Daily Papers

Large language models are increasingly used as decision aids whose probability judgments shape downstream choices. Whether those judgments carry a systematic directional tilt has been hard to detect: calibration metrics aggregate unsigned errors, and naturalistic uncertainty offers no ground-truth probability. When an LLM rates a startup's success at 70% but its failure at 15%, the missing 15 points expose a distortion no aggregate score flags. We introduce OptimismBench, which detects directional bias with inverted pairs: each scenario elicits both P(success) and P(failure), and asymmetry between the two framings yields a signed bias score without ground truth. Across 16 models from 8 providers, fourteen are optimistic; pessimism appears only in Anthropic's frontier tier. Eleven matched base-versus-chat pairs across four families show post-training sets the sign of the bias, with opposite shifts in different families. The pattern survives prompt, temperature, perspective, and self-debiasing ablations. A seventeen-model six-language comparison further shows model identity dominates language, with inter-model variance at 4.7x inter-language variance. We release 3,870 items across 10 languages for per-model directional-bias auditing. When alignment makes a model more helpful, it also tilts its probabilities; downstream pipelines inherit the tilt by default.

Does structured intent representation generalize across languages and models? We study PPS (Prompt Protocol Specification), a 5W3H-based framework for structured intent representation in human-AI interaction, and extend prior Chinese-only evidence along three dimensions: two additional languages (English and Japanese), a fourth condition in which a user's simple prompt is automatically expanded into a full 5W3H specification by an AI-assisted authoring interface, and a new research question on cross-model output consistency. Across 2,160 model outputs (3 languages x 4 conditions x 3 LLMs x 60 tasks), we find that AI-expanded 5W3H prompts (Condition D) show no statistically significant difference in goal alignment from manually crafted 5W3H prompts (Condition C) across all three languages, while requiring only a single-sentence input from the user. Structured PPS conditions often reduce or reshape cross-model output variance, though this effect is not uniform across languages and metrics; the strongest evidence comes from identifying spurious low variance in unconstrained baselines. We also show that unstructured prompts exhibit a systematic dual-inflation bias: artificially high composite scores and artificially low apparent cross-model variance. These findings suggest that structured 5W3H representations can improve intent alignment and accessibility across languages and models, especially when AI-assisted authoring lowers the barrier for non-expert users.

Recently, multi-expert methods have led to significant improvements in long-tail recognition (LTR). We summarize two aspects that need further enhancement to contribute to LTR boosting: (1) More diverse experts; (2) Lower model variance. However, the previous methods didn't handle them well. To this end, we propose More Diverse experts with Consistency Self-distillation (MDCS) to bridge the gap left by earlier methods. Our MDCS approach consists of two core components: Diversity Loss (DL) and Consistency Self-distillation (CS). In detail, DL promotes diversity among experts by controlling their focus on different categories. To reduce the model variance, we employ KL divergence to distill the richer knowledge of weakly augmented instances for the experts' self-distillation. In particular, we design Confident Instance Sampling (CIS) to select the correctly classified instances for CS to avoid biased/noisy knowledge. In the analysis and ablation study, we demonstrate that our method compared with previous work can effectively increase the diversity of experts, significantly reduce the variance of the model, and improve recognition accuracy. Moreover, the roles of our DL and CS are mutually reinforcing and coupled: the diversity of experts benefits from the CS, and the CS cannot achieve remarkable results without the DL. Experiments show our MDCS outperforms the state-of-the-art by 1% sim 2% on five popular long-tailed benchmarks, including CIFAR10-LT, CIFAR100-LT, ImageNet-LT, Places-LT, and iNaturalist 2018. The code is available at https://github.com/fistyee/MDCS.

Natural data are often long-tail distributed over semantic classes. Existing recognition methods tackle this imbalanced classification by placing more emphasis on the tail data, through class re-balancing/re-weighting or ensembling over different data groups, resulting in increased tail accuracies but reduced head accuracies. We take a dynamic view of the training data and provide a principled model bias and variance analysis as the training data fluctuates: Existing long-tail classifiers invariably increase the model variance and the head-tail model bias gap remains large, due to more and larger confusion with hard negatives for the tail. We propose a new long-tailed classifier called RoutIng Diverse Experts (RIDE). It reduces the model variance with multiple experts, reduces the model bias with a distribution-aware diversity loss, reduces the computational cost with a dynamic expert routing module. RIDE outperforms the state-of-the-art by 5% to 7% on CIFAR100-LT, ImageNet-LT and iNaturalist 2018 benchmarks. It is also a universal framework that is applicable to various backbone networks, long-tailed algorithms, and training mechanisms for consistent performance gains. Our code is available at: https://github.com/frank-xwang/RIDE-LongTailRecognition.

Current preference learning methods achieve high accuracy on standard benchmarks but exhibit significant performance degradation when objective quality signals are removed. We introduce WritingPreferenceBench, a dataset of 1,800 human-annotated preference pairs (1,200 English, 600 Chinese) across 8 creative writing genres, where responses are matched for objective correctness, factual accuracy, and length. On this benchmark, sequence-based reward models--the standard architecture for RLHF--achieve only 52.7% mean accuracy, while zero-shot language model judges perform at 53.9%. In contrast, generative reward models that produce explicit reasoning chains achieve 81.8% accuracy. We observe high within-model variance across genres: individual models range from 18.2% to 81.8% accuracy across different writing categories, with standard deviations averaging 10.1%. This variance persists regardless of model scale, with 27B parameter models showing no consistent improvement over 8B variants. Our results suggest that current RLHF methods primarily learn to detect objective errors rather than capture subjective quality preferences (e.g., creativity, stylistic flair, and emotional resonance), and that successful preference modeling may require intermediate reasoning representations rather than direct classification.

Federated and decentralized machine learning leverage end-user devices for privacy-preserving training of models at lower operating costs than within a data center. In a round of Federated Learning (FL), a random sample of participants trains locally, then a central server aggregates the local models to produce a single model for the next round. In a round of Decentralized Learning (DL), all participants train locally and then aggregate with their immediate neighbors, resulting in many local models with residual variance between them. On the one hand, FL's sampling and lower model variance provides lower communication costs and faster convergence. On the other hand, DL removes the need for a central server and distributes the communication costs more evenly amongst nodes, albeit at a larger total communication cost and slower convergence. In this paper, we present MoDeST: Mostly-Consistent Decentralized Sampling Training. MoDeST implements decentralized sampling in which a random subset of nodes is responsible for training and aggregation every round: this provides the benefits of both FL and DL without their traditional drawbacks. Our evaluation of MoDeST on four common learning tasks: (i) confirms convergence as fast as FL, (ii) shows a 3x-14x reduction in communication costs compared to DL, and (iii) demonstrates that MoDeST quickly adapts to nodes joining, leaving, or failing, even when 80% of all nodes become unresponsive.

Deepfake detection has become increasingly important due to the rise of synthetic media, which poses significant risks to digital identity and cyber presence for security and trust. While multiple approaches have improved detection accuracy, challenges remain in achieving consistent performance across diverse datasets and manipulation types. In response, we propose a novel two-tier ensemble framework for deepfake detection based on deep learning that hierarchically combines multiple instances of three state-of-the-art architectures: Xception, Res2Net101, and EfficientNet-B7. Our framework employs a unique approach where each architecture is instantiated three times with different initializations to enhance model diversity, followed by a learnable weighting mechanism that dynamically combines their predictions. Unlike traditional fixed-weight ensembles, our first-tier averages predictions within each architecture family to reduce model variance, while the second tier learns optimal contribution weights through backpropagation, automatically adjusting each architecture's influence based on their detection reliability. Our experiments achieved state-of-the-art intra-dataset performance with AUC scores of 99.22% (FF++) and 100.00% (CelebDF-v2), and F1 scores of 98.06% (FF++) and 99.94% (CelebDF-v2) without augmentation. With augmentation, we achieve AUC scores of 99.47% (FF++) and 100.00% (CelebDF-v2), and F1 scores of 98.43% (FF++) and 99.95% (CelebDF-v2). The framework demonstrates robust cross-dataset generalization, achieving AUC scores of 88.20% and 72.52%, and F1 scores of 93.16% and 80.62% in cross-dataset evaluations.

We present ThinkProbe, a framework for structural analysis of LLM reasoning traces. ThinkProbe converts each trace into a Thought Graph a directed graph with cycles, 8 node types, and 6 edge types and derives a 19-metric five-dimensional cognitive profile (5D-CP: Breadth, Depth, Structure, Metacognitive, Efficiency) through a fully non-generative pipeline combining rule-based segmentation and discriminative semantic linking. Applied to 4{,}200 traces from 7 native reasoning models across 200 open-ended questions and 10 cognitive domains, ThinkProbe reveals that reasoning structure is a stable, model-level property: between-model variance exceeds between-domain variance by up to fourfold across four of five cognitive dimensions, with Structure showing genuine sensitivity to question domain, exposing qualitatively distinct cognitive profiles invisible to accuracy-based evaluation.

The paper introduces AniTalker, an innovative framework designed to generate lifelike talking faces from a single portrait. Unlike existing models that primarily focus on verbal cues such as lip synchronization and fail to capture the complex dynamics of facial expressions and nonverbal cues, AniTalker employs a universal motion representation. This innovative representation effectively captures a wide range of facial dynamics, including subtle expressions and head movements. AniTalker enhances motion depiction through two self-supervised learning strategies: the first involves reconstructing target video frames from source frames within the same identity to learn subtle motion representations, and the second develops an identity encoder using metric learning while actively minimizing mutual information between the identity and motion encoders. This approach ensures that the motion representation is dynamic and devoid of identity-specific details, significantly reducing the need for labeled data. Additionally, the integration of a diffusion model with a variance adapter allows for the generation of diverse and controllable facial animations. This method not only demonstrates AniTalker's capability to create detailed and realistic facial movements but also underscores its potential in crafting dynamic avatars for real-world applications. Synthetic results can be viewed at https://github.com/X-LANCE/AniTalker.

This position paper argues that, for long-horizon tasks evaluated across models with comparable frontier capability, the agent execution harness, namely the infrastructure layer that governs context construction, tool interaction, orchestration, and verification around a language model, is often a stronger determinant of agent performance than the model it wraps. We formalize and defend the Binding Constraint Thesis: in this regime, performance variance is governed more by harness configuration than by model choice, and current evaluation protocols therefore systematically misattribute harness-level gains to model improvements. We support this thesis along three lines. First, a control-theoretic formalization treats the harness as the controller of a closed-loop dynamical system and the LLM as the stochastic policy it governs, which explains why small harness changes can produce performance shifts that exceed those obtained by substituting one model for another. Second, published benchmarks, industry deployments, and a controlled variance decomposition show that harness-induced variance can substantially exceed model-induced variance, including cases of model ranking reversal. Third, we propose a harness-aware evaluation framework with a disclosure standard and a variance decomposition protocol. Until harness specifications are disclosed, leaderboard comparisons for long-horizon agents should be treated as incomplete and potentially misleading.

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

The classification of Intangible Cultural Heritage (ICH) images in the Mekong Delta poses unique challenges due to limited annotated data, high visual similarity among classes, and domain heterogeneity. In such low-resource settings, conventional deep learning models often suffer from high variance or overfit to spurious correlations, leading to poor generalization. To address these limitations, we propose a robust framework that integrates the hybrid CoAtNet architecture with model soups, a lightweight weight-space ensembling technique that averages checkpoints from a single training trajectory without increasing inference cost. CoAtNet captures both local and global patterns through stage-wise fusion of convolution and self-attention. We apply two ensembling strategies - greedy and uniform soup - to selectively combine diverse checkpoints into a final model. Beyond performance improvements, we analyze the ensembling effect through the lens of bias-variance decomposition. Our findings show that model soups reduces variance by stabilizing predictions across diverse model snapshots, while introducing minimal additional bias. Furthermore, using cross-entropy-based distance metrics and Multidimensional Scaling (MDS), we show that model soups selects geometrically diverse checkpoints, unlike Soft Voting, which blends redundant models centered in output space. Evaluated on the ICH-17 dataset (7,406 images across 17 classes), our approach achieves state-of-the-art results with 72.36% top-1 accuracy and 69.28% macro F1-score, outperforming strong baselines including ResNet-50, DenseNet-121, and ViT. These results underscore that diversity-aware checkpoint averaging provides a principled and efficient way to reduce variance and enhance generalization in culturally rich, data-scarce classification tasks.

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general ``affine variance'' noise model and provides sharp rates of convergence in both the low-noise and high-noise~regimes.

With the success of deep neural networks, Neural Architecture Search (NAS) as a way of automatic model design has attracted wide attention. As training every child model from scratch is very time-consuming, recent works leverage weight-sharing to speed up the model evaluation procedure. These approaches greatly reduce computation by maintaining a single copy of weights on the super-net and share the weights among every child model. However, weight-sharing has no theoretical guarantee and its impact has not been well studied before. In this paper, we conduct comprehensive experiments to reveal the impact of weight-sharing: (1) The best-performing models from different runs or even from consecutive epochs within the same run have significant variance; (2) Even with high variance, we can extract valuable information from training the super-net with shared weights; (3) The interference between child models is a main factor that induces high variance; (4) Properly reducing the degree of weight sharing could effectively reduce variance and improve performance.

While tokenization is a key step in language modeling, with effects on model training and performance, it remains unclear how to effectively evaluate tokenizer quality. One proposed dimension of tokenizer quality is the extent to which tokenizers preserve linguistically meaningful subwords, aligning token boundaries with morphological boundaries within a word. We expand MorphScore (Arnett & Bergen, 2025), which previously covered 22 languages, to support a total of 70 languages. The updated MorphScore offers more flexibility in evaluation and addresses some of the limitations of the original version. We then correlate our alignment scores with downstream task performance for five pre-trained languages models on seven tasks, with at least one task in each of the languages in our sample. We find that morphological alignment does not explain very much variance in model performance, suggesting that morphological alignment alone does not measure dimensions of tokenization quality relevant to model performance.

We identify first-mover bias -- path-dependent concentration of SHAP feature importance from sequential residual fitting in gradient boosting -- as a mechanistic contributor to attribution instability under multicollinearity. Scaling up a single model amplifies this effect: a Large Single Model matching our method's total tree count produces the poorest attribution reproducibility of any approach tested. We show that model independence largely neutralizes first-mover bias. Both DASH (Diversified Aggregation of SHAP) and simple seed-averaging (Stochastic Retrain) restore stability by breaking the sequential dependency chain. At rho=0.9, both achieve stability ~0.977, while Single Best degrades to 0.958 and LSM to 0.938. On Breast Cancer, DASH improves stability from 0.376 to 0.925 (+0.549), outperforming Stochastic Retrain by +0.063. Under nonlinear DGPs, the advantage emerges at rho>=0.7. DASH provides two diagnostic tools -- the Feature Stability Index and Importance-Stability Plot -- that detect first-mover bias without ground truth. A crossed ANOVA with formal F-statistics confirms the mechanism: DASH shifts variance from model-dominated (40.6%) to data-dominated (73.6%). Software at https://github.com/DrakeCaraker/dash-shap

Cross-lingual evaluation of large language models (LLMs) typically conflates two sources of variance: genuine model performance differences and measurement instability. We investigate evaluation reliability by holding generation conditions constant while varying target language. Using synthetic customer-support dialogues generated with identical parameters across Estonian, Finnish, and Hungarian, we test whether automatic metrics and LLM-as-a-judge scoring produce stable model rankings across these morphologically rich, related Finno-Ugric languages. With a small set of Estonian native speaker annotations as a reference point, we find systematic ranking instabilities: surface-level metrics (lexical diversity, surface and semantic similarity) maintain cross-language stability, but pragmatic judgments (coherence, instruction-following) exhibit rank inversions and near-zero correlations. Because generation is controlled, these inconsistencies reflect how judge scoring behaves differently across languages rather than true model differences. This controlled design provides a diagnostic probe: evaluation methods that fail to maintain stability under identical generation conditions signal transfer failure before deployment. Our findings suggest that zero-shot judge transfer is unreliable for discourse-level assessment in morphologically rich languages, motivating language-specific calibration against targeted human baselines. We release our controlled generation protocol, synthetic data, and evaluation framework to enable replication across language families at https://github.com/isaac-chung/cross-lingual-stability-judges.

This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a maximal point of a real function. Based on a two-dimensional fully coupled ordinary differential equation (ODE), we construct an explicit viscosity solution to the Hamilton-Jacobi-Bellman equation of the constrained LQ problem. Together with the Meyer-Itô formula and a verification procedure, we obtain the optimal feedback controls of the constrained LQ problem and the original MV problem, which corrects the flawed results in some existing literatures. In addition, closed-form efficient portfolio and efficient frontier are derived. In the end, we present several examples where the two-dimensional ODE is decoupled.

Post-training plays a crucial role in refining and aligning large language models to meet specific tasks and human preferences. While recent advancements in post-training techniques, such as Group Relative Policy Optimization (GRPO), leverage increased sampling with relative reward scoring to achieve superior performance, these methods often suffer from training instability that limits their practical adoption. To address this challenge, we present Group Variance Policy Optimization (GVPO). GVPO incorporates the analytical solution to KL-constrained reward maximization directly into its gradient weights, ensuring alignment with the optimal policy. The method provides intuitive physical interpretations: its gradient mirrors the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly the KL-constrained reward maximization objective, (2) it supports flexible sampling distributions that avoids on-policy and importance sampling limitations. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Strong empirical evidence that one machine-learning algorithm A outperforms another one B ideally calls for multiple trials optimizing the learning pipeline over sources of variation such as data sampling, data augmentation, parameter initialization, and hyperparameters choices. This is prohibitively expensive, and corners are cut to reach conclusions. We model the whole benchmarking process, revealing that variance due to data sampling, parameter initialization and hyperparameter choice impact markedly the results. We analyze the predominant comparison methods used today in the light of this variance. We show a counter-intuitive result that adding more sources of variation to an imperfect estimator approaches better the ideal estimator at a 51 times reduction in compute cost. Building on these results, we study the error rate of detecting improvements, on five different deep-learning tasks/architectures. This study leads us to propose recommendations for performance comparisons.

Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through the stochastic sampling of their latent variables, a process that inherently introduces estimation variance, which can slow convergence and degrade performance. In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients. Instead of improving stochastic estimators, we leverage specific decoder architectures to analytically compute the expected ELBO, yielding a gradient with zero variance. We first provide a theoretical foundation for this method and demonstrate its superiority over existing estimators in a controlled setting with a linear decoder. To generalize our approach for practical use with complex, expressive decoders, we introduce a novel training dynamic that uses the exact, zero-variance gradient to guide the early stages of encoder training before annealing to a standard stochastic estimator. Our experiments show that this technique consistently improves the performance of established baselines, including reparameterization, Gumbel-Softmax, and REINFORCE, across multiple datasets. This work opens a new direction for training generative models by combining the stability of analytical computation with the expressiveness of deep, nonlinear architecture.

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an O(mathsf{Var^star M Gamma S A K}) regret bound where O hides logarithm factors, M is the number of contexts, S is the number of states, A is the number of actions, K is the number of episodes, Gamma le S is the maximum transition degree of any state-action pair, and Var^star is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel Omega(mathsf{Var^star M S A K}) regret lower bound with Gamma = 2, which shows our upper bound minimax optimal when Gamma is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k_2=2k_1=0.2 h/Mpc by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

The outcome of Large Language Model (LLM) pre-training strongly depends on weight initialization and variance control strategies. Although the importance of initial variance control has been well documented in neural networks in general, the literature on initialization and management of its growth during LLM pre-training, specifically, is somewhat sparse. In this paper, we introduce the Layer Index Rescaling (LIR) weight initialization scheme, and the Target Variance Rescaling (TVR) variance control strategy. Experiments on a 1B parameter LLaMA model demonstrate that better variance management using these techniques yields substantial improvements in downstream task performance (up to 4.6% on common pre-training benchmarks) and reduces extreme activation values, thus mitigating challenges associated with quantization and low-precision training. Our code is available at: https://github.com/bluorion-com/weight_rescaling.

Text-to-video diffusion models are notoriously limited in their ability to model temporal aspects such as motion, physics, and dynamic interactions. Existing approaches address this limitation by retraining the model or introducing external conditioning signals to enforce temporal consistency. In this work, we explore whether a meaningful temporal representation can be extracted directly from the predictions of a pre-trained model without any additional training or auxiliary inputs. We introduce FlowMo, a novel training-free guidance method that enhances motion coherence using only the model's own predictions in each diffusion step. FlowMo first derives an appearance-debiased temporal representation by measuring the distance between latents corresponding to consecutive frames. This highlights the implicit temporal structure predicted by the model. It then estimates motion coherence by measuring the patch-wise variance across the temporal dimension and guides the model to reduce this variance dynamically during sampling. Extensive experiments across multiple text-to-video models demonstrate that FlowMo significantly improves motion coherence without sacrificing visual quality or prompt alignment, offering an effective plug-and-play solution for enhancing the temporal fidelity of pre-trained video diffusion models.

This paper presents a dynamic cryptocurrency portfolio optimization strategy that integrates technical indicators and sentiment analysis to enhance investment decision-making. The proposed method employs the 14-day Relative Strength Index (RSI) and 14-day Simple Moving Average (SMA) to capture market momentum, while sentiment scores are extracted from news articles using the VADER (Valence Aware Dictionary and sEntiment Reasoner) model, with compound scores quantifying overall market tone. The large language model Google Gemini is used to further verify the sentiment scores predicted by VADER and give investment decisions. These technical indicator and sentiment signals are incorporated into the expected return estimates before applying mean-variance optimization with constraints on asset weights. The strategy is evaluated through a rolling-window backtest over cryptocurrency market data, with Bitcoin (BTC) and an equal-weighted portfolio of selected cryptocurrencies serving as benchmarks. Experimental results show that the proposed approach achieves a cumulative return of 38.72, substantially exceeding Bitcoin's 8.85 and the equal-weighted portfolio's 21.65 over the same period, and delivers a higher Sharpe ratio (1.1093 vs. 0.8853 and 1.0194, respectively). However, the strategy exhibits a larger maximum drawdown (-18.52%) compared to Bitcoin (-4.48%) and the equal-weighted portfolio (-11.02%), indicating higher short-term downside risk. These results highlight the potential of combining sentiment and technical signals to improve cryptocurrency portfolio performance, while also emphasizing the need to address risk exposure in volatile markets.

Despite the remarkable progress in generative modelling, current diffusion models lack a quantitative approach to assess image quality. To address this limitation, we propose to estimate the pixel-wise aleatoric uncertainty during the sampling phase of diffusion models and utilise the uncertainty to improve the sample generation quality. The uncertainty is computed as the variance of the denoising scores with a perturbation scheme that is specifically designed for diffusion models. We then show that the aleatoric uncertainty estimates are related to the second-order derivative of the diffusion noise distribution. We evaluate our uncertainty estimation algorithm and the uncertainty-guided sampling on the ImageNet and CIFAR-10 datasets. In our comparisons with the related work, we demonstrate promising results in filtering out low quality samples. Furthermore, we show that our guided approach leads to better sample generation in terms of FID scores.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Multi-turn, multi-agent LLM game evaluations often exhibit substantial run-to-run variance. In long-horizon interactions, small early deviations compound across turns and are amplified by multi-agent coupling. This biases win rate estimates and makes rankings unreliable across repeated tournaments. Prompt choice worsens this further by producing different effective policies. We address both instability and underperformance with MEMO (Memory-augmented MOdel context optimization), a self-play framework that optimizes inference-time context by coupling retention and exploration. Retention maintains a persistent memory bank that stores structured insights from self-play trajectories and injects them as priors during later play. Exploration runs tournament-style prompt evolution with uncertainty-aware selection via TrueSkill, and uses prioritized replay to revisit rare and decisive states. Across five text-based games, MEMO raises mean win rate from 25.1% to 49.5% for GPT-4o-mini and from 20.9% to 44.3% for Qwen-2.5-7B-Instruct, using 2,000 self-play games per task. Run-to-run variance also drops, giving more stable rankings across prompt variations. These results suggest that multi-agent LLM game performance and robustness have substantial room for improvement through context optimization. MEMO achieves the largest gains in negotiation and imperfect-information games, while RL remains more effective in perfect-information settings.

Large Language Models (LLMs) achieve competitive performance across diverse natural language processing (NLP) tasks, yet pretraining is computationally demanding, making optimizer efficiency an important practical consideration. Muon accelerates LLM pretraining via orthogonal momentum updates that serve as a matrix analogue of the element-wise sign operator. Motivated by the recent perspective that Adam is a variance-adaptive sign update algorithm, we propose two variants of Muon, Muon-NSR and Muon-VS, which apply variance-adaptive normalization to momentum before orthogonalization. Muon-NSR applies noise-to-signal ratio (NSR) modulation, while Muon-VS performs variance-based scaling without introducing additional hyperparameters. Experiments on GPT-2 and LLaMA pretraining demonstrate that our proposed methods accelerate convergence and consistently achieve lower validation loss than both competitive, well-tuned AdamW and Muon baselines. For example, on the LLaMA-1.2B model, Muon-NSR and Muon-VS reduce the iterations required to reach the target validation loss by 1.36times relative to the well-tuned Muon following the recent benchmark.

Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.

Model merging offers a promising avenue for knowledge integration and parallel development without retraining. Yet, existing methods either ignore the geometry of the loss landscape or rely on intractable full-space Hessian approximations. We propose EpiMer, a framework that casts model merging as solving the Fréchet mean on a Riemannian manifold and restricts the computation to a low-rank subspace spanned by the task vectors. With the expected Hessian as the metric, we reveal a connection between local curvature and epistemic uncertainty of the parameters. Our theoretical analysis decomposes the merging error bound into the subspace Fréchet variance and the residual energy, and provides a closed-form characterization of when curvature-aware merging provably outperforms flat-geometry methods. In addition, our framework unifies both curvature-aware methods and recent spectral methods as special cases of the subspace Fréchet mean with different geometric metrics. Merging fine-tuned CLIP-ViT models on eight image classification tasks, Epistemic Merging strictly outperforms the baselines on all three CLIP-ViT backbones at matched rank, improving the across-task average accuracy and worst-task accuracy on every backbone.

This paper presents TEVR, a speech recognition model designed to minimize the variation in token entropy w.r.t. to the language model. This takes advantage of the fact that if the language model will reliably and accurately predict a token anyway, then the acoustic model doesn't need to be accurate in recognizing it. We train German ASR models with 900 million parameters and show that on CommonVoice German, TEVR scores a very competitive 3.64% word error rate, which outperforms the best reported results by a relative 16.89% reduction in word error rate. We hope that releasing our fully trained speech recognition pipeline to the community will lead to privacy-preserving offline virtual assistants in the future.

Given a set of pre-trained models, how can we quickly and accurately find the most useful pre-trained model for a downstream task? Transferability measurement is to quantify how transferable is a pre-trained model learned on a source task to a target task. It is used for quickly ranking pre-trained models for a given task and thus becomes a crucial step for transfer learning. Existing methods measure transferability as the discrimination ability of a source model for a target data before transfer learning, which cannot accurately estimate the fine-tuning performance. Some of them restrict the application of transferability measurement in selecting the best supervised pre-trained models that have classifiers. It is important to have a general method for measuring transferability that can be applied in a variety of situations, such as selecting the best self-supervised pre-trained models that do not have classifiers, and selecting the best transferring layer for a target task. In this work, we propose TMI (TRANSFERABILITY MEASUREMENT WITH INTRA-CLASS FEATURE VARIANCE), a fast and accurate algorithm to measure transferability. We view transferability as the generalization of a pre-trained model on a target task by measuring intra-class feature variance. Intra-class variance evaluates the adaptability of the model to a new task, which measures how transferable the model is. Compared to previous studies that estimate how discriminative the models are, intra-class variance is more accurate than those as it does not require an optimal feature extractor and classifier. Extensive experiments on real-world datasets show that TMI outperforms competitors for selecting the top-5 best models, and exhibits consistently better correlation in 13 out of 17 cases.

Electrocardiogram (ECG) is a widely used tool for assessing cardiac function due to its low cost and accessibility. Emergent research shows that ECGs can help make predictions on key outcomes traditionally derived from more complex modalities such as echocardiograms (ECHO), enabling the use of ECGs as a more accessible method to predict broader measurements of cardiac function. ECHO, in particular, are of great importance because they require considerable hospital resources while playing a key role in clinical cardiac assessment. To aid this use case, we introduce EchoingECG, a probabilistic student-teacher model that leverages uncertainty-aware ECG embeddings and ECHO supervision to improve ECG-based cardiac function prediction. Our approach integrates Probabilistic Cross-Modal Embeddings (PCME++), a probabilistic contrastive framework, with ECHO-CLIP, a vision-language pre-trained model trained on ECHO-text pairs, to distill ECHO knowledge into ECG representations. Through experiments and external validation, we showed that EchoingECG outperforms state-of-the-art foundation ECG models in zero-shot, few-shot, and fine-tune settings for ECHO predictions based on ECG. We also highlighted that variance estimation (enabled through our method) enhanced our understanding of model performance by identifying underlying regions of uncertainty within ECGs. The code is available: https://github.com/mcintoshML/EchoingECG.

Increasingly expensive training of ever larger models such as Vision Transfomers motivate reusing the vast library of already trained state-of-the-art networks. However, their latency, high computational costs and memory demands pose significant challenges for deployment, especially on resource-constrained hardware. While structured pruning methods can reduce these factors, they often require costly retraining, sometimes for up to hundreds of epochs, or even training from scratch to recover the lost accuracy resulting from the structural modifications. Maintaining the provided performance of trained models after structured pruning and thereby avoiding extensive retraining remains a challenge. To solve this, we introduce Variance-Based Pruning, a simple and structured one-shot pruning technique for efficiently compressing networks, with minimal finetuning. Our approach first gathers activation statistics, which are used to select neurons for pruning. Simultaneously the mean activations are integrated back into the model to preserve a high degree of performance. On ImageNet-1k recognition tasks, we demonstrate that directly after pruning DeiT-Base retains over 70% of its original performance and requires only 10 epochs of fine-tuning to regain 99% of the original accuracy while simultaneously reducing MACs by 35% and model size by 36%, thus speeding up the model by 1.44x.

Spontaneous speech emotion data usually contain perceptual grades where graders assign emotion score after listening to the speech files. Such perceptual grades introduce uncertainty in labels due to grader opinion variation. Grader variation is addressed by using consensus grades as groundtruth, where the emotion with the highest vote is selected. Consensus grades fail to consider ambiguous instances where a speech sample may contain multiple emotions, as captured through grader opinion uncertainty. We demonstrate that using the probability density function of the emotion grades as targets instead of the commonly used consensus grades, provide better performance on benchmark evaluation sets compared to results reported in the literature. We show that a saliency driven foundation model (FM) representation selection helps to train a state-of-the-art speech emotion model for both dimensional and categorical emotion recognition. Comparing representations obtained from different FMs, we observed that focusing on overall test-set performance can be deceiving, as it fails to reveal the models generalization capacity across speakers and gender. We demonstrate that performance evaluation across multiple test-sets and performance analysis across gender and speakers are useful in assessing usefulness of emotion models. Finally, we demonstrate that label uncertainty and data-skew pose a challenge to model evaluation, where instead of using the best hypothesis, it is useful to consider the 2- or 3-best hypotheses.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

We present ACAR (Adaptive Complexity and Attribution Routing), a measurement framework for studying multi-model orchestration under auditable conditions. ACAR uses self-consistency variance (sigma) computed from N=3 probe samples to route tasks across single-model, two-model, and three-model execution modes. The system is implemented on top of TEAMLLM, a deterministic execution substrate with immutable artifacts and complete decision traces. We evaluate ACAR on 1,510 tasks spanning four benchmarks: MathArena, Reasoning Gym, LiveCodeBench, and SuperGPQA, using Claude Sonnet 4, GPT-4o, and Gemini 2.0 Flash, producing more than 7,550 auditable runs. Results show that sigma-based routing achieves 55.6 percent accuracy, exceeding the two-model baseline of 54.4 percent while avoiding full ensembling on 54.2 percent of tasks. The routing mechanism is model-agnostic and requires no learned components. We also document negative results. First, retrieval augmentation reduced accuracy by 3.4 percentage points, as median retrieval similarity was only 0.167, demonstrating that experience injection without semantic alignment introduces noise rather than grounding. Second, when models agree on incorrect answers (sigma equals zero), no downstream ensemble can recover; this agreement-but-wrong failure mode is intrinsic to self-consistency and bounds achievable accuracy at approximately eight percentage points below full ensembling. Third, attribution estimates based on proxy signals such as response similarity and entropy showed weak correlation with ground-truth leave-one-out values, indicating that practical attribution requires explicit counterfactual computation. This work documents which assumptions fail in practice and provides falsifiable baselines for future research on routing, retrieval, and multi-model attribution.

As LLM-based agents are deployed in production systems, understanding their behavioral consistency (whether they produce similar action sequences when given identical tasks) becomes critical for reliability. We study consistency in the context of SWE-bench, a challenging software engineering benchmark requiring complex, multi-step reasoning. Comparing Claude~4.5~Sonnet, GPT-5, and Llama-3.1-70B across 50 runs each (10 tasks times 5 runs), we find that across models, higher consistency aligns with higher accuracy: Claude achieves the lowest variance (CV: 15.2\%) and highest accuracy (58\%), GPT-5 is intermediate (CV: 32.2\%, accuracy: 32\%), and Llama shows the highest variance (CV: 47.0\%) with lowest accuracy (4\%). However, within a model, consistency can amplify both correct and incorrect interpretations. Our analysis reveals a critical nuance: consistency amplifies outcomes rather than guaranteeing correctness. 71\% of Claude's failures stem from "consistent wrong interpretation": making the same incorrect assumption across all runs. Interestingly, GPT-5 achieves similar early strategic agreement as Claude (diverging at step 3.4 vs.\ 3.2) but exhibits 2.1times higher variance, suggesting that divergence timing alone does not determine consistency. These findings suggest that for production deployment, interpretation accuracy matters more than execution consistency, with implications for agent evaluation and training.

Visual tokens dominate inference cost in vision-language models (VLMs), yet many carry redundant information. Existing pruning methods alleviate this but typically rely on attention magnitude or similarity scores. We reformulate visual token pruning as capacity constrained communication: given a fixed budget K, the model must allocate limited bandwidth to maximally preserve visual information. We propose AutoSelect, which attaches a lightweight Scorer and Denoiser to a frozen VLM and trains with only the standard next token prediction loss, without auxiliary objectives or extra annotations. During training, a variance preserving noise gate modulates each token's information flow according to its predicted importance so that gradients propagate through all tokens; a diagonal attention Denoiser then recovers the perturbed representations. At inference, only the Scorer and a hard top-K selection remain, adding negligible latency. On ten VLM benchmarks, AutoSelect retains 96.5% of full model accuracy while accelerating LLM prefill by 2.85x with only 0.69 ms overhead, and transfers to different VLM backbones without architecture-specific tuning. Code is available at https://github.com/MedHK23/AutoSelect.

Deep neural networks are vulnerable to adversarial examples that mislead the models with imperceptible perturbations. Though adversarial attacks have achieved incredible success rates in the white-box setting, most existing adversaries often exhibit weak transferability in the black-box setting, especially under the scenario of attacking models with defense mechanisms. In this work, we propose a new method called variance tuning to enhance the class of iterative gradient based attack methods and improve their attack transferability. Specifically, at each iteration for the gradient calculation, instead of directly using the current gradient for the momentum accumulation, we further consider the gradient variance of the previous iteration to tune the current gradient so as to stabilize the update direction and escape from poor local optima. Empirical results on the standard ImageNet dataset demonstrate that our method could significantly improve the transferability of gradient-based adversarial attacks. Besides, our method could be used to attack ensemble models or be integrated with various input transformations. Incorporating variance tuning with input transformations on iterative gradient-based attacks in the multi-model setting, the integrated method could achieve an average success rate of 90.1% against nine advanced defense methods, improving the current best attack performance significantly by 85.1% . Code is available at https://github.com/JHL-HUST/VT.

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.

In this paper, we present OtterHD-8B, an innovative multimodal model evolved from Fuyu-8B, specifically engineered to interpret high-resolution visual inputs with granular precision. Unlike conventional models that are constrained by fixed-size vision encoders, OtterHD-8B boasts the ability to handle flexible input dimensions, ensuring its versatility across various inference requirements. Alongside this model, we introduce MagnifierBench, an evaluation framework designed to scrutinize models' ability to discern minute details and spatial relationships of small objects. Our comparative analysis reveals that while current leading models falter on this benchmark, OtterHD-8B, particularly when directly processing high-resolution inputs, outperforms its counterparts by a substantial margin. The findings illuminate the structural variances in visual information processing among different models and the influence that the vision encoders' pre-training resolution disparities have on model effectiveness within such benchmarks. Our study highlights the critical role of flexibility and high-resolution input capabilities in large multimodal models and also exemplifies the potential inherent in the Fuyu architecture's simplicity for handling complex visual data.

The use of positional embeddings in transformer language models is widely accepted. However, recent research has called into question the necessity of such embeddings. We further extend this inquiry by demonstrating that a randomly initialized and frozen transformer language model, devoid of positional embeddings, inherently encodes strong positional information through the shrinkage of self-attention variance. To quantify this variance, we derive the underlying distribution of each step within a transformer layer. Through empirical validation using a fully pretrained model, we show that the variance shrinkage effect still persists after extensive gradient updates. Our findings serve to justify the decision to discard positional embeddings and thus facilitate more efficient pretraining of transformer language models.

Mamba is an efficient sequence model that rivals Transformers and demonstrates significant potential as a foundational architecture for various tasks. Quantization is commonly used in neural networks to reduce model size and computational latency. However, applying quantization to Mamba remains underexplored, and existing quantization methods, which have been effective for CNN and Transformer models, appear inadequate for Mamba models (e.g., Quarot suffers a 21% accuracy drop on Vim-T^dagger even under W8A8). We have pioneered the exploration of this issue and identified several key challenges. First, significant outliers are present in gate projections, output projections, and matrix multiplications. Second, Mamba's unique parallel scan further amplifies these outliers, leading to uneven and heavy-tailed data distributions. Third, even with the application of the Hadamard transform, the variance across channels in weights and activations still remains inconsistent. To these ends, we propose MambaQuant, a post-training quantization (PTQ) framework consisting of: 1) Karhunen-Loeve Transformation (KLT) enhanced rotation, rendering the rotation matrix adaptable to diverse channel distributions. 2) Smooth-Fused rotation, which equalizes channel variances and can merge additional parameters into model weights. Experiments show that MambaQuant can quantize both weights and activations into 8-bit with less than 1% accuracy loss for Mamba-based vision and language tasks. To the best of our knowledge, MambaQuant is the first comprehensive PTQ design for the Mamba family, paving the way for further advancements in its application.

While Masked Diffusion Models (MDMs), such as LLaDA, present a promising paradigm for language modeling, there has been relatively little effort in aligning these models with human preferences via reinforcement learning. The challenge primarily arises from the high variance in Evidence Lower Bound (ELBO)-based likelihood estimates required for preference optimization. To address this issue, we propose Variance-Reduced Preference Optimization (VRPO), a framework that formally analyzes the variance of ELBO estimators and derives bounds on both the bias and variance of preference optimization gradients. Building on this theoretical foundation, we introduce unbiased variance reduction strategies, including optimal Monte Carlo budget allocation and antithetic sampling, that significantly improve the performance of MDM alignment. We demonstrate the effectiveness of VRPO by applying it to LLaDA, and the resulting model, LLaDA 1.5, outperforms its SFT-only predecessor consistently and significantly across mathematical (GSM8K +4.7), code (HumanEval +3.0, MBPP +1.8), and alignment benchmarks (IFEval +4.0, Arena-Hard +4.3). Furthermore, LLaDA 1.5 demonstrates a highly competitive mathematical performance compared to strong language MDMs and ARMs. Project page: https://ml-gsai.github.io/LLaDA-1.5-Demo/.

Zero-shot, training-free, image-based text-to-video generation is an emerging area that aims to generate videos using existing image-based diffusion models. Current methods in this space require specific architectural changes to image generation models, which limit their adaptability and scalability. In contrast to such methods, we provide a model-agnostic approach. We use intersections in diffusion trajectories, working only with the latent values. We could not obtain localized frame-wise coherence and diversity using only the intersection of trajectories. Thus, we instead use a grid-based approach. An in-context trained LLM is used to generate coherent frame-wise prompts; another is used to identify differences between frames. Based on these, we obtain a CLIP-based attention mask that controls the timing of switching the prompts for each grid cell. Earlier switching results in higher variance, while later switching results in more coherence. Therefore, our approach can ensure appropriate control between coherence and variance for the frames. Our approach results in state-of-the-art performance while being more flexible when working with diverse image-generation models. The empirical analysis using quantitative metrics and user studies confirms our model's superior temporal consistency, visual fidelity and user satisfaction, thus providing a novel way to obtain training-free, image-based text-to-video generation.

We present the first evaluation harness that enables any out-of-the-box, local, Large Language Models (LLMs) to play full-press Diplomacy without fine-tuning or specialized training. Previous work required frontier LLMs, or fine-tuning, due to the high complexity and information density of Diplomacy's game state. Combined with the high variance of matches, these factors made Diplomacy prohibitive for study. In this work, we used data-driven iteration to optimize a textual game state representation such that a 24B model can reliably complete matches without any fine tuning. We develop tooling to facilitate hypothesis testing and statistical analysis, and we present case studies on persuasion, aggressive playstyles, and performance across a range of models. We conduct a variety of experiments across many popular LLMs, finding the larger models perform the best, but the smaller models still play adequately. We also introduce Critical State Analysis: an experimental protocol for rapidly iterating and analyzing key moments in a game at depth. Our harness democratizes the evaluation of strategic reasoning in LLMs by eliminating the need for fine-tuning, and it provides insights into how these capabilities emerge naturally from widely used LLMs. Our code is available in the supplement and will be open sourced.

We present a vision-action policy that won 1st place in the 2025 BEHAVIOR Challenge - a large-scale benchmark featuring 50 diverse long-horizon household tasks in photo-realistic simulation, requiring bimanual manipulation, navigation, and context-aware decision making. Building on the Pi0.5 architecture, we introduce several innovations. Our primary contribution is correlated noise for flow matching, which improves training efficiency and enables correlation-aware inpainting for smooth action sequences. We also apply learnable mixed-layer attention and System 2 stage tracking for ambiguity resolution. Training employs multi-sample flow matching to reduce variance, while inference uses action compression and challenge-specific correction rules. Our approach achieves 26% q-score across all 50 tasks on both public and private leaderboards.

When searching for information, a human reader first glances over a document, spots relevant sections and then focuses on a few sentences for resolving her intention. However, the high variance of document structure complicates to identify the salient topic of a given section at a glance. To tackle this challenge, we present SECTOR, a model to support machine reading systems by segmenting documents into coherent sections and assigning topic labels to each section. Our deep neural network architecture learns a latent topic embedding over the course of a document. This can be leveraged to classify local topics from plain text and segment a document at topic shifts. In addition, we contribute WikiSection, a publicly available dataset with 242k labeled sections in English and German from two distinct domains: diseases and cities. From our extensive evaluation of 20 architectures, we report a highest score of 71.6% F1 for the segmentation and classification of 30 topics from the English city domain, scored by our SECTOR LSTM model with bloom filter embeddings and bidirectional segmentation. This is a significant improvement of 29.5 points F1 compared to state-of-the-art CNN classifiers with baseline segmentation.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Generative models trained using self-supervision of tokenized electronic health record (EHR) timelines show promise for clinical outcome prediction. This is typically done using Monte Carlo simulation for future patient trajectories. However, existing approaches suffer from three key limitations: sparse estimate distributions that poorly differentiate patient risk levels, extreme computational costs, and high sampling variance. We propose two new estimators: the Sum of Conditional Outcome Probability Estimator (SCOPE) and Risk Estimation from Anticipated Conditional Hazards (REACH), that leverage next-token probability distributions discarded by standard Monte Carlo. We prove both estimators are unbiased and that REACH guarantees variance reduction over Monte Carlo sampling for any model and outcome. Empirically, on hospital mortality prediction in MIMIC-IV using the ETHOS-ARES framework, SCOPE and REACH match 100-sample Monte Carlo performance using only 10-11 samples (95% CI: [9,11]), representing a ~10x reduction in inference cost without degrading calibration. For ICU admission prediction, efficiency gains are more modest (~1.2x), which we attribute to the outcome's lower "spontaneity," a property we characterize theoretically and empirically. These methods substantially improve the feasibility of deploying generative EHR models in resource-constrained clinical settings.

Pretrained diffusion models serve as frozen teachers feeding downstream pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are Monte Carlo (MC) expectations over noise levels and Gaussian noise samples; their estimator variance dominates compute cost because each draw requires expensive upstream work (rendering, simulation, encoding). We introduce CARV, a compute-aware variance-accounting framework that motivates a hierarchical MC estimator: amortize the expensive upstream computation over cheap diffusion-noise resamples, sharpened by timestep importance sampling and a stratified-inverse-CDF construction. In our text-to-3D distillation and attribution experiments, CARV delivers 2-3x effective compute multipliers (most from amortized reuse; ~25% additional from IS+stratification) without changing the objective; in single-step distillation, the same techniques cut gradient variance by an order of magnitude but do not improve downstream FID, marking the regime where MC variance is no longer the bottleneck.

The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability. We propose a principled, attack-agnostic robustness metric based on the spectral norm of the Fisher Information Matrix (FIM), which quantifies the worst-case sensitivity of the model's output distribution to input perturbations. Theoretically, we establish that the FIM equals the variance of the input Jacobian and derive closed-form spectral bounds for common architectures, including VGG, ResNet, DenseNet, and Transformer, providing the first theoretical robustness ranking. To enable scalable evaluation, we develop efficient algorithms, including power iteration and Hutchinson-based estimation, that support both white-box and black-box settings. Extensive experiments across multiple datasets, including CIFAR, ImageNet, and medical images, and across multiple architectures show a strong correlation between our metric and adversarial vulnerability. Our framework serves as an interpretable diagnostic tool that complements attack-based evaluations, offering insights into architectural sensitivity and guiding the design of more robust models. Code is available at: https://github.com/franz-chang/SRP/.

The Frechet Inception Distance (FID) is the de facto arbiter of image generation, yet most papers report just a single number from a single trained model using a single sampling seed. How reproducible is that number if we retrain the model, or merely resample from it? In this paper, we treat FID as a random variable on a two-axis panel of training and generation seeds, and measure its variance directly on several hundred SiT networks trained on class-conditional ImageNet 256x256. We report surprising findings: (a) Retraining the model using the same recipe with a different seed moves FID 3.2x more (in Inception feature space) than redrawing samples from a fixed network. (b) That gap is driven by three factors: random initialisation, data ordering, and the per-step Gaussian noise of the flow-matching loss. (c) Increasing compute or model size barely tightens the spread, holding the FID coefficient of variation (CoV) inside a 1-2% band. (d) Per-cell classifier-free-guidance tuning halves the spread but reshuffles which seeds work best, and a lucky training seed reaches the same FID with up to 2x less compute than an unlucky one. Based on these findings, we recommend a new FID evaluation protocol: evaluate under per-cell optimal guidance, treat any FID gap below the empirically measured ~1.3% CoV as inconclusive, and report an error bar over several training seeds rather than a single FID number.

Supervised proxy-based deep cross-modal hashing has become the dominant paradigm for large-scale retrieval. However, prevalent methods model class proxies as deterministic points in the embedding space. This rigid assumption causes severe gradient conflicts in multi-label scenarios, where gradient conflicts arising from label co-occurrence lead to severe gradient contention and optimization collapse. To resolve this, we propose Kent-based Distributional Proxy Hashing (KDPH), a novel framework that shifts proxy representation from static points to flexible anisotropic Kent distributions on the hypersphere. Unlike point proxies that must shift their positions to accommodate conflicting gradients, KDPH absorbs these conflicts by dynamically adjusting its directional variance. This allows the proxy to maintain a stable semantic mean direction while stretching to cover diverse label correlations. Furthermore, to ensure stable training of these geometric parameters, we derive a tailored loss function incorporating the Cayley transform to enforce strict orthogonality. To the best of our knowledge, KDPH is the first framework to successfully introduce the Kent distributions into cross-modal hashing. Experiments on three benchmark datasets demonstrate that KDPH mitigates proxy collapse and chaotic oscillation, significantly outperforms state-of-the-art methods. Code is available at https://github.com/Senmo996/KDPH-official-code.

Due to privacy, storage, and other constraints, there is a growing need for unsupervised domain adaptation techniques in machine learning that do not require access to the data used to train a collection of source models. Existing methods for multi-source-free domain adaptation (MSFDA) typically train a target model using pseudo-labeled data produced by the source models, which focus on improving the pseudo-labeling techniques or proposing new training objectives. Instead, we aim to analyze the fundamental limits of MSFDA. In particular, we develop an information-theoretic bound on the generalization error of the resulting target model, which illustrates an inherent bias-variance trade-off. We then provide insights on how to balance this trade-off from three perspectives, including domain aggregation, selective pseudo-labeling, and joint feature alignment, which leads to the design of novel algorithms. Experiments on multiple datasets validate our theoretical analysis and demonstrate the state-of-art performance of the proposed algorithm, especially on some of the most challenging datasets, including Office-Home and DomainNet.

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

Recent research on texture synthesis for 3D shapes benefits a lot from dramatically developed 2D text-to-image diffusion models, including inpainting-based and optimization-based approaches. However, these methods ignore the modal gap between the 2D diffusion model and 3D objects, which primarily render 3D objects into 2D images and texture each image separately. In this paper, we revisit the texture synthesis and propose a Variance alignment based 3D-2D Collaborative Denoising framework, dubbed VCD-Texture, to address these issues. Formally, we first unify both 2D and 3D latent feature learning in diffusion self-attention modules with re-projected 3D attention receptive fields. Subsequently, the denoised multi-view 2D latent features are aggregated into 3D space and then rasterized back to formulate more consistent 2D predictions. However, the rasterization process suffers from an intractable variance bias, which is theoretically addressed by the proposed variance alignment, achieving high-fidelity texture synthesis. Moreover, we present an inpainting refinement to further improve the details with conflicting regions. Notably, there is not a publicly available benchmark to evaluate texture synthesis, which hinders its development. Thus we construct a new evaluation set built upon three open-source 3D datasets and propose to use four metrics to thoroughly validate the texturing performance. Comprehensive experiments demonstrate that VCD-Texture achieves superior performance against other counterparts.

Stable pre-training is essential for achieving better-performing language models. However, tracking pre-training stability by calculating gradient variance at every step is impractical due to the significant computational costs. We explore Token Embedding Variability (TEV) as a simple and efficient proxy for assessing pre-training stability in language models with pre-layer normalization, given that shallower layers are more prone to gradient explosion (section 2.2). Moreover, we propose Multi-head Low-Rank Attention (MLRA) as an architecture to alleviate such instability by limiting the exponential growth of output embedding variance, thereby preventing the gradient explosion (section 3.2). Empirical results on GPT-2 with MLRA demonstrate increased stability and lower perplexity, particularly in deeper models.

As AI becomes more capable, we entrust it with more general and consequential tasks. The risks from failure grow more severe with increasing task scope. It is therefore important to understand how extremely capable AI models will fail: Will they fail by systematically pursuing goals we do not intend? Or will they fail by being a hot mess, and taking nonsensical actions that do not further any goal? We operationalize this question using a bias-variance decomposition of the errors made by AI models: An AI's incoherence on a task is measured over test-time randomness as the fraction of its error that stems from variance rather than bias in task outcome. Across all tasks and frontier models we measure, the longer models spend reasoning and taking actions, the more incoherent their failures become. Incoherence changes with model scale in a way that is experiment dependent. However, in several settings, larger, more capable models are more incoherent than smaller models. Consequently, scale alone seems unlikely to eliminate incoherence. Instead, as more capable AIs pursue harder tasks, requiring more sequential action and thought, our results predict failures to be accompanied by more incoherent behavior. This suggests a future where AIs sometimes cause industrial accidents (due to unpredictable misbehavior), but are less likely to exhibit consistent pursuit of a misaligned goal. This increases the relative importance of alignment research targeting reward hacking or goal misspecification.

Portfolio Management is the process of overseeing a group of investments, referred to as a portfolio, with the objective of achieving predetermined investment goals. Portfolio optimization is a key component that involves allocating the portfolio assets so as to maximize returns while minimizing risk taken. It is typically carried out by financial professionals who use a combination of quantitative techniques and investment expertise to make decisions about the portfolio allocation. Recent applications of Deep Reinforcement Learning (DRL) have shown promising results when used to optimize portfolio allocation by training model-free agents on historical market data. Many of these methods compare their results against basic benchmarks or other state-of-the-art DRL agents but often fail to compare their performance against traditional methods used by financial professionals in practical settings. One of the most commonly used methods for this task is Mean-Variance Portfolio Optimization (MVO), which uses historical time series information to estimate expected asset returns and covariances, which are then used to optimize for an investment objective. Our work is a thorough comparison between model-free DRL and MVO for optimal portfolio allocation. We detail the specifics of how to make DRL for portfolio optimization work in practice, also noting the adjustments needed for MVO. Backtest results demonstrate strong performance of the DRL agent across many metrics, including Sharpe ratio, maximum drawdowns, and absolute returns.

Excluding irrelevant features in a pattern recognition task plays an important role in maintaining a simpler machine learning model and optimizing the computational efficiency. Nowadays with the rise of large scale datasets, feature selection is in great demand as it becomes a central issue when facing high-dimensional datasets. The present study provides a new measure of saliency for features by employing a Sensitivity Analysis (SA) technique called the extended Fourier amplitude sensitivity test, and a well-trained Feedforward Neural Network (FNN) model, which ultimately leads to the selection of a promising optimal feature subset. Ideas of the paper are mainly demonstrated based on adopting FNN model for feature selection in classification problems. But in the end, a generalization framework is discussed in order to give insights into the usage in regression problems as well as expressing how other function approximate models can be deployed. Effectiveness of the proposed method is verified by result analysis and data visualization for a series of experiments over several well-known datasets drawn from UCI machine learning repository.

Post-training quantization (PTQ) is a practical path to deploy large diffusion models, but quantization noise can accumulate over the denoising trajectory and degrade generation quality. We propose Q-Drift, a principled sampler-side correction that treats quantization error as an implicit stochastic perturbation on each denoising step and derives a marginal-distribution-preserving drift adjustment. Q-Drift estimates a timestep-wise variance statistic from calibration, in practice requiring as few as 5 paired full-precision/quantized calibration runs. The resulting sampler correction is plug-and-play with common samplers, diffusion models, and PTQ methods, while incurring negligible overhead at inference. Across six diverse text-to-image models (spanning DiT and U-Net), three samplers (Euler, flow-matching, DPM-Solver++), and two PTQ methods (SVDQuant, MixDQ), Q-Drift improves FID over the corresponding quantized baseline in most settings, with up to 4.59 FID reduction on PixArt-Sigma (SVDQuant W3A4), while preserving CLIP scores.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance σ^2, while the component means are estimated using a likelihood with variance τ^2, yielding a family of mismatched likelihood functions parameterized by the ratio ρ=τ/σ. We show that the interplay between ρ and the signal-to-noise ratio (SNR) induces a sharp phase diagram. Under correct specification (ρ=1), maximum likelihood recovers the true means, independently of the SNR. However, once the model is misspecified, two different regimes emerge. Under under-smoothing (ρ<1), the estimated Gaussian means are displaced from the truth, and in low SNR this discrepancy grows as the SNR decreases: for every fixed ρ<1, the squared error scales as SNR^{-1}. Under over-smoothing (ρ>1), the fitted likelihood blurs the cluster separation, causing distinct component means to collapse towards the overall mixture center once ρ^2 exceeds a threshold of the form 1 + λ,SNR, where λ depends on the geometry of the true means. We further show that the hard assignment objective arises as the limit τto 0 of the same mismatched likelihood family, and derive corresponding low- and high-SNR results for hard-assignment mean estimation and latent-label recovery. Furthermore, in low SNR, Bayes-optimal clustering is close to random guessing, and the hard-assignment target remains far from the true means. These results show that in low-SNR applications, even mild variance misspecification or hard-assignment procedures can induce substantial bias, whereas in high SNR these effects are largely absent.

Mitigating social bias in Large Language Models (LLMs) presents a distinct alignment challenge: unlike verifiable tasks, bias lacks a single ground truth, creating a high-variance, subjective reward landscape. Previous preference-based fine-tuning methods have major trade-offs: Direct Preference Optimization (DPO) is limited by the lack of exploration inherent in offline training, while Proximal Policy Optimization (PPO) can lead to training instability due to potentially unreliable critic estimates. In this paper, we propose BiasGRPO, a framework using Group Relative Policy Optimization (GRPO) to stabilize alignment by normalizing rewards across a group of sampled completions. By substituting the value function with a group-relative baseline, our approach reduces instability while maintaining the exploration benefits of online training. We find that BiasGRPO outperforms DPO and PPO across multiple benchmarks, indicating its effectiveness. To adapt GRPO, we synthetically extend a dataset spanning multiple domains and contexts. We also create and release a custom bias reward model that effectively guides generation while being highly compute-efficient and avoiding knowledge degradation, providing a valuable resource that can be seamlessly integrated into multi-objective RLHF pipelines.

Mixed-precision quantization must decide which parts of a model to keep at higher precision. A common premise, shared by sensitivity-based methods such as HAWQ and CoopQ, is that the loss from quantizing a set of layers can be reconstructed from per-layer or pairwise sensitivities measured in isolation. We test this premise at the 4-bit weight-and-activation precisions now being deployed, treating the change in loss f(S) from quantizing a layer set S as a set function on the Boolean cube and analyzing it through two classical changes of basis. This analysis yields two findings. First, across configurations drawn from the deployment distribution, 85--93\% of the variance of f is explained by per-layer effects alone. Second, a monotone transform of a sum of per-layer terms reproduces f's ranking of configurations, misordering at most 2\% of pairs. We propose the coverage model f(S)=cbigl(1-prod_{iin S}(1-a_i)bigr), which reproduces the measured variance profile of f to within a few percent from its L fitted break-rates. This structure supports two predictors of a configuration's loss, each with L+1 parameters. The additive model is the optimal first-order predictor. By Parseval's identity its mean-squared error equals the variance of f left unexplained by per-layer effects, which we measure on full lattices, estimate out of sample at full-network scale, and report with every result as a certificate of how well any additive model can do. The coverage model itself is the second predictor. As allocators at matched memory, they attain the lowest KL divergence among the compared allocators on models from 30B to 355B parameters. Below four bits, the resulting allocations continue to solve code and reasoning tasks at budgets where allocations from gradient sensitivities no longer produce terminating generations.

Production deployments often swap between different-sized models in a family for cost-quality cascading, mid-conversation switching, and routing, and each swap forces the receiver to repay the prefill from scratch. We propose cross-model KV cache transfer, where the receiver reuses the source's KV cache, skipping prefill. We find that cross-model KV has substantial linear structure across matched-KV pairs, where source and target share KV head count and per-head dimension. On Qwen3 14B->32B, one source layer explains 56% of variance in the target's keys and 32% in values, rising to 79% and 65% with multiple source layers. Building on this, we design a closed-form ridge mapper that operates per head and proceeds in three steps. First, for each target layer we select the top-k most predictive source layers and concatenate their KV as input. Second, we strip RoPE from the keys before mapping, so the fit is position-free and reusable across context lengths. Third, we fit ridge regression on a small calibration set of 500 FineWeb-Edu sequences of 1,024 tokens each. Surprisingly, across six pairs in three families, this linear mapper retains 73-98% of the receiver's standalone-prefill accuracy on four pairs, while two degrade sharply. A nonlinear MLP recovers up to +37 pp HellaSwag retention on the failures. The mapper runs 2.7-25x faster than re-prefill and remains stable across multi-turn handoff, making cross-model KV cache transfer practical.

Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-level distribution-valued characteristics can instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed from Qwen3-Embedding-8B news representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reported frozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.

Denoising diffusion probabilistic models (DDPMs) have recently achieved leading performances in many generative tasks. However, the inherited iterative sampling process costs hinder their applications to text-to-speech deployment. Through the preliminary study on diffusion model parameterization, we find that previous gradient-based TTS models require hundreds or thousands of iterations to guarantee high sample quality, which poses a challenge for accelerating sampling. In this work, we propose ProDiff, on progressive fast diffusion model for high-quality text-to-speech. Unlike previous work estimating the gradient for data density, ProDiff parameterizes the denoising model by directly predicting clean data to avoid distinct quality degradation in accelerating sampling. To tackle the model convergence challenge with decreased diffusion iterations, ProDiff reduces the data variance in the target site via knowledge distillation. Specifically, the denoising model uses the generated mel-spectrogram from an N-step DDIM teacher as the training target and distills the behavior into a new model with N/2 steps. As such, it allows the TTS model to make sharp predictions and further reduces the sampling time by orders of magnitude. Our evaluation demonstrates that ProDiff needs only 2 iterations to synthesize high-fidelity mel-spectrograms, while it maintains sample quality and diversity competitive with state-of-the-art models using hundreds of steps. ProDiff enables a sampling speed of 24x faster than real-time on a single NVIDIA 2080Ti GPU, making diffusion models practically applicable to text-to-speech synthesis deployment for the first time. Our extensive ablation studies demonstrate that each design in ProDiff is effective, and we further show that ProDiff can be easily extended to the multi-speaker setting. Audio samples are available at https://ProDiff.github.io/.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which n component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter L. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is mathcal{O}( n + nLvarepsilon^{-1}), which improves upon existing methods by a factor up to n. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

Sampling-based algorithms, which eliminate ''unimportant'' computations during forward and/or back propagation (BP), offer potential solutions to accelerate neural network training. However, since sampling introduces approximations to training, such algorithms may not consistently maintain accuracy across various tasks. In this work, we introduce a variance-controlled adaptive sampling (VCAS) method designed to accelerate BP. VCAS computes an unbiased stochastic gradient with fine-grained layerwise importance sampling in data dimension for activation gradient calculation and leverage score sampling in token dimension for weight gradient calculation. To preserve accuracy, we control the additional variance by learning the sample ratio jointly with model parameters during training. We assessed VCAS on multiple fine-tuning and pre-training tasks in both vision and natural language domains. On all the tasks, VCAS can preserve the original training loss trajectory and validation accuracy with an up to 73.87% FLOPs reduction of BP and 49.58% FLOPs reduction of the whole training process. The implementation is available at https://github.com/thu-ml/VCAS .

Dueling bandits is a prominent framework for decision-making involving preferential feedback, a valuable feature that fits various applications involving human interaction, such as ranking, information retrieval, and recommendation systems. While substantial efforts have been made to minimize the cumulative regret in dueling bandits, a notable gap in the current research is the absence of regret bounds that account for the inherent uncertainty in pairwise comparisons between the dueling arms. Intuitively, greater uncertainty suggests a higher level of difficulty in the problem. To bridge this gap, this paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM). We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound tilde Obig(dsum_{t=1^Tsigma_t^2} + dbig), where sigma_t is the variance of the pairwise comparison in round t, d is the dimension of the context vectors, and T is the time horizon. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an tilde O(d) regret. We perform empirical experiments on synthetic data to confirm the advantage of our method over previous variance-agnostic algorithms.

The choice of embedding model is a crucial step in the design of Retrieval Augmented Generation (RAG) systems. Given the sheer volume of available options, identifying clusters of similar models streamlines this model selection process. Relying solely on benchmark performance scores only allows for a weak assessment of model similarity. Thus, in this study, we evaluate the similarity of embedding models within the context of RAG systems. Our assessment is two-fold: We use Centered Kernel Alignment to compare embeddings on a pair-wise level. Additionally, as it is especially pertinent to RAG systems, we evaluate the similarity of retrieval results between these models using Jaccard and rank similarity. We compare different families of embedding models, including proprietary ones, across five datasets from the popular Benchmark Information Retrieval (BEIR). Through our experiments we identify clusters of models corresponding to model families, but interestingly, also some inter-family clusters. Furthermore, our analysis of top-k retrieval similarity reveals high-variance at low k values. We also identify possible open-source alternatives to proprietary models, with Mistral exhibiting the highest similarity to OpenAI models.

Vision-language models (VLMs) have demonstrated remarkable zero-shot performance across various classification tasks. Nonetheless, their reliance on hand-crafted text prompts for each task hinders efficient adaptation to new tasks. While prompt learning offers a promising solution, most studies focus on maximizing the utilization of given few-shot labeled datasets, often overlooking the potential of careful data selection strategies, which enable higher accuracy with fewer labeled data. This motivates us to study a budget-efficient active prompt learning framework. Specifically, we introduce a class-guided clustering that leverages the pre-trained image and text encoders of VLMs, thereby enabling our cluster-balanced acquisition function from the initial round of active learning. Furthermore, considering the substantial class-wise variance in confidence exhibited by VLMs, we propose a budget-saving selective querying based on adaptive class-wise thresholds. Extensive experiments in active learning scenarios across nine datasets demonstrate that our method outperforms existing baselines.

The success of Reinforcement Learning from Human Feedback (RLHF) critically depends on the quality of the reward model. While this quality is primarily evaluated through accuracy, it remains unclear whether accuracy fully captures what makes a reward model an effective teacher. We address this question from an optimization perspective. First, we prove that regardless of how accurate a reward model is, if it induces low reward variance, then the RLHF objective suffers from a flat landscape. Consequently, even a perfectly accurate reward model can lead to extremely slow optimization, underperforming less accurate models that induce higher reward variance. We additionally show that a reward model that works well for one language model can induce low reward variance, and thus a flat objective landscape, for another. These results establish a fundamental limitation of evaluating reward models solely based on accuracy or independently of the language model they guide. Experiments using models of up to 8B parameters corroborate our theory, demonstrating the interplay between reward variance, accuracy, and reward maximization rate. Overall, our findings highlight that beyond accuracy, a reward model needs to induce sufficient variance for efficient optimization.

This paper first answers the question "why do the two most powerful techniques Dropout and Batch Normalization (BN) often lead to a worse performance when they are combined together?" in both theoretical and statistical aspects. Theoretically, we find that Dropout would shift the variance of a specific neural unit when we transfer the state of that network from train to test. However, BN would maintain its statistical variance, which is accumulated from the entire learning procedure, in the test phase. The inconsistency of that variance (we name this scheme as "variance shift") causes the unstable numerical behavior in inference that leads to more erroneous predictions finally, when applying Dropout before BN. Thorough experiments on DenseNet, ResNet, ResNeXt and Wide ResNet confirm our findings. According to the uncovered mechanism, we next explore several strategies that modifies Dropout and try to overcome the limitations of their combination by avoiding the variance shift risks.

Language model (LM) benchmarking faces several challenges: comprehensive evaluations are costly, benchmarks often fail to measure the intended capabilities, and evaluation quality can degrade due to labeling errors and benchmark saturation. Although various strategies have been proposed to mitigate these issues, they tend to address individual aspects in isolation, neglecting broader questions about overall evaluation quality. Here, we introduce Fluid Benchmarking, a new evaluation approach that advances LM benchmarking across multiple dimensions. Inspired by psychometrics, Fluid Benchmarking is based on the insight that the relative value of benchmark items depends on an LM's capability level, suggesting that evaluation should adapt to each LM. Methodologically, Fluid Benchmarking estimates an item response model based on existing LM evaluation results and uses the inferred quantities to select evaluation items dynamically, similar to computerized adaptive testing in education. In our experiments, we compare Fluid Benchmarking against the common practice of random item sampling as well as more sophisticated baselines, including alternative methods grounded in item response theory. We examine four dimensions -- efficiency, validity, variance, and saturation -- and find that Fluid Benchmarking achieves superior performance in all of them (e.g., higher validity and less variance on MMLU with fifty times fewer items). Our analysis shows that the two components of Fluid Benchmarking have distinct effects: item response theory, used to map performance into a latent ability space, increases validity, while dynamic item selection reduces variance. Overall, our results suggest that LM benchmarking can be substantially improved by moving beyond static evaluation.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to the same input differ in correctness, while ignoring those where all responses receive the same reward - so-called zero-variance prompts. In this work, we argue that such prompts are not useless but can, in fact, provide meaningful feedback for policy optimization. To this end, we introduce RL with Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes errors even without contrasting responses, modulating feedback with token-level characteristics to preserve informative, nuanced signals. Across six math reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO, while consistently outperforming other baselines that filter out zero-variance prompts. These results highlight the untapped potential of learning from zero-variance prompts in RLVR.

Reinforcement learning with verifiable rewards (RLVR) has been shown to enhance the reasoning capabilities of large language models (LLMs), enabling the development of large reasoning models (LRMs). However, LRMs such as DeepSeek-R1 and OpenAI o1 often generate verbose responses containing redundant or irrelevant reasoning step-a phenomenon known as overthinking-which substantially increases computational costs. Prior efforts to mitigate this issue commonly incorporate length penalties into the reward function, but we find they frequently suffer from two critical issues: length collapse and training collapse, resulting in sub-optimal performance. To address them, we propose a pipeline for training a Conciseness Reward Model (CRM) that scores the conciseness of reasoning path. Additionally, we introduce a novel reward formulation named Conciseness Reward Function (CRF) with explicit dependency between the outcome reward and conciseness score, thereby fostering both more effective and more efficient reasoning. From a theoretical standpoint, we demonstrate the superiority of the new reward from the perspective of variance reduction and improved convergence properties. Besides, on the practical side, extensive experiments on five mathematical benchmark datasets demonstrate the method's effectiveness and token efficiency, which achieves an 8.1% accuracy improvement and a 19.9% reduction in response token length on Qwen2.5-7B. Furthermore, the method generalizes well to other LLMs including Llama and Mistral. The implementation code and datasets are publicly available for reproduction: https://anonymous.4open.science/r/CRM.

In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an varepsilon-optimal policy when varepsilon is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.

Large Language Models (LLMs) have demonstrated impressive generative capabilities across diverse tasks but remain susceptible to hallucinations, confidently generated yet factually incorrect outputs. We introduce a reference-free, token-level hallucination detection framework that leverages the variance in token log-probabilities across multiple stochastic generations. Unlike prior methods that require ground-truth references or sentence-level verification, our approach is model-agnostic, interpretable, and suited for real-time or post-hoc analysis. We evaluate our method on unanswerable question prompts from the SQuAD v2 dataset and benchmark across three autoregressive models of varying scales: GPT-Neo 125M, Falcon 1B, and Mistral 7B. Through both quantitative metrics and visual diagnostics, we show that token-level variance reliably highlights instability in model outputs and correlates with hallucination patterns. Our framework is lightweight, reproducible, and adaptable to multiple domains, offering a valuable diagnostic tool for analyzing generative reliability in LLMs.

The Cox proportional hazards model is widely used in survival analysis to model time-to-event data. However, it faces significant computational challenges in the era of large-scale data, particularly when dealing with time-dependent covariates. This paper proposes a moment-assisted subsampling method that is both statistically and computationally efficient for inference under the Cox model. This efficiency is achieved by integrating the computationally efficient uniform subsampling estimator and whole data sample moments that are easy to compute even for large datasets. The resulting estimator is asymptotically normal with a smaller variance than the uniform subsampling estimator. Additionally, we derive the optimal sample moment for the Cox model that minimizes the asymptotic variance in Loewner order. With the optimal moment, the proposed estimator can achieve the same estimation efficiency as the whole data-based partial likelihood estimator while maintaining the computational advantages of subsampling. Simulation studies and real data analyses demonstrate the promising finite sample performance of the proposed estimator in terms of both estimation and computational efficiency.

Systems based on Large Language Models (LLMs) have become formidable tools for automating research and software production. However, their governance remains a challenge when technical requirements demand absolute consistency, auditability, and predictable control over cost and latency. Recent literature highlights two phenomena that aggravate this scenario: the stochastic variance inherent in the model's judgment (often treated as "systemic noise") and the substantial degradation of context utilization in long inputs, with critical losses when decisive information is diluted in the middle of the prompt. This article proposes PARCER as an engineering response to these limitations. The framework acts as a declarative "operational contract" in YAML, transforming unstructured interactions into versioned and executable artifacts. PARCER imposes strict governance structured into seven operational phases, introducing decision hygiene practices inspired by legal judgments to mitigate noise, adaptive token budgeting, formalized recovery routes (fallbacks) for context preservation, and systemic observability via OpenTelemetry. The objective of this work is to present the conceptual and technical architecture of PARCER, positioning it as a necessary transition from simple "prompt engineering" to "context engineering with governable governance".

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.

Sofroniew et al. (2026) report that emotion concepts in Claude Sonnet 4.5 are represented as vectors whose geometry mirrors human affect psychology. We replicate the representational core of that study on the base pretrained model google/gemma-2-27b, inheriting every disclosed parameter, resolving unspecified steps by disclosed rules, and changing only the subject model. From 205,200 newly generated Claude Sonnet 4.5 stories matching the original corpus design, we extract 171 emotion vectors and recover the core results. The leading principal components form an affective circumplex (PC1 carries 26.7% of variance against the original study's ~27%, PC2 13.4% against ~14%), emotions cluster into similar intuitive families, and the geometry holds across a broad late-middle band. The valence axis aligns with human norms (r = 0.72, against 0.81) and is stable across scales and depth. Arousal aligns at r = 0.67 (against 0.66) but only at the full 171-emotion scale and late depth, so we do not classify it as replicated. Extending the original analysis, a 46-layer sweep locates a sharp seam at L22-26, where the geometry consolidates and the vocabulary readout becomes legible. An embedding-layer baseline finds much of the geometry already present in the static token embeddings, with arousal as the exception. On top-activating held-out text, the geometry predicts token-level co-activation at r = 0.907. At least 52% of vectors peak on structurally non-conceptual tokens, a measured floor for max-activation confounds. Even when a document contains the vector's emotion word, the peak lands on that word only 6.1% of the time. Because the subject is a base model and the stimuli are Claude-generated fiction, the recovered structure is a property of the pretrained representation of Claude-rendered emotion. The original's causal and assistant-facing analyses are out of scope. Code and data are released.

In observational settings, where the data generating process and possibly the sample size are not controlled, it is typically impossible to guarantee a priori that quantities of interest will be estimated with sufficient precision. However, even when the data do not determine the quantities of interest, they may still allow determination of what is missing -- unobserved information which, if observed, would meaningfully reduce uncertainty. We propose an interactive visualization system, termed variance deltas, to enable the discovery of such missing information from a Bayesian posterior distribution. This system, which we provide as a software package, represents missing information as subsets of unobserved model quantities, organized into a tree based on how well each subset explains uncertainty about the quantity of interest. This system both automates the construction of candidate subsets from minimal user input and implements interactive operations for the division and combination of subsets, allowing the efficient discovery of interesting and useful explanations. We demonstrate this system by using it to discover nonobvious explanations of uncertainty for (1) a treatment effect parameter in a simulated causal inference problem and (2) a population proportion in a forecasting model of real polling data with many sources of bias.

Reasoning has emerged as the next major frontier for language models (LMs), with rapid advances from both academic and industrial labs. However, this progress often outpaces methodological rigor, with many evaluations relying on benchmarking practices that lack transparency, robustness, or statistical grounding. In this work, we conduct a comprehensive empirical study and find that current mathematical reasoning benchmarks are highly sensitive to subtle implementation choices - including decoding parameters, random seeds, prompt formatting, and even hardware and software-framework configurations. Performance gains reported in recent studies frequently hinge on unclear comparisons or unreported sources of variance. To address these issues, we propose a standardized evaluation framework with clearly defined best practices and reporting standards. Using this framework, we reassess recent methods and find that reinforcement learning (RL) approaches yield only modest improvements - far below prior claims - and are prone to overfitting, especially on small-scale benchmarks like AIME24. In contrast, supervised finetuning (SFT) methods show consistently stronger generalization. To foster reproducibility, we release all code, prompts, and model outputs, for reasoning benchmarks, establishing more rigorous foundations for future work.

Large language models achieve high performance on many but not all downstream tasks. The interaction between pretraining data and task data is commonly assumed to determine this variance: a task with data that is more similar to a model's pretraining data is assumed to be easier for that model. We test whether distributional and example-specific similarity measures (embedding-, token- and model-based) correlate with language model performance through a large-scale comparison of the Pile and C4 pretraining datasets with downstream benchmarks. Similarity correlates with performance for multilingual datasets, but in other benchmarks, we surprisingly find that similarity metrics are not correlated with accuracy or even each other. This suggests that the relationship between pretraining data and downstream tasks is more complex than often assumed.

The alignment of language models with human preferences is vital for their application in real-world tasks. The problem is formulated as optimizing the model's policy to maximize the expected reward that reflects human preferences with minimal deviation from the initial policy. While considered as a straightforward solution, reinforcement learning (RL) suffers from high variance in policy updates, which impedes efficient policy improvement. Recently, direct preference optimization (DPO) was proposed to directly optimize the policy from preference data. Though simple to implement, DPO is derived based on the optimal policy that is not assured to be achieved in practice, which undermines its convergence to the intended solution. In this paper, we propose efficient exact optimization (EXO) of the alignment objective. We prove that EXO is guaranteed to optimize in the same direction as the RL algorithms asymptotically for arbitary parametrization of the policy, while enables efficient optimization by circumventing the complexities associated with RL algorithms. We compare our method to DPO with both theoretical and empirical analyses, and further demonstrate the advantages of our method over existing approaches on realistic human preference data.

The goal of meta-learning is to learn to adapt to a new task with only a few labeled examples. To tackle this problem in NLP, we propose in-context tuning, which recasts adaptation and prediction as a simple sequence prediction problem: to form the input sequence, we concatenate the task instruction, the labeled examples, and the target input to predict; to meta-train the model to learn from in-context examples, we fine-tune a pre-trained language model (LM) to predict the target label from the input sequences on a collection of tasks. We benchmark our method on two collections of text classification tasks: LAMA and BinaryClfs. Compared to first-order MAML which adapts the model with gradient descent, our method better leverages the inductive bias of LMs to perform pattern matching, and outperforms MAML by an absolute 6% AUC ROC score on BinaryClfs, with increasing advantage w.r.t. model size. Compared to non-fine-tuned in-context learning (i.e. prompting a raw LM), in-context tuning directly learns to learn from in-context examples. On BinaryClfs, in-context tuning improves the average AUC-ROC score by an absolute 10%, and reduces the variance with respect to example ordering by 6x and example choices by 2x.

We introduce a new framework for sample-efficient model evaluation that we call active testing. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications, where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. As actively selecting labels introduces a bias; we further show how to remove this bias while reducing the variance of the estimator at the same time. Active testing is easy to implement and can be applied to any supervised machine learning method. We demonstrate its effectiveness on models including WideResNets and Gaussian processes on datasets including Fashion-MNIST and CIFAR-100.

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.

We develop task scaling laws and model ladders to predict the individual task performance of pretrained language models (LMs) in the overtrained setting. Standard power laws for language modeling loss cannot accurately model task performance. Therefore, we leverage a two-step prediction approach: first use model and data size to predict a task-specific loss, and then use this task loss to predict task performance. We train a set of small-scale "ladder" models, collect data points to fit the parameterized functions of the two prediction steps, and make predictions for two target models: a 7B model trained to 4T tokens and a 13B model trained to 5T tokens. Training the ladder models only costs 1% of the compute used for the target models. On four multiple-choice tasks written in ranked classification format, we can predict the accuracy of both target models within 2 points of absolute error. We have higher prediction error on four other tasks (average absolute error 6.9) and find that these are often tasks with higher variance in task metrics. We also find that using less compute to train fewer ladder models tends to deteriorate predictions. Finally, we empirically show that our design choices and the two-step approach lead to superior performance in establishing scaling laws.

Text generation with Large Language Models (LLMs) is known to be memory bound due to the combination of their auto-regressive nature, huge parameter counts, and limited memory bandwidths, often resulting in low token rates. Speculative decoding has been proposed as a solution for LLM inference acceleration. However, since draft models are often unavailable in the modern open-source LLM families, e.g., for Llama 2 7B, training a high-quality draft model is required to enable inference acceleration via speculative decoding. In this paper, we propose a simple draft model training framework for direct alignment to chat-capable target models. With the proposed framework, we train Llama 2 Chat Drafter 115M, a draft model for Llama 2 Chat 7B or larger, with only 1.64\% of the original size. Our training framework only consists of pretraining, distillation dataset generation, and finetuning with knowledge distillation, with no additional alignment procedure. For the finetuning step, we use instruction-response pairs generated by target model for distillation in plausible data distribution, and propose a new Total Variation Distance++ (TVD++) loss that incorporates variance reduction techniques inspired from the policy gradient method in reinforcement learning. Our empirical results show that Llama 2 Chat Drafter 115M with speculative decoding achieves up to 2.3 block efficiency and 2.4times speed-up relative to autoregressive decoding on various tasks with no further task-specific fine-tuning.

Large reasoning models (LRMs) generate intermediate reasoning traces before producing final answers, yielding strong gains on multi-step and mathematical tasks. Yet aligning LRMs with human preferences, a crucial prerequisite for model deployment, remains underexplored. The statistically correct objective for preference alignment requires marginalizing over reasoning traces, but this computation is intractable in practice. A common workaround optimizes a single sampled trajectory, which introduces substantial gradient variance from stochastic trace sampling. To address this challenge, we frame preference optimization for LRMs through the lens of the bias--variance trade-off and propose Bias--Variance Optimized Preference Optimization (BVPO), a simple, drop-in method that mixes two gradient estimators: a high-variance trace-based estimator and a low-variance empty-trace estimator obtained by disabling reasoning trace generation. Our theory shows that BVPO strictly reduces trace-induced variance for any nontrivial mixture, provides a closed-form choice of the mixing weight that minimizes mean-squared error relative to the true marginal gradient, and under standard smoothness and step-size conditions, tightens classical convergence bounds for stochastic gradient descent. Empirically, BVPO improves alignment over the best baseline by up to 7.8 points on AlpacaEval~2 and 6.8 points on Arena-Hard. Despite being trained only on general conversational data, BVPO also boosts reasoning performance for base models by up to 4.0 points on the average of six math reasoning benchmarks. These results identify variance from trace sampling as a key bottleneck and demonstrate that directly optimizing the bias--variance trade-off yields more stable training and stronger overall performance.

Nuclei segmentation and classification is a significant process in pathology image analysis. Deep learning-based approaches have greatly contributed to the higher accuracy of this task. However, those approaches suffer from the imbalanced nuclei data composition, which shows lower classification performance on the rare nuclei class. In this paper, we propose a realistic data synthesis method using a diffusion model. We generate two types of virtual patches to enlarge the training data distribution, which is for balancing the nuclei class variance and for enlarging the chance to look at various nuclei. After that, we use a semantic-label-conditioned diffusion model to generate realistic and high-quality image samples. We demonstrate the efficacy of our method by experiment results on two imbalanced nuclei datasets, improving the state-of-the-art networks. The experimental results suggest that the proposed method improves the classification performance of the rare type nuclei classification, while showing superior segmentation and classification performance in imbalanced pathology nuclei datasets.

Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator variance and inefficient sampling. Prior approaches mitigate this via explicit smoothness penalties, trajectory regularization, or modified probability paths and solvers. We introduce Temporal Pair Consistency (TPC), a lightweight variance-reduction principle that couples velocity predictions at paired timesteps along the same probability path, operating entirely at the estimator level without modifying the model architecture, probability path, or solver. We provide a theoretical analysis showing that TPC induces a quadratic, trajectory-coupled regularization that provably reduces gradient variance while preserving the underlying flow-matching objective. Instantiated within flow matching, TPC improves sample quality and efficiency across CIFAR-10 and ImageNet at multiple resolutions, achieving lower FID at identical or lower computational cost than prior methods, and extends seamlessly to modern SOTA-style pipelines with noise-augmented training, score-based denoising, and rectified flow.

The trade-off between interpretability and accuracy remains a core challenge in machine learning. Standard Generalized Additive Models (GAMs) offer clear feature attributions but are often constrained by their strictly additive nature, which can limit predictive performance. Introducing feature interactions can boost accuracy yet may obscure individual feature contributions. To address these issues, we propose Neural Additive Experts (NAEs), a novel framework that seamlessly balances interpretability and accuracy. NAEs employ a mixture of experts framework, learning multiple specialized networks per feature, while a dynamic gating mechanism integrates information across features, thereby relaxing rigid additive constraints. Furthermore, we propose targeted regularization techniques to mitigate variance among expert predictions, facilitating a smooth transition from an exclusively additive model to one that captures intricate feature interactions while maintaining clarity in feature attributions. Our theoretical analysis and experiments on synthetic data illustrate the model's flexibility, and extensive evaluations on real-world datasets confirm that NAEs achieve an optimal balance between predictive accuracy and transparent, feature-level explanations. The code is available at https://github.com/Teddy-XiongGZ/NAE.

Speaker anonymization aims to conceal cues to speaker identity while preserving linguistic content. Current machine learning based approaches require substantial computational resources, hindering real-time streaming applications. To address these concerns, we propose a streaming model that achieves speaker anonymization with low latency. The system is trained in an end-to-end autoencoder fashion using a lightweight content encoder that extracts HuBERT-like information, a pretrained speaker encoder that extract speaker identity, and a variance encoder that injects pitch and energy information. These three disentangled representations are fed to a decoder that re-synthesizes the speech signal. We present evaluation results from two implementations of our system, a full model that achieves a latency of 230ms, and a lite version (0.1x in size) that further reduces latency to 66ms while maintaining state-of-the-art performance in naturalness, intelligibility, and privacy preservation.

The Segment Anything Model 2 (SAM2) is a powerful foundation model for promptable segmentation. However, its high computational and memory costs are a major barrier to deployment on resource-constrained devices. In this paper, we present Q-SAM2, an accurate low-bit quantization method that achieves high compression and high fidelity. To address performance degradation arising from challenging weight and activation distributions during quantization, Q-SAM2 introduces two novel contributions: Variance-Reduced Calibration (VRC), an initialization method that reduces weight statistical variance by minimizing the Frobenius norm over a small calibration batch; and Learnable Statistical Clipping (LSC), a Quantization-Aware Training (QAT) method that learns momentum-stabilized clipping factors to manage outliers in weights and activations. Comprehensive experiments demonstrate that Q-SAM2 achieves highly accurate inference with substantial efficiency gains, significantly surpassing state-of-the-art general QAT schemes, particularly in the ultra-low 2-bit regime. Specifically, Q-SAM2 achieves an accuracy gain of up to 9.7 ppt in J&F on the video segmentation benchmark and 7.3 ppt in mIoU for instance segmentation over the best competing QAT model, all while achieving an 8x reduction in model size compared to the BF16 baseline.

Asynchronous reinforcement learning has become increasingly central to scaling LLM post-training, delivering major throughput gains by decoupling rollout generation from policy updates. However, widely used policy-gradient objectives such as REINFORCE and GRPO suffer under high asynchrony: stale rollouts produce heavy-tailed importance weights, so a small number of trajectories dominate updates and the policy-gradient estimator becomes markedly higher variance. Through systematic analysis on math, reasoning, and tool-use benchmarks, we find that this increasing variance is reliably predicted by collapsing effective sample size (ESS), which prior stabilization methods largely fail to address. Motivated by this diagnosis, we introduce Variance Controlled Policy Optimization (VCPO), a method that (i) dynamically scales the learning rate with ESS to dampen unreliable updates and (ii) applies a closed-form minimum-variance baseline for off-policy settings, without a critic model and adding minimal overhead. Empirically, across math and general reasoning benchmarks, this enables robustly stable asynchronous training compared to previous stabilization and algorithmic methods, even in highly off-policy regimes (128 steps off-policy). In a long-horizon, tool-use task, VCPO matches synchronous performance while delivering a 2.5times speedup in training time. Code is available at: https://github.com/mit-han-lab/vcpo

The Unconstrained Feature Model (UFM) is a mathematical framework that enables closed-form approximations for minimal training loss and related performance measures in deep neural networks (DNNs). This paper leverages the UFM to provide qualitative insights into neural multivariate regression, a critical task in imitation learning, robotics, and reinforcement learning. Specifically, we address two key questions: (1) How do multi-task models compare to multiple single-task models in terms of training performance? (2) Can whitening and normalizing regression targets improve training performance? The UFM theory predicts that multi-task models achieve strictly smaller training MSE than multiple single-task models when the same or stronger regularization is applied to the latter, and our empirical results confirm these findings. Regarding whitening and normalizing regression targets, the UFM theory predicts that they reduce training MSE when the average variance across the target dimensions is less than one, and our empirical results once again confirm these findings. These findings highlight the UFM as a powerful framework for deriving actionable insights into DNN design and data pre-processing strategies.

Large language models (LLMs) have demonstrated several emergent behaviors with scale, including reasoning and fluency in long-form text generation. However, they continue to struggle with tasks requiring precise spatial and positional reasoning. ASCII art, a symbolic medium where characters encode structure and form, provides a unique probe of this limitation. We introduce ASCIIBench, a novel benchmark for evaluating both the generation and classification of ASCII-text images. ASCIIBench consists of a filtered dataset of 5,315 class-labeled ASCII images and is, to our knowledge, the first publicly available benchmark of its kind. Alongside the dataset, we release weights for a fine-tuned CLIP model adapted to capture ASCII structure, enabling the evaluation of LLM-generated ASCII art. Our analysis shows that cosine similarity over CLIP embeddings fails to separate most ASCII categories, yielding chance-level performance even for low-variance classes. In contrast, classes with high internal mean similarity exhibit clear discriminability, revealing that the bottleneck lies in representation rather than generational variance. These findings position ASCII art as a stress test for multimodal representations and motivate the development of new embedding methods or evaluation metrics tailored to symbolic visual modalities. All resources are available at https://github.com/ASCIIBench/ASCIIBench.

Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability p_0 is small. Using the Tsallis q-logarithm, we define a loss family J_Q that interpolates between RLVR (at q{=}0, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at q{=}1, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification P_{θ^{-q}} that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires Ω(1{p_0}) time to escape cold start, while the density-estimation pole escapes in Θbig(log(1{p_0})big); intermediate q trades escape speed against noise memorization. Because P_θ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias Obig(q{M P_θ^{q+1}}big); GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at q{=}0.75 substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low q dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at q{=}0.75 provides stable gradients (best overall on HotPotQA at 47.9 maj@16, +14.4 over GRPO).

Large Language Models (LLMs) have achieved strong performance across natural language and multimodal tasks, yet their practical deployment remains constrained by inference latency and kernel launch overhead, particularly in interactive, short-sequence settings. This paper presents a hybrid runtime framework that combines Just-In-Time (JIT) compilation with CUDA Graph execution to reduce launch overhead while preserving runtime flexibility during autoregressive decoding. The framework partitions transformer inference into static components executed via CUDA Graph replay and dynamic components handled through JIT-compiled kernels, enabling asynchronous graph capture and reuse across decoding steps. We evaluate the proposed approach on LLaMA-2 7B using single-GPU, batch-size-one inference across prompt lengths from 10 to 500 tokens. Experimental results show that the hybrid runtime reduces Time-to-First-Token (TTFT) by up to 66.0% and achieves lower P99 latency compared with TensorRT-LLM in this regime. These results indicate that hybrid JIT-CUDA Graph execution can effectively reduce inference latency and variance for short-sequence LLM workloads, making it a practical optimization strategy for latency-sensitive AI applications.

Self-paced learning and hard example mining re-weight training instances to improve learning accuracy. This paper presents two improved alternatives based on lightweight estimates of sample uncertainty in stochastic gradient descent (SGD): the variance in predicted probability of the correct class across iterations of mini-batch SGD, and the proximity of the correct class probability to the decision threshold. Extensive experimental results on six datasets show that our methods reliably improve accuracy in various network architectures, including additional gains on top of other popular training techniques, such as residual learning, momentum, ADAM, batch normalization, dropout, and distillation.

Learning predictive world models from raw visual observations is a central challenge in reinforcement learning (RL), especially for robotics and continuous control. Conventional model-based RL frameworks directly condition future predictions on absolute actions, which makes optimization unstable: the optimal action distributions are task-dependent, unknown a priori, and often lead to oscillatory or inefficient control. To address this, we introduce the Residual-Action World Model (ResWM), a new framework that reformulates the control variable from absolute actions to residual actions -- incremental adjustments relative to the previous step. This design aligns with the inherent smoothness of real-world control, reduces the effective search space, and stabilizes long-horizon planning. To further strengthen the representation, we propose an Observation Difference Encoder that explicitly models the changes between adjacent frames, yielding compact latent dynamics that are naturally coupled with residual actions. ResWM is integrated into a Dreamer-style latent dynamics model with minimal modifications and no extra hyperparameters. Both imagination rollouts and policy optimization are conducted in the residual-action space, enabling smoother exploration, lower control variance, and more reliable planning. Empirical results on the DeepMind Control Suite demonstrate that ResWM achieves consistent improvements in sample efficiency, asymptotic returns, and control smoothness, significantly surpassing strong baselines such as Dreamer and TD-MPC. Beyond performance, ResWM produces more stable and energy-efficient action trajectories, a property critical for robotic systems deployed in real-world environments. These findings suggest that residual action modeling provides a simple yet powerful principle for bridging algorithmic advances in RL with the practical requirements of robotics.

We present WebFovea, a vision-based web agent that placed 2nd in the WebRetriever Challenge 2026 with a final score of 57.0 out of 100. The challenge evaluates agents end to end on Protocol III of the WebRetriever benchmark (arXiv:2607.06118): starting from an entry URL on a live website, the agent must operate the site's own interface and return a verifiable answer. A capable multimodal large language model (LLM) is necessary for this, but not sufficient. The model's decisions reach the browser through the harness, the code between the model and the page. At every step, four things must go right: the model's reply must be parsed into the intended action, the action must take effect on the page, the result must be reported back accurately, and the model must be shown the information it needs. On real websites, many of the failures we observed occurred at one of these four stages rather than in the model's reasoning. A coordinate-space mismatch placed every click at 3/4 of its intended coordinates; actions on native dropdowns, inside iframes, and in text boxes failed silently; and self-generated chat-template tokens contaminated 4.9% of task episodes. WebFovea hardens each stage and surrounds the loop with guardrails that keep the agent within the rules and its budget. The four-stage view does not depend on the model, although some individual fixes do. Because we used the same model in all four submissions, the rise of our official hidden-set score from 31.0 to 57.0 reflects changes to the harness, up to run-to-run variance on live sites. We describe the design, the evidence for each component (including negative results), a failure analysis, the limitations, and a roadmap that includes routing different steps to different models. Code is available at https://github.com/jianganghan/WebFovea.

Data selection for language models is often framed as balancing example quality and diversity. We argue that both are consequences of a more fundamental principle: selected examples should preserve the downstream query space induced by instructions, task signals, or retrieval needs. We present Greedy Information Projection (GIP), a query-aligned method that requires only candidate embeddings and a score signal from LLM judgments, metadata, or intrinsic geometry. GIP greedily selects examples whose embedding span explains the largest residual component of task/query scores, yielding a fast matching-pursuit selector. A Gaussian projection view connects this update to maximizing mutual information, equivalently minimizing the residual volume of the query subspace left unexplained by selected data; this explains how quality and diversity emerge from one objective. Empirically, GIP matches or surpasses full-data fine-tuning using small instruction and reasoning subsets, while pretraining and RAG passage-selection experiments show that the same residual principle transfers beyond supervised fine-tuning.

We reimplement the dynamics model of the Robotic World Model (RWM) and test the uncertainty estimate that its follow-up, RWM-U, uses to penalize reward in offline policy optimization. Our implementation matches the released model's gradients. On held-out data, training on the model's own rollouts beats one-step training at the preregistered long horizon for all ten episodes, but loses on short one-step windows. RWM-U's ensemble disagreement ranks rollout errors better than forecast step (Spearman rho = 0.90 at 100 steps), yet its spread substantially understates error: one-sigma coverage on the released checkpoint is 4.6% at 100 steps, versus 68% for a calibrated Gaussian. Rolling ensemble members on their own predictions raises coverage to 33%. The implemented squared-error loss on sampled predictions drives each member's variance toward zero. A horizon-specific rescaling restores one-sigma coverage under leave-one-episode-out evaluation, but not two-sigma coverage. We also identify two defects in the released evaluation pipeline. The study covers one robot, one gait and one dataset; it trains no policy.

Video generation models internalize physical realism as their prior. Anime deliberately violates physics: smears, impact frames, chibi shifts; and its thousands of coexisting artistic conventions yield no single "physics of anime" a model can absorb. Physics-biased models therefore flatten the artistry that defines the medium or collapse under its stylistic variance. We present AniMatrix, a video generation model that targets artistic rather than physical correctness through a dual-channel conditioning mechanism and a three-step transition: redefine correctness, override the physics prior, and distinguish art from failure. First, a Production Knowledge System encodes anime as a structured taxonomy of controllable production variables (Style, Motion, Camera, VFX), and AniCaption infers these variables from pixels as directorial directives. A trainable tag encoder preserves the field-value structure of this taxonomy while a frozen T5 encoder handles free-form narrative; dual-path injection (cross-attention for fine-grained control, AdaLN modulation for global enforcement) ensures categorical directives are never diluted by open-ended text. Second, a style-motion-deformation curriculum transitions the model from near-physical motion to full anime expressiveness. Third, deformation-aware preference optimization with a domain-specific reward model separates intentional artistry from pathological collapse. On an anime-specific human evaluation with five production dimensions scored by professional animators, AniMatrix ranks first on four of five, with the largest gains over Seedance-Pro 1.0 on Prompt Understanding (+0.70, +22.4 percent) and Artistic Motion (+0.55, +16.9 percent). We are preparing accompanying resources for public release to support reproducibility and follow-up research.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT