Daily Papers

We characterise and enumerate permutations that are sortable by n-4 passes through a stack. We conjecture the number of permutations sortable by n-5 passes, and also the form of a formula for the general case n-k, which involves a polynomial expression.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

The democratization of machine learning systems has made the process of fine-tuning accessible to practitioners, leading to a wide range of open-source models fine-tuned on specialized tasks and datasets. Recent work has proposed to merge such models to combine their functionalities. However, prior approaches are usually restricted to models that are fine-tuned from the same base model. Furthermore, the final merged model is typically required to be of the same size as the original models. In this work, we propose a new two-step algorithm to merge models -- termed PLeaS -- which relaxes these constraints. First, leveraging the Permutation symmetries inherent in the two models, PLeaS partially matches nodes in each layer by maximizing alignment. Next, PLeaS computes the weights of the merged model as a layer-wise Least Squares solution to minimize the approximation error between the features of the merged model and the permuted features of the original models. PLeaS allows a practitioner to merge two models sharing the same architecture into a single performant model of a desired size, even when the two original models are fine-tuned from different base models. We also demonstrate how our method can be extended to address a challenging scenario where no data is available from the fine-tuning domains. We demonstrate our method to merge ResNet and ViT models trained with shared and different label spaces, and show improvement over the state-of-the-art merging methods of up to 15 percentage points for the same target compute while merging models trained on DomainNet and fine-grained classification tasks. Our code is open-sourced at https://github.com/SewoongLab/PLeaS-Merging .

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components n and the number of epochs K, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number kappa. For SGD with Random Reshuffling, we present lower bounds that have tighter kappa dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of n and kappa and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

A universal word (u-word) for d-dimensional permutations of length n is a 2-dimensional word with d-1 rows, any size n window of which is order-isomorphic to exactly one permutation of length n, and all permutations of length n are covered. It is known that u-words (in fact, even u-cycles, a stronger claim) for d-dimensional permutations exist. In this paper, we use the idea of incomparable elements to prove that u-words of length (n!)^{d-1}+n-1-i(n-1), for dgeq 2 and $0leq ileq 2^{d-1}{n-1}left[(1+(n-1)!)^{d-1}-left(1+(n-1)!{2}right)^{d-1}right], for d-dimensional permutations of length n exist, which generalizes the respective result of Kitaev, Potapov and Vajnovszki for ``usual'' permutations (d=2$).

A key to knowledge graph embedding (KGE) is to choose a proper representation space, e.g., point-wise Euclidean space and complex vector space. In this paper, we propose a unified perspective of embedding and introduce uncertainty into KGE from the view of group theory. Our model can incorporate existing models (i.e., generality), ensure the computation is tractable (i.e., efficiency) and enjoy the expressive power of complex random variables (i.e., expressiveness). The core idea is that we embed entities/relations as elements of a symmetric group, i.e., permutations of a set. Permutations of different sets can reflect different properties of embedding. And the group operation of symmetric groups is easy to compute. In specific, we show that the embedding of many existing models, point vectors, can be seen as elements of a symmetric group. To reflect uncertainty, we first embed entities/relations as permutations of a set of random variables. A permutation can transform a simple random variable into a complex random variable for greater expressiveness, called a normalizing flow. We then define scoring functions by measuring the similarity of two normalizing flows, namely NFE. We construct several instantiating models and prove that they are able to learn logical rules. Experimental results demonstrate the effectiveness of introducing uncertainty and our model. The code is available at https://github.com/changyi7231/NFE.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Self-supervised learning of convolutional neural networks can harness large amounts of cheap unlabeled data to train powerful feature representations. As surrogate task, we jointly address ordering of visual data in the spatial and temporal domain. The permutations of training samples, which are at the core of self-supervision by ordering, have so far been sampled randomly from a fixed preselected set. Based on deep reinforcement learning we propose a sampling policy that adapts to the state of the network, which is being trained. Therefore, new permutations are sampled according to their expected utility for updating the convolutional feature representation. Experimental evaluation on unsupervised and transfer learning tasks demonstrates competitive performance on standard benchmarks for image and video classification and nearest neighbor retrieval.

Panoptic segmentation assigns semantic and instance ID labels to every pixel of an image. As permutations of instance IDs are also valid solutions, the task requires learning of high-dimensional one-to-many mapping. As a result, state-of-the-art approaches use customized architectures and task-specific loss functions. We formulate panoptic segmentation as a discrete data generation problem, without relying on inductive bias of the task. A diffusion model is proposed to model panoptic masks, with a simple architecture and generic loss function. By simply adding past predictions as a conditioning signal, our method is capable of modeling video (in a streaming setting) and thereby learns to track object instances automatically. With extensive experiments, we demonstrate that our simple approach can perform competitively to state-of-the-art specialist methods in similar settings.

This work presents DAVINCI, a unified architecture for single-stage Computer-Aided Design (CAD) sketch parameterization and constraint inference directly from raster sketch images. By jointly learning both outputs, DAVINCI minimizes error accumulation and enhances the performance of constrained CAD sketch inference. Notably, DAVINCI achieves state-of-the-art results on the large-scale SketchGraphs dataset, demonstrating effectiveness on both precise and hand-drawn raster CAD sketches. To reduce DAVINCI's reliance on large-scale annotated datasets, we explore the efficacy of CAD sketch augmentations. We introduce Constraint-Preserving Transformations (CPTs), i.e. random permutations of the parametric primitives of a CAD sketch that preserve its constraints. This data augmentation strategy allows DAVINCI to achieve reasonable performance when trained with only 0.1% of the SketchGraphs dataset. Furthermore, this work contributes a new version of SketchGraphs, augmented with CPTs. The newly introduced CPTSketchGraphs dataset includes 80 million CPT-augmented sketches, thus providing a rich resource for future research in the CAD sketch domain.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

Multimodal learning holds promise for richer information extraction by capturing dependencies across data sources. Yet, current training methods often underperform due to modality competition, a phenomenon where modalities contend for training resources leaving some underoptimized. This raises a pivotal question: how can we address training imbalances, ensure adequate optimization across all modalities, and achieve consistent performance improvements as we transition from unimodal to multimodal data? This paper proposes the Multimodal Competition Regularizer (MCR), inspired by a mutual information (MI) decomposition designed to prevent the adverse effects of competition in multimodal training. Our key contributions are: 1) A game-theoretic framework that adaptively balances modality contributions by encouraging each to maximize its informative role in the final prediction 2) Refining lower and upper bounds for each MI term to enhance the extraction of both task-relevant unique and shared information across modalities. 3) Proposing latent space permutations for conditional MI estimation, significantly improving computational efficiency. MCR outperforms all previously suggested training strategies and simple baseline, clearly demonstrating that training modalities jointly leads to important performance gains on both synthetic and large real-world datasets. We release our code and models at https://github.com/kkontras/MCR.

Over the past few years, the acceleration of computing resources and research in deep learning has led to significant practical successes in a range of tasks, including in particular in computer vision. Building on these advances, reinforcement learning has also seen a leap forward with the emergence of agents capable of making decisions directly from visual observations. Despite these successes, the over-parametrization of neural architectures leads to memorization of the data used during training and thus to a lack of generalization. Reinforcement learning agents based on visual inputs also suffer from this phenomenon by erroneously correlating rewards with unrelated visual features such as background elements. To alleviate this problem, we introduce a new regularization technique consisting of channel-consistent local permutations (CLOP) of the feature maps. The proposed permutations induce robustness to spatial correlations and help prevent overfitting behaviors in RL. We demonstrate, on the OpenAI Procgen Benchmark, that RL agents trained with the CLOP method exhibit robustness to visual changes and better generalization properties than agents trained using other state-of-the-art regularization techniques. We also demonstrate the effectiveness of CLOP as a general regularization technique in supervised learning.

Neural field is an emerging paradigm in data representation that trains a neural network to approximate the given signal. A key obstacle that prevents its widespread adoption is the encoding speed-generating neural fields requires an overfitting of a neural network, which can take a significant number of SGD steps to reach the desired fidelity level. In this paper, we delve into the impacts of data transformations on the speed of neural field training, specifically focusing on how permuting pixel locations affect the convergence speed of SGD. Counterintuitively, we find that randomly permuting the pixel locations can considerably accelerate the training. To explain this phenomenon, we examine the neural field training through the lens of PSNR curves, loss landscapes, and error patterns. Our analyses suggest that the random pixel permutations remove the easy-to-fit patterns, which facilitate easy optimization in the early stage but hinder capturing fine details of the signal.

Large language models (LLMs) are now widely used to evaluate the quality of text, a field commonly referred to as LLM-as-a-judge. While prior works mainly focus on point-wise and pair-wise evaluation paradigms. Rubric-based evaluation, where LLMs select a score from multiple rubrics, has received less analysis. In this work, we show that rubric-based evaluation implicitly resembles a multi-choice setting and therefore has position bias: LLMs prefer score options appearing at specific positions in the rubric list. Through controlled experiments across multiple models and datasets, we demonstrate consistent position bias. To mitigate this bias, we propose a balanced permutation strategy that evenly distributes each score option across positions. We show that aggregating scores across balanced permutations not only reveals latent position bias, but also improves correlation between the LLM-as-a-Judge and human. Our results suggest that rubric-based LLM-as-a-Judge is not inherently point-wise and that simple permutation-based calibration can substantially improve its reliability.

Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series data. In this study, we propose an efficient architecture, Temporal-Guided Network (TGNet), which utilizes graph networks and temporal-guided embedding. Graph networks extract invariant features to permutations of adjacent regions instead of convolutional layers. Temporal-guided embedding explicitly learns temporal contexts from training data and is substituted for the input of long-term histories from days/weeks ago. TGNet learns an autoregressive model, conditioned on temporal contexts of forecasting targets from temporal-guided embedding. Finally, our model achieves competitive performances with other baselines on three spatiotemporal demand dataset from real-world, but the number of trainable parameters is about 20 times smaller than a state-of-the-art baseline. We also show that temporal-guided embedding learns temporal contexts as intended and TGNet has robust forecasting performances even to atypical event situations.

Condorcet domains are subsets of permutations that ensure pairwise majority voting yields acyclic outcomes, and they form an active area of research at the intersection of social choice theory and combinatorics. In this paper, we extend the theory of Condorcet domains to the broader setting of arbitrary finite Coxeter groups. The core contribution of our approach is the introduction of Condorcet root posets, defined on the chosen root systems. Notably, we establish a natural bijection between closed Condorcet domains and Condorcet root posets, which facilitates the study of Condorcet domains. Using this correspondence, we extend the median graph representation of closed Condorcet domains to arbitrary finite Coxeter groups, demonstrating that these domains can be characterized by the skeletons of their associated Condorcet root posets. These results are novel even in type A. Furthermore, these posets give a unified language that efficiently captures a wide range of desirable properties of Condorcet domains, such as being maximal, connected, peak-pit, and of tiling type. Using this framework, we strengthen and generalize several classical results: we establish that a maximal Condorcet domain is connected if and only if it is peak-pit; we prove that the tiling-type property is equivalent to the combination of being maximal and connected, and having maximal width; and we show that strictly positive voting profiles on connected Condorcet domains yield outcomes with only simple ties.

Syntactic parsing remains a critical tool for relation extraction and information extraction, especially in resource-scarce languages where LLMs are lacking. Yet in morphologically rich languages (MRLs), where parsers need to identify multiple lexical units in each token, existing systems suffer in latency and setup complexity. Some use a pipeline to peel away the layers: first segmentation, then morphology tagging, and then syntax parsing; however, errors in earlier layers are then propagated forward. Others use a joint architecture to evaluate all permutations at once; while this improves accuracy, it is notoriously slow. In contrast, and taking Hebrew as a test case, we present a new "flipped pipeline": decisions are made directly on the whole-token units by expert classifiers, each one dedicated to one specific task. The classifiers are independent of one another, and only at the end do we synthesize their predictions. This blazingly fast approach sets a new SOTA in Hebrew POS tagging and dependency parsing, while also reaching near-SOTA performance on other Hebrew NLP tasks. Because our architecture does not rely on any language-specific resources, it can serve as a model to develop similar parsers for other MRLs.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

The whole-brain connectome of a fruit fly comprises over 130K neurons connected with a probability of merely 0.02%, yet achieves an average shortest path of only 4.4 hops. Despite being highly structured at the circuit level, the network's long-range connections are broadly distributed across brain regions, functioning as stochastic shortcuts that enable efficient global communication. Inspired by this observation, we propose Stochastic Attention (SA), a drop-in enhancement for sliding-window attention (SWA) that applies a random permutation to the token sequence before windowed attention and restores the original order afterward. This transforms the fixed local window into a stochastic global one within the same O(nw) per-layer budget. Through depth, independently sampled permutations yield exponentially growing receptive fields, achieving full sequence coverage in O(log_w n) layers versus O(n/w) for SWA. We validate SA in two settings: pre-training language models from scratch, where a gated SA + SWA combination achieves the best average zero-shot accuracy, and training-free inference on Qwen3-8B and Qwen3-30B-A3B, where SA consistently outperforms SWA and matches or exceeds Mixture of Block Attention at comparable compute budgets. These results suggest that connectome-inspired stochastic routing is a practical primitive for improving the expressivity of efficient attention, complementary to existing linear and sparse approaches.

When primed with only a handful of training samples, very large, pretrained language models such as GPT-3 have shown competitive results when compared to fully-supervised, fine-tuned, large, pretrained language models. We demonstrate that the order in which the samples are provided can make the difference between near state-of-the-art and random guess performance: essentially some permutations are "fantastic" and some not. We analyse this phenomenon in detail, establishing that: it is present across model sizes (even for the largest current models), it is not related to a specific subset of samples, and that a given good permutation for one model is not transferable to another. While one could use a development set to determine which permutations are performant, this would deviate from the true few-shot setting as it requires additional annotated data. Instead, we use the generative nature of language models to construct an artificial development set and based on entropy statistics of the candidate permutations on this set, we identify performant prompts. Our method yields a 13% relative improvement for GPT-family models across eleven different established text classification tasks.

Retrieval-Augmented Generation (RAG) has become a key paradigm for reducing factual hallucinations in large language models (LLMs), yet little is known about how the order of retrieved documents affects model behavior. We empirically show that under Top-5 retrieval with the gold document included, LLM answers vary substantially across permutations of the retrieved set, even when the gold document is fixed in the first position. This reveals a previously underexplored sensitivity to retrieval permutations. Although robust RAG methods primarily focus on enhancing LLM robustness to low-quality retrieval and mitigating positional bias to distribute attention fairly over long contexts, neither approach directly addresses permutation sensitivity. In this paper, we propose Stable-RAG, which exploits permutation sensitivity estimation to mitigate permutation-induced hallucinations. Stable-RAG runs the generator under multiple retrieval orders, clusters hidden states, and decodes from a cluster-center representation that captures the dominant reasoning pattern. It then uses these reasoning results to align hallucinated outputs toward the correct answer, encouraging the model to produce consistent and accurate predictions across document permutations. Experiments on three QA datasets show that Stable-RAG significantly improves answer accuracy, reasoning consistency and robust generalization across datasets, retrievers, and input lengths compared with baselines.

Transformers are central to recent successes in natural language processing and computer vision. Transformers have a mostly uniform backbone where layers alternate between feed-forward and self-attention in order to build a deep network. Here we investigate this design choice and find that more complex blocks that have different permutations of layer primitives can be more efficient. Using this insight, we develop a complex block, named Brainformer, that consists of a diverse sets of layers such as sparsely gated feed-forward layers, dense feed-forward layers, attention layers, and various forms of layer normalization and activation functions. Brainformer consistently outperforms the state-of-the-art dense and sparse Transformers, in terms of both quality and efficiency. A Brainformer model with 8 billion activated parameters per token demonstrates 2x faster training convergence and 5x faster step time compared to its GLaM counterpart. In downstream task evaluation, Brainformer also demonstrates a 3% higher SuperGLUE score with fine-tuning compared to GLaM with a similar number of activated parameters. Finally, Brainformer largely outperforms a Primer dense model derived with NAS with similar computation per token on fewshot evaluations.

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~li2022permutation showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that Omega(2^N) evaluations are typically required in TNLS for reaching the objective reduction in the neighborhood, while ideally O(N^2R) evaluations are sufficient in TnALE, where N denotes the tensor order and R reflects the ``low-rankness'' of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

Neural networks often suffer from catastrophic interference (CI): performance on previously learned tasks drops off significantly when learning a new task. This contrasts strongly with humans, who can sequentially learn new tasks without appreciably forgetting previous tasks. Prior work has explored various techniques for mitigating CI such as regularization, rehearsal, generative replay, and distillation methods. The current work takes a different approach, one guided by cognitive science research showing that in naturalistic environments, the probability of encountering a task decreases as a power-law of the time since it was last performed. We argue that a realistic evaluation of techniques for the mitigation of CI should be performed in simulated naturalistic learning environments. Thus, we evaluate the extent of mitigation of CI when training simple rehearsal-based methods in power-law environments similar to the ones humans face. Our work explores this novel rehearsal-based approach for a domain-incremental task: learning permutations in the MNIST task. We compare our rehearsal environment with other baselines to show its efficacy in promoting continual learning. Additionally, we investigate whether this environment shows forward facilitation, i.e., faster learning of later tasks. Next, we explore the robustness of our learning environment to the number of tasks, model size, and amount of data rehearsed after each task. Notably, our results show that the performance is comparable or superior to that of models trained using popular regularization methods and also to rehearsals in non-power-law environments. The benefits of this training paradigm include simplicity and the lack of a need for extra neural circuitry. In addition, because our method is orthogonal to other methods, future research can combine training in power-law environments with other continual learning mechanisms.

The output structure of database-like tables, consisting of values structured in horizontal rows and vertical columns identifiable by name, can cover a wide range of NLP tasks. Following this constatation, we propose a framework for text-to-table neural models applicable to problems such as extraction of line items, joint entity and relation extraction, or knowledge base population. The permutation-based decoder of our proposal is a generalized sequential method that comprehends information from all cells in the table. The training maximizes the expected log-likelihood for a table's content across all random permutations of the factorization order. During the content inference, we exploit the model's ability to generate cells in any order by searching over possible orderings to maximize the model's confidence and avoid substantial error accumulation, which other sequential models are prone to. Experiments demonstrate a high practical value of the framework, which establishes state-of-the-art results on several challenging datasets, outperforming previous solutions by up to 15%.

Effective evaluation of the reasoning capabilities of large language models (LLMs) are susceptible to overestimation due to data exposure of evaluation benchmarks. We introduce a framework for producing linguistic reasoning problems that reduces the effect of memorisation in model performance estimates and apply this framework to develop LINGOLY-TOO, a challenging evaluation benchmark for linguistic reasoning. By developing orthographic templates, we dynamically obfuscate the writing systems of real languages to generate numerous question variations. These variations preserve the reasoning steps required for each solution while reducing the likelihood of specific problem instances appearing in model training data. Our experiments demonstrate that frontier models, including OpenAI o1-preview and DeepSeem R1, struggle with advanced reasoning. Our analysis also shows that LLMs exhibit noticeable variance in accuracy across permutations of the same problem, and on average perform better on questions appearing in their original orthography. Our findings highlight the opaque nature of response generation in LLMs and provide evidence that prior data exposure contributes to overestimating the reasoning capabilities of frontier models.

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose REOrder, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. REOrder improves top-1 accuracy over row-major ordering on ImageNet-1K by up to 3.01% and Functional Map of the World by 13.35%.

Prior research indicates that LID model performance significantly declines on accented speech; however, the specific causes, extent, and characterization of these errors remain under-explored. (i) We identify a common failure mode on accented speech whereby LID systems often misclassify L2 accented speech as the speaker's native language or a related language. (ii) We present evidence suggesting that state-of-the-art models are invariant to permutations of short spans of speech, implying they classify on the basis of short phonotactic features indicative of accent rather than language. Our analysis reveals a simple method to enhance model robustness to accents through input chunking. (iii) We present an approach that integrates sequence-level information into our model without relying on monolingual ASR systems; this reduces accent-language confusion and significantly enhances performance on accented speech while maintaining comparable results on standard LID.

Revolutionizing the field of deep learning, Transformer-based models have achieved remarkable performance in many tasks. Recent research has recognized these models are robust to shuffling but are limited to inter-token permutation in the forward propagation. In this work, we propose our definition of permutation equivariance, a broader concept covering both inter- and intra- token permutation in the forward and backward propagation of neural networks. We rigorously proved that such permutation equivariance property can be satisfied on most vanilla Transformer-based models with almost no adaptation. We examine the property over a range of state-of-the-art models including ViT, Bert, GPT, and others, with experimental validations. Further, as a proof-of-concept, we explore how real-world applications including privacy-enhancing split learning, and model authorization, could exploit the permutation equivariance property, which implicates wider, intriguing application scenarios.

In passage reranking, response ranking and multi-document question answering, LLMs can score several candidate documents or responses together in one prompt, each still receiving its own score. Such scorers are selected on ranking quality, but their scores determine a decision: what a score threshold retains, a reader answers, or which chosen/rejected pair enters preference training. Because the candidates share that prompt, reordering them changes their scores. The same query over the same candidates should still yield the same decision. However, equal ranking quality does not imply equal decisions: on passage reranking, five trained scorers within 0.010 nDCG@10 retain sets that overlap by only 0.66-0.84 when reordered. No prompt-time change we test resolves that dependence: the only one that improves ranking quality does not measurably improve decision stability. We introduce order-consistency SFT (OC-SFT), which attenuates it in the weights by penalizing disagreement between a candidate's scores across orderings. It holds ranking quality and leads every decision-stability measure among trained scorers on all three tasks. It is also more stable on 12 base models than order-averaged distillation, which trains on labels averaged across permutations. One OC-SFT permutation retains sets that overlap more than ten averaged off-the-shelf permutations. A comparison of such scorers should therefore report what a threshold retains and a reader answers, not ranking quality alone. Code is available at https://github.com/thomsonreuters/presentation-dependence.

Decoding the linguistic intricacies of the genome is a crucial problem in biology, and pre-trained foundational models such as DNABERT and Nucleotide Transformer have made significant strides in this area. Existing works have largely hinged on k-mer, fixed-length permutations of A, T, C, and G, as the token of the genome language due to its simplicity. However, we argue that the computation and sample inefficiencies introduced by k-mer tokenization are primary obstacles in developing large genome foundational models. We provide conceptual and empirical insights into genome tokenization, building on which we propose to replace k-mer tokenization with Byte Pair Encoding (BPE), a statistics-based data compression algorithm that constructs tokens by iteratively merging the most frequent co-occurring genome segment in the corpus. We demonstrate that BPE not only overcomes the limitations of k-mer tokenization but also benefits from the computational efficiency of non-overlapping tokenization. Based on these insights, we introduce DNABERT-2, a refined genome foundation model that adapts an efficient tokenizer and employs multiple strategies to overcome input length constraints, reduce time and memory expenditure, and enhance model capability. Furthermore, we identify the absence of a comprehensive and standardized benchmark for genome understanding as another significant impediment to fair comparative analysis. In response, we propose the Genome Understanding Evaluation (GUE), a comprehensive multi-species genome classification dataset that amalgamates 28 distinct datasets across 7 tasks, with input lengths ranging from 70 to 1000. Through comprehensive experiments on the GUE benchmark, we demonstrate that DNABERT-2 achieves comparable performance to the state-of-the-art model with 21 times fewer parameters and approximately 56 times less GPU time in pre-training.

We study the problem of recovering an underlying 3D shape from a set of images. Existing learning based approaches usually resort to recurrent neural nets, e.g., GRU, or intuitive pooling operations, e.g., max/mean poolings, to fuse multiple deep features encoded from input images. However, GRU based approaches are unable to consistently estimate 3D shapes given different permutations of the same set of input images as the recurrent unit is permutation variant. It is also unlikely to refine the 3D shape given more images due to the long-term memory loss of GRU. Commonly used pooling approaches are limited to capturing partial information, e.g., max/mean values, ignoring other valuable features. In this paper, we present a new feed-forward neural module, named AttSets, together with a dedicated training algorithm, named FASet, to attentively aggregate an arbitrarily sized deep feature set for multi-view 3D reconstruction. The AttSets module is permutation invariant, computationally efficient and flexible to implement, while the FASet algorithm enables the AttSets based network to be remarkably robust and generalize to an arbitrary number of input images. We thoroughly evaluate FASet and the properties of AttSets on multiple large public datasets. Extensive experiments show that AttSets together with FASet algorithm significantly outperforms existing aggregation approaches.

3D Gaussian Splatting has recently emerged as a highly promising technique for modeling of static 3D scenes. In contrast to Neural Radiance Fields, it utilizes efficient rasterization allowing for very fast rendering at high-quality. However, the storage size is significantly higher, which hinders practical deployment, e.g.~on resource constrained devices. In this paper, we introduce a compact scene representation organizing the parameters of 3D Gaussian Splatting (3DGS) into a 2D grid with local homogeneity, ensuring a drastic reduction in storage requirements without compromising visual quality during rendering. Central to our idea is the explicit exploitation of perceptual redundancies present in natural scenes. In essence, the inherent nature of a scene allows for numerous permutations of Gaussian parameters to equivalently represent it. To this end, we propose a novel highly parallel algorithm that regularly arranges the high-dimensional Gaussian parameters into a 2D grid while preserving their neighborhood structure. During training, we further enforce local smoothness between the sorted parameters in the grid. The uncompressed Gaussians use the same structure as 3DGS, ensuring a seamless integration with established renderers. Our method achieves a reduction factor of 8x to 26x in size for complex scenes with no increase in training time, marking a substantial leap forward in the domain of 3D scene distribution and consumption. Additional information can be found on our project page: https://fraunhoferhhi.github.io/Self-Organizing-Gaussians/

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

Retrieval-augmented generation (RAG) has emerged as a popular approach to steering the output of a large language model (LLM) by incorporating retrieved contexts as inputs. However, existing work observed the generator bias, such that improving the retrieval results may negatively affect the outcome. In this work, we show such bias can be mitigated, from inference scaling, aggregating inference calls from the permuted order of retrieved contexts. The proposed Mixture-of-Intervention (MOI) explicitly models the debiased utility of each passage with multiple forward passes to construct a new ranking. We also show that MOI can leverage the retriever's prior knowledge to reduce the computational cost by minimizing the number of permutations considered and lowering the cost per LLM call. We showcase the effectiveness of MOI on diverse RAG tasks, improving ROUGE-L on MS MARCO and EM on HotpotQA benchmarks by ~7 points.

Many environmental remediation and energy applications (conversion and storage) for sustainability need design and development of green novel materials. Discovery processes of such novel materials are time taking and cumbersome due to large number of possible combinations and permutations of materials structures. Often theoretical studies based on Density Functional Theory (DFT) and other theories, coupled with Simulations are conducted to narrow down sample space of candidate materials, before conducting laboratory-based synthesis and analytical process. With the emergence of artificial intelligence (AI), AI techniques are being tried in this process too to ease out simulation time and cost. However tremendous values of previously published research from various parts of the world are still left as labor-intensive manual effort and discretion of individual researcher and prone to human omissions. AIMS-EREA is our novel framework to blend best of breed of Material Science theory with power of Generative AI to give best impact and smooth and quickest discovery of material for sustainability. This also helps to eliminate the possibility of production of hazardous residues and bye-products of the reactions. AIMS-EREA uses all available resources -- Predictive and Analytical AI on large collection of chemical databases along with automated intelligent assimilation of deep materials knowledge from previously published research works through Generative AI. We demonstrate use of our own novel framework with an example, how this framework can be successfully applied to achieve desired success in development of thermoelectric material for waste heat conversion.

The paper proposes a solution based on Generative Adversarial Network (GAN) for solving jigsaw puzzles. The problem assumes that an image is divided into equal square pieces, and asks to recover the image according to information provided by the pieces. Conventional jigsaw puzzle solvers often determine the relationships based on the boundaries of pieces, which ignore the important semantic information. In this paper, we propose JigsawGAN, a GAN-based auxiliary learning method for solving jigsaw puzzles with unpaired images (with no prior knowledge of the initial images). We design a multi-task pipeline that includes, (1) a classification branch to classify jigsaw permutations, and (2) a GAN branch to recover features to images in correct orders. The classification branch is constrained by the pseudo-labels generated according to the shuffled pieces. The GAN branch concentrates on the image semantic information, where the generator produces the natural images to fool the discriminator, while the discriminator distinguishes whether a given image belongs to the synthesized or the real target domain. These two branches are connected by a flow-based warp module that is applied to warp features to correct the order according to the classification results. The proposed method can solve jigsaw puzzles more efficiently by utilizing both semantic information and boundary information simultaneously. Qualitative and quantitative comparisons against several representative jigsaw puzzle solvers demonstrate the superiority of our method.

Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose two improvements to relative representations. First, we introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. The latter coincides with the symmetries in parameter space induced by common activation functions. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes. We provide an empirical investigation on a natural language task, where both the proposed variations yield improved performance on zero-shot model stitching.

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18times speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.

Multi-arm collaboration is becoming a core capability in embodied manipulation. Recent vision-language-action (VLA) models integrate perception, language, and control, but most represent language as a single global instruction and do not provide an explicit mechanism for assigning and composing arm-specific behaviors. This design limits transfer to collaboration patterns that differ from those observed during training. We present MA-VLA, a unified framework for multi-arm collaboration via atomic action assignment. MA-VLA decomposes cooperative behavior into mid-level atomic prompts and allocates them to individual arms, enabling explicit subgoal specification and compositional reuse across tasks. To reduce reliance on fixed execution roles, we introduce Arm Shuffle, a training-time permutation of the observation, state, and assigned atomic prompts for each arm. This permutation enforces role-agnostic instruction following and supports recomposition into unseen coordination patterns, which we term multi-arm compositional generalization. We also construct a benchmark in which test-time collaboration patterns are absent in training set. Across simulation and real-world evaluations, prior state-of-the-art VLAs largely fail under these unseen collaborations, while MA-VLA consistently succeeds. These results indicate that structured, per-arm atomic action assignment offers a practical route to scalable generalization in multi-arm embodied systems. Code, models, and data are available at https://github.com/zhangzaibin/future-robots

Multi-View Representation Learning (MVRL) aims to derive a unified representation from multi-view data by leveraging shared and complementary information across views. However, when views are irregularly missing, the incomplete data can lead to representations that lack sufficiency and consistency. To address this, we propose Multi-View Permutation of Variational Auto-Encoders (MVP), which excavates invariant relationships between views in incomplete data. MVP establishes inter-view correspondences in the latent space of Variational Auto-Encoders, enabling the inference of missing views and the aggregation of more sufficient information. To derive a valid Evidence Lower Bound (ELBO) for learning, we apply permutations to randomly reorder variables for cross-view generation and then partition them by views to maintain invariant meanings under permutations. Additionally, we enhance consistency by introducing an informational prior with cyclic permutations of posteriors, which turns the regularization term into a similarity measure across distributions. We demonstrate the effectiveness of our approach on seven diverse datasets with varying missing ratios, achieving superior performance in multi-view clustering and generation tasks.

The kernel of a binary code containing the zero word partitions the binary coordinates into blocks, two coordinates lying in the same block when every kernel word takes the same value in both, and the kernel-block rank profile is the multiset of the dimensions of its linear span punctured on those blocks. For the family H^{t_1,t_2,t_3} of Z_2Z_4Z_8-linear Hadamard codes, this invariant is known explicitly and gives a complete classification of the family. In this paper, we compute it for the Z_2Z_4-linear and Z_{2^s}-linear Hadamard families with which those codes are compared, and we prove that it is constant for every nonlinear Z_2Z_4-linear Hadamard code and for every nonlinear Z_{2^s}-linear Hadamard code bar H^{a_1,dots,a_s} with sgeq2. The second statement is obtained without any rank formula, by exhibiting coordinate permutations that preserve the code and act transitively on its kernel blocks, which makes the argument uniform in s. We also prove a descent theorem: if bar H^{a_1,dots,a_s} is nonlinear and a_1geq2, then the code punctured on one kernel block is the Z_{2^{s-1}}-linear Hadamard code bar H^{a_1,dots,a_{s-1}}. Consequently, the constant local rank equals rank(bar H^{a_1,dots,a_{s-1}}) and is at least t-κ+2, where 2^t is the length and κ the kernel dimension. These results separate every nonlinear Z_2Z_4Z_8-linear Hadamard code from every Z_4-linear, Z_2Z_4-linear and Z_{2^s}-linear Hadamard code of the same length, except for the single infinite family H^{1,1,t-4} and bar H^{2,0,t-5} with tgeq5. The members of this infinite family agree in the rank, kernel dimension and the kernel-block rank profile, but a two-block refinement separates them.

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

Scene text recognition (STR) suffers from challenges of either less realistic synthetic training data or the difficulty of collecting sufficient high-quality real-world data, limiting the effectiveness of trained models. Meanwhile, despite producing holistically appealing text images, diffusion-based visual text generation methods struggle to synthesize accurate and realistic instance-level text at scale. To tackle this, we introduce TextSSR: a novel pipeline for Synthesizing Scene Text Recognition training data. TextSSR targets three key synthesizing characteristics: accuracy, realism, and scalability. It achieves accuracy through a proposed region-centric text generation with position-glyph enhancement, ensuring proper character placement. It maintains realism by guiding style and appearance generation using contextual hints from surrounding text or background. This character-aware diffusion architecture enjoys precise character-level control and semantic coherence preservation, without relying on natural language prompts. Therefore, TextSSR supports large-scale generation through combinatorial text permutations. Based on these, we present TextSSR-F, a dataset of 3.55 million quality-screened text instances. Extensive experiments show that STR models trained on TextSSR-F outperform those trained on existing synthetic datasets by clear margins on common benchmarks, and further improvements are observed when mixed with real-world training data. Code is available at https://github.com/YesianRohn/TextSSR.

In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the full picture. Such systems have inspired development of artificial intelligence algorithms in areas such as swarm optimization and cellular automata. Motivated by the emergence of collective behavior from complex cellular systems, we build systems that feed each sensory input from the environment into distinct, but identical neural networks, each with no fixed relationship with one another. We show that these sensory networks can be trained to integrate information received locally, and through communication via an attention mechanism, can collectively produce a globally coherent policy. Moreover, the system can still perform its task even if the ordering of its inputs is randomly permuted several times during an episode. These permutation invariant systems also display useful robustness and generalization properties that are broadly applicable. Interactive demo and videos of our results: https://attentionneuron.github.io/

Audio decisions often depend on evidence that a transcript does not preserve, while their probability estimates can depend on how answer options are ordered. AudioJev maps a waveform, question and supplied alternatives directly to a candidate distribution through one shared full-parameter model. We define order calibration as preserving an answer's probability under meaning-preserving option permutations. Random-derangement SKL training pairs each question with a reordered view in which every alternative changes position, supervises both answers, and aligns the two distributions before applying a symmetric KL penalty. Inference retains a single candidate-scoring forward, with no calibration head or order ensemble. Across three training seeds, AudioJev reaches 68.88%/55.33% mean accuracy on complete MMAU/MMAR and reduces random-order SKL by 43.8%/60.5% relative to the single-view removal ablation. The same model handles intent, environmental sound, note properties, speech activity and conversational transitions. Paired removal ablations and multi-order evaluation measure predictive accuracy and probability stability together, establishing a direct audio interface whose calibration objective acts on candidate meaning rather than presentation position. Inference code and model weights are available at https://github.com/SihanLv/AudioJev-Inference and https://huggingface.co/shlv/AudioJev.

With the capability of modeling bidirectional contexts, denoising autoencoding based pretraining like BERT achieves better performance than pretraining approaches based on autoregressive language modeling. However, relying on corrupting the input with masks, BERT neglects dependency between the masked positions and suffers from a pretrain-finetune discrepancy. In light of these pros and cons, we propose XLNet, a generalized autoregressive pretraining method that (1) enables learning bidirectional contexts by maximizing the expected likelihood over all permutations of the factorization order and (2) overcomes the limitations of BERT thanks to its autoregressive formulation. Furthermore, XLNet integrates ideas from Transformer-XL, the state-of-the-art autoregressive model, into pretraining. Empirically, under comparable experiment settings, XLNet outperforms BERT on 20 tasks, often by a large margin, including question answering, natural language inference, sentiment analysis, and document ranking.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.

Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. In geometric quantum machine learning, one achieves this by encoding group structure into parameterised quantum circuits to include the symmetries of a problem as an inductive bias. However, constructing such circuits is challenging as a concrete guiding principle has yet to emerge. In this paper, we propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans\"atze -- circuits possessing spin rotation symmetry. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits. We prove that our construction is mathematically equivalent to other known constructions, such as those based on twirling and generalised permutations, but more direct to implement on quantum hardware. The efficacy of our constructed circuits is tested by solving the ground state problem of SU(2) symmetric Heisenberg models on the one-dimensional triangular lattice and on the Kagome lattice. Our results highlight that our equivariant circuits boost the performance of quantum variational algorithms, indicating broader applicability to other real-world problems.

The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks structures). We found that across model architectures (e.g., RNNs, Transformers, Perceivers, etc.), models with multiple attention layers, or models that leveraged cross-attention mechanisms between input domains, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, either cross-modal attention or models with deeper attention layers are key architectural features required to integrate multimodal inputs. On the other hand, neither of these architectural features led to productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

As we show in this paper, the prediction for output token n+1 of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens 1, 2, ..., n-1. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location k in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.

Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of features matters, set function learning demands methods that are invariant to permutations of the input set, presenting a unique and complex problem. This survey provides a comprehensive overview of the current development in set function learning, covering foundational theories, key methodologies, and diverse applications. We categorize and discuss existing approaches, focusing on deep learning approaches, such as DeepSets and Set Transformer based methods, as well as other notable alternative methods beyond deep learning, offering a complete view of current models. We also introduce various applications and relevant datasets, such as point cloud processing and multi-label classification, highlighting the significant progress achieved by set function learning methods in these domains. Finally, we conclude by summarizing the current state of set function learning approaches and identifying promising future research directions, aiming to guide and inspire further advancements in this promising field.

Large Language Models (LLMs) have transformed listwise document reranking by enabling global reasoning over candidate sets, yet single models often struggle to balance fine-grained relevance scoring with holistic cross-document analysis. We propose DeepAgentRank (\DeAR), an open-source framework that decouples these tasks through a dual-stage approach, achieving superior accuracy and interpretability. In Stage 1, we distill token-level relevance signals from a frozen 13B LLaMA teacher into a compact \{3, 8\}B student model using a hybrid of cross-entropy, RankNet, and KL divergence losses, ensuring robust pointwise scoring. In Stage 2, we attach a second LoRA adapter and fine-tune on 20K GPT-4o-generated chain-of-thought permutations, enabling listwise reasoning with natural-language justifications. Evaluated on TREC-DL19/20, eight BEIR datasets, and NovelEval-2306, \DeAR surpasses open-source baselines by +5.1 nDCG@5 on DL20 and achieves 90.97 nDCG@10 on NovelEval, outperforming GPT-4 by +3.09. Without fine-tuning on Wikipedia, DeAR also excels in open-domain QA, achieving 54.29 Top-1 accuracy on Natural Questions, surpassing baselines like MonoT5, UPR, and RankGPT. Ablations confirm that dual-loss distillation ensures stable calibration, making \DeAR a highly effective and interpretable solution for modern reranking systems.Dataset and code available at https://github.com/DataScienceUIBK/DeAR-Reranking..

Large-scale models are pretrained on massive web-crawled datasets containing documents of mixed quality, making data filtering essential. A popular method is Classifier-based Quality Filtering (CQF), which trains a binary classifier to distinguish between pretraining data and a small, high-quality set. It assigns each pretraining document a quality score defined as the classifier's score and retains only the top-scoring ones. We provide an in-depth analysis of CQF. We show that while CQF improves downstream task performance, it does not necessarily enhance language modeling on the high-quality dataset. We explain this paradox by the fact that CQF implicitly filters the high-quality dataset as well. We further compare the behavior of models trained with CQF to those trained on synthetic data of increasing quality, obtained via random token permutations, and find starkly different trends. Our results challenge the view that CQF captures a meaningful notion of data quality.

Low-discrepancy (LD) sequences have been extensively used as efficient experimental designs across many scientific disciplines. QMCPy (https://qmcsoftware.github.io/QMCSoftware/) is an accessible Python library which provides a unified implementation of randomized LD sequences, automatic variable transformations, adaptive Quasi-Monte Carlo error estimation algorithms, and fast kernel methods. This article focuses on recent updates to QMCPy which broaden support for randomized LD sequences and add new tools to enable fast kernel methods using LD sequences. Specifically, we give a unified description of the supported LD lattices, digital nets, and Halton point sets, along with randomization options including random permutations / shifts, linear matrix scrambling (LMS), and nested uniform scrambling (NUS). We also support higher-order digital nets, higher-order scrambling with LMS or NUS, and Halton scrambling with LMS or NUS. For fast kernel methods, we provide shift-invariant (SI) and digitally-shift-invariant (DSI) kernels, including a new set of higher-order smoothness DSI kernels. When SI and DSI kernels are respectively paired with n LD lattice and digital net points, the resulting Gram matrices permit multiplication and inversion at only O(n log n) cost. These fast operations utilize QMCPy's implementation of the fast Fourier transform in bit-reversed order (FFTBR), inverse FFTBR (IFFTBR), and fast Walsh--Hadamard transform (FWHT).

Multimodal large language models (MLLMs) are now routinely deployed for visual understanding, generation, and curation. A substantial fraction of these applications require an explicit aesthetic judgment. Most existing solutions reduce this judgment to predicting a scalar score for a single image. We first ask whether such scores faithfully capture comparative preference: in a controlled study with eight expert annotators, score-derived rankings align poorly with the same annotators' direct comparisons, while direct ranking yields substantially higher inter-annotator agreement on best- and worst-image labels. Motivated by this finding, we introduce the Visual Aesthetic Benchmark (VAB), which casts aesthetic evaluation as comparative selection over candidate sets with matched subject matter. VAB contains 400 tasks and 1,195 images across fine art, photography, and illustration, with labels derived from the consensus of 10 independent expert judges per task. Evaluating 20 frontier MLLMs and six dedicated visual-quality reward models, we find that the strongest system identifies both the best and the worst image correctly across three random permutations of the candidate order in only 26.5% of tasks, far below the 68.9% achieved by human experts. Fine-tuning a 35B-parameter model on 2,000 expert examples brings its accuracy close to that of a 397B-parameter open-weight model, suggesting that the comparative signal in VAB is transferable. Together, these results expose a clear and measurable gap between current multimodal models and expert aesthetic judgment, and VAB provides the first set-based, expert-grounded testbed on which that gap can be tracked and closed.

As large language models (LLMs) continue to advance, their deployment often involves fine-tuning to enhance performance on specific downstream tasks. However, this customization is sometimes accompanied by misleading claims about the origins, raising significant concerns about transparency and trust within the open-source community. Existing model verification techniques typically assess functional, representational, and weight similarities. However, these approaches often struggle against obfuscation techniques, such as permutations and scaling transformations. To address this limitation, we propose a novel detection method Origin-Tracer that rigorously determines whether a model has been fine-tuned from a specified base model. This method includes the ability to extract the LoRA rank utilized during the fine-tuning process, providing a more robust verification framework. This framework is the first to provide a formalized approach specifically aimed at pinpointing the sources of model fine-tuning. We empirically validated our method on thirty-one diverse open-source models under conditions that simulate real-world obfuscation scenarios. We empirically analyze the effectiveness of our framework and finally, discuss its limitations. The results demonstrate the effectiveness of our approach and indicate its potential to establish new benchmarks for model verification.

In this work, we present a modular and interpretable framework that uses Large Language Models (LLMs) to automate candidate assessment in recruitment. The system integrates diverse sources, including job descriptions, CVs, interview transcripts, and HR feedback; to generate structured evaluation reports that mirror expert judgment. Unlike traditional ATS tools that rely on keyword matching or shallow scoring, our approach employs role-specific, LLM-generated rubrics and a multi-agent architecture to perform fine-grained, criteria-driven evaluations. The framework outputs detailed assessment reports, candidate comparisons, and ranked recommendations that are transparent, auditable, and suitable for real-world hiring workflows. Beyond rubric-based analysis, we introduce an LLM-Driven Active Listwise Tournament mechanism for candidate ranking. Instead of noisy pairwise comparisons or inconsistent independent scoring, the LLM ranks small candidate subsets (mini-tournaments), and these listwise permutations are aggregated using a Plackett-Luce model. An active-learning loop selects the most informative subsets, producing globally coherent and sample-efficient rankings. This adaptation of listwise LLM preference modeling (previously explored in financial asset ranking) provides a principled and highly interpretable methodology for large-scale candidate ranking in talent acquisition.

As AI labs approach a data ceiling where compute capacity outpaces the rate of new high-quality text generation, language model pretraining is shifting toward a data-constrained, compute-abundant regime that demands productive multi-epoch training on fixed corpora. Standard autoregressive (AR) pretraining overfits severely in this setting, reaching its optimum early and then continuously deteriorating. We investigate training-time data augmentation as a regularizer to mitigate this overfitting and enable productive training for hundreds of epochs on the same data. We introduce three orthogonal categories of augmentation for AR pretraining: token-level noise (masking, random replacement), sequence permutations (right-to-left prediction, Fill-in-the-Middle), and target offset prediction (x_{t+i} for i > 1). Through systematic ablations, we find that individual augmentations delay overfitting and lower validation loss relative to the baseline, with random token replacement achieving the best minimum loss among individual methods. Combining augmentation categories further lowers the minimum validation loss. Our experiments demonstrate that data augmentations mitigate AR pretraining's data inefficiency and offer a promising solution to the data-constrained regime~\footnote{All code and data are available at https://github.com/ michaelchen-lab/ data-augmentations-for-pretraining.

Simon's algorithm is a polynomial period-finding algorithm that has been used to exploit the algebraic structure of specific symmetric ciphers, showing that exponential speedups in their cryptanalysis are theoretically possible. While the theoretical framework for an attack using Simon's algorithm on the Even-Mansour cipher is well-established, practical implementations on noisy intermediate-scale quantum (NISQ) hardware remain limited. This paper presents a proof of concept quantum cryptanalysis of the Even-Mansour cipher using Simon's period-finding algorithm on NISQ hardware. For N = 3 and N = 4, we successfully demonstrate secret key recovery for N-bit constructions on the ibm_miami processor. Our experiments also identify a scaling limitation in the classical pre-processing stage: The DORCIS circuit optimization tool encountered a memory bottleneck at N = 5, preventing the generation of optimized circuits for larger key lengths. Our results suggest firstly that Simon's algorithm is effective for the Even-Mansour cipher for short bit lengths on current quantum hardware. Secondly, while DORCIS is effective for the small-scale S-boxes for which it was designed, there remains a need for the investigation of more scalable and efficient synthesis tools capable of handling larger and more general permutations in the context of Even-Mansour ciphers.

We tackle the problem of sparse novel view synthesis (NVS) using video diffusion models; given K (approx 5) multi-view images of a scene and their camera poses, we predict the view from a target camera pose. Many prior approaches leverage generative image priors encoded via diffusion models. However, models trained on single images lack multi-view knowledge. We instead argue that video models already contain implicit multi-view knowledge and so should be easier to adapt for NVS. Our key insight is to formulate sparse NVS as a low frame-rate video completion task. However, one challenge is that sparse NVS is defined over an unordered set of inputs, often too sparse to admit a meaningful order, so the models should be invariant to permutations of that input set. To this end, we present FrameCrafter, which adapts video models (naturally trained with coherent frame orderings) to permutation-invariant NVS through several architectural modifications, including per-frame latent encodings and removal of temporal positional embeddings. Our results suggest that video models can be easily trained to "forget" about time with minimal supervision, producing competitive performance on sparse-view NVS benchmarks. Project page: https://frame-crafter.github.io/

High-definition (HD) map provides abundant and precise environmental information of the driving scene, serving as a fundamental and indispensable component for planning in autonomous driving system. We present MapTR, a structured end-to-end Transformer for efficient online vectorized HD map construction. We propose a unified permutation-equivalent modeling approach, i.e., modeling map element as a point set with a group of equivalent permutations, which accurately describes the shape of map element and stabilizes the learning process. We design a hierarchical query embedding scheme to flexibly encode structured map information and perform hierarchical bipartite matching for map element learning. MapTR achieves the best performance and efficiency with only camera input among existing vectorized map construction approaches on nuScenes dataset. In particular, MapTR-nano runs at real-time inference speed (25.1 FPS) on RTX 3090, 8times faster than the existing state-of-the-art camera-based method while achieving 5.0 higher mAP. Even compared with the existing state-of-the-art multi-modality method, MapTR-nano achieves 0.7 higher mAP, and MapTR-tiny achieves 13.5 higher mAP and 3times faster inference speed. Abundant qualitative results show that MapTR maintains stable and robust map construction quality in complex and various driving scenes. MapTR is of great application value in autonomous driving. Code and more demos are available at https://github.com/hustvl/MapTR.

Modern Text-to-SQL systems often follow generate-execute-select pipelines, generating multiple candidate queries then selecting the best one. Listwise selection, by jointly comparing multiple candidates, has been widely adopted, but fine-tuning listwise selectors is costly. We thus propose a fine-tuning-free listwise selector. We replace two major fine-tuning objectives with inference-time strategies: (1) learning selection criteria as ordering and (2) mitigating positional bias. First, we build reusable structured memories instead of learning selection behavior as model parameters. Given a question, MaP-SQL retrieves memories distilled from training data that encode how natural language maps to schema elements, SQL operations, and expected outputs. These memories serve as explicit decision criteria for evaluating candidates in a listwise manner. Second, to mitigate ordering bias of listwise selectors, we aggregate rankings across multiple input permutations, with inference cost optimized by execution results and pointwise scoring. Our approach improves selection accuracy while maintaining efficiency and compatibility with existing large language models. Across Text-to-SQL benchmarks, it produces more stable selection without fine-tuning and fewer unnecessary comparisons than existing methods. On BIRD-dev, it outperforms the previous state-of-the-art selector-based method R^3-SQL by 2.02 execution accuracy points on average using the same candidate sets, with 2.92x fewer tokens.

An Erdös matrix E is a bistochastic matrix whose sum of squares of entries (Frobenius norm squared) equals its maxtrace (maximum of all the σ-traces for permutations σ's). We characterize all Erdös E by the patterns of their zero entries; showing that each such skeleton has at most one E. We present an algorithm to find all ntimes n Erdös matrices, which finds them up to nleqslant 5 quickly and also size n=6. We further show some presently known RCDS matrices to be Erdös.

Position bias in multiple-choice LLM evaluation is widely cited as a confound in capability comparisons, but published measurements rely on single answer-order shuffles whose results confound the bias signal with content-level noise and sampling stochasticity. I introduce inspect_permute, an open-source extension to the inspect_ai evaluation framework that runs exhaustive answer-order permutations per question and reports the chi-squared / Cramer V signature of position bias with bootstrap confidence intervals. I apply the tool across four vendors (gpt-4o-mini, claude-haiku-4-5, gemini-2.5-flash, grok-3) on five MMLU subjects, 24,000 API calls under temperature-0 generation, with falsifier predictions pre-registered via a public SHA-256 hash before half the data was observed. Position bias turns out to be statistically detectable only within a roughly 60-95% base-accuracy Goldilocks zone. Below it, processing-load dominance swamps subject-specific signal; above it, ceiling effects compress the variance below the chi-squared test resolution. Detectable cells separate into two mechanism types: monotone A-to-D decrease (processing_load, in low-tier models) and non-monotone D-drop (content_ambiguity, in a narrow capability band). Standard MMLU places every frontier-tier model above the detection band, so absence of signal there should be read as not measurable, not unbiased. Together with the ceiling-effect characterisation in arXiv:2606.26185, this work brackets the detectable region of position-bias measurement and makes the field central question askable in a verifiable form. Package, data, preregistration under MIT.

Large language models (LLMs) can memorize sensitive facts, motivating unlearning methods that remove targeted knowledge without costly retraining. However, unlearning research remains heavily English-centric. We study multilingual unlearning by extending the TOFU benchmark to five languages, and fine-tune, unlearn, and query our models with different permutations of languages. We find that unlearning transfer, the ability of an unlearned model to "forget" facts in languages other than the unlearning language, is highly variable: e.g., it is strongest between languages sharing scripts and families, and we show that the unlearning language predicts which query languages are most likely to yield the strongest transfer. Layer-wise analysis reveals that unlearning leaves the shared cross-lingual latent space largely intact in early layers, instead operating primarily in later decoding layers. This suggests that unlearning does not truly erase knowledge, but rather induces superficial suppression. Exploiting this structure, a single inference-time steering direction reverses much of this suppression across languages, recovering 50% (Qwen) and 90% (Gemma) of the unlearned knowledge.

We focus on addressing the dense backward propagation issue for training efficiency of N:M fine-grained sparsity that preserves at most N out of M consecutive weights and achieves practical speedups supported by the N:M sparse tensor core. Therefore, we present a novel method of Bi-directional Masks (Bi-Mask) with its two central innovations in: 1) Separate sparse masks in the two directions of forward and backward propagation to obtain training acceleration. It disentangles the forward and backward weight sparsity and overcomes the very dense gradient computation. 2) An efficient weight row permutation method to maintain performance. It picks up the permutation candidate with the most eligible N:M weight blocks in the backward to minimize the gradient gap between traditional uni-directional masks and our bi-directional masks. Compared with existing uni-directional scenario that applies a transposable mask and enables backward acceleration, our Bi-Mask is experimentally demonstrated to be more superior in performance. Also, our Bi-Mask performs on par with or even better than methods that fail to achieve backward acceleration. Project of this paper is available at https://github.com/zyxxmu/Bi-Mask.

It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Existing cross-encoder models can be categorized as pointwise, pairwise, or listwise. Pairwise and listwise models allow passage interactions, which typically makes them more effective than pointwise models but less efficient and less robust to input passage order permutations. To enable efficient permutation-invariant passage interactions during re-ranking, we propose a new cross-encoder architecture with inter-passage attention: the Set-Encoder. In experiments on TREC Deep Learning and TIREx, the Set-Encoder is as effective as state-of-the-art listwise models while being more efficient and invariant to input passage order permutations. Compared to pointwise models, the Set-Encoder is particularly more effective when considering inter-passage information, such as novelty, and retains its advantageous properties compared to other listwise models. Our code is publicly available at https://github.com/webis-de/ECIR-25.

Language models pretrained on large collections of tabular data have demonstrated their effectiveness in several downstream tasks. However, many of these models do not take into account the row/column permutation invariances, hierarchical structure, etc. that exist in tabular data. To alleviate these limitations, we propose HYTREL, a tabular language model, that captures the permutation invariances and three more structural properties of tabular data by using hypergraphs - where the table cells make up the nodes and the cells occurring jointly together in each row, column, and the entire table are used to form three different types of hyperedges. We show that HYTREL is maximally invariant under certain conditions for tabular data, i.e., two tables obtain the same representations via HYTREL iff the two tables are identical up to permutations. Our empirical results demonstrate that HYTREL consistently outperforms other competitive baselines on four downstream tasks with minimal pretraining, illustrating the advantages of incorporating the inductive biases associated with tabular data into the representations. Finally, our qualitative analyses showcase that HYTREL can assimilate the table structures to generate robust representations for the cells, rows, columns, and the entire table.

Protecting the intellectual property of open-source Large Language Models (LLMs) is very important, because training LLMs costs extensive computational resources and data. Therefore, model owners and third parties need to identify whether a suspect model is a subsequent development of the victim model. To this end, we propose a training-free REEF to identify the relationship between the suspect and victim models from the perspective of LLMs' feature representations. Specifically, REEF computes and compares the centered kernel alignment similarity between the representations of a suspect model and a victim model on the same samples. This training-free REEF does not impair the model's general capabilities and is robust to sequential fine-tuning, pruning, model merging, and permutations. In this way, REEF provides a simple and effective way for third parties and models' owners to protect LLMs' intellectual property together. The code is available at https://github.com/tmylla/REEF.

Automatic video captioning aims for a holistic visual scene understanding. It requires a mechanism for capturing temporal context in video frames and the ability to comprehend the actions and associations of objects in a given timeframe. Such a system should additionally learn to abstract video sequences into sensible representations as well as to generate natural written language. While the majority of captioning models focus solely on the visual inputs, little attention has been paid to the audiovisual modality. To tackle this issue, we propose a novel two-fold approach. First, we implement a reward-guided KL Divergence to train a video captioning model which is resilient towards token permutations. Second, we utilise a Bi-Modal Hierarchical Reinforcement Learning (BMHRL) Transformer architecture to capture long-term temporal dependencies of the input data as a foundation for our hierarchical captioning module. Using our BMHRL, we show the suitability of the HRL agent in the generation of content-complete and grammatically sound sentences by achieving 4.91, 2.23, and 10.80 in BLEU3, BLEU4, and METEOR scores, respectively on the ActivityNet Captions dataset. Finally, we make our BMHRL framework and trained models publicly available for users and developers at https://github.com/d-rothen/bmhrl.

CLIP models learn transferable multi-modal features via image-text contrastive learning on internet-scale data. They are widely used in zero-shot classification, multi-modal retrieval, text-to-image diffusion, and as image encoders in large vision-language models. However, CLIP's pretraining is dominated by images paired with short captions, biasing the model toward encoding simple descriptions of salient objects and leading to coarse alignment on complex scenes and dense descriptions. While recent work mitigates this by fine-tuning on small-scale long-caption datasets, we identify an important common bias: both human- and LLM-generated long captions typically begin with a one-sentence summary followed by a detailed description. We show that this acts as a shortcut during training, concentrating attention on the opening sentence and early tokens and weakening alignment over the rest of the caption. To resolve this, we introduce DeBias-CLIP, which removes the summary sentence during training and applies sentence sub-sampling and text token padding to distribute supervision across all token positions. DeBias-CLIP achieves state-of-the-art long-text retrieval, improves short-text retrieval, and is less sensitive to sentence order permutations. It is a drop-in replacement for Long-CLIP with no additional trainable parameters.

Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.

This technical report presents our solution, EgoAdapt (Egocentric Adaptation via Category, Calibration, and Consistency), to the CVPR 2026 HD-EPIC VQA challenge. HD-EPIC evaluates whether a vision-language model can reason over realistic first-person kitchen videos, where the evidence for an answer may be a short hand-object interaction, a long recipe trajectory, a spatial relation to a fixture, or a subtle gaze cue. The benchmark contains 26K multiple-choice questions across seven macro-categories: recipe, ingredient, nutrition, fine-grained action, 3D perception, object motion, and gaze. We observe that the main difficulty is not only model capacity, but also the mismatch between a single generic inference recipe and the heterogeneous temporal, spatial, and semantic structure of the benchmark. Our method, EgoAdapt, introduces three inference-time components: (1) category-conditioned routing with per-category prompts, frame budgets, and sampling rates; (2) calibrated option scoring that evaluates all candidate answers with letter-token likelihoods and generation agreement instead of relying only on direct generation; and (3) test-time consistency adaptation that aggregates predictions across option permutations and verification-style prompts for ambiguous cases. This design substantially improves over the available HD-EPIC baselines.