With diffusion and flow matching models achieving state-of-the-art generating performance, the interest of the community now turned to reducing the inference time without sacrificing sample quality. Consistency Models (CMs), which are trained to be consistent on diffusion or probability flow ordinary differential equation (PF-ODE) trajectories, enable one or two-step flow or diffusion sampling. However, CMs typically require prolonged training with large batch sizes to obtain competitive sample quality. In this paper, we examine the training dynamics of CMs near convergence and discover that CM trajectory tangents -- CM output update directions -- are quite oscillatory, in the sense that they move parallel to the data manifold, not towards the manifold. To mitigate oscillatory trajectory tangents, we propose a new loss function, called the {\em manifold feature distance (MFD)}, which provides manifold-aligned trajectory tangents that point toward the data manifold. Consequently, our method -- dubbed {\em Align Your Trajectory Tangent (AYT)} -- can accelerate CM training by orders of magnitude and even out-perform the learned perceptual image patch similarity metric (LPIPS). Furthermore, we find that our loss enables training with extremely small batch sizes without compromising sample quality.
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Theory · Optimization
Many machine learning problems are geometric at their core, relying on metric representations of data for tasks such as clustering, prototype selection, nearest-neighbor search, and graph-based learning. Furthermore, data is constantly evolving and it is routinely transformed through dimensionality reduction, random projections, feature embeddings, compression, or privacy-preserving mechanisms. These transformations are designed to preserve geometry approximately. As a result, they preserve objective values for many geometric optimization problems, but they fail to guarantee that algorithmic outcomes remain consistent. In this work, we study \emph{resilient data summaries} for geometric optimization. Building on the notion of \emph{$\gamma$-resilient algorithms} from Ahmadian, we introduce $\gamma$-resilient coresets. A $\gamma$-resilient $(k,\varepsilon)$-coreset is a compact, weighted summary that guarantees a $(1+\varepsilon)$ approximation to the objective and enforces stability at the level of assignments. We complement our positive result with a lower bound showing that to obtain a tight approximation for resilient clustering it is necessary to use a bi-criteria solution.
Theory · Reinforcement Learning and Planning
Behavior cloning is a fundamental paradigm in machine learning, enabling policy learning from expert demonstrations across robotics, autonomous driving, and generative models. Autoregressive models like transformer have proven remarkably effective, from large language models (LLMs) to vision-language-action systems (VLAs). However, applying autoregressive models to continuous control requires discretizing actions through quantization, a practice widely adopted yet poorly understood theoretically. This paper provides theoretical foundations for this practice. We analyze how quantization error propagates along the horizon and interacts with statistical sample complexity. We show that behavior cloning with quantized actions and log-loss achieves optimal sample complexity—matching existing lower bounds—and incurs only polynomial horizon dependence on quantization error, provided the dynamics are stable and the policy satisfies a probabilistic smoothness condition. We further characterize when different quantization schemes satisfy or violate these requirements, and propose a model-based augmentation that provably improves the error bound without requiring policy smoothness. Finally, we establish fundamental limits that jointly capture the effects of quantization error and statistical complexity.
Applications · Language, Speech and Dialog
Listwise reranking is a critical yet costly component in vision-centric retrieval and multimodal retrieval-augmented generation (M-RAG) over long documents. Although recent VLM-based rerankers achieve strong accuracy, they are often impractical due to long visual-token inputs and autoregressive decoding, resulting in high latency. We propose ZipRerank, a very efficient listwise multimodal reranker that directly addresses both bottlenecks: it shortens the input via query-image early interaction and eliminates multi-step generation by scoring all candidates in a single forward pass. ZipRerank is trained with a two-stage recipe: listwise pretraining on large-scale text reranking data rendered as images, followed by multimodal finetuning with VLM-teacher supervision and a soft-ranking objective to handle noisy rankings. Extensive experiments on the MMDocIR benchmark demonstrate that ZipRerank matches or surpasses state-of-the-art multimodal rerankers while reducing LLM inference latency by up to an order of magnitude, making it well-suited for latency-sensitive real-world systems. Source code is available at https://anonymous.4open.science/r/ZipRerank.
Social Aspects · Alignment
As Large Reasoning Models (LRMs) are increasingly deployed, auditing their chain-of-thought (CoT) traces for safety becomes critical. Recent work has reported that monitorability—the degree to which CoT faithfully and informatively reflects internal computation—can appear as a "free gift" during the early stages of Reinforcement Learning with Verifiable Rewards (RLVR). We make this observation concrete through a systematic evaluation across model families and training domains. Our results show that this effect is not universal: monitorability improvements are strongly data-dependent. In particular, we demonstrate the critical role of data diversity and instruction-following data during RLVR training. We further show that monitorability is orthogonal to capability—improvements in reasoning performance do not imply increased transparency. Through mechanistic analysis, we attribute monitorability gains primarily to response distribution sharpening (entropy reduction) and increased attention to the prompt, rather than stronger causal reliance on reasoning traces. We also reveal how monitorability dynamics vary with controlled training and evaluation difficulty. Together, these findings provide a holistic view of how monitorability emerges under RLVR, clarifying when gains are likely to occur and when they are not.
Social Aspects · Fairness
Fair graph clustering has emerged as a critical research area for addressing algorithmic bias in machine learning. The objective is to ensure that the proportion of each protected group within a cluster is consistent with its representation in the entire dataset. However, most existing spectral solutions rely on computationally expensive eigendecompositions of the graph Laplacian, limiting their scalability. In this paper, we propose Riemannian Fair Spectral Clustering (R-FairSC), a novel method that formulates fair spectral clustering as a constrained optimization problem on a Riemannian manifold. We develop a Riemannian alternating direction method of multipliers employing a variable-splitting strategy to efficiently solve the associated subproblems. Numerical experiments on large synthetic and real-world graphs demonstrate that R-FairSC significantly improves computational efficiency over state-of-the-art methods while maintaining high clustering quality and fairness.
Social Aspects · Robustness
Chain-of-Thought (CoT) prompting enables multi-step reasoning in large language models, yet long-horizon generation remains brittle under distribution shift and context interference: irrelevant cues persist, small deviations compound into inference drift, and late-stage corrections can destabilize the trajectory. We recast autoregressive decoding as a perturbed long-horizon dynamical system and introduce an *inference-time stabilization operator* that targets *trajectory-level* reliability rather than token-level fluency. Specifically, we propose *ODE-guided language models*, which augment a base Transformer with a persistent continuous-time *thought state* whose dynamics are explicitly designed to be dissipative, enabling stable evidence accumulation with controlled forgetting. Instantiating this framework, *Thinking in Flow* (TiF) equips the model with a lightweight Neural ODE controller and injects its output through post-norm residual updates to achieve numerically stable, low-intrusion steering. A demand--supply (uncertainty--capacity) gate determines *when* intervention is warranted, while a direction gate determines *how* to steer in representation space, yielding selective, do-no-harm corrections instead of persistent bias. We establish well-posedness, dissipativity, and incremental stability of the controlled thought dynamics, implying bounded interventions over arbitrarily long contexts, and empirically demonstrate improved robustness to distractions and semantic perturbations, while matching or improving accuracy on mathematical reasoning benchmarks across both the Llama and Qwen model families; we further observe gains on non-mathematical BBH reasoning tasks when training TiF on Llama.
Social Aspects · Alignment
Foundation models are increasingly trained on synthetic data generated by prior model iterations rather than exclusively on real data. This *self-consuming* training paradigm can lead to model collapse, divergence, or bias amplification. Recent work (Ferbach et al., 2024) shows that incorporating human curation into the loop can steer a self-consuming model toward human-aligned behavior, but these analyses focus on a single, isolated model that solely consumes its own outputs. In practice, however, models often interact and train on input output pairs produced by other models. This paper studies self-consuming training in the *multi-model* regime. We first formalize a framework for interacting self-consuming models and characterize when the resulting dynamical system converges to a stable point. We then examine how human curation of one model affects its own alignment (self-influence) and how such effects propagate to other models (cross-influence). Unlike isolated settings where human curation always enhances model alignment, we show that cross-model interactions can dampen or even invert this effect, ultimately degrading long-term alignment.
How can we use AI to discover a new state of the art for a scientific problem? Prior work in test-time scaling, such as AlphaEvolve, performs search by prompting a frozen LLM. We perform reinforcement learning at test time, so the LLM can continue to train, but now with experience specific to the test problem. This form of continual learning is quite special, because its goal is to produce one great solution rather than many good ones on average, and to solve this very problem rather than generalize to other problems. Therefore, our learning objective and search subroutine are designed to prioritize the most promising solutions. We call this method Test-Time Training to Discover (TTT-Discover). Following prior work, we focus on problems with continuous rewards. We report results for every problem we attempted, across mathematics, GPU kernel engineering, algorithm design, and biology. TTT-Discover sets the new state of the art in almost all of them: (i) Erdős' minimum overlap problem and an autocorrelation inequality; (ii) a GPUMode kernel competition (up to 2× faster than prior art); (iii) past AtCoder algorithm competitions; and (iv) denoising problem in single-cell analysis. Our solutions are reviewed by experts or the organizers. All our results are achieved with an open model, OpenAI gpt-oss-120b, and can be reproduced with our publicly available code, in contrast to previous best results that required closed frontier models. Our test-time training runs are performed using Tinker, an API by Thinking Machines, with a cost of only a few hundred dollars per problem.
Applications · Computer Vision
Existing referring video object segmentation (RVOS) is largely built on passive perception and assumes the target is already visible in the observed video, which limits real-world use when queries refer to objects beyond the current view. To address this gap, we introduce **Referring Video Active Exploration and Segmentation** (**RVAS**), a new task that focuses on reasoning about exploration policy and then locating and segmenting the object according to an input referring expression. To support RVAS, we build a large-scale dataset with manually annotated exploration actions and reference reasoning traces, enabling supervised training and evaluation. We benchmark representative RVOS and related video understanding baselines and find that they struggle to perform active target search and incur substantial overhead when coupled with online decision making. Motivated by these challenges, we propose LESA, a baseline framework that introduces a state controller and hierarchical memory for efficient streaming processing and sparse MLLM reasoning. LESA substantially reduces inference cost while maintaining competitive planning quality, and consistently improves segmentation accuracy on the RVAS dataset.
Social Aspects · Safety
Despite the advanced capabilities of Large Vision-Language Models (LVLMs), they frequently suffer from object hallucination. One reason is that visual features and pretrained textual representations often become intertwined in the deeper network layers. To address this, we propose REVIS, a training-free framework designed to explicitly re-activate this suppressed visual information. Rooted in latent space geometry, REVIS extracts the pure visual information vector via orthogonal projection and employs a calibrated strategy to perform sparse intervention only at the precise depth where suppression occurs. This surgical approach effectively restores visual information with minimal computational cost. Empirical evaluations on standard benchmarks demonstrate that REVIS reduces object hallucination rates by approximately 19% compared to state-of-the-art baselines, while preserving general reasoning capabilities.
General Machine Learning · Clustering
Capacitated fair-range $k$-clustering generalizes classical $k$-clustering by incorporating both capacity constraints and demographic fairness. In this setting, data points are categorized as clients and facilities; each facility has a capacity and may belong to one or more possibly intersecting demographic groups. The task is to select $k$ facilities as centers and assign each client to a center so that: ($a$) no center exceeds its capacity, ($b$) the number of centers selected from each group lies within specified lower and upper bounds (fair-range constraints), and ($c$) the clustering cost (e.g., $k$-median or $k$-means) is minimized. Prior work by Thejaswi et al. (KDD 2022) showed that even satisfying fair-range constraints is \np-hard, thereby making the problem inapproximable to any polynomial factor. Our first main result strengthens this by showing that inapproximability persists even when the fair-range constraints are trivially satisfiable, highlighting the intrinsic computational complexity of the clustering task itself. These inapproximability results hold even on tree metrics and when the number of groups is logarithmic in the size of the facility set. In light of strong inapproximability results, we focus on a practical setting where the number of groups is constant. Our second main result is a polynomial-time $O(\log k)$- and $O(\log^2 k)$-approximation algorithm for $k$-median and $k$-means objectives, respectively, in this regime. Next, we design constant factor approximation algorithms for these problems that run in fixed parameterized tractable time in $k$. All our approximation guarantees match the best bounds for capacitated clustering without fair-range constraints. Finally, as our third main contribution, we show that our polynomial-time algorithms are, to our knowledge, the first to have provable approximation guarantees that can practically solve problem instances of modest size.
Applications · Computer Vision
Polarization information is valuable for many computer vision applications. However, in hazy environments, polarization information is severely attenuated due to the degradation of captured polarized images. Existing dehazing methods struggle to effectively restore polarization information, as single-image methods are unaware of polarization, and polarization-based methods are constrained by the traditional polarization models. These deficiencies lead to inaccurate polarimetric signatures and physical inconsistencies in scattering environments. To overcome these limitations and achieve the joint restoration of scene radiance and polarization information, we propose DuRP, a dual-stage physics-embedded learning framework. Specifically, we derive generalized polarization physics models that relax the ideal assumptions of traditional theory to provide a more precise foundation for the joint restoration of polarimetric and amplitude information. We then design a dual-stage neural network to estimate latent physical parameters through differentiable operators, ensuring that both the polarimetric state and radiance are accurately recovered. Experimental results show that DuRP achieves state-of-the-art performance in joint restoration and significantly enhances polarization-based vision tasks.
Applications · Time Series
Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from “more interaction” to “more effective interaction”.
Applications · Computer Vision
Visual data is typically a prerequisite for training existing video anomaly detection (VAD) methods. However, obtaining sufficient annotated anomaly data for training is challenging and not scalable due to the rarity of anomaly data and the wide variety of abnormal events. In this work, we advocate that the effectiveness of treating texts as video sequences for the VAD model and propose a novel Text-Driven Video Anomaly Detection (TD-VAD) approach to break visual dependence. In contrast to the anomaly video data, text descriptions of abnormal events are easy to collect, and their class labels can be directly derived. Specifically, our method utilizes video-like text descriptions with temporal characteristics generated by LLM to train a VAD model, without any reliance on target-domain anomaly data. To capture the long and short-range temporal logic of events, we design the event evolution causal attention module to model contextual dependencies across time. During inference, considering the domain gap between the texts and video sequences, we use the frozen CLIP encoder to extract embeddings of video frames to align the text modality while retaining crucial visual information. Comprehensive experiments on two large-scale VAD datasets, XD-Violence and UCF-Crime, demonstrate that our method outperforms prior one-class and unsupervised VAD methods by a large margin.
Deep Learning · Large Language Models
We study how Large Language Models (LLMs) process negation mechanistically. First, we establish that even though open-weight models often provide wrong answers to questions involving negation, they do possess internal components that process negation correctly. Their poor accuracy is due to late-layer attention behavior that promotes simple shortcuts; ablating those attention modules greatly improves accuracy on negation-related questions. Second, we uncover how models process negation. We consider two hypotheses: models could use attention heads that attend to the phrase being negated and suppress related concepts, or they could directly construct a representation of the entire negative phrase (e.g., representing "not gas" as a vector that promotes liquids and solids). We apply a range of observational and causal interpretability techniques on Mistral-7B and Llama-3.1-8B to show that models implement both mechanisms, with the "constructive" mechanism being more prominent. Combined, our work deepens the understanding of LLMs' internals, highlighting construction-dominant computations and the coexistence of competing mechanisms within LLMs.
Deep Learning · Large Language Models
Diffusion large language models (dLLMs), which offer a promising alternative to traditional autoregressive LLMs, have recently shown strong results in pretraining. However, due to their lack of tractable sequence-level likelihoods, they have yet to benefit from modern LLM post-training techniques such as reinforcement learning (RL), limiting their real-world applicability. Existing attempts at dLLM post-training rely on heuristic approximations or lower bounds of the true likelihood. In this work, we propose Amortized Group Relative Policy Optimization (AGRPO), a policy gradient algorithm that leverages the multi-step Markovian nature of dLLM generation, optimizing individual denoising steps rather than entire sequences. We demonstrate AGRPO's effectiveness on different math and reasoning tasks, achieving +9.9\% absolute gain on GSM8K, +4.6\% on MATH-500, +59.4\% on Countdown, and +69.7\% on Sudoku over the base LLaDA model, improving upon comparable dLLM RL methods such as diffu-GRPO. Furthermore, we analyze how post-training gains persist across different inference configurations, revealing that models trained with AGRPO can sample 4x faster with minimal performance sacrifices.
Optimization · Non-Convex
Sharpness-Aware Minimization (SAM) is widely used to seek flatter minima—often linked to better generalization. In its standard implementation, SAM updates the current iterate using the loss gradient evaluated at a point perturbed by distance $\rho$ along the normalized gradient direction. We show that, for some choices of $\rho$, SAM can stall at points where this shifted (perturbed-point) gradient vanishes despite a nonzero original gradient, and therefore, they are not stationary points of the original loss. We call these points hallucinated minimizers, prove their existence under simple nonconvex landscape conditions (e.g., the presence of a local minimizer and a local maximizer), and establish sufficient conditions for local convergence of the SAM iterates to them. We corroborate this failure mode in neural network training and observe that it aligns with SAM's performance degradation often seen at large $\rho$. Finally, as a practical safeguard, we find that a short initial SGD warm-start before enabling SAM mitigates this failure mode and reduces sensitivity to the choice of $\rho$.
Deep Learning · Generative Models and Autoencoders
Diffusion models have achieved state-of-the-art performance in image generation tasks. However, training powerful diffusion models remains time-consuming, which limits their practical deployment. In this paper, we revisit the learning dynamics of diffusion models through the lens of *spectral bias*, a phenomenon in which deep neural networks prioritize learning low-frequency modes. Through an empirical analysis of diffusion training, we observe that diffusion models exhibit a **dual** spectral bias. First, over training iterations, they fit low-frequency components earlier than high-frequency details. Second, along the diffusion timesteps, early denoising steps mainly reconstruct coarse low-frequency content, while high-frequency details emerge in later steps. Motivated by this observation, we propose Frequency-aware Patch Selection **(FaPS)**, a general and fast training method for diffusion models that can be applied to both UNet and DiT backbones. Specifically, FaPS introduces a *frequency-aware gating* that adaptively selects image patches based on their frequency information and focuses computation only on the selected patches. Since the selection decisions are discrete and thus non-differentiable, we model the gating as a stochastic policy network and optimize it end-to-end using a policy gradient method. Our experiments demonstrate that FaPS achieves up to $\mathbf{3}\times$ faster training while maintaining comparable or superior generation quality, and improves the performance of diffusion models in limited-data settings.
Theory · Optimization
Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines.