Daily Papers

Learning super-resolution (SR) network without the paired low resolution (LR) and high resolution (HR) image is difficult because direct supervision through the corresponding HR counterpart is unavailable. Recently, many real-world SR researches take advantage of the unpaired image-to-image translation technique. That is, they used two or more generative adversarial networks (GANs), each of which translates images from one domain to another domain, \eg, translates images from the HR domain to the LR domain. However, it is not easy to stably learn such a translation with GANs using unpaired data. In this study, we present a simple and efficient method of training of real-world SR network. To stably train the network, we use statistics of an image patch, such as means and variances. Our real-world SR framework consists of two GANs, one for translating HR images to LR images (degradation task) and the other for translating LR to HR (SR task). We argue that the unpaired image translation using GANs can be learned efficiently with our proposed data sampling strategy, namely, variance matching. We test our method on the NTIRE 2020 real-world SR dataset. Our method outperforms the current state-of-the-art method in terms of the SSIM metric as well as produces comparable results on the LPIPS metric.

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

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.

We introduce Vision Bridge Transformer (ViBT), a large-scale instantiation of Brownian Bridge Models designed for conditional generation. Unlike traditional diffusion models that transform noise into data, Bridge Models directly model the trajectory between inputs and outputs, creating an efficient data-to-data translation paradigm. By scaling these models to 20B and 1.3B parameters, we demonstrate their effectiveness for image and video translation tasks. To support this scale, we adopt a Transformer architecture and propose a variance-stabilized velocity-matching objective for robust training. Together, these advances highlight the power of scaling Bridge Models for instruction-based image editing and complex video translation.

Motivated by the success of coarse-grained or fine-grained contrast in text-video retrieval, there emerge multi-grained contrastive learning methods which focus on the integration of contrasts with different granularity. However, due to the wider semantic range of videos, the text-agnostic video representations might encode misleading information not described in texts, thus impeding the model from capturing precise cross-modal semantic correspondence. To this end, we propose a Text-Conditioned Multi-Grained Contrast framework, dubbed TC-MGC. Specifically, our model employs a language-video attention block to generate aggregated frame and video representations conditioned on the word's and text's attention weights over frames. To filter unnecessary similarity interactions and decrease trainable parameters in the Interactive Similarity Aggregation (ISA) module, we design a Similarity Reorganization (SR) module to identify attentive similarities and reorganize cross-modal similarity vectors and matrices. Next, we argue that the imbalance problem among multigrained similarities may result in over- and under-representation issues. We thereby introduce an auxiliary Similarity Decorrelation Regularization (SDR) loss to facilitate cooperative relationship utilization by similarity variance minimization on matching text-video pairs. Finally, we present a Linear Softmax Aggregation (LSA) module to explicitly encourage the interactions between multiple similarities and promote the usage of multi-grained information. Empirically, TC-MGC achieves competitive results on multiple text-video retrieval benchmarks, outperforming X-CLIP model by +2.8% (+1.3%), +2.2% (+1.0%), +1.5% (+0.9%) relative (absolute) improvements in text-to-video retrieval R@1 on MSR-VTT, DiDeMo and VATEX, respectively. Our code is publicly available at https://github.com/JingXiaolun/TC-MGC.

While flow matching is elegant, its reliance on single-sample conditional velocities leads to high-variance training targets that destabilize optimization and slow convergence. By explicitly characterizing this variance, we identify 1) a high-variance regime near the prior, where optimization is challenging, and 2) a low-variance regime near the data distribution, where conditional and marginal velocities nearly coincide. Leveraging this insight, we propose Stable Velocity, a unified framework that improves both training and sampling. For training, we introduce Stable Velocity Matching (StableVM), an unbiased variance-reduction objective, along with Variance-Aware Representation Alignment (VA-REPA), which adaptively strengthen auxiliary supervision in the low-variance regime. For inference, we show that dynamics in the low-variance regime admit closed-form simplifications, enabling Stable Velocity Sampling (StableVS), a finetuning-free acceleration. Extensive experiments on ImageNet 256times256 and large pretrained text-to-image and text-to-video models, including SD3.5, Flux, Qwen-Image, and Wan2.2, demonstrate consistent improvements in training efficiency and more than 2times faster sampling within the low-variance regime without degrading sample quality. Our code is available at https://github.com/linYDTHU/StableVelocity.

Large and demographically balanced datasets are essential for reliable neuroimaging biomarkers. Full-resolution 3D brain MRI synthesis can support data augmentation in this setting, but existing approaches either incur prohibitive computational cost at volumetric scale or rely on lossy latent compression that may compromise anatomical detail. As a result, practical 3D generative augmentation often requires specialized compute infrastructure. We propose WaveDiT, a conditional flow matching framework operating in the coefficient space of a 3D Haar Discrete Wavelet Transform. The model combines factorized spatio-depth attention with band-wise heteroscedastic uncertainty modeling derived from higher-order wavelet statistics. Predicted log-variance is integrated directly into both the flow objective and conditioning pathway, enabling adaptive precision consistent with the heavy-tailed and input-dependent variance structure of anatomical detail. This formulation supports full-resolution 3D synthesis under practical memory and time constraints on a single modern GPU. Evaluation on a multi-site cohort demonstrates improved alignment between generated and real MRI distributions, together with enhanced downstream brain age prediction and region-level anatomical agreement relative to diffusion, latent, and wavelet-based baselines. Code is available at https://github.com/sisinflab/WaveDiT

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

Post-training of flow matching models-aligning the output distribution with a high-quality target-is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization. Code and data are available at https://github.com/HansPolo113/FAIL.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

Distribution matching is central to many vision and graphics tasks, where the widely used Wasserstein distance is too costly to compute for high dimensional distributions. The Sliced Wasserstein Distance (SWD) offers a scalable alternative, yet its Monte Carlo estimator suffers from high variance, resulting in noisy gradients and slow convergence. We introduce Reservoir SWD (ReSWD), which integrates Weighted Reservoir Sampling into SWD to adaptively retain informative projection directions in optimization steps, resulting in stable gradients while remaining unbiased. Experiments on synthetic benchmarks and real-world tasks such as color correction and diffusion guidance show that ReSWD consistently outperforms standard SWD and other variance reduction baselines. Project page: https://reservoirswd.github.io/

We present a novel method for efficiently producing semi-dense matches across images. Previous detector-free matcher LoFTR has shown remarkable matching capability in handling large-viewpoint change and texture-poor scenarios but suffers from low efficiency. We revisit its design choices and derive multiple improvements for both efficiency and accuracy. One key observation is that performing the transformer over the entire feature map is redundant due to shared local information, therefore we propose an aggregated attention mechanism with adaptive token selection for efficiency. Furthermore, we find spatial variance exists in LoFTR's fine correlation module, which is adverse to matching accuracy. A novel two-stage correlation layer is proposed to achieve accurate subpixel correspondences for accuracy improvement. Our efficiency optimized model is sim 2.5times faster than LoFTR which can even surpass state-of-the-art efficient sparse matching pipeline SuperPoint + LightGlue. Moreover, extensive experiments show that our method can achieve higher accuracy compared with competitive semi-dense matchers, with considerable efficiency benefits. This opens up exciting prospects for large-scale or latency-sensitive applications such as image retrieval and 3D reconstruction. Project page: https://zju3dv.github.io/efficientloftr.

Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular framework that decouples forecasting from spatial resolution by applying learned generative super-resolution as a post-processing step to coarse-resolution forecast trajectories. We formulate super-resolution as a stochastic inverse problem, using a residual formulation to preserve large-scale structure while reconstructing unresolved variability. The model is trained with flow matching exclusively on reanalysis data and is applied to global medium-range forecasts. We evaluate (i) design consistency by re-coarsening super-resolved forecasts and comparing them to the original coarse trajectories, and (ii) high-resolution forecast quality using standard ensemble verification metrics and spectral diagnostics. Results show that super-resolution preserves large-scale structure and variance after re-coarsening, introduces physically consistent small-scale variability, and achieves competitive probabilistic forecast skill at 0.25° resolution relative to an operational ensemble baseline, while requiring only a modest additional training cost compared with end-to-end high-resolution forecasting.

Existing few-shot medical image segmentation (FSMIS) models fail to address a practical issue in medical imaging: the domain shift caused by different imaging techniques, which limits the applicability to current FSMIS tasks. To overcome this limitation, we focus on the cross-domain few-shot medical image segmentation (CD-FSMIS) task, aiming to develop a generalized model capable of adapting to a broader range of medical image segmentation scenarios with limited labeled data from the novel target domain. Inspired by the characteristics of frequency domain similarity across different domains, we propose a Frequency-aware Matching Network (FAMNet), which includes two key components: a Frequency-aware Matching (FAM) module and a Multi-Spectral Fusion (MSF) module. The FAM module tackles two problems during the meta-learning phase: 1) intra-domain variance caused by the inherent support-query bias, due to the different appearances of organs and lesions, and 2) inter-domain variance caused by different medical imaging techniques. Additionally, we design an MSF module to integrate the different frequency features decoupled by the FAM module, and further mitigate the impact of inter-domain variance on the model's segmentation performance. Combining these two modules, our FAMNet surpasses existing FSMIS models and Cross-domain Few-shot Semantic Segmentation models on three cross-domain datasets, achieving state-of-the-art performance in the CD-FSMIS task.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

Flow matching (FM) trains a time-dependent vector field that transports samples from a simple prior to a complex data distribution. However, for high-dimensional images, each training sample supervises only a single trajectory and intermediate point, yielding an extremely sparse and high-variance training signal. This under-constrained supervision can cause flow collapse, where the learned dynamics memorize specific source-target pairings, mapping diverse inputs to overly similar outputs, failing to generalize. We introduce Posterior-Augmented Flow Matching (PAFM), a theoretically grounded generalization of FM that replaces single-target supervision with an expectation over an approximate posterior of valid target completions for a given intermediate state and condition. PAFM factorizes this intractable posterior into (i) the likelihood of the intermediate under a hypothesized endpoint and (ii) the prior probability of that endpoint under the condition, and uses an importance sampling scheme to construct a mixture over multiple candidate targets. We prove that PAFM yields an unbiased estimator of the original FM objective while substantially reducing gradient variance during training by aggregating information from many plausible continuation trajectories per intermediate. Finally, we show that PAFM improves over FM by up to 3.4 FID50K across different model scales (SiT-B/2 and SiT-XL/2), different architectures (SiT and MMDiT), and in both class and text conditioned benchmarks (ImageNet and CC12M), with a negligible increase in the compute overhead. Code: https://github.com/gstoica27/PAFM.git.

Recent progress in flow-based generative models and reinforcement learning (RL) has improved text-image alignment and visual quality. However, current RL training for flow models still has two main problems: (i) GRPO-style fixed per-prompt group sizes ignore variation in sampling importance across prompts, which leads to inefficient sampling and slower training; and (ii) trajectory-level advantages are reused as per-step estimates, which biases credit assignment along the flow. We propose SuperFlow, an RL training framework for flow-based models that adjusts group sizes with variance-aware sampling and computes step-level advantages in a way that is consistent with continuous-time flow dynamics. Empirically, SuperFlow reaches promising performance while using only 5.4% to 56.3% of the original training steps and reduces training time by 5.2% to 16.7% without any architectural changes. On standard text-to-image (T2I) tasks, including text rendering, compositional image generation, and human preference alignment, SuperFlow improves over SD3.5-M by 4.6% to 47.2%, and over Flow-GRPO by 1.7% to 16.0%.

Correlation based stereo matching has achieved outstanding performance, which pursues cost volume between two feature maps. Unfortunately, current methods with a fixed model do not work uniformly well across various datasets, greatly limiting their real-world applicability. To tackle this issue, this paper proposes a new perspective to dynamically calculate correlation for robust stereo matching. A novel Uncertainty Guided Adaptive Correlation (UGAC) module is introduced to robustly adapt the same model for different scenarios. Specifically, a variance-based uncertainty estimation is employed to adaptively adjust the sampling area during warping operation. Additionally, we improve the traditional non-parametric warping with learnable parameters, such that the position-specific weights can be learned. We show that by empowering the recurrent network with the UGAC module, stereo matching can be exploited more robustly and effectively. Extensive experiments demonstrate that our method achieves state-of-the-art performance over the ETH3D, KITTI, and Middlebury datasets when employing the same fixed model over these datasets without any retraining procedure. To target real-time applications, we further design a lightweight model based on UGAC, which also outperforms other methods over KITTI benchmarks with only 0.6 M parameters.

Latent world models enable efficient planning by predicting future states in a compact representation space, but their performance depends critically on the quality of the learned latent distribution. LeWorldModel (LeWM) regularizes its latents toward an isotropic Gaussian using the Epps-Pulley (EP) objective. We show that the corrective gradients of EP rapidly vanish for isolated tail samples, leaving heavy-tailed deviations insufficiently controlled. To address this limitation, we propose QQWorld, which replaces EP with a quantile-quantile matching objective that directly aligns projected latent samples with rank-matched Gaussian quantiles, thereby maintaining effective corrective gradients in the tails. We further develop cross-batch QQ, which enlarges the effective ranking pool using detached samples from previous batches, and characterize its bias-variance trade-off. Across four control environments, QQWorld effectively improves the average planning success rate of LeWM, while consistently yielding better Gaussian alignment and thinner latent tails.

Tracking a point through a video can be a challenging task due to uncertainty arising from visual obfuscations, such as appearance changes and occlusions. Although current state-of-the-art discriminative models excel in regressing long-term point trajectory estimates -- even through occlusions -- they are limited to regressing to a mean (or mode) in the presence of uncertainty, and fail to capture multi-modality. To overcome this limitation, we introduce Generative Point Tracker (GenPT), a generative framework for modelling multi-modal trajectories. GenPT is trained with a novel flow matching formulation that combines the iterative refinement of discriminative trackers, a window-dependent prior for cross-window consistency, and a variance schedule tuned specifically for point coordinates. We show how our model's generative capabilities can be leveraged to improve point trajectory estimates by utilizing a best-first search strategy on generated samples during inference, guided by the model's own confidence of its predictions. Empirically, we evaluate GenPT against the current state of the art on the standard PointOdyssey, Dynamic Replica, and TAP-Vid benchmarks. Further, we introduce a TAP-Vid variant with additional occlusions to assess occluded point tracking performance and highlight our model's ability to capture multi-modality. GenPT is capable of capturing the multi-modality in point trajectories, which translates to state-of-the-art tracking accuracy on occluded points, while maintaining competitive tracking accuracy on visible points compared to extant discriminative point trackers.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Recently, GRPO-based reinforcement learning has shown remarkable progress in optimizing flow-matching models, effectively improving their alignment with task-specific rewards. Within these frameworks, the policy update relies on importance-ratio clipping to constrain overconfident positive and negative gradients. However, in practice, we observe a systematic shift in the importance-ratio distribution-its mean falls below 1 and its variance differs substantially across timesteps. This left-shifted and inconsistent distribution prevents positive-advantage samples from entering the clipped region, causing the mechanism to fail in constraining overconfident positive updates. As a result, the policy model inevitably enters an implicit over-optimization stage-while the proxy reward continues to increase, essential metrics such as image quality and text-prompt alignment deteriorate sharply, ultimately making the learned policy impractical for real-world use. To address this issue, we introduce GRPO-Guard, a simple yet effective enhancement to existing GRPO frameworks. Our method incorporates ratio normalization, which restores a balanced and step-consistent importance ratio, ensuring that PPO clipping properly constrains harmful updates across denoising timesteps. In addition, a gradient reweighting strategy equalizes policy gradients over noise conditions, preventing excessive updates from particular timestep regions. Together, these designs act as a regulated clipping mechanism, stabilizing optimization and substantially mitigating implicit over-optimization without relying on heavy KL regularization. Extensive experiments on multiple diffusion backbones (e.g., SD3.5M, Flux.1-dev) and diverse proxy tasks demonstrate that GRPO-Guard significantly reduces over-optimization while maintaining or even improving generation quality.

Recent breakthroughs in instruction-based image editing have captured significant attention, as models are now capable of handling real-world editing demands with the practicality required by everyday users. However, editing models trained primarily for single-turn edits often break down in multi-turn editing--the natural interactive setting where a user iteratively refines an image based on the model's own previous outputs. This failure stems from the all-or-nothing requirement, where a single failed turn compromises the entire sequence, and error propagation, where exposure bias leads to compounding editing errors. To address these challenges, we introduce MT-EditFlow, a flow-matching reinforcement learning framework designed to optimize reward signals for sequential image editing. MT-EditFlow integrates a multi-turn perspective with a multi-reward formulation to provide a unified structure applicable to both GRPO and NFT-based reinforcement learning methods. We systematically analyze and optimize the reward signal by investigating effective scoring strategies for turn-level aggregation, VLM reasoning modes to trade off reward bias and variance, and advantage fusion levels to prevent reward hacking. Our findings reveal that broadcasting the aggregated advantage across the entire editing trajectory effectively bridges the gap between local planning and global multi-turn task success. Extensive experiments demonstrate that MT-EditFlow significantly improves performance across diverse base models. Notably, it boosts FLUX.1-Kontext-dev by 6.85 points in turn-3 overall performance, surpassing state-of-the-art open-source models such as Qwen-Image-Edit. By maintaining high marginal success rates and reducing exposure bias, MT-EditFlow provides a foundation for more reliable and natural human-AI collaboration in visual content creation.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Diffusion-based neural solvers have shown strong promise for combinatorial optimization (CO), but existing methods typically rely on supervised training with large collections of near-optimal solutions. In this work, we extend adjoint-based trajectory optimization methods to discrete combinatorial domains. We formulate diffusion-based CO as a stochastic control problem over Continuous-Time Markov Chains and introduce discrete adjoint dynamics for propagating optimization signals through discrete generative trajectories. Building on this formulation, we propose Combinatorial Adjoint Matching (CAM), an unsupervised training framework for discrete diffusion solvers with structured and low-variance trajectory-level optimization signals. Empirically, CAM consistently outperforms existing unsupervised diffusion baselines and achieves performance competitive with strong supervised diffusion solvers and even traditional solvers across diverse combinatorial optimization problems. Our code is available at https://github.com/Shengyu-Feng/CAM.

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely on a standard Gaussian distribution, a choice inherited from diffusion models, and rarely consider the source distribution itself as an optimization target in such settings. In this work, we show that principled design of the source distribution is not only feasible but also beneficial at the scale of modern text-to-image systems. Specifically, we propose learning a condition-dependent source distribution under flow matching objective that better exploit rich conditioning signals. We identify key failure modes that arise when directly incorporating conditioning into the source, including distributional collapse and instability, and show that appropriate variance regularization and directional alignment between source and target are critical for stable and effective learning. We further analyze how the choice of target representation space impacts flow matching with structured sources, revealing regimes in which such designs are most effective. Extensive experiments across multiple text-to-image benchmarks demonstrate consistent and robust improvements, including up to a 3x faster convergence in FID, highlighting the practical benefits of a principled source distribution design for conditional flow matching.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

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 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.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

Contactless fingerprint matching using smartphone cameras can alleviate major challenges of traditional fingerprint systems including hygienic acquisition, portability and presentation attacks. However, development of practical and robust contactless fingerprint matching techniques is constrained by the limited availability of large scale real-world datasets. To motivate further advances in contactless fingerprint matching across sensors, we introduce the RidgeBase benchmark dataset. RidgeBase consists of more than 15,000 contactless and contact-based fingerprint image pairs acquired from 88 individuals under different background and lighting conditions using two smartphone cameras and one flatbed contact sensor. Unlike existing datasets, RidgeBase is designed to promote research under different matching scenarios that include Single Finger Matching and Multi-Finger Matching for both contactless- to-contactless (CL2CL) and contact-to-contactless (C2CL) verification and identification. Furthermore, due to the high intra-sample variance in contactless fingerprints belonging to the same finger, we propose a set-based matching protocol inspired by the advances in facial recognition datasets. This protocol is specifically designed for pragmatic contactless fingerprint matching that can account for variances in focus, polarity and finger-angles. We report qualitative and quantitative baseline results for different protocols using a COTS fingerprint matcher (Verifinger) and a Deep CNN based approach on the RidgeBase dataset. The dataset can be downloaded here: https://www.buffalo.edu/cubs/research/datasets/ridgebase-benchmark-dataset.html

Black-box adversarial attacks on Large Vision-Language Models (LVLMs) are challenging due to missing gradients and complex multimodal boundaries. While prior state-of-the-art transfer-based approaches like M-Attack perform well using local crop-level matching between source and target images, we find this induces high-variance, nearly orthogonal gradients across iterations, violating coherent local alignment and destabilizing optimization. We attribute this to (i) ViT translation sensitivity that yields spike-like gradients and (ii) structural asymmetry between source and target crops. We reformulate local matching as an asymmetric expectation over source transformations and target semantics, and build a gradient-denoising upgrade to M-Attack. On the source side, Multi-Crop Alignment (MCA) averages gradients from multiple independently sampled local views per iteration to reduce variance. On the target side, Auxiliary Target Alignment (ATA) replaces aggressive target augmentation with a small auxiliary set from a semantically correlated distribution, producing a smoother, lower-variance target manifold. We further reinterpret momentum as Patch Momentum, replaying historical crop gradients; combined with a refined patch-size ensemble (PE+), this strengthens transferable directions. Together these modules form M-Attack-V2, a simple, modular enhancement over M-Attack that substantially improves transfer-based black-box attacks on frontier LVLMs: boosting success rates on Claude-4.0 from 8% to 30%, Gemini-2.5-Pro from 83% to 97%, and GPT-5 from 98% to 100%, outperforming prior black-box LVLM attacks. Code and data are publicly available at: https://github.com/vila-lab/M-Attack-V2.

MeanFlow (MF) is a diffusion-motivated generative model that enables efficient few-step generation by learning long jumps directly from noise to data. In practice, it is often used as a latent MF by leveraging the pre-trained Stable Diffusion variational autoencoder (SD-VAE) for high-dimensional data modeling. However, MF training remains computationally demanding and is often unstable. During inference, the SD-VAE decoder dominates the generation cost, and MF depends on complex guidance hyperparameters for class-conditional generation. In this work, we develop an efficient training and sampling scheme for MF in the latent space of a Representation Autoencoder (RAE), where a pre-trained vision encoder (e.g., DINO) provides semantically rich latents paired with a lightweight decoder. We observe that naive MF training in the RAE latent space suffers from severe gradient explosion. To stabilize and accelerate training, we adopt Consistency Mid-Training for trajectory-aware initialization and use a two-stage scheme: distillation from a pre-trained flow matching teacher to speed convergence and reduce variance, followed by an optional bootstrapping stage with a one-point velocity estimator to further reduce deviation from the oracle mean flow. This design removes the need for guidance, simplifies training configurations, and reduces computation in both training and sampling. Empirically, our method achieves a 1-step FID of 2.03, outperforming vanilla MF's 3.43, while reducing sampling GFLOPS by 38% and total training cost by 83% on ImageNet 256. We further scale our approach to ImageNet 512, achieving a competitive 1-step FID of 3.23 with the lowest GFLOPS among all baselines. Code is available at https://github.com/sony/mf-rae.

Post-training for long-horizon agentic tasks has a tension between compute efficiency and generalization. While supervised fine-tuning (SFT) is compute efficient, it often suffers from out-of-domain (OOD) degradation. Conversely, end-to-end reinforcement learning (E2E RL) preserves OOD capabilities, but incurs high compute costs due to many turns of on-policy rollout. We introduce PivotRL, a novel framework that operates on existing SFT trajectories to combine the compute efficiency of SFT with the OOD accuracy of E2E RL. PivotRL relies on two key mechanisms: first, it executes local, on-policy rollouts and filters for pivots: informative intermediate turns where sampled actions exhibit high variance in outcomes; second, it utilizes rewards for functional-equivalent actions rather than demanding strict string matching with the SFT data demonstration. We theoretically show that these mechanisms incentivize strong learning signals with high natural gradient norm, while maximally preserving policy probability ordering on actions unrelated to training tasks. In comparison to standard SFT on identical data, we demonstrate that PivotRL achieves +4.17% higher in-domain accuracy on average across four agentic domains, and +10.04% higher OOD accuracy in non-agentic tasks. Notably, on agentic coding tasks, PivotRL achieves competitive accuracy with E2E RL with 4x fewer rollout turns. PivotRL is adopted by NVIDIA's Nemotron-3-Super-120B-A12B, acting as the workhorse in production-scale agentic post-training.

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.

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.

In modern recommendation systems, the standard pipeline involves training machine learning models on historical data to predict user behaviors and improve recommendations continuously. However, these data training loops can introduce interference in A/B tests, where data generated by control and treatment algorithms, potentially with different distributions, are combined. To address these challenges, we introduce a novel approach called weighted training. This approach entails training a model to predict the probability of each data point appearing in either the treatment or control data and subsequently applying weighted losses during model training. We demonstrate that this approach achieves the least variance among all estimators that do not cause shifts in the training distributions. Through simulation studies, we demonstrate the lower bias and variance of our approach compared to other methods.

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate hatβ of the hidden parameter β^{star} of an underlying linear model. The key challenge of this work lies in the heteroscedasticity assumption that we make, meaning that each covariate has a different and unknown variance. The goal of the decision maker is then to figure out on the fly the optimal way to allocate the total budget of T samples between covariates, as sampling several times a specific one will reduce the variance of the estimated model around it (but at the cost of a possible higher variance elsewhere). By trying to minimize the ell^2-loss E [lVerthatβ-β^{star}rVert^2] the decision maker is actually minimizing the trace of the covariance matrix of the problem, which corresponds then to online A-optimal design. Combining techniques from bandit and convex optimization we propose a new active sampling algorithm and we compare it with existing ones. We provide theoretical guarantees of this algorithm in different settings, including a O(T^{-2}) regret bound in the case where the covariates form a basis of the feature space, generalizing and improving existing results. Numerical experiments validate our theoretical findings.

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.

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

We study contextual combinatorial bandits with probabilistically triggered arms (C^2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C^2-UCB-T algorithm and propose a novel analysis that achieves an O(dKT) regret bound, removing a potentially exponentially large factor O(1/p_{min}), where d is the dimension of contexts, p_{min} is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC^2-UCB and derive a regret bound O(dT), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C^2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

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.

Static word embeddings are ubiquitous in computational social science applications and contribute to practical decision-making in a variety of fields including law and healthcare. However, assessing the statistical uncertainty in downstream conclusions drawn from word embedding statistics has remained challenging. When using only point estimates for embeddings, researchers have no streamlined way of assessing the degree to which their model selection criteria or scientific conclusions are subject to noise due to sparsity in the underlying data used to generate the embeddings. We introduce a method to obtain approximate, easy-to-use, and scalable reconstruction error variance estimates for GloVe (Pennington et al., 2014), one of the most widely used word embedding models, using an analytical approximation to a multivariate normal model. To demonstrate the value of embeddings with variance (GloVe-V), we illustrate how our approach enables principled hypothesis testing in core word embedding tasks, such as comparing the similarity between different word pairs in vector space, assessing the performance of different models, and analyzing the relative degree of ethnic or gender bias in a corpus using different word lists.

Client selection strategies are widely adopted to handle the communication-efficient problem in recent studies of Federated Learning (FL). However, due to the large variance of the selected subset's update, prior selection approaches with a limited sampling ratio cannot perform well on convergence and accuracy in heterogeneous FL. To address this problem, in this paper, we propose a novel stratified client selection scheme to reduce the variance for the pursuit of better convergence and higher accuracy. Specifically, to mitigate the impact of heterogeneity, we develop stratification based on clients' local data distribution to derive approximate homogeneous strata for better selection in each stratum. Concentrating on a limited sampling ratio scenario, we next present an optimized sample size allocation scheme by considering the diversity of stratum's variability, with the promise of further variance reduction. Theoretically, we elaborate the explicit relation among different selection schemes with regard to variance, under heterogeneous settings, we demonstrate the effectiveness of our selection scheme. Experimental results confirm that our approach not only allows for better performance relative to state-of-the-art methods but also is compatible with prevalent FL algorithms.

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.

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.

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.

LLM-as-a-judge has emerged as a cornerstone technique for evaluating large language models by leveraging LLM reasoning to score prompt-response pairs. Since LLM judgments are stochastic, practitioners commonly query each pair multiple times to estimate mean scores accurately. This raises a critical challenge: given a fixed computational budget B, how to optimally allocate queries across K prompt-response pairs to minimize estimation error? % We present a principled variance-adaptive approach leveraging multi-armed bandit theory and concentration inequalities. Our method dynamically allocates queries based on estimated score variances, concentrating resources where uncertainty is highest. Further, our algorithm is shown to achieve a worst-case score-estimation error of Oleft(frac{sum_{i=1^K σ_i^2}{B}}right), σ_i^2 being the unknown score variance for pair i in [K] with near-optimal budget allocation. % Experiments on Summarize-From-Feedback and HelpSteer2 demonstrate that our method significantly outperforms uniform allocation, reducing worst-case estimation error while maintaining identical budgets. Our work establishes a theoretical foundation for efficient LLM evaluation with practical implications for AI safety, model alignment, and automated assessment at scale.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain performance. Across tuned hyperparameters across the board, all flavors of matrix-whitening methods reliably outperform elementwise counterparts, such as Adam. Matrix-whitening is often related to spectral descent -- however, experiments reveal that performance gains are *not explained solely by accurate spectral normalization* -- particularly, SOAP displays the largest per-step gain, even though Muon more accurately descends along the steepest spectral descent direction. Instead, we argue that matrix-whitening serves two purposes, and the variance adaptation component of matrix-whitening is the overlooked ingredient explaining this performance gap. Experiments show that variance-adapted versions of optimizers consistently outperform their sign-descent counterparts, including an adaptive version of Muon. We further ablate variance adaptation strategies, finding that while lookahead style approximations are not as effective, low-rank variance estimators can effectively reduce memory costs without a performance loss.

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.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

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/.

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned on a downstream task for a specific application. The most successful and most commonly used fine-tuning method is to update the pre-trained weights via a low-rank adaptation (LoRA). LoRA introduces new weight matrices that are usually initialized at random with a uniform rank distribution across model weights. Recent works focus on weight-driven initialization or learning of adaptive ranks during training. Both approaches have only been investigated in isolation, resulting in slow convergence or a uniform rank distribution, in turn leading to sub-optimal performance. We propose to enhance LoRA by initializing the new weights in a data-driven manner by computing singular value decomposition on minibatches of activation vectors. Then, we initialize the LoRA matrices with the obtained right-singular vectors and re-distribute ranks among all weight matrices to explain the maximal amount of variance and continue the standard LoRA fine-tuning procedure. This results in our new method Explained Variance Adaptation (EVA). We apply EVA to a variety of fine-tuning tasks ranging from language generation and understanding to image classification and reinforcement learning. EVA exhibits faster convergence than competitors and attains the highest average score across a multitude of tasks per domain.

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose p1, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that p1 substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.

We consider whether off-policy experience from a smaller, weaker model can elicit capability in a stronger learner that on-policy RL fine-tuning (e.g., GRPO) does not reach. We find that injecting mathematically wrong drafts from a smaller but more domain-trained model -- mismatched to the current problem -- into a stronger learner's GRPO context consistently outperforms standard on-policy GRPO on held-out MATH-500 and out-of-distribution AIME 2025/2026. Concretely, we use Mathstral-7B as the learner, Qwen2.5-Math-1.5B as the draft model, 8.8K Level 3--5 MATH problems (with MATH-500 held out), and train with Dr. GRPO. Mismatch is an active ingredient: shuffling drafts to mismatched problems while holding everything else constant yields +1.62pp on MATH-500 (greedy pass@1) over the matched-wrong variant (n=10 seeds, p=0.0015, Welch's t). In fact, the mismatched-wrong variant leads all other variants we tested on MATH-500 across both greedy pass@1 and sampling pass@k. On out-of-distribution AIME 2025 and 2026, the mismatched-wrong variant uniquely lifts pass@k above both Mathstral-7B (in its native [INST] format) and the Qwen2.5-Math-1.5B draft model at every sample budget from k=1 to k=1024 across 2 seeds (+14.2pp on 2025 and +9.0pp on 2026 at pass@1024 over Mathstral-7B), and at pass@1024 also leads no-draft, matched-wrong, and mismatched-correct variants on both years. All variants use the same prompt with no draft injection at test time. The recipe -- trained on a single GPU with no SFT, no reward models, no synthesized data, and no produce-critique-revise inner loop -- reaches 71.98% MATH-500 on Mathstral-7B-v0.1, the highest published result on this model to our knowledge, surpassing the heavier WizardMath pipeline at 70.9% on full MATH (SFT + PPO with process/instruction reward models).

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate, recent approaches have focused on learning the data term with deep neural networks without explicitly modeling the prior, assuming that the model itself has the capacity to learn an optimal prior from a large-scale dataset. The performance improvement was obvious, however, they often fail to address inherent ambiguities of matching, such as textureless regions, repetitive patterns, and large displacements. To address this, we propose DiffMatch, a novel conditional diffusion-based framework designed to explicitly model both the data and prior terms. Unlike previous approaches, this is accomplished by leveraging a conditional denoising diffusion model. DiffMatch consists of two main components: conditional denoising diffusion module and cost injection module. We stabilize the training process and reduce memory usage with a stage-wise training strategy. Furthermore, to boost performance, we introduce an inference technique that finds a better path to the accurate matching field. Our experimental results demonstrate significant performance improvements of our method over existing approaches, and the ablation studies validate our design choices along with the effectiveness of each component. Project page is available at https://ku-cvlab.github.io/DiffMatch/.

Clinical trial matching is the task of identifying trials for which patients may be potentially eligible. Typically, this task is labor-intensive and requires detailed verification of patient electronic health records (EHRs) against the stringent inclusion and exclusion criteria of clinical trials. This process is manual, time-intensive, and challenging to scale up, resulting in many patients missing out on potential therapeutic options. Recent advancements in Large Language Models (LLMs) have made automating patient-trial matching possible, as shown in multiple concurrent research studies. However, the current approaches are confined to constrained, often synthetic datasets that do not adequately mirror the complexities encountered in real-world medical data. In this study, we present the first, end-to-end large-scale empirical evaluation of clinical trial matching using real-world EHRs. Our study showcases the capability of LLMs to accurately match patients with appropriate clinical trials. We perform experiments with proprietary LLMs, including GPT-4 and GPT-3.5, as well as our custom fine-tuned model called OncoLLM and show that OncoLLM, despite its significantly smaller size, not only outperforms GPT-3.5 but also matches the performance of qualified medical doctors. All experiments were carried out on real-world EHRs that include clinical notes and available clinical trials from a single cancer center in the United States.

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of flow matching is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, FID = 10.05).

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.

Some security-development settings require local models that map an objective to an ordered, checkable plan. We present a low-rank decomposition adapter and release a case-disjoint corpus with 24 authored decompositions and 83 derived next-step examples across 24 satellite-security cases. To prevent reference-plan leakage, prompts contain one objective and eight shuffled SPARTA candidates. The evaluation candidate sets are constructed with oracle inclusion of every reference technique, so this study measures selection from a controlled set, not retrieval. On six fixed cases and five decoding seeds, mean scores vary across adapters and prompted Qwen2.5 baselines; a separate greedy check over three adapter training seeds shows non-negligible training variance. A 24-fold greedy leave-one-case-out control at the two compact sizes likewise shows tradeoffs: at 1.5B, adapter precision is 0.583 against 0.480 for two-shot prompting, while recall is 0.586 against 0.660. Case-resampling intervals for adapter precision relative to the strongest prompted baseline cross zero at 1.5B and 7B. The adapter is also substantially more format-compliant, which prevents attributing all score differences to selection. Autoregressive next-step accuracy is 0.08, 0.06, and 0.29 at 0.5B, 1.5B, and 7B. We therefore offer the formulation, leakage-controlled dataset, reproducibility package, and descriptive analysis as a proof of concept, not evidence of a reliable stand-alone decomposition system or a general adapter advantage. A separate diagnostic tests contract reuse.

Arbitrary style transfer (AST) and domain generalization (DG) are important yet challenging visual learning tasks, which can be cast as a feature distribution matching problem. With the assumption of Gaussian feature distribution, conventional feature distribution matching methods usually match the mean and standard deviation of features. However, the feature distributions of real-world data are usually much more complicated than Gaussian, which cannot be accurately matched by using only the first-order and second-order statistics, while it is computationally prohibitive to use high-order statistics for distribution matching. In this work, we, for the first time to our best knowledge, propose to perform Exact Feature Distribution Matching (EFDM) by exactly matching the empirical Cumulative Distribution Functions (eCDFs) of image features, which could be implemented by applying the Exact Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play manner with minimal cost. The effectiveness of our proposed EFDM method is verified on a variety of AST and DG tasks, demonstrating new state-of-the-art results. Codes are available at https://github.com/YBZh/EFDM.

Recent advancements in visual autoregressive models (VAR) have demonstrated their effectiveness in image generation, highlighting their potential for real-world image super-resolution (Real-ISR). However, adapting VAR for ISR presents critical challenges. The next-scale prediction mechanism, constrained by causal attention, fails to fully exploit global low-quality (LQ) context, resulting in blurry and inconsistent high-quality (HQ) outputs. Additionally, error accumulation in the iterative prediction severely degrades coherence in ISR task. To address these issues, we propose VARestorer, a simple yet effective distillation framework that transforms a pre-trained text-to-image VAR model into a one-step ISR model. By leveraging distribution matching, our method eliminates the need for iterative refinement, significantly reducing error propagation and inference time. Furthermore, we introduce pyramid image conditioning with cross-scale attention, which enables bidirectional scale-wise interactions and fully utilizes the input image information while adapting to the autoregressive mechanism. This prevents later LQ tokens from being overlooked in the transformer. By fine-tuning only 1.2\% of the model parameters through parameter-efficient adapters, our method maintains the expressive power of the original VAR model while significantly enhancing efficiency. Extensive experiments show that VARestorer achieves state-of-the-art performance with 72.32 MUSIQ and 0.7669 CLIPIQA on DIV2K dataset, while accelerating inference by 10 times compared to conventional VAR inference.

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters.

Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Yet, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

Reinforcement learning is structurally harder than supervised learning because the policy changes the data distribution it learns from. The resulting fragility is especially visible in large-model training, where the training and rollout systems differ in numerical precision, sampling, and other implementation details. Existing methods manage this fragility by adding hyper-parameters to the training objective, which makes the algorithm more sensitive to its configuration and requires retuning whenever the task, model scale, or distribution mismatch changes. This fragility traces to two concerns that current objectives entangle through hyper-parameters set before training begins: a trust-region concern, that updates should not move the policy too far from its current value, and an off-policy concern, that data from older or different behavior policies should influence the update only to the extent that it remains reliable. Neither concern is a constant to set in advance, and their severity is reflected in the policy-ratio distribution of the current batch. We present a simple yet effective batch-adaptive objective that replaces fixed clipping with the normalized effective sample size of the policy ratios. The same statistic caps the score-function weight and sets the strength of an off-policy regularizer, so the update stays close to the usual on-policy score-function update when ratios are nearly uniform, and tightens automatically when stale or mismatched data cause ratio concentration, while retaining a nonzero learning signal on high-ratio tokens. Experiments across a wide range of settings show that our method matches or exceeds tuned baselines, introducing no new objective hyper-parameters and removing several existing ones. The code is available at https://github.com/FeynRL-project/FeynRL.

Run the same LLM agent on the same task twice: do you get the same behavior? We find the answer is often no. In a study of 3,000 agent runs across three models (Llama 3.1 70B, GPT-4o, and Claude Sonnet 4.5) on HotpotQA, we observe that ReAct-style agents produce 2.0--4.2 distinct action sequences per 10 runs on average, even with identical inputs. More importantly, this variance predicts failure: tasks with consistent behavior (leq2 unique paths) achieve 80--92% accuracy, while highly inconsistent tasks (geq6 unique paths) achieve only 25--60%, a 32--55 percentage point gap depending on model. We trace variance to early decisions: 69% of divergence occurs at step 2, the first search query. Our results suggest that monitoring behavioral consistency during execution could enable early error detection and improve agent reliability.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

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

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation σ^2 mapsto κ(σ^2), explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: anisotropy across eigenmodes, inhomogeneity across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation, introducing complex pipelines including extra noising and denoising steps. Second, they use a pretrained and frozen VAE encoder, resulting in suboptimal reconstruction and generation quality. In this paper, we find that the two issues can be solved in a very simple way: just fixing the variance (which would otherwise be predicted by the VAE encoder) to a constant (e.g., 0.5). On the one hand, this method allows the encoder to output a broader distribution of tokens and the decoder to learn to reconstruct clean images from the augmented token distribution, avoiding additional noise or denoising design. On the other hand, fixed variance simplifies the VAE evidence lower bound, making it stable to train an NF with a VAE jointly. On the ImageNet 256 times 256 generation task, our model SimFlow obtains a gFID score of 2.15, outperforming the state-of-the-art method STARFlow (gFID 2.40). Moreover, SimFlow can be seamlessly integrated with the end-to-end representation alignment (REPA-E) method and achieves an improved gFID of 1.91, setting a new state of the art among NFs.

We consider the problem of finding an input to a stochastic black box function such that the scalar output of the black box function is as close as possible to a target value in the sense of the expected squared error. While the optimization of stochastic black boxes is classic in (robust) Bayesian optimization, the current approaches based on Gaussian processes predominantly focus either on i) maximization/minimization rather than target value optimization or ii) on the expectation, but not the variance of the output, ignoring output variations due to stochasticity in uncontrollable environmental variables. In this work, we fill this gap and derive acquisition functions for common criteria such as the expected improvement, the probability of improvement, and the lower confidence bound, assuming that aleatoric effects are Gaussian with known variance. Our experiments illustrate that this setting is compatible with certain extensions of Gaussian processes, and show that the thus derived acquisition functions can outperform classical Bayesian optimization even if the latter assumptions are violated. An industrial use case in billet forging is presented.

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of the random variables, making them suitable for sequential decision making contexts. The results are instantiated for both the batch setting (where the sample size is fixed) and the sequential setting (where the sample size is a stopping time). Our bounds are asymptotically sharp: when the data are iid, our CI adpats optimally to both unknown mean μ and unknown V[(X-μ)^2], meaning that the first order term of our CI exactly matches that of the oracle Bernstein inequality which knows those quantities. We compare our results to a widely used (non-sharp) concentration inequality for the variance based on self-bounding random variables, showing both the theoretical gains and improved empirical performance of our approach. We finally extend our methods to work in any separable Hilbert space.

Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining. However, most existing TSFMs remain univariate, and recent efforts to enable cross-variate modeling still operate directly within the raw variate space. This design introduces fundamental limitations in semantic alignment and relational expressivity. Specifically, raw-space group mixing lacks a dedicated mechanism to align heterogeneous physical quantities, while standard non-negative attention fails to capture the complex synergistic and antagonistic interactions ubiquitous in real-world systems. To address these challenges, we propose Falcon-X, decouples variates from the raw space and maps them into a unified latent prototype space. Falcon-X employs a Unified Prototype Diff-Attention mechanism that explicitly evaluates both positive and negative semantic affinities to explicitly align heterogeneous variates. Cross-variate interactions are then efficiently performed within this shared space via Latent Entity Attention, naturally facilitating zero-shot structural transfer. Finally, a Variate Reassembly Router robustly reconstructs variate-specific trajectories via a request-and-dispatch mechanism. Extensive evaluations on the GIFT-Eval and fev-bench benchmarks demonstrate that Falcon-X achieves state-of-the-art forecasting performance, offering a principled and scalable paradigm for complex multivariate environments. Falcon-X is publicly released to support future research.

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 .

Self-tuning algorithms that adapt the learning process online encourage more effective and robust learning. Among all the methods available, meta-gradients have emerged as a promising approach. They leverage the differentiability of the learning rule with respect to some hyper-parameters to adapt them in an online fashion. Although meta-gradients can be accumulated over multiple learning steps to avoid myopic updates, this is rarely used in practice. In this work, we demonstrate that whilst multi-step meta-gradients do provide a better learning signal in expectation, this comes at the cost of a significant increase in variance, hindering performance. In the light of this analysis, we introduce a novel method mixing multiple inner steps that enjoys a more accurate and robust meta-gradient signal, essentially trading off bias and variance in meta-gradient estimation. When applied to the Snake game, the mixing meta-gradient algorithm can cut the variance by a factor of 3 while achieving similar or higher performance.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

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.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

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.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

Agentic systems are evaluated on benchmarks where agents interact with environments to solve tasks. Most papers report a pass@1 score computed from a single run per task, assuming this gives a reliable performance estimate. We test this assumption by collecting 60,000 agentic trajectories on SWE-Bench-Verified, spanning three models and two scaffolds. We find substantial variance: single-run pass@1 estimates vary by 2.2 to 6.0 percentage points depending on which run is selected, with standard deviations exceeding 1.5 percentage points even at temperature 0. This variance has critical implications: reported improvements of 2--3 percentage points may reflect evaluation noise rather than genuine algorithmic progress. Through token-level analysis, we show that trajectories diverge early, often within the first few percent of tokens, and that these small differences cascade into different solution strategies. To enable reliable evaluation of agentic systems, we recommend three concrete practices: (1) estimate pass@1 from multiple independent runs per task, especially when measuring small improvements, (2) use statistical power analysis to determine the number of runs needed to detect expected effect sizes, and (3) consider metrics like pass@k (optimistic bound) and pass^k (pessimistic bound) with k>1 to better characterize the full performance envelope. While these practices increase evaluation cost, they are essential for distinguishing genuine scientific progress from statistical noise.

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at https://voldemort108x.github.io/hetero_uncertainty/.

Based on the weight-sharing mechanism, one-shot NAS methods train a supernet and then inherit the pre-trained weights to evaluate sub-models, largely reducing the search cost. However, several works have pointed out that the shared weights suffer from different gradient descent directions during training. And we further find that large gradient variance occurs during supernet training, which degrades the supernet ranking consistency. To mitigate this issue, we propose to explicitly minimize the gradient variance of the supernet training by jointly optimizing the sampling distributions of PAth and DAta (PA&DA). We theoretically derive the relationship between the gradient variance and the sampling distributions, and reveal that the optimal sampling probability is proportional to the normalized gradient norm of path and training data. Hence, we use the normalized gradient norm as the importance indicator for path and training data, and adopt an importance sampling strategy for the supernet training. Our method only requires negligible computation cost for optimizing the sampling distributions of path and data, but achieves lower gradient variance during supernet training and better generalization performance for the supernet, resulting in a more consistent NAS. We conduct comprehensive comparisons with other improved approaches in various search spaces. Results show that our method surpasses others with more reliable ranking performance and higher accuracy of searched architectures, showing the effectiveness of our method. Code is available at https://github.com/ShunLu91/PA-DA.

This tutorial gives a concise overview of existing PAC-Bayesian theory focusing on three generalization bounds. The first is an Occam bound which handles rules with finite precision parameters and which states that generalization loss is near training loss when the number of bits needed to write the rule is small compared to the sample size. The second is a PAC-Bayesian bound providing a generalization guarantee for posterior distributions rather than for individual rules. The PAC-Bayesian bound naturally handles infinite precision rule parameters, L_2 regularization, {\em provides a bound for dropout training}, and defines a natural notion of a single distinguished PAC-Bayesian posterior distribution. The third bound is a training-variance bound --- a kind of bias-variance analysis but with bias replaced by expected training loss. The training-variance bound dominates the other bounds but is more difficult to interpret. It seems to suggest variance reduction methods such as bagging and may ultimately provide a more meaningful analysis of dropouts.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

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

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

The sliced Wasserstein (SW) distances between two probability measures are defined as the expectation of the Wasserstein distance between two one-dimensional projections of the two measures. The randomness comes from a projecting direction that is used to project the two input measures to one dimension. Due to the intractability of the expectation, Monte Carlo integration is performed to estimate the value of the SW distance. Despite having various variants, there has been no prior work that improves the Monte Carlo estimation scheme for the SW distance in terms of controlling its variance. To bridge the literature on variance reduction and the literature on the SW distance, we propose computationally efficient control variates to reduce the variance of the empirical estimation of the SW distance. The key idea is to first find Gaussian approximations of projected one-dimensional measures, then we utilize the closed-form of the Wasserstein-2 distance between two Gaussian distributions to design the control variates. In particular, we propose using a lower bound and an upper bound of the Wasserstein-2 distance between two fitted Gaussians as two computationally efficient control variates. We empirically show that the proposed control variate estimators can help to reduce the variance considerably when comparing measures over images and point-clouds. Finally, we demonstrate the favorable performance of the proposed control variate estimators in gradient flows to interpolate between two point-clouds and in deep generative modeling on standard image datasets, such as CIFAR10 and CelebA.

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.

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.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-t prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-t priors and primal-space guarantees for constrained generation, under varepsilon-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

We elucidate the design space of Representation Distribution Matching (RDM), our name for the paradigm that trains a one-step image generator by matching generated and reference feature distributions under frozen pretrained encoders. We identify two design axes, how the distributions are compared and the representations they are compared in, and controlled studies along them yield three findings. First, the classical MMD, which could not train convincing generators a decade ago, becomes a strong and scalable objective once estimated right. Second, the generated batch is then the operative variable, with an optimum above 2048, far beyond customary batch sizes. Third, any single representation can be gamed, driven below the real score while images stay visibly fake, so we match against a balanced battery of encoders and evaluate with SW_r14, a Sliced-Wasserstein distance over 14 encoders that is independent of the training loss and resists gaming. Combining the preferred choices yields improved RDM (iRDM): it sets the one-step state of the art on ImageNet at SW_r14 1.30, corroborated by PickScore, a human-preference proxy our objective never optimizes, which prefers it over the prior best one-step generator on 71.2% of matched samples. The same recipe post-trains the four-step FLUX.2 [klein] into a one-step generator, surpassing the four-step version on GenEval, 0.826 to 0.794, and on PickScore, 22.76 to 22.58, in 90 H200 GPU-hours. Project page: https://alan-lanfeng.github.io/rdm/.

Pre-training data mixtures are commonly tuned by running small-scale experiments and extrapolating to the target training budget. When high-quality data is scarce and must be repeated, this extrapolation frequently fails, but the source of the failure has not been isolated. We show that a primary culprit is a repetition mismatch: because high-quality datasets are small, their repetition rate changes as the training budget grows, shifting the optimal mixture in ways that small-scale proxy experiments do not anticipate. A subsampling procedure that matches the target repetition rate controls for this effect. In a two-source setting combining limited high-quality data with web crawl, a single repetition-controlled experiment using only 1/16 of the target tokens recovers a mixture within 0.05 of the optimum for a 757M parameter model, compared to an error of 0.75 without repetition control. Achieving comparable accuracy without repetition control requires three to four horizons, consuming 44 to 94% of the target token budget. With three data sources, the larger mixture space requires more than a single experiment to constrain, but the approach remains effective: at the 757M scale, just two repetition-controlled horizons recover the optimal mixture, outperforming baselines that instead require the full two-source experiments to construct. Our results reveal that repetition dynamics, not scale alone, shape whether small-scale mixture experiments generalize. More broadly, they suggest that data repetition deserves treatment as a first-class variable in mixture optimization, rather than an inconvenient side effect of limited data.

Feature embeddings acquired from pretrained models are widely used in medical applications of deep learning to assess the characteristics of datasets; e.g. to determine the quality of synthetic, generated medical images. The Fréchet Inception Distance (FID) is one popular synthetic image quality metric that relies on the assumption that the characteristic features of the data can be detected and encoded by an InceptionV3 model pretrained on ImageNet1K (natural images). While it is widely known that this makes it less effective for applications involving medical images, the extent to which the metric fails to capture meaningful differences in image characteristics is not obviously known. Here, we use Monte Carlo dropout to compute the predictive variance in the FID as well as a supplemental estimate of the predictive variance in the feature embedding model's latent representations. We show that the magnitudes of the predictive variances considered exhibit varying degrees of correlation with the extent to which test inputs (ImageNet1K validation set augmented at various strengths, and other external datasets) are out-of-distribution relative to its training data, providing some insight into the effectiveness of their use as indicators of the trustworthiness of the FID.

Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space without explicitly shaping its distribution, making it unclear which types of distributions are optimal for modeling. We introduce Distribution-Matching VAE (DMVAE), which explicitly aligns the encoder's latent distribution with an arbitrary reference distribution via a distribution matching constraint. This generalizes beyond the Gaussian prior of conventional VAEs, enabling alignment with distributions derived from self-supervised features, diffusion noise, or other prior distributions. With DMVAE, we can systematically investigate which latent distributions are more conducive to modeling, and we find that SSL-derived distributions provide an excellent balance between reconstruction fidelity and modeling efficiency, reaching gFID equals 3.2 on ImageNet with only 64 training epochs. Our results suggest that choosing a suitable latent distribution structure (achieved via distribution-level alignment), rather than relying on fixed priors, is key to bridging the gap between easy-to-model latents and high-fidelity image synthesis. Code is avaliable at https://github.com/sen-ye/dmvae.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.

The rapid advancement of Large Language Models (LLMs) necessitates robust evaluation methodologies. Current benchmarking approaches often rely on comparing model outputs against predefined prompts and reference outputs. Relying on predefined reference outputs hinders flexible adaptation of benchmarks to the rapidly evolving capabilities of LLMs. This limitation necessitates periodic efforts to prepare new benchmarks. To keep pace with rapidly evolving LLM capabilities, we propose a more flexible benchmarking approach. Our method, \textbf{Varco Arena}, provides reference-free benchmarking of LLMs in tournament style. \textbf{Varco Arena} directly compares LLM outputs across a diverse set of prompts, determining model rankings through a single-elimination tournament structure. This direct pairwise comparison offers two key advantages: (1) Direct comparison, unmediated by reference text, more effectively orders competing LLMs, resulting in more reliable rankings, and (2) reference-free approach to benchmarking adds flexibility in updating benchmark prompts by eliminating the need for quality references. Our empirical results, supported by simulation experiments, demonstrate that the \textbf{Varco Arena} tournament approach aligns better with the current Elo model for benchmarking LLMs. The alignment is measured in terms of Spearman correlation, showing improvement over current practice of benchmarking that use reference outputs as comparison anchors.

We seek to identify the most relevant benefits offered by Medicare Advantage Health Plans that drive membership and market share. As an example, we explore plans operating in a single county in New Jersey between 2018 and 2023. A dataset of benefits from publicly available data sources was created and the variance inflation factor was applied to identify the correlation between the extracted features, to avoid multicollinearity and overparameterization problems. We categorized the variable Market Share and used it as a multinomial response variable with three categories: less than 0.3\%, 0.3\% to 1.5\%, and over 1.5\%. Categories were chosen to achieve approximately uniform distribution of plans (47, 60, and 65 respectively). We built a multinomial Lasso model using 5-fold cross-validation to tune the penalty parameter. Lasso forced some features to be dropped from the model, which reduces the risk of overfitting and increases the interpretability of the results. For each category, important variables are different. Certain brands drive market share, as do PPO plans and prescription drug coverage. Benefits, particularly ancillary benefits that are not part of CMS's required benefits, appear to have little influence, while financial terms such as deductibles, copays, and out-of-pocket limits are associated with higher market share. Finally, we evaluated the predictive accuracy of the Lasso model with the test set. The accuracy is 0.76.

Policy-gradient methods usually optimize expected return, but many real world applications care about distributional properties of returns: tail risk, outlier robustness, or best-of-K discovery. We introduce OrderGrad, a family of likelihood-ratio and reparameterization gradient estimators for order-statistic objectives. OrderGrad optimizes finite-sample L-statistics, i.e., weighted averages of sorted rewards or costs, recovering objectives such as VaR, CVaR, trimmed means, medians, and top-m/best-of-K criteria by changing only the rank weights. For any fixed sample size and rank-weight vector, OrderGrad provides an unbiased gradient estimator for the corresponding order-statistic objective. The method is implemented as a simple reward transformation that can then be used in an otherwise standard policy-gradient or reparameterized update. We study the resulting estimator's variance behavior and evaluate it on tasks where mean optimization is mismatched to the deployment objective, including LLM math post-training and other tasks. OrderGrad provides a unified, plug-and-play route to risk-averse, robust, and exploratory learning. Code: https://github.com/paavo5/ordergrad

The high cost of fine-tuning LLMs poses a significant economic barrier; pre-hoc performance prediction offers a critical solution to substantially reduce this expense. However, the theoretical limits of pre-hoc performance prediction remain unexplored. We formulate it as a stochastic estimation problem under information constraints, decomposing prediction risk into two components: an intrinsic limit (static data-model compatibility) and a reducible optimization variance. We prove that optimization variance admits a necessary lower bound on its decay rate, implying fundamental constraints on how quickly uncertainty dissipates, regardless of the predictor used. Based on these dynamics, we derive a budget-optimal probing principle and introduce a predictability phase diagram that organizes tasks into three distinct regimes: Static-Sufficient, Dynamic-Critical, and Noise-Dominant. Extensive experiments on synthetic and real-world benchmarks validate these theoretical regimes and demonstrate the efficiency of our probing strategy.

Stock price prediction is a challenging task and a lot of propositions exist in the literature in this area. Portfolio construction is a process of choosing a group of stocks and investing in them optimally to maximize the return while minimizing the risk. Since the time when Markowitz proposed the Modern Portfolio Theory, several advancements have happened in the area of building efficient portfolios. An investor can get the best benefit out of the stock market if the investor invests in an efficient portfolio and could take the buy or sell decision in advance, by estimating the future asset value of the portfolio with a high level of precision. In this project, we have built an efficient portfolio and to predict the future asset value by means of individual stock price prediction of the stocks in the portfolio. As part of building an efficient portfolio we have studied multiple portfolio optimization methods beginning with the Modern Portfolio theory. We have built the minimum variance portfolio and optimal risk portfolio for all the five chosen sectors by using past daily stock prices over the past five years as the training data, and have also conducted back testing to check the performance of the portfolio. A comparative study of minimum variance portfolio and optimal risk portfolio with equal weight portfolio is done by backtesting.

Cross-modal optical-SAR (Synthetic Aperture Radar) registration is a bottleneck for disaster-response via remote sensing, yet modern image matchers are developed and benchmarked almost exclusively on natural-image domains. We evaluate twenty-four pretrained matcher families--in a zero-shot setting with no fine-tuning or domain adaptation on satellite or SAR data--on SpaceNet9 and two additional cross-modal benchmarks under a deterministic protocol with tiled large-image inference, robust geometric filtering, and tie-point-grounded metrics. Our results reveal asymmetric transfer--matchers with explicit cross-modal training do not uniformly outperform those without it. While XoFTR (trained for visible-thermal matching) and RoMa achieve the lowest reported mean error at 3.0 px on the labeled SpaceNet9 training scenes, RoMa achieves this without any cross-modal training, and MatchAnything-ELoFTR (3.4 px)--trained on synthetic cross-modal pairs--matches closely, suggesting (as a working hypothesis) that foundation-model features (DINOv2) may contribute to modality invariance that partially substitutes for explicit cross-modal supervision. 3D-reconstruction matchers (MASt3R, DUSt3R), which are not designed for traditional 2D image matching, are highly protocol-sensitive and remain fragile under default settings. Deployment protocol choices (geometry model, tile size, inlier gating) shift accuracy by up to 33times for a single matcher, sometimes exceeding the effect of swapping matchers entirely within the evaluated sweep--affine geometry alone reduces mean error from 12.34 to 9.74 px. These findings inform both practical deployment of existing matchers and future matcher design for cross-modal satellite registration.

Visual generation is dominated by three paradigms: AutoRegressive (AR), diffusion, and Visual AutoRegressive (VAR) models. Unlike AR and diffusion, VARs operate on heterogeneous input structures across their generation steps, which creates severe asynchronous policy conflicts. This issue becomes particularly acute in reinforcement learning (RL) scenarios, leading to unstable training and suboptimal alignment. To resolve this, we propose a novel framework to enhance Group Relative Policy Optimization (GRPO) by explicitly managing these conflicts. Our method integrates three synergistic components: 1) a stabilizing intermediate reward to guide early-stage generation; 2) a dynamic time-step reweighting scheme for precise credit assignment; and 3) a novel mask propagation algorithm, derived from principles of Reward Feedback Learning (ReFL), designed to isolate optimization effects both spatially and temporally. Our approach demonstrates significant improvements in sample quality and objective alignment over the vanilla GRPO baseline, enabling robust and effective optimization for VAR models.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

The recent success of distributed word representations has led to an increased interest in analyzing the properties of their spatial distribution. Several studies have suggested that contextualized word embedding models do not isotropically project tokens into vector space. However, current methods designed to measure isotropy, such as average random cosine similarity and the partition score, have not been thoroughly analyzed and are not appropriate for measuring isotropy. We propose IsoScore: a novel tool that quantifies the degree to which a point cloud uniformly utilizes the ambient vector space. Using rigorously designed tests, we demonstrate that IsoScore is the only tool available in the literature that accurately measures how uniformly distributed variance is across dimensions in vector space. Additionally, we use IsoScore to challenge a number of recent conclusions in the NLP literature that have been derived using brittle metrics of isotropy. We caution future studies from using existing tools to measure isotropy in contextualized embedding space as resulting conclusions will be misleading or altogether inaccurate.

Mean Field Variational Inference (MFVI) is widely understood to underestimate posterior variance. By analysing conjugate Bayesian Linear Regression (BLR), we show that this characterization is incomplete: while MFVI underestimates the variance in parameter space, it can overestimate the predictive variance compared to the exact posterior. We show that if the MFVI posterior underestimates predictive variances in some directions, it necessarily overestimates them in others. Crucially, this overestimation occurs in directions where the training data concentrates. This leads to the surprising result that, for a test point drawn from the training distribution, MFVI's expected predictive variance exceeds that of the exact posterior. We demonstrate a pathological case of this effect, where the MFVI posterior fails to reduce predictive variance compared to the prior on in distribution data. We connect these results to the Cold Posterior Effect, arguing that varying the temperature can correct this overestimation, yielding predictions closer to those of the exact posterior. We validate our theory on synthetic and real-world regression tasks.

Latent diffusion models have emerged as the dominant framework for high-fidelity and efficient image generation, owing to their ability to learn diffusion processes in compact latent spaces. However, while previous research has focused primarily on reconstruction accuracy and semantic alignment of the latent space, we observe that another critical factor, robustness to sampling perturbations, also plays a crucial role in determining generation quality. Through empirical and theoretical analyses, we show that the commonly used β-VAE-based tokenizers in latent diffusion models, tend to produce overly compact latent manifolds that are highly sensitive to stochastic perturbations during diffusion sampling, leading to visual degradation. To address this issue, we propose a simple yet effective solution that constructs a latent space robust to sampling perturbations while maintaining strong reconstruction fidelity. This is achieved by introducing a Variance Expansion loss that counteracts variance collapse and leverages the adversarial interplay between reconstruction and variance expansion to achieve an adaptive balance that preserves reconstruction accuracy while improving robustness to stochastic sampling. Extensive experiments demonstrate that our approach consistently enhances generation quality across different latent diffusion architectures, confirming that robustness in latent space is a key missing ingredient for stable and faithful diffusion sampling.

Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR) serves as a convenient alternative: the measurement model is fitted to obtain factor scores in the first stage, which are then used to fit the structural model in the subsequent stage. However, naive application of FSR is known to yield biased estimates of structural parameters. In this paper, we develop a generic bias-correction framework for two-stage estimation of parametric statistical models and tailor it specifically to FSR. Unlike existing bias-corrected FSR solutions, the proposed method applies to a broader class of LV models and does not require computing specific types of factor scores. We establish the root-n consistency of the proposed bias-corrected two-stage estimator under mild regularity conditions. To ensure broad applicability and minimize reliance on complex analytical derivations, we introduce a stochastic approximation algorithm for point estimation and a Monte Carlo-based procedure for variance estimation. In a sequence of Monte Carlo experiments, we demonstrate that the bias-corrected FSR estimator performs comparably to the ``gold standard'' one-stage maximum likelihood estimator. These results suggest that our approach offers a straightforward yet effective alternative for estimating LV models.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

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.