuristic pruning of low intensity field interactions is commonly used to accelerate inference. In this work we propose an alternative to the pruning heuristic in FwFMs using a diagonal plus symmetric low-rank decomposition. Our technique reduces the computational cost of inference, by allowing it to be proportional to the number of item fields only. Using a set of experiments on real-world datasets, we show that aggressive rank reduction outperforms similarly aggressive pruning, both in terms of accuracy and item recommendation speed. We corroborate our claim of faster inference experimentally, both via a synthetic test, and by having deployed our solution to a major online advertising system. The code to reproduce our experimental results is at https://github.com/michaelviderman/pytorch-fm/tree/dev.

Topic modeling is a technique for organizing and extracting themes from large collections of unstructured text. Non-negative matrix factorization (NMF) is a common unsupervised approach that decomposes a term frequency-inverse document frequency (TF-IDF) matrix to uncover latent topics and segment the dataset accordingly. While useful for highlighting patterns and clustering documents, NMF does not provide explicit topic labels, necessitating subject matter experts (SMEs) to assign labels manually. We present a methodology for automating topic labeling in documents clustered via NMF with automatic model determination (NMFk). By leveraging the output of NMFk and employing prompt engineering, we utilize large language models (LLMs) to generate accurate topic labels. Our case study on over 34,000 scientific abstracts on Knowledge Graphs demonstrates the effectiveness of our method in enhancing knowledge management and document organization.

To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance with side information encoded. Due to the overlook of the relations among instances or items (e.g., the director of a movie is also an actor of another movie), these methods are insufficient to distill the collaborative signal from the collective behaviors of users. In this work, we investigate the utility of knowledge graph (KG), which breaks down the independent interaction assumption by linking items with their attributes. We argue that in such a hybrid structure of KG and user-item graph, high-order relations --- which connect two items with one or multiple linked attributes --- are an essential factor for successful recommendation. We propose a new method named Knowledge Graph Attention Network (KGAT) which explicitly models the high-order connectivities in KG in an end-to-end fashion. It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors. Our KGAT is conceptually advantageous to existing KG-based recommendation methods, which either exploit high-order relations by extracting paths or implicitly modeling them with regularization. Empirical results on three public benchmarks show that KGAT significantly outperforms state-of-the-art methods like Neural FM and RippleNet. Further studies verify the efficacy of embedding propagation for high-order relation modeling and the interpretability benefits brought by the attention mechanism.

With the overwhelming amount of data available both on and offline today, recommender systems have become much needed to help users find items tailored to their interests. When social network information exists there are methods that utilize this information to make better recommendations, however the methods are often clunky with complex architectures and training procedures. Furthermore many of the existing methods utilize graph neural networks which are notoriously difficult to train. To address this, we propose Socially-aware Temporally caUsal Decoder recommender sYstems (STUDY). STUDY does joint inference over groups of users who are adjacent in the social network graph using a single forward pass of a modified transformer decoder network. We test our method in a school-based educational content setting, using classroom structure to define social networks. Our method outperforms both social and sequential methods while maintaining the design simplicity of a single homogeneous network that models all interactions in the data. We also carry out ablation studies to understand the drivers of our performance gains and find that our model depends on leveraging a social network structure that effectively models the similarities in user behavior.

Building recommendation systems via federated learning (FL) is a new emerging challenge for advancing next-generation Internet service and privacy protection. Existing approaches train shared item embedding by FL while keeping the user embedding private on client side. However, item embedding identical for all clients cannot capture users' individual differences on perceiving the same item and thus leads to poor personalization. Moreover, dense item embedding in FL results in expensive communication cost and latency. To address these challenges, we propose Federated Recommendation with Additive Personalization (FedRAP), which learns a global view of items via FL and a personalized view locally on each user. FedRAP enforces sparsity of the global view to save FL's communication cost and encourages difference between the two views through regularization. We propose an effective curriculum to learn the local and global views progressively with increasing regularization weights. To produce recommendations for an user, FedRAP adds the two views together to obtain a personalized item embedding. FedRAP achieves the best performance in FL setting on multiple benchmarks. It outperforms recent federated recommendation methods and several ablation study baselines.

Social recommendation, which seeks to leverage social ties among users to alleviate the sparsity issue of user-item interactions, has emerged as a popular technique for elevating personalized services in recommender systems. Despite being effective, existing social recommendation models are mainly devised for recommending regular items such as blogs, images, and products, and largely fail for community recommendations due to overlooking the unique characteristics of communities. Distinctly, communities are constituted by individuals, who present high dynamicity and relate to rich structural patterns in social networks. To our knowledge, limited research has been devoted to comprehensively exploiting this information for recommending communities. To bridge this gap, this paper presents CASO, a novel and effective model specially designed for social community recommendation. Under the hood, CASO harnesses three carefully-crafted encoders for user embedding, wherein two of them extract community-related global and local structures from the social network via social modularity maximization and social closeness aggregation, while the third one captures user preferences using collaborative filtering with observed user-community affiliations. To further eliminate feature redundancy therein, we introduce a mutual exclusion between social and collaborative signals. Finally, CASO includes a community detection loss in the model optimization, thereby producing community-aware embeddings for communities. Our extensive experiments evaluating CASO against nine strong baselines on six real-world social networks demonstrate its consistent and remarkable superiority over the state of the art in terms of community recommendation performance.

Collaborative filtering generates recommendations based on user-item similarities through rating data, which may involve numerous unrated items. To predict scores for unrated items, matrix factorization techniques, such as nonnegative matrix factorization (NMF), are often employed to predict scores for unrated items. Nonnegative/binary matrix factorization (NBMF), which is an extension of NMF, approximates a nonnegative matrix as the product of nonnegative and binary matrices. Previous studies have employed NBMF for image analysis where the data were dense. In this paper, we propose a modified NBMF algorithm that can be applied to collaborative filtering where data are sparse. In the modified method, unrated elements in a rating matrix are masked, which improves the collaborative filtering performance. Utilizing a low-latency Ising machine in NBMF is advantageous in terms of the computation time, making the proposed method beneficial.

Collaborative filtering (CF) is widely used to learn informative latent representations of users and items from observed interactions. Existing CF-based methods commonly adopt negative sampling to discriminate different items. Training with negative sampling on large datasets is computationally expensive. Further, negative items should be carefully sampled under the defined distribution, in order to avoid selecting an observed positive item in the training dataset. Unavoidably, some negative items sampled from the training dataset could be positive in the test set. In this paper, we propose a self-supervised collaborative filtering framework (SelfCF), that is specially designed for recommender scenario with implicit feedback. The proposed SelfCF framework simplifies the Siamese networks and can be easily applied to existing deep-learning based CF models, which we refer to as backbone networks. The main idea of SelfCF is to augment the output embeddings generated by backbone networks, because it is infeasible to augment raw input of user/item ids. We propose and study three output perturbation techniques that can be applied to different types of backbone networks including both traditional CF models and graph-based models. The framework enables learning informative representations of users and items without negative samples, and is agnostic to the encapsulated backbones. We conduct comprehensive experiments on four datasets to show that our framework may achieve even better recommendation accuracy than the encapsulated supervised counterpart with a 2times--4times faster training speed. We also show that SelfCF can boost up the accuracy by up to 17.79% on average, compared with a self-supervised framework BUIR.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

Personalized book recommendation in Bangla literature has been constrained by the lack of structured, large-scale, and publicly available datasets. This work introduces RokomariBG, a large-scale, multi-entity heterogeneous book graph dataset designed to support research on personalized recommendation in a low-resource language setting. The dataset comprises 127,302 books, 63,723 users, 16,601 authors, 1,515 categories, 2,757 publishers, and 209,602 reviews, connected through eight relation types and organized as a comprehensive knowledge graph. To demonstrate the utility of the dataset, we provide a systematic benchmarking study on the Top-N recommendation task, evaluating a diverse set of representative recommendation models, including classical collaborative filtering methods, matrix factorization models, content-based approaches, graph neural networks, a hybrid matrix factorization model with side information, and a neural two-tower retrieval architecture. The benchmarking results highlight the importance of leveraging multi-relational structure and textual side information, with neural retrieval models achieving the strongest performance (NDCG@10 = 0.204). Overall, this work establishes a foundational benchmark and a publicly available resource for Bangla book recommendation research, enabling reproducible evaluation and future studies on recommendation in low-resource cultural domains. The dataset and code are publicly available at https://github.com/backlashblitz/Bangla-Book-Recommendation-Dataset

Multi-vector retrieval (MVR) models, exemplified by ColBERT, have established new benchmarks in retrieval accuracy by preserving fine-grained token-level interactions. However, this granularity imposes prohibitive storage and retrieval efficiency bottlenecks: to manage the immense memory footprint and computational overhead of billion-scale token vectors, state-of-the-art systems are forced to rely on aggressive dimension reduction and complex clustering (e.g., K-means). This compromise introduces two critical limitations: excessive indexing latency of clustering large-scale corpora and semantic information loss inherent to compression. In this paper, we propose Single-stage Sparse Retrieval (SSR}, a paradigm shift that replaces expensive clustering with efficient sparse coding. Instead of compressing features into low-dimensional dense vectors, we utilize Sparse Autoencoder (SAE) to project token embeddings into a high-dimensional but highly sparse representation. This transformation enables us to bypass vector clustering entirely and leverage inverted indexing for precise, high-throughput retrieval. Extensive experiments on the BEIR benchmark demonstrate that SSR achieves a "trifecta" of improvements: it reduces indexing time by 15x compared to ColBERTv2, halves retrieval latency, and simultaneously improves retrieval performance over leading baselines.

Recommender systems in concert with Large Language Models (LLMs) present promising avenues for generating semantically-informed recommendations. However, LLM-based recommenders exhibit a tendency to overemphasize semantic correlations within users' interaction history. When taking pretrained collaborative ID embeddings as input, LLM-based recommenders progressively weaken the inherent collaborative signals as the embeddings propagate through LLM backbones layer by layer, as opposed to traditional Transformer-based sequential models in which collaborative signals are typically preserved or even enhanced for state-of-the-art performance. To address this limitation, we introduce FreLLM4Rec, an approach designed to balance semantic and collaborative information from a spectral perspective. Item embeddings that incorporate both semantic and collaborative information are first purified using a Global Graph Low-Pass Filter (G-LPF) to preliminarily remove irrelevant high-frequency noise. Temporal Frequency Modulation (TFM) then actively preserves collaborative signal layer by layer. Note that the collaborative preservation capability of TFM is theoretically guaranteed by establishing a connection between the optimal but hard-to-implement local graph fourier filters and the suboptimal yet computationally efficient frequency-domain filters. Extensive experiments on four benchmark datasets demonstrate that FreLLM4Rec successfully mitigates collaborative signal attenuation and achieves competitive performance, with improvements of up to 8.00\% in NDCG@10 over the best baseline. Our findings provide insights into how LLMs process collaborative information and offer a principled approach for improving LLM-based recommendation systems.

We present ROCKET, a training-free model compression method that achieves state-of-the-art performance in comparison with factorization, structured-sparsification and dynamic compression baselines. Operating under a global compression budget, ROCKET comprises two key innovations: First, it formulates layer-wise compression allocation as a multi-choice knapsack problem, selecting the optimal compression level for each layer to minimize total reconstruction error while adhering to a target model size. Second, it introduces a single-step sparse matrix factorization inspired by dictionary learning: using only a small calibration set, it sparsifies weight coefficients based on activation-weights sensitivity and then updates the dictionary in closed form via least squares bypassing iterative optimization, sparse coding, or backpropagation entirely. ROCKET consistently outperforms existing compression approaches across different model architectures at 20-50\% compression rates. Notably, it retains over 90\% of the original model's performance at 30\% compression without any fine-tuning. Moreover, when applying a light fine-tuning phase, recovery is substantially enhanced: for instance, compressing Qwen3-14B to an 8B-parameter model and healing it with just 30 million tokens yields performance nearly on par with the original Qwen3-8B. The code for ROCKET is at github.com/mts-ai/ROCKET/tree/main.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy enables parameter sharing and efficient reconstruction and has been widely adopted across domains ranging from multi-view learning and signal processing to neural network compression. However, it leaves a fundamental question unanswered: which matrices can be safely concatenated and compressed together under explicit reconstruction error constraints? Existing approaches rely on heuristic or architecture-specific grouping and provide no principled guarantees on the resulting SVD approximation error. In the present work, we introduce a theory-driven framework for compression-aware clustering of matrices under SVD compression constraints. Our analysis establishes new spectral bounds for horizontally concatenated matrices, deriving global upper bounds on the optimal rank-r SVD reconstruction error from lower bounds on singular value growth. The first bound follows from Weyl-type monotonicity under blockwise extensions, while the second leverages singular values of incremental residuals to yield tighter, per-block guarantees. We further develop an efficient approximate estimator based on incremental truncated SVD that tracks dominant singular values without forming the full concatenated matrix. Therefore, we propose three clustering algorithms that merge matrices only when their predicted joint SVD compression error remains below a user-specified threshold. The algorithms span a trade-off between speed, provable accuracy, and scalability, enabling compression-aware clustering with explicit error control. Code is available online.

Collaborative filtering models, particularly graph-based approaches, have demonstrated strong performance in capturing user-item interactions for recommendation systems. However, they continue to struggle in cold-start and data-sparse scenarios. The emergence of large language models (LLMs) like GPT and LLaMA presents new possibilities for enhancing recommendation performance, especially in cold-start settings. Despite their promise, LLMs pose challenges related to scalability and efficiency due to their high computational demands and limited ability to model complex user-item relationships effectively. In this work, we introduce a novel perspective on leveraging LLMs for CF model initialization. Through experiments, we uncover an embedding collapse issue when scaling CF models to larger embedding dimensions. To effectively harness large-scale LLM embeddings, we propose innovative selective initialization strategies utilizing random, uniform, and variance-based index sampling. Our comprehensive evaluation on multiple real-world datasets demonstrates significant performance gains across various CF models while maintaining a lower computational cost compared to existing LLM-based recommendation approaches.

The new barrier mode in Apache Spark allows embedding distributed deep learning training as a Spark stage to simplify the distributed training workflow. In Spark, a task in a stage does not depend on any other tasks in the same stage, and hence it can be scheduled independently. However, several algorithms require more sophisticated inter-task communications, similar to the MPI paradigm. By combining distributed message passing (using asynchronous network IO), OpenJDK's new auto-vectorization and Spark's barrier execution mode, we can add non-map/reduce based algorithms, such as Cannon's distributed matrix multiplication to Spark. We document an efficient distributed matrix multiplication using Cannon's algorithm, which improves significantly on the performance of the existing MLlib implementation. Used within a barrier task, the algorithm described herein results in an up to 24 percent performance increase on a 10,000x10,000 square matrix with a significantly lower memory footprint. Applications of efficient matrix multiplication include, among others, accelerating the training and implementation of deep convolutional neural network based workloads, and thus such efficient algorithms can play a ground-breaking role in faster, more efficient execution of even the most complicated machine learning tasks.

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular challenge has been to design universal initialization strategies which provably lead to implicit regularization in gradient-descent methods. At the same time, it has been argued by Cohen et. al. 2016 that more general classes of neural networks can be captured by considering tensor factorizations. However, in the tensor case, implicit regularization has only been rigorously established for gradient flow or in the lazy training regime. In this paper, we prove the first tensor result of its kind for gradient descent rather than gradient flow. We focus on the tubal tensor product and the associated notion of low tubal rank, encouraged by the relevance of this model for image data. We establish that gradient descent in an overparametrized tensor factorization model with a small random initialization exhibits an implicit bias towards solutions of low tubal rank. Our theoretical findings are illustrated in an extensive set of numerical simulations show-casing the dynamics predicted by our theory as well as the crucial role of using a small random initialization.

Utilizing powerful Large Language Models (LLMs) for generative recommendation has attracted much attention. Nevertheless, a crucial challenge is transforming recommendation data into the language space of LLMs through effective item tokenization. Current approaches, such as ID, textual, and codebook-based identifiers, exhibit shortcomings in encoding semantic information, incorporating collaborative signals, or handling code assignment bias. To address these limitations, we propose LETTER (a LEarnable Tokenizer for generaTivE Recommendation), which integrates hierarchical semantics, collaborative signals, and code assignment diversity to satisfy the essential requirements of identifiers. LETTER incorporates Residual Quantized VAE for semantic regularization, a contrastive alignment loss for collaborative regularization, and a diversity loss to mitigate code assignment bias. We instantiate LETTER on two models and propose a ranking-guided generation loss to augment their ranking ability theoretically. Experiments on three datasets validate the superiority of LETTER, advancing the state-of-the-art in the field of LLM-based generative recommendation.

Sequential recommender systems aim to predict a user's future interests by extracting temporal patterns from their behavioral history. Existing approaches typically employ transformer-based architectures to process long sequences of user interactions, capturing preference shifts by modeling temporal relationships between items. However, these methods often overlook the influence of group-level features that capture the collective behavior of similar users. We hypothesize that explicitly modeling temporally evolving group features alongside individual user histories can significantly enhance next-item recommendation. Our approach introduces latent group representations, where each user's affiliation to these groups is modeled through learnable, time-varying membership weights. The membership weights at each timestep are computed by modeling shifts in user preferences through their interaction history, where we incorporate both short-term and long-term user preferences. We extract a set of statistical features that capture the dynamics of user behavior and further refine them through a series of transformations to produce the final drift-aware membership weights. A group-based representation is derived by weighting latent group embeddings with the learned membership scores. This representation is integrated with the user's sequential representation within the transformer block to jointly capture personal and group-level temporal dynamics, producing richer embeddings that lead to more accurate, context-aware recommendations. We validate the effectiveness of our approach through extensive experiments on five benchmark datasets, where it consistently outperforms state-of-the-art sequential recommendation methods.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

Over the last few years, multi-vector retrieval methods, spearheaded by ColBERT, have become an increasingly popular approach to Neural IR. By storing representations at the token level rather than at the document level, these methods have demonstrated very strong retrieval performance, especially in out-of-domain settings. However, the storage and memory requirements necessary to store the large number of associated vectors remain an important drawback, hindering practical adoption. In this paper, we introduce a simple clustering-based token pooling approach to aggressively reduce the number of vectors that need to be stored. This method can reduce the space & memory footprint of ColBERT indexes by 50% with virtually no retrieval performance degradation. This method also allows for further reductions, reducing the vector count by 66%-to-75% , with degradation remaining below 5% on a vast majority of datasets. Importantly, this approach requires no architectural change nor query-time processing, and can be used as a simple drop-in during indexation with any ColBERT-like model.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

Contemporary generative recommendation systems face significant challenges in handling multimodal data, eliminating algorithmic biases, and providing transparent decision-making processes. This paper introduces an enhanced generative recommendation framework that addresses these limitations through five key innovations: multimodal fusion architecture, retrieval-augmented generation mechanisms, causal inference-based debiasing, explainable recommendation generation, and real-time adaptive learning capabilities. Our framework leverages advanced large language models as the backbone while incorporating specialized modules for cross-modal understanding, contextual knowledge integration, bias mitigation, explanation synthesis, and continuous model adaptation. Extensive experiments on three benchmark datasets (MovieLens-25M, Amazon-Electronics, Yelp-2023) demonstrate consistent improvements in recommendation accuracy, fairness, and diversity compared to existing approaches. The proposed framework achieves up to 2.3% improvement in NDCG@10 and 1.4% enhancement in diversity metrics while maintaining computational efficiency through optimized inference strategies.

A recommendation system uses the past purchases or ratings of n products by a group of m users, in order to provide personalized recommendations to individual users. The information is modeled as an m times n preference matrix which is assumed to have a good rank-k approximation, for a small constant k. In this work, we present a quantum algorithm for recommendation systems that has running time O(poly(k)polylog(mn)). All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time polynomial in the matrix dimension. Our algorithm provides good recommendations by sampling efficiently from an approximation of the preference matrix, without reconstructing the entire matrix. For this, we design an efficient quantum procedure to project a given vector onto the row space of a given matrix. This is the first algorithm for recommendation systems that runs in time polylogarithmic in the dimensions of the matrix and provides an example of a quantum machine learning algorithm for a real world application.

Many deep learning applications benefit from using large models with billions of parameters. Training these models is notoriously expensive due to the need for specialized HPC clusters. In this work, we consider alternative setups for training large models: using cheap "preemptible" instances or pooling existing resources from multiple regions. We analyze the performance of existing model-parallel algorithms in these conditions and find configurations where training larger models becomes less communication-intensive. Based on these findings, we propose SWARM parallelism, a model-parallel training algorithm designed for poorly connected, heterogeneous and unreliable devices. SWARM creates temporary randomized pipelines between nodes that are rebalanced in case of failure. We empirically validate our findings and compare SWARM parallelism with existing large-scale training approaches. Finally, we combine our insights with compression strategies to train a large Transformer language model with 1B shared parameters (approximately 13B before sharing) on preemptible T4 GPUs with less than 200Mb/s network.

We propose SMMF (Square-Matricized Momentum Factorization), a memory-efficient optimizer that reduces the memory requirement of the widely used adaptive learning rate optimizers, such as Adam, by up to 96%. SMMF enables flexible and efficient factorization of an arbitrary rank (shape) of the first and second momentum tensors during optimization, based on the proposed square-matricization and one-time single matrix factorization. From this, it becomes effectively applicable to any rank (shape) of momentum tensors, i.e., bias, matrix, and any rank-d tensors, prevalent in various deep model architectures, such as CNNs (high rank) and Transformers (low rank), in contrast to existing memory-efficient optimizers that applies only to a particular (rank-2) momentum tensor, e.g., linear layers. We conduct a regret bound analysis of SMMF, which shows that it converges similarly to non-memory-efficient adaptive learning rate optimizers, such as AdamNC, providing a theoretical basis for its competitive optimization capability. In our experiment, SMMF takes up to 96% less memory compared to state-of-the-art memory efficient optimizers, e.g., Adafactor, CAME, and SM3, while achieving comparable model performance on various CNN and Transformer tasks.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

Recent work has explored generative recommender systems as an alternative to traditional ID-based models, reframing item recommendation as a sequence generation task over discrete item tokens. While promising, such methods often underperform in practice compared to well-tuned ID-based baselines like SASRec. In this paper, we identify two key limitations holding back generative approaches: the lack of collaborative signal in item tokenization, and inefficiencies in the commonly used encoder-decoder architecture. To address these issues, we introduce COSETTE, a contrastive tokenization method that integrates collaborative information directly into the learned item representations, jointly optimizing for both content reconstruction and recommendation relevance. Additionally, we propose MARIUS, a lightweight, audio-inspired generative model that decouples timeline modeling from item decoding. MARIUS reduces inference cost while improving recommendation accuracy. Experiments on standard sequential recommendation benchmarks show that our approach narrows, or even eliminates, the performance gap between generative and modern ID-based models, while retaining the benefits of the generative paradigm.

Deep recommender systems rely heavily on large embedding tables to handle high-cardinality categorical features such as user/item identifiers, and face significant memory constraints at scale. To tackle this challenge, hashing techniques are often employed to map multiple entities to the same embedding and thus reduce the size of the embedding tables. Concurrently, graph-based collaborative signals have emerged as powerful tools in recommender systems, yet their potential for optimizing embedding table reduction remains unexplored. This paper introduces GraphHash, the first graph-based approach that leverages modularity-based bipartite graph clustering on user-item interaction graphs to reduce embedding table sizes. We demonstrate that the modularity objective has a theoretical connection to message-passing, which provides a foundation for our method. By employing fast clustering algorithms, GraphHash serves as a computationally efficient proxy for message-passing during preprocessing and a plug-and-play graph-based alternative to traditional ID hashing. Extensive experiments show that GraphHash substantially outperforms diverse hashing baselines on both retrieval and click-through-rate prediction tasks. In particular, GraphHash achieves on average a 101.52% improvement in recall when reducing the embedding table size by more than 75%, highlighting the value of graph-based collaborative information for model reduction. Our code is available at https://github.com/snap-research/GraphHash.

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

Given a (machine learning) classifier and a collection of unlabeled data, how can we efficiently identify misclassification patterns presented in this dataset? To address this problem, we propose a human-machine collaborative framework that consists of a team of human annotators and a sequential recommendation algorithm. The recommendation algorithm is conceptualized as a stochastic sampler that, in each round, queries the annotators a subset of samples for their true labels and obtains the feedback information on whether the samples are misclassified. The sampling mechanism needs to balance between discovering new patterns of misclassification (exploration) and confirming the potential patterns of classification (exploitation). We construct a determinantal point process, whose intensity balances the exploration-exploitation trade-off through the weighted update of the posterior at each round to form the generator of the stochastic sampler. The numerical results empirically demonstrate the competitive performance of our framework on multiple datasets at various signal-to-noise ratios.

Federated Learning (FL) traditionally assumes homogeneous client tasks; however, in real-world scenarios, clients often specialize in diverse tasks, introducing task heterogeneity. To address this challenge, Many-Task FL (MaT-FL) has emerged, enabling clients to collaborate effectively despite task diversity. Existing MaT-FL approaches rely on client grouping or personalized layers, requiring the server to manage individual models and failing to account for clients handling multiple tasks. We propose MaTU, a MaT-FL approach that enables joint learning of task vectors across clients, eliminating the need for clustering or client-specific weight storage at the server. Our method introduces a novel aggregation mechanism that determines task similarity based on the direction of clients task vectors and constructs a unified task vector encapsulating all tasks. To address task-specific requirements, we augment the unified task vector with lightweight modulators that facilitate knowledge transfer among related tasks while disentangling dissimilar ones. Evaluated across 30 datasets, MaTU achieves superior performance over state-of-the-art MaT-FL approaches, with results comparable to per-task fine-tuning, while delivering significant communication savings.

Conventional recommendation systems (RSs) are typically optimized to enhance performance metrics uniformly across all training samples, inadvertently overlooking the needs of diverse user populations. The performance disparity among various populations can harm the model's robustness to sub-populations due to the varying user properties. While large language models (LLMs) show promise in enhancing RS performance, their practical applicability is hindered by high costs, inference latency, and degraded performance on long user queries. To address these challenges, we propose a hybrid task allocation framework designed to promote social good by equitably serving all user groups. By adopting a two-phase approach, we promote a strategic assignment of tasks for efficient and responsible adaptation of LLMs. Our strategy works by first identifying the weak and inactive users that receive a suboptimal ranking performance by RSs. Next, we use an in-context learning approach for such users, wherein each user interaction history is contextualized as a distinct ranking task. We evaluate our hybrid framework by incorporating eight different recommendation algorithms and three different LLMs -- both open and close-sourced. Our results on three real-world datasets show a significant reduction in weak users and improved robustness to subpopulations without disproportionately escalating costs.

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training samples. Our workhorse is a novel representer theorem for general regularized high-dimensional models, which decomposes the model prediction in terms of contributions from each of the training samples: with positive (negative) values corresponding to positive (negative) impact training samples to the model's prediction. We derive consequences for the canonical instances of ell_1 regularized sparse models, and nuclear norm regularized low-rank models. As a case study, we further investigate the application of low-rank models in the context of collaborative filtering, where we instantiate high-dimensional representers for specific popular classes of models. Finally, we study the empirical performance of our proposed methods on three real-world binary classification datasets and two recommender system datasets. We also showcase the utility of high-dimensional representers in explaining model recommendations.

Multi-vector models, such as ColBERT, are a significant advancement in neural information retrieval (IR), delivering state-of-the-art performance by representing queries and documents by multiple contextualized token-level embeddings. However, this increased representation size introduces considerable storage and computational overheads which have hindered widespread adoption in practice. A common approach to mitigate this overhead is to cluster the model's frozen vectors, but this strategy's effectiveness is fundamentally limited by the intrinsic clusterability of these embeddings. In this work, we introduce CRISP (Clustered Representations with Intrinsic Structure Pruning), a novel multi-vector training method which learns inherently clusterable representations directly within the end-to-end training process. By integrating clustering into the training phase rather than imposing it post-hoc, CRISP significantly outperforms post-hoc clustering at all representation sizes, as well as other token pruning methods. On the BEIR retrieval benchmarks, CRISP achieves a significant rate of ~3x reduction in the number of vectors while outperforming the original unpruned model. This indicates that learned clustering effectively denoises the model by filtering irrelevant information, thereby generating more robust multi-vector representations. With more aggressive clustering, CRISP achieves an 11x reduction in the number of vectors with only a 3.6% quality loss.

Nonnegative matrix factorization (NMF) seeks a low-rank approximation X approx UV^T with nonnegative factors and is commonly solved using interior methods that enforce feasibility throughout optimization. We show that such constraint-driven approaches can impede progress in the nonconvex landscape, leading to slow convergence or convergence to suboptimal stationary points. We propose an exterior framework for NMF (eNMF) that separates low-rank approximation from nonnegativity enforcement. Our method initializes from the optimal unconstrained factorization and introduces a rotation procedure that maps unconstrained factors to an exterior point closest to the nonnegative orthant. This viewpoint yields an algorithmic framework in which simple iterative updates converge to KKT-satisfying stationary points on the boundary of the positive orthant. The exterior formulation also enables a geometric interpretation of NMF solutions, clarifying equivalence classes of factorizations under permutation and orthogonal transformations. An intriguing numerical result, involving 400 NMF experiments across both real and synthetic datasets, show that in 99% of the cases, different algorithms tend to converge towards equivalent factor matrices. We benchmark eNMF against 9 state-of-the-art NMF algorithms with 9 initialization schemes across 3 real-world and 2 synthetic datasets. eNMF consistently outperforms all 81 competitors, achieving up to 30% lower reconstruction error under equal-time settings and up to 150% speedup under equal-error settings. The downstream experiments further demonstrate substantial performance gains in audio processing and recommendation tasks, corroborating the practical benefits of the proposed exterior optimization framework. Code is available at https://github.com/roychowdhuryresearch/eNMF

Generative recommendation has recently emerged as a transformative paradigm that directly generates target items, surpassing traditional cascaded approaches. It typically involves two components: a tokenizer that learns item identifiers and a recommender trained on them. Existing methods often decouple tokenization from recommendation or rely on asynchronous alternating optimization, limiting full end-to-end alignment. To address this, we unify the tokenizer and recommender under the ultimate recommendation objective via differentiable soft item identifiers, enabling joint end-to-end training. However, this introduces three challenges: training-inference discrepancy due to soft-to-hard mismatch, item identifier collapse from codeword usage imbalance, and collaborative signal deficiency due to an overemphasis on fine-grained token-level semantics. To tackle these challenges, we propose UniGRec, a unified generative recommendation framework that addresses them from three perspectives. UniGRec employs Annealed Inference Alignment during tokenization to smoothly bridge soft training and hard inference, a Codeword Uniformity Regularization to prevent identifier collapse and encourage codebook diversity, and a Dual Collaborative Distillation mechanism that distills collaborative priors from a lightweight teacher model to jointly guide both the tokenizer and the recommender. Extensive experiments on real-world datasets demonstrate that UniGRec consistently outperforms state-of-the-art baseline methods. Our codes are available at https://github.com/Jialei-03/UniGRec.

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To overcome this limitation, dynamical low-rank training methods have been developed, utilizing robust time integration techniques for low-rank matrix differential equations. Although these approaches facilitate efficient training, they still depend on computationally intensive QR and singular value decompositions of matrices with small rank. In this work, we introduce a novel low-rank training method that reduces the number of required QR decompositions. Our approach integrates an augmentation step into a projector-splitting scheme, ensuring convergence to a locally optimal solution. We provide a rigorous theoretical analysis of the proposed method and demonstrate its effectiveness across multiple benchmarks.

The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is group selection: given an M-dimensional observation with unknown covariance structure, find the finite group whose spectral decomposition best matches the covariance. Naive enumeration of all subgroups of the symmetric group S_M requires exponential time in M. We prove that this combinatorial problem reduces to a generalized eigenvalue problem derived from the double commutator of the covariance matrix, yielding a polynomial-time algorithm with complexity O(d^2M^2 + d^3), where d is the dimension of a generator basis. The minimum eigenvector of the double-commutator matrix directly constructs the optimal group generator in closed form, with no iterative optimization. The reduction is exact: the double-commutator minimum eigenvalue is zero if and only if the optimal generator lies in the span of the basis, and its magnitude provides a certifiable optimality gap when it does not. This problem does not appear in the standard catalogs of computational complexity (Garey and Johnson, 1979) and represents a new class linking group theory, matrix analysis, and statistical estimation. We establish connections to independent component analysis (JADE), structured matrix nearness problems, and simultaneous matrix diagonalization, and we show that the double-commutator formulation is the unique approach that is simultaneously polynomial-time, closed-form, and certifiable. We extend the framework to non-Abelian symmetry recovery via a Sequential GEVP with deflation, and add two identifiability theorems characterizing the commutant-lattice ambiguity and the dichotomy on whether Aut(R) recovers a generative subgroup or only a supergroup.

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.

Multi-agent systems (MAS) increasingly solve complex tasks by orchestrating agents and tools selected from rapidly growing marketplaces. As these marketplaces expand, many candidates become functionally overlapping, making selection not just a retrieval problem: beyond filtering relevant agents, an orchestrator must choose options that are reliable, compatible with the current execution context, and able to cooperate with other selected agents. Existing recommender systems -- largely built for item-level ranking from flat user-item logs -- do not directly address the structured, sequential, and interaction-dependent nature of agent orchestration. We address this gap by formulating agent recommendation in MAS as a constrained decision problem and introducing a generic constrained recommendation framework that first uses retrieval to build a compact candidate set conditioned on the current subtask and context, and then performs utility optimization within this feasible set using a learned scorer that accounts for relevance, reliability, and interaction effects. We ground both the formulation and learning signals in historical calling trees, which capture the execution structure of MAS (parent-child calls, branching dependencies, and local cooperation patterns) beyond what flat logs provide. The framework supports two complementary settings: agent-level recommendation (select the next agent/tool) and system-level recommendation (select a small, connected agent team/subgraph for coordinated execution). To enable systematic evaluation, we construct a unified calling-tree benchmark by normalizing invocation logs from eight heterogeneous multi-agent corpora into a shared structured representation.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

The dominant retrieve-then-rank pipeline in large-scale recommender systems suffers from mis-calibration and engineering overhead due to its architectural split and differing optimization objectives. While recent generative sequence models have shown promise in unifying retrieval and ranking by auto-regressively generating ranked items, existing solutions typically address either personalized search or query-free recommendation, often exhibiting performance trade-offs when attempting to unify both. We introduce SynerGen, a novel generative recommender model that bridges this critical gap by providing a single generative backbone for both personalized search and recommendation, while simultaneously excelling at retrieval and ranking tasks. Trained on behavioral sequences, our decoder-only Transformer leverages joint optimization with InfoNCE for retrieval and a hybrid pointwise-pairwise loss for ranking, allowing semantic signals from search to improve recommendation and vice versa. We also propose a novel time-aware rotary positional embedding to effectively incorporate time information into the attention mechanism. SynerGen achieves significant improvements on widely adopted recommendation and search benchmarks compared to strong generative recommender and joint search and recommendation baselines. This work demonstrates the viability of a single generative foundation model for industrial-scale unified information access.

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby boosting expressivity and accuracy but at the same time resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible without sacrificing accuracy. Specifically, a lightweight meta-learner, trained jointly with the KAN, is used to map low-dimensional embedding to coefficient vectors, shaping them to lie on a low-dimensional manifold that is amenable to clustering. We then run K-means in coefficient space and replace per-edge vectors with shared centroids. Afterwards, the meta-learner can be discarded, and a brief fine-tuning of the centroid codebook recovers any residual accuracy loss. The resulting model stores only a small codebook and per-edge indices, exploiting the vector nature of KAN parameters to amortize storage across multiple coefficients. On MNIST, CIFAR-10, and CIFAR-100, across standard KANs and ConvKANs using multiple basis functions, MetaCluster achieves a reduction of up to 80times in parameter storage, with no loss in accuracy. Code will be released upon publication.

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors and enable us to recover the informative eigenvectors representing the global structure. We show applications of our method in several inference problems: community detection in networks, clustering from pairwise similarities, rank estimation and matrix completion problems. Using extensive experiments, we illustrate that our method solves the localization problem and works down to the theoretical detectability limits in different kinds of synthetic data. This is in contrast with existing spectral algorithms based on data matrix, non-backtracking matrix, Laplacians and those with rank-one regularizations, which perform poorly in the sparse case with noise.

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.

We present LLM-KT, a flexible framework designed to enhance collaborative filtering (CF) models by seamlessly integrating LLM (Large Language Model)-generated features. Unlike existing methods that rely on passing LLM-generated features as direct inputs, our framework injects these features into an intermediate layer of any CF model, allowing the model to reconstruct and leverage the embeddings internally. This model-agnostic approach works with a wide range of CF models without requiring architectural changes, making it adaptable to various recommendation scenarios. Our framework is built for easy integration and modification, providing researchers and developers with a powerful tool for extending CF model capabilities through efficient knowledge transfer. We demonstrate its effectiveness through experiments on the MovieLens and Amazon datasets, where it consistently improves baseline CF models. Experimental studies showed that LLM-KT is competitive with the state-of-the-art methods in context-aware settings but can be applied to a broader range of CF models than current approaches.

Generative recommendation is an emerging paradigm that has shown promise in industrial recommendation systems, aiming to predict users' next interactions from their historical behaviors. At the core of generative recommendation lies item tokenization, which bridges item semantics and recommendation models. However, existing methods often struggle to effectively organize and inject complex user-behavioral and item-semantic contexts into recommendation models simultaneously. On the one hand, existing graph-based integration methods, such as graph serialization and graph neural networks, either suffer from scalability issues or exploit only local graph information. On the other hand, existing semantic tokenization methods typically rely on heuristics and lack explicit supervision signals, which may lead to inaccurate or suboptimal semantic representations. To address these limitations in user interest context modeling, we propose G2Rec, a scalable framework that unifies holistic graph-based user co-engagement modeling with semantic tokenization for industrial-scale generative recommendation. Overall, G2Rec enables recommendation models to capture holistic and semantically grounded user interest prototypes without requiring ground-truth user interests, thereby providing more comprehensive and accurate modeling of user behavior contexts in industrial sequential recommendation. Online deployment across product surfaces and extensive experiments on public datasets demonstrate the superiority of G2Rec over existing methods.

We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the problem of DP mechanisms for adaptive streams with multiple participations and introduce a non-trivial extension of online matrix factorization DP mechanisms to our setting. This includes establishing the necessary theory for sensitivity calculations and efficient computation of optimal matrices. For some applications like >!! 10,000 SGD steps, applying these optimal techniques becomes computationally expensive. We thus design an efficient Fourier-transform-based mechanism with only a minor utility loss. Extensive empirical evaluation on both example-level DP for image classification and user-level DP for language modeling demonstrate substantial improvements over all previous methods, including the widely-used DP-SGD . Though our primary application is to ML, our main DP results are applicable to arbitrary linear queries and hence may have much broader applicability.

Generative recommendation autoregressively generates item identifiers to recommend potential items. Existing methods typically adopt a one-to-one mapping strategy, where each item is represented by a single identifier. However, this scheme poses issues, such as suboptimal semantic modeling for low-frequency items and limited diversity in token sequence data. To overcome these limitations, we propose MTGRec, which leverages Multi-identifier item Tokenization to augment token sequence data for Generative Recommender pre-training. Our approach involves two key innovations: multi-identifier item tokenization and curriculum recommender pre-training. For multi-identifier item tokenization, we leverage the RQ-VAE as the tokenizer backbone and treat model checkpoints from adjacent training epochs as semantically relevant tokenizers. This allows each item to be associated with multiple identifiers, enabling a single user interaction sequence to be converted into several token sequences as different data groups. For curriculum recommender pre-training, we introduce a curriculum learning scheme guided by data influence estimation, dynamically adjusting the sampling probability of each data group during recommender pre-training. After pre-training, we fine-tune the model using a single tokenizer to ensure accurate item identification for recommendation. Extensive experiments on three public benchmark datasets demonstrate that MTGRec significantly outperforms both traditional and generative recommendation baselines in terms of effectiveness and scalability.

Modern transformers pair impressive capabilities with substantial memory and compute demands. Low-rank weight factorization reduces both while keeping the matrices dense, and thus efficient on standard hardware. Existing methods, however, choose the subspace to remove from each weight matrix with local closed-form criteria: activation energy, layer-wise reconstruction error, or a quadratic approximation of the loss. These criteria ignore how errors propagate through the network, so at high compression the errors compound with depth and performance collapses. We introduce Learnable Subspace Projections (LSP), which instead learns the subspaces to discard end-to-end. Each linear layer, or tied group of layers that read the same activations, is assigned an orthogonal projector. All projectors are optimized jointly against a global objective--the KL divergence to the dense model's output distribution or the model's original training loss--while the pretrained weights remain frozen. Projectors are initialized from a whitened SVD truncation, and ranks are allocated by the output KL each projector induces per parameter saved. After training, the projectors merge into standard low-rank factors, with each tied group sharing one factor. In attention, this also lets the model cache one narrow latent in place of full keys and values. Across LLMs (OPT-125M/1.3B, Qwen3-4B, Llama-2-7B) and ViT-B/16, LSP outperforms baselines, and its advantage widens as compression increases. At -70% compression, LSP brings Llama-2-7B to 10.9 WikiText-2 perplexity and 42.2% mean zero-shot accuracy, versus 13.3 and 36.0% for the strongest baseline. The factorized model decodes up to 1.6x faster than the dense model at small batch sizes, and aching the shared latent shrinks the combined memory of weights and KV cache by 13.5x at a 128k-token context, versus at most 6.5x for untied baseline factorizations.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

Personalized recommendation systems shape much of user choice online, yet their targeted nature makes separating out the value of recommendation and the underlying goods challenging. We build a discrete choice model that embeds recommendation-induced utility, low-rank heterogeneity, and flexible state dependence and apply the model to viewership data at Netflix. We exploit idiosyncratic variation introduced by the recommendation algorithm to identify and separately value these components as well as to recover model-free diversion ratios that we can use to validate our structural model. We use the model to evaluate counterfactuals that quantify the incremental engagement generated by personalized recommendations. First, we show that replacing the current recommender system with a matrix factorization or popularity-based algorithm would lead to 4% and 12% reduction in engagement, respectively, and decreased consumption diversity. Second, most of the consumption increase from recommendations comes from effective targeting, not mechanical exposure, with the largest gains for mid-popularity goods (as opposed to broadly appealing or very niche goods).

Building a scalable and real-time recommendation system is vital for many businesses driven by time-sensitive customer feedback, such as short-videos ranking or online ads. Despite the ubiquitous adoption of production-scale deep learning frameworks like TensorFlow or PyTorch, these general-purpose frameworks fall short of business demands in recommendation scenarios for various reasons: on one hand, tweaking systems based on static parameters and dense computations for recommendation with dynamic and sparse features is detrimental to model quality; on the other hand, such frameworks are designed with batch-training stage and serving stage completely separated, preventing the model from interacting with customer feedback in real-time. These issues led us to reexamine traditional approaches and explore radically different design choices. In this paper, we present Monolith, a system tailored for online training. Our design has been driven by observations of our application workloads and production environment that reflects a marked departure from other recommendations systems. Our contributions are manifold: first, we crafted a collisionless embedding table with optimizations such as expirable embeddings and frequency filtering to reduce its memory footprint; second, we provide an production-ready online training architecture with high fault-tolerance; finally, we proved that system reliability could be traded-off for real-time learning. Monolith has successfully landed in the BytePlus Recommend product.

In recent years, the scaling laws of recommendation models have attracted increasing attention, which govern the relationship between performance and parameters/FLOPs of recommenders. Currently, there are three mainstream architectures for achieving scaling in recommendation models, namely attention-based, TokenMixer-based, and factorization-machine-based methods, which exhibit fundamental differences in both design philosophy and architectural structure. In this paper, we propose a unified scaling architecture for recommendation systems, namely UniMixer, to improve scaling efficiency and establish a unified theoretical framework that unifies the mainstream scaling blocks. By transforming the rule-based TokenMixer to an equivalent parameterized structure, we construct a generalized parameterized feature mixing module that allows the token mixing patterns to be optimized and learned during model training. Meanwhile, the generalized parameterized token mixing removes the constraint in TokenMixer that requires the number of heads to be equal to the number of tokens. Furthermore, we establish a unified scaling module design framework for recommender systems, which bridges the connections among attention-based, TokenMixer-based, and factorization-machine-based methods. To further boost scaling ROI, a lightweight UniMixing module is designed, UniMixing-Lite, which further compresses the model parameters and computational cost while significantly improve the model performance. The scaling curves are shown in the following figure. Extensive offline and online experiments are conducted to verify the superior scaling abilities of UniMixer.

Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising, representation learning, clustering, and latent variable modeling. In this work, we focus primarily on spectral estimators for high-dimensional factor models, where leading singular vectors of the data matrix are used to estimate latent structure and covariance parameters. In many modern applications, however, data are collected across related but heterogeneous tasks, studies, domains, or populations. Applying such estimators separately to each task can lead to unstable estimates when sample sizes are limited relative to dimension, while completely pooling the data can obscure meaningful task-specific structure. We introduce Hierarchical Spectral Shrinkage (HSS), a scalable empirical-Bayes framework for partially pooling task-specific spectral estimators. The method regularizes the leading spectral directions of each task toward a data-adaptivelylearned common basis, while allowing the amount of shrinkage to vary across tasks and spectral components. The proposed estimator arises as the posterior mean in a surrogate Bayesian regression formulation of the empirical singular vectors. For factor models, HSS yields partially pooled estimators of the group-specific loading spaces and covariance matrices and can be combined with different spectral estimators by replacing their empirical singular vectors with hierarchically regularized counterparts. More broadly, the same construction provides a mechanism for extending spectral estimators to collections of related but heterogeneous datasets. We demonstrate substantial improvements in estimation accuracy and out-of-sample performance over separate, fully pooled, and shared-subspace approaches in synthetic experiments and multi-study gene-expression data.

Active learning promises to alleviate the massive data needs of supervised machine learning: it has successfully improved sample efficiency by an order of magnitude on traditional tasks like topic classification and object recognition. However, we uncover a striking contrast to this promise: across 5 models and 4 datasets on the task of visual question answering, a wide variety of active learning approaches fail to outperform random selection. To understand this discrepancy, we profile 8 active learning methods on a per-example basis, and identify the problem as collective outliers -- groups of examples that active learning methods prefer to acquire but models fail to learn (e.g., questions that ask about text in images or require external knowledge). Through systematic ablation experiments and qualitative visualizations, we verify that collective outliers are a general phenomenon responsible for degrading pool-based active learning. Notably, we show that active learning sample efficiency increases significantly as the number of collective outliers in the active learning pool decreases. We conclude with a discussion and prescriptive recommendations for mitigating the effects of these outliers in future work.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using learning based methods, but did not examine the underlying connection to MWFAS. In this paper, we investigate this relationship and introduce efficient combinatorial algorithms for solving MWFAS as a means of addressing the ranking problem. Our experimental results show that these simple, learning free methods achieve substantially faster runtimes than recent learning based approaches, while also delivering competitive, and in many cases superior, ranking accuracy. These findings suggest that lightweight combinatorial techniques offer a scalable and effective alternative to deep learning for large scale ranking tasks.

Modern Large Language Models (LLMs) are composed of matrices with billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Being significantly large, such matrices can often be expressed in low-rank format with potential to relax resource requirements. Unlike prior works which focus on developing novel matrix decomposition algorithms, in this work we first study the emergence of low-rank structures across matrices within different layers of LLMs and establish a consequential relationship between the gradient dynamics and emerging low-rank expressiveness of matrices. Our findings reveal that different layers exhibit varying levels of converged low-rank structure, necessitating a non-uniform rank reduction across them to minimize performance drop due to compression. In view of that, we present Weight Low-Rank Projection (WeLore) that unifies weight compression and memory-efficient fine-tuning as ONE, in a data-agnostic and one-shot way. WeLore capitalizes the heavy-tail distribution of singular values to identify a suitable rank reduction ratio for matrices within LLMs. Going beyond only as a compression technique, WeLore categorizes weight matrices into Low-rank Components (LRCs) and Non-Low-rank Components (N-LRCs) based on their ability to express themselves as low-rank. Our gradient perspective and extensive experiments illustrate that LRCs tend to have better finetuning capabilities and can closely mimic (sometimes outperform) the training loss trajectory and performance of full-finetuning with notable memory and compute footprint reduction. For example, finetuning a 50\% compressed LLaMa-2 7B model using only a fraction of parameters in LRCs (WeLore) can outperform its full finetuning with ~3x better throughput and ~0.6x GPU requirement. Our codes are available at https://github.com/VITA-Group/welore

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method from the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly.

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking and node embedding. While prior work on local graph clustering mainly focuses on graphs without node attributes, modern real-world graph datasets typically come with node attributes that provide valuable additional information. We present a simple local graph clustering algorithm for graphs with node attributes, based on the idea of diffusing mass locally in the graph while accounting for both structural and attribute proximities. Using high-dimensional concentration results, we provide statistical guarantees on the performance of the algorithm for the recovery of a target cluster with a single seed node. We give conditions under which a target cluster generated from a fairly general contextual random graph model, which includes both the stochastic block model and the planted cluster model as special cases, can be fully recovered with bounded false positives. Empirically, we validate all theoretical claims using synthetic data, and we show that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Recommender systems are essential components of modern online platforms which presents personalized content in various domain. The traditional collaborative filtering methods depends on static user-item interaction graphs and a limited subset of similarity measures which fail to capture the changing nature of preferences of an individual. Recent graph neural network (GNN) based approaches focus on user-item bipartite graphs which do not use explicit user-user relational modelling and dynamic graph evolution during training. To address these limitations, this paper proposes a Dynamic Graph SimilarityAware Attention Graph Neural Network (DG-SA-GNN) framework that integrates dynamic user similarity graph construction with multi-similarity propagation and attention-based aggregation. The proposed architecture constructs four parallel user similarity graphs using Cosine, Jaccard, Discounted Pearson Correlation Coefficient (Discount PCC), and IPIJ similarity functions, each processed by a dedicated UserGNN module. A Graph Transformer fuses the four graph views, and a CrossAttention module refines user embeddings through interaction with item embeddings. Crucially, the graphs are reconstructed at scheduled epochs during training, enabling the model to adapt to the learned embedding space constituting the dynamic graph component. Mini-batch training with hard negative sampling improves scalability and convergence. Experiments on the MovieLens100K benchmark demonstrate that DG-SA-GNN achieves a Recall@20 of 0.162 and NDCG@20 of 0.065 which is better than the LightGCN baseline in recall. The results validate that dynamic multi-similarity graph construction coupled with attention-based fusion which produce recommendation performance

Generative recommendation (GR) typically first quantizes continuous item embeddings into multi-level semantic IDs (SIDs), and then generates the next item via autoregressive decoding. Although existing methods are already competitive in terms of recommendation performance, directly inheriting the autoregressive decoding paradigm from language models still suffers from three key limitations: (1) autoregressive decoding struggles to jointly capture global dependencies among the multi-dimensional features associated with different positions of SID; (2) using a unified, fixed decoding path for the same item implicitly assumes that all users attend to item attributes in the same order; (3) autoregressive decoding is inefficient at inference time and struggles to meet real-time requirements. To tackle these challenges, we propose MDGR, a Masked Diffusion Generative Recommendation framework that reshapes the GR pipeline from three perspectives: codebook, training, and inference. (1) We adopt a parallel codebook to provide a structural foundation for diffusion-based GR. (2) During training, we adaptively construct masking supervision signals along both the temporal and sample dimensions. (3) During inference, we develop a warm-up-based two-stage parallel decoding strategy for efficient generation of SIDs. Extensive experiments on multiple public and industrial-scale datasets show that MDGR outperforms ten state-of-the-art baselines by up to 10.78%. Furthermore, by deploying MDGR on a large-scale online advertising platform, we achieve a 1.20% increase in revenue, demonstrating its practical value.

Current recommender systems employ large-sized embedding tables with uniform dimensions for all features, leading to overfitting, high computational cost, and suboptimal generalizing performance. Many techniques aim to solve this issue by feature selection or embedding dimension search. However, these techniques typically select a fixed subset of features or embedding dimensions for all instances and feed all instances into one recommender model without considering heterogeneity between items or users. This paper proposes a novel instance-wise Hierarchical Architecture Search framework, iHAS, which automates neural architecture search at the instance level. Specifically, iHAS incorporates three stages: searching, clustering, and retraining. The searching stage identifies optimal instance-wise embedding dimensions across different field features via carefully designed Bernoulli gates with stochastic selection and regularizers. After obtaining these dimensions, the clustering stage divides samples into distinct groups via a deterministic selection approach of Bernoulli gates. The retraining stage then constructs different recommender models, each one designed with optimal dimensions for the corresponding group. We conduct extensive experiments to evaluate the proposed iHAS on two public benchmark datasets from a real-world recommender system. The experimental results demonstrate the effectiveness of iHAS and its outstanding transferability to widely-used deep recommendation models.

In modern machine learning problems we deal with datasets that are either distributed by nature or potentially large for which distributing the computations is usually a standard way to proceed, since centralized algorithms are in general ineffective. We propose a distributed learning approach for mixtures of experts (MoE) models with an aggregation strategy to construct a reduction estimator from local estimators fitted parallelly to distributed subsets of the data. The aggregation is based on an optimal minimization of an expected transportation divergence between the large MoE composed of local estimators and the unknown desired MoE model. We show that the provided reduction estimator is consistent as soon as the local estimators to be aggregated are consistent, and its construction is performed by a proposed majorization-minimization (MM) algorithm that is computationally effective. We study the statistical and numerical properties for the proposed reduction estimator on experiments that demonstrate its performance compared to namely the global estimator constructed in a centralized way from the full dataset. For some situations, the computation time is more than ten times faster, for a comparable performance. Our source codes are publicly available on Github.

Recommender Systems are built to retrieve relevant items to satisfy users' information needs. The candidate corpus usually consists of a finite set of items that are ready to be served, such as videos, products, or articles. With recent advances in Generative AI such as GPT and Diffusion models, a new form of recommendation task is yet to be explored where items are to be created by generative models with personalized prompts. Taking image generation as an example, with a single prompt from the user and access to a generative model, it is possible to generate hundreds of new images in a few minutes. How shall we attain personalization in the presence of "infinite" items? In this preliminary study, we propose a two-stage framework, namely Prompt-Model Retrieval and Generated Item Ranking, to approach this new task formulation. We release GEMRec-18K, a prompt-model interaction dataset with 18K images generated by 200 publicly-available generative models paired with a diverse set of 90 textual prompts. Our findings demonstrate the promise of generative model recommendation as a novel personalization problem and the limitations of existing evaluation metrics. We highlight future directions for the RecSys community to advance towards generative recommender systems. Our code and dataset are available at https://github.com/MAPS-research/GEMRec.

Recently, generative retrieval-based recommendation systems have emerged as a promising paradigm. However, most modern recommender systems adopt a retrieve-and-rank strategy, where the generative model functions only as a selector during the retrieval stage. In this paper, we propose OneRec, which replaces the cascaded learning framework with a unified generative model. To the best of our knowledge, this is the first end-to-end generative model that significantly surpasses current complex and well-designed recommender systems in real-world scenarios. Specifically, OneRec includes: 1) an encoder-decoder structure, which encodes the user's historical behavior sequences and gradually decodes the videos that the user may be interested in. We adopt sparse Mixture-of-Experts (MoE) to scale model capacity without proportionally increasing computational FLOPs. 2) a session-wise generation approach. In contrast to traditional next-item prediction, we propose a session-wise generation, which is more elegant and contextually coherent than point-by-point generation that relies on hand-crafted rules to properly combine the generated results. 3) an Iterative Preference Alignment module combined with Direct Preference Optimization (DPO) to enhance the quality of the generated results. Unlike DPO in NLP, a recommendation system typically has only one opportunity to display results for each user's browsing request, making it impossible to obtain positive and negative samples simultaneously. To address this limitation, We design a reward model to simulate user generation and customize the sampling strategy. Extensive experiments have demonstrated that a limited number of DPO samples can align user interest preferences and significantly improve the quality of generated results. We deployed OneRec in the main scene of Kuaishou, achieving a 1.6\% increase in watch-time, which is a substantial improvement.

Large nonlinear recurrent neural networks with random couplings generate high-dimensional, potentially chaotic activity whose structure is of interest in neuroscience and other fields. A fundamental object encoding the collective structure of this activity is the N times N covariance matrix. Prior analytical work on the covariance matrix has been limited to low-dimensional summary statistics. Recent work proposed an ansatz in which, at large N, the covariance matrix for a typical quenched realization takes the same form as that of a linear network with the same couplings, driven by independent noise, with DMFT order parameters setting the transfer function and the noise spectrum. Here, we derive this ansatz using the two-site cavity method, providing two derivations with complementary perspectives. The first decomposes each unit's activity into a linear response to its local field and a nonlinear residual, and shows that cross-covariances between residuals at distinct sites are strongly suppressed, so the residuals act as independent noise driving a linear network. The second derives a self-consistent matrix equation for the covariance matrix. A naive Gaussian closure for the joint statistics of local fields at distinct sites misses cross terms that, in a linear network, would be generated by an external drive. The cavity method recovers these terms from non-Gaussian contributions, revealing an emergent external drive. Higher-order cross-site moments follow a Wick-like decomposition into products of pairwise covariances at leading order, reducing them to the linear-equivalent form. We verify the predictions in simulations. These results extend linear equivalence from feedforward high-dimensional nonlinear systems, where the activations are independent of the weights, to recurrent networks, where the activations are correlated with the couplings that generate them.

Generative retrieval has emerged as a powerful paradigm for LLM-based recommendation. However, industrial recommender systems often benefit from restricting the output space to a constrained subset of items based on business logic (e.g. enforcing content freshness or product category), which standard autoregressive decoding cannot natively support. Moreover, existing constrained decoding methods that make use of prefix trees (Tries) incur severe latency penalties on hardware accelerators (TPUs/GPUs). In this work, we introduce STATIC (Sparse Transition Matrix-Accelerated Trie Index for Constrained Decoding), an efficient and scalable constrained decoding technique designed specifically for high-throughput LLM-based generative retrieval on TPUs/GPUs. By flattening the prefix tree into a static Compressed Sparse Row (CSR) matrix, we transform irregular tree traversals into fully vectorized sparse matrix operations, unlocking massive efficiency gains on hardware accelerators. We deploy STATIC on a large-scale industrial video recommendation platform serving billions of users. STATIC produces significant product metric impact with minimal latency overhead (0.033 ms per step and 0.25% of inference time), achieving a 948x speedup over a CPU trie implementation and a 47-1033x speedup over a hardware-accelerated binary-search baseline. Furthermore, the runtime overhead of STATIC remains extremely low across a wide range of practical configurations. To the best of our knowledge, STATIC enables the first production-scale deployment of strictly constrained generative retrieval. In addition, evaluation on academic benchmarks demonstrates that STATIC can considerably improve cold-start performance for generative retrieval. Our code is available at https://github.com/youtube/static-constraint-decoding.

Recommendation foundation model utilizes large language models (LLM) for recommendation by converting recommendation tasks into natural language tasks. It enables generative recommendation which directly generates the item(s) to recommend rather than calculating a ranking score for each and every candidate item in traditional recommendation models, simplifying the recommendation pipeline from multi-stage filtering to single-stage filtering. To avoid generating excessively long text and hallucinated recommendation when deciding which item(s) to recommend, creating LLM-compatible item IDs to uniquely identify each item is essential for recommendation foundation models. In this study, we systematically examine the item indexing problem for recommendation foundation models, using P5 as an example of backbone model. To emphasize the importance of item indexing, we first discuss the issues of several trivial item indexing methods, such as independent indexing, title indexing, and random indexing. We then propose four simple yet effective solutions, including sequential indexing, collaborative indexing, semantic (content-based) indexing, and hybrid indexing. Our study highlights the significant influence of item indexing methods on the performance of LLM-based recommendation, and our results on real-world datasets validate the effectiveness of our proposed solutions. The research also demonstrates how recent advances on language modeling and traditional IR principles such as indexing can help each other for better learning and inference.

Multi-Task Learning (MTL) aims to boost predictive performance by sharing information across related tasks, yet conventional methods often suffer from negative transfer when unrelated or noisy tasks are forced to share representations. We propose Robust Multi-Task Boosting using Clustering and Local Ensembling (RMB-CLE), a principled MTL framework that integrates error-based task clustering with local ensembling. Unlike prior work that assumes fixed clusters or hand-crafted similarity metrics, RMB-CLE derives inter-task similarity directly from cross-task errors, which admit a risk decomposition into functional mismatch and irreducible noise, providing a theoretically grounded mechanism to prevent negative transfer. Tasks are grouped adaptively via agglomerative clustering, and within each cluster, a local ensemble enables robust knowledge sharing while preserving task-specific patterns. Experiments show that RMB-CLE recovers ground-truth clusters in synthetic data and consistently outperforms multi-task, single-task, and pooling-based ensemble methods across diverse real-world and synthetic benchmarks. These results demonstrate that RMB-CLE is not merely a combination of clustering and boosting but a general and scalable framework that establishes a new basis for robust multi-task learning.

Large-scale machine learning and data mining methods routinely distribute computations across multiple agents to parallelize processing. The time required for the computations at the agents is affected by the availability of local resources and/or poor channel conditions giving rise to the "straggler problem". As a remedy to this problem, we employ Unequal Error Protection (UEP) codes to obtain an approximation of the matrix product in the distributed computation setting to provide higher protection for the blocks with higher effect on the final result. We characterize the performance of the proposed approach from a theoretical perspective by bounding the expected reconstruction error for matrices with uncorrelated entries. We also apply the proposed coding strategy to the computation of the back-propagation step in the training of a Deep Neural Network (DNN) for an image classification task in the evaluation of the gradients. Our numerical experiments show that it is indeed possible to obtain significant improvements in the overall time required to achieve the DNN training convergence by producing approximation of matrix products using UEP codes in the presence of stragglers.

Large scale recommender models find most relevant items from huge catalogs, and they play a critical role in modern search and recommendation systems. To model the input space with large-vocab categorical features, a typical recommender model learns a joint embedding space through neural networks for both queries and items from user feedback data. However, with millions to billions of items in the corpus, users tend to provide feedback for a very small set of them, causing a power-law distribution. This makes the feedback data for long-tail items extremely sparse. Inspired by the recent success in self-supervised representation learning research in both computer vision and natural language understanding, we propose a multi-task self-supervised learning (SSL) framework for large-scale item recommendations. The framework is designed to tackle the label sparsity problem by learning better latent relationship of item features. Specifically, SSL improves item representation learning as well as serving as additional regularization to improve generalization. Furthermore, we propose a novel data augmentation method that utilizes feature correlations within the proposed framework. We evaluate our framework using two real-world datasets with 500M and 1B training examples respectively. Our results demonstrate the effectiveness of SSL regularization and show its superior performance over the state-of-the-art regularization techniques. We also have already launched the proposed techniques to a web-scale commercial app-to-app recommendation system, with significant improvements top-tier business metrics demonstrated in A/B experiments on live traffic. Our online results also verify our hypothesis that our framework indeed improves model performance even more on slices that lack supervision.

In this era of information explosion, a personalized recommendation system is convenient for users to get information they are interested in. To deal with billions of users and items, large-scale online recommendation services usually consist of three stages: candidate generation, coarse-grained ranking, and fine-grained ranking. The success of each stage depends on whether the model accurately captures the interests of users, which are usually hidden in users' behavior data. Previous research shows that users' interests are diverse, and one vector is not sufficient to capture users' different preferences. Therefore, many methods use multiple vectors to encode users' interests. However, there are two unsolved problems: (1) The similarity of different vectors in existing methods is too high, with too much redundant information. Consequently, the interests of users are not fully represented. (2) Existing methods model the long-term and short-term behaviors together, ignoring the differences between them. This paper proposes a Hierarchical Multi-Interest Co-Network (HCN) to capture users' diverse interests in the coarse-grained ranking stage. Specifically, we design a hierarchical multi-interest extraction layer to update users' diverse interest centers iteratively. The multiple embedded vectors obtained in this way contain more information and represent the interests of users better in various aspects. Furthermore, we develop a Co-Interest Network to integrate users' long-term and short-term interests. Experiments on several real-world datasets and one large-scale industrial dataset show that HCN effectively outperforms the state-of-the-art methods. We deploy HCN into a large-scale real world E-commerce system and achieve extra 2.5\% improvements on GMV (Gross Merchandise Value).

Generative Recommendation (GR) has emerged as a transformative paradigm that reformulates the traditional cascade ranking system into a sequence-to-item generation task, facilitated by the use of discrete Semantic IDs (SIDs). However, current SIDs are suboptimal as the indexing objectives (Stage 1) are misaligned with the actual recommendation goals (Stage 2). Since these identifiers remain static (Stage 2), the backbone model lacks the flexibility to adapt them to the evolving complexities of user interactions. Furthermore, the prevailing strategy of flattening hierarchical SIDs into token sequences leads to sequence length inflation, resulting in prohibitive computational overhead and inference latency. To address these challenges, we propose IntRR, a novel framework that integrates objective-aligned SID Redistribution and structural Length Reduction. By leveraging item-specific Unique IDs (UIDs) as collaborative anchors, this approach dynamically redistributes semantic weights across hierarchical codebook layers. Concurrently, IntRR handles the SID hierarchy recursively, eliminating the need to flatten sequences. This ensures a fixed cost of one token per item. Extensive experiments on benchmark datasets demonstrate that IntRR yields substantial improvements over representative generative baselines, achieving superior performance in both recommendation accuracy and efficiency.