This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has been a promising approach for studying the discrete optimization methods. Despite the crucial role of momentum in gradient-based optimization methods, the gap between the original dynamics and the continuous time approximations due to the discretization error has not been comprehensively bridged yet. In this work, we study the HB momentum method in continuous time while putting more focus on the discretization error to provide additional theoretical tools to this area. In particular, we design a first-order piece-wise continuous differential equation, where we add a number of counter terms to account for the discretization error explicitly. As a result, we provide a continuous time model for the HB momentum method that allows the control of discretization error to arbitrary order of the learning rate. As an application, we leverage it to find a new implicit regularization of the directional smoothness and investigate the implicit bias of HB for diagonal linear networks, indicating how our results can be used in deep learning. Our theoretical findings are further supported by numerical experiments.

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents sparse observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

Modern Text-to-Image (T2I) models deploy multi-layered defenses to block Not-Safe-For-Work (NSFW) content generation. These defenses typically include sequential layers such as prompt filters, concept erasers and image filters. While existing adversarial attacks have demonstrated vulnerabilities in isolated defense layers, they prove largely ineffective against multi-layered defenses deployed in real-world T2I systems. In this paper, we demonstrate that exploiting overlapping vulnerabilities across these distinct defense layers enables adversaries to systematically bypass the entire safeguard of T2I systems. We propose Transstratal Adversarial Attack (TAA), a novel black-box framework to compromise T2I models with multi-layered protection. It generates transstratal adversarial prompts to evade all defense layers simultaneously. This is accomplished through transstratal adversarial candidate generation using LLMs to fulfill implicit and subjective adversarial requirements against different defense layers, combined with adversarial genetic optimization for efficient black-box search to maximize the bypass rates and generated image harmfulness. Evaluated across 14 T2I models (e.g., Stable Diffusion, DALL E, and Midjourney) and 17 safety modules, our attack achieves an average attack success rate of 85.6\%, surpassing state-of-the-art methods by 73.5\%. Our findings challenge the isolated design of safety mechanisms and establish the first benchmark for holistic robustness evaluation in multi-layered safeguarded T2I models.

In strategic classification, the standard supervised learning setting is extended to support the notion of strategic user behavior in the form of costly feature manipulations made in response to a classifier. While standard learning supports a broad range of model classes, the study of strategic classification has, so far, been dedicated mostly to linear classifiers. This work aims to expand the horizon by exploring how strategic behavior manifests under non-linear classifiers and what this implies for learning. We take a bottom-up approach showing how non-linearity affects decision boundary points, classifier expressivity, and model class complexity. Our results show how, unlike the linear case, strategic behavior may either increase or decrease effective class complexity, and that the complexity decrease may be arbitrarily large. Another key finding is that universal approximators (e.g., neural nets) are no longer universal once the environment is strategic. We demonstrate empirically how this can create performance gaps even on an unrestricted model class.

This paper investigates Reinforcement Learning (RL) on data without explicit labels for reasoning tasks in Large Language Models (LLMs). The core challenge of the problem is reward estimation during inference while not having access to ground-truth information. While this setting appears elusive, we find that common practices in Test-Time Scaling (TTS), such as majority voting, yield surprisingly effective rewards suitable for driving RL training. In this work, we introduce Test-Time Reinforcement Learning (TTRL), a novel method for training LLMs using RL on unlabeled data. TTRL enables self-evolution of LLMs by utilizing the priors in the pre-trained models. Our experiments demonstrate that TTRL consistently improves performance across a variety of tasks and models. Notably, TTRL boosts the pass@1 performance of Qwen-2.5-Math-7B by approximately 211% on the AIME 2024 with only unlabeled test data. Furthermore, although TTRL is only supervised by the Maj@N metric, TTRL has demonstrated performance to consistently surpass the upper limit of the initial model, and approach the performance of models trained directly on test data with ground-truth labels. Our experimental findings validate the general effectiveness of TTRL across various tasks and highlight TTRL's potential for broader tasks and domains.

Large language models with Mixture-of-Experts (MoE) architectures achieve efficiency and scalability, yet their routing mechanisms introduce safety alignment challenges insufficiently addressed by techniques developed for dense models. In this work, the MoE-specific safety risk of positional vulnerability--that safety-aligned behaviors rely on specific expert modules--is formalized and systematically analyzed. An analytical framework, SAFEx, is presented to robustly identify, characterize, and validate safety-critical experts via a stability-based expert selection procedure, and to decompose them into two functional groups: the Harmful Content Detection Group (HCDG), which specializes in identifying and recognizing harmful content within user inputs, and the Harmful Response Control Group (HRCG), which specializes in controlling and enforcing model behaviors to generate appropriate safety responses. Expert-level interventions are conducted to probe causality and to test mitigation. Targeted masking of SAFEx-selected experts reveals that safety behavior is highly concentrated. On Qwen3-30B-A3B, configured with 48 MoE-FFN layers and 128 experts per layer under top-8 routing (48 128=6,144 experts in total), disabling 12 selected experts reduces the refusal rate by 22%. In addition, lightweight adaptation is performed using LoRA under three configurations--the HRCG, the union of HCDG and HRCG, and all experts--and the resulting updates are composed through negative weight merging targeted at the HRCG, leading to improved refusal under adversarial prompts without full-model retraining. These results establish positional vulnerability as a distinct MoE-specific safety challenge and provide a practical, compute-efficient pathway for expert-level safety interventions within routed architectures.

Extracting optical flow from videos remains a core computer vision problem. Motivated by the recent success of large general-purpose models, we ask whether frozen self-supervised video models trained only to predict future frames can be prompted, without fine-tuning, to output flow. Prior attempts to read out depth or illumination from video generators required fine-tuning; that strategy is ill-suited for flow, where labeled data is scarce and synthetic datasets suffer from a sim-to-real gap. Inspired by the Counterfactual World Model (CWM) paradigm, which can obtain point-wise correspondences by injecting a small tracer perturbation into a next-frame predictor and tracking its propagation, we extend this idea to generative video models for zero-shot flow extraction. We explore several popular architectures and find that successful zero-shot flow extraction in this manner is aided by three model properties: (1) distributional prediction of future frames (avoiding blurry or noisy outputs); (2) factorized latents that treat each spatio-temporal patch independently; and (3) random-access decoding that can condition on any subset of future pixels. These properties are uniquely present in the recently introduced Local Random Access Sequence (LRAS) architecture. Building on LRAS, we propose KL-tracing: a novel test-time inference procedure that injects a localized perturbation into the first frame, rolls out the model one step, and computes the Kullback-Leibler divergence between perturbed and unperturbed predictive distributions. Without any flow-specific fine-tuning, our method is competitive with state-of-the-art, task-specific models on the real-world TAP-Vid DAVIS benchmark and the synthetic TAP-Vid Kubric. Our results show that counterfactual prompting of controllable generative video models is an effective alternative to supervised or photometric-loss methods for high-quality flow.

Artificial intelligence (AI) has played a transformative role in chemical research, greatly facilitating the prediction of small molecule properties, simulation of catalytic processes, and material design. These advances are driven by increases in computing power, open source machine learning frameworks, and extensive chemical datasets. However, a persistent challenge is the limited amount of high-quality real-world data, while models calculated based on large amounts of theoretical data are often costly and difficult to deploy, which hinders the applicability of AI models in real-world scenarios. In this study, we enhance the prediction of solute-solvent properties by proposing a novel sample selection method: the iterative core subset extraction (CSIE) framework. CSIE iteratively updates the core sample subset based on information gain to remove redundant features in theoretical data and optimize the performance of the model on real chemical datasets. Furthermore, we introduce an asymmetric molecular interaction graph neural network (AMGNN) that combines positional information and bidirectional edge connections to simulate real-world chemical reaction scenarios to better capture solute-solvent interactions. Experimental results show that our method can accurately extract the core subset and improve the prediction accuracy.

Speech is a fundamental form of human communication, and speech perception constitutes the initial stage of language comprehension. Although brain-to-speech interface technologies have made significant progress in recent years, most existing studies focus on neural decoding during speech production. Such approaches heavily rely on articulatory motor regions, rendering them unsuitable for individuals with speech motor impairments, such as those with aphasia or locked-in syndrome. To address this limitation, we construct and release NeuroListen, the first publicly available stereo-electroencephalography (sEEG) dataset specifically designed for auditory reconstruction. It contains over 10 hours of neural-speech paired recordings from 5 clinical participants, covering a wide range of semantic categories. Building on this dataset, we propose HyperSpeech, a multi-band neural decoding framework that employs dynamic spatio-temporal hypergraph neural networks to capture high-order dependencies across frequency, spatial, and temporal dimensions. Experimental results demonstrate that HyperSpeech significantly outperforms existing methods across multiple objective speech quality metrics, and achieves superior performance in human subjective evaluations, validating its effectiveness and advancement. This study provides a dedicated dataset and modeling framework for auditory speech decoding, offering foundations for neural language processing and assistive communication systems.

The tremendous potential has been demonstrated by large language models (LLMs) in intelligent decision-making problems, with unprecedented capabilities shown across diverse applications ranging from gaming AI systems to complex strategic planning frameworks. However, the StarCraft II platform, which has been widely adopted for validating decision-making algorithms in the past decade, has not yet provided substantial support for this emerging domain. To address issues that LLMs cannot interface with the hundreds of actions of the pysc2 backend and the lack of native support for multi-agent (MA) collaboration, we propose the LLM-PySC2 environment. This is the first environment that offers LLMs the complete pysc2 action space with sufficient multi-modal information and game Wiki knowledge. With an asynchronous query architecture, the environment efficiently interacts with LLMs that maintain a constant latency regardless of the scale of the agents' population. In the experiments, we evaluated LLMs' decision-making performance in both the macro-decision and micro-operation scenarios, with traditional StarCraft II Multi-Agent Challenge (SMAC) tasks and a series of new proposed. Results indicate that LLMs possess the potential to achieve victories in complex scenarios but cannot constantly generate correct decisions, especially in the recovered pysc2 action space and MA settings. Without task-relevant instructions, the pre-trained models suffer from issues such as hallucinations and inefficient collaboration. Our findings suggest that StarCraft II still challenges in the era of large models, revealing that there is a lot to do to develop an advanced LLM decision-making system, and the proposed LLM-PySC2 environment will support future development of LLM-based decision-making solutions.