Tunneling the Loss Landscape: Bypassing Memorization with Monte Carlo Parameter Swapping

Grokking is a striking phenomenon in neural network training, where a model can undergo a prolonged period of pure memorization before abrupt generalization. While previous works have attempted to interpret it through classical machine learning mechanisms like weight norm, recent research draws an analogy from statistical physics, framing grokking as a form of computational glass relaxation. This theory defines the initial memorization as a result of `fast cooling' where the training loss is reduced so quickly that a glass state is formed, followed by a `slow relaxation' towards final generalization. Although providing a unifying framework for representative grokking theories, this perspective has remained largely at the theoretical on macroscopic level without direct empirical validation on training dynamics. Here we introduce a three-component framework to directly characterize the training dynamics via parameter mobility (PM), and two representative measurements from glassy dynamics: replica correlation (RC) and fractal dimension (FD). We demonstrate that standard optimization presents clear signatures of glass dynamics and inherently traps the grokking network in a kinetic arrested memorization state with a collapsed mobility, strong history dependence, and channel-like motions. This quantitative agreement motivates us to introduce State-Aware Monte Carlo Parameter Swapping (SAM-Swap), an optimization plug-in that can accelerate generalization, inspired by swap Monte Carlo algorithm widely used in glass dynamics. Comparing SAM-Swap, weight decay, and Gaussian gradient noise, we find that accelerated generalization is consistently associated with random exploration in the parameter space, similar to diffusion in physics.

The Grokked Illusion: True Equilibrium Mitigates Catastrophic Forgetting

While neural networks are typically evaluated by their training and test performance, these metrics do not reveal how robust a learned representation is. Recent studies have shown that solutions occupying larger volumes in parameter space, as quantified by Boltzmann entropy, often exhibit superior generalizability compared to those reached by conventional optimization, a phenomenon known as the high entropy advantage. Here we ask whether this advantage persists beyond generalization. Specifically, we investigate models' robustness, the ability to retain the learned knowledge when the model is subsequently trained to acquire new information. Using grokking in modular arithmetic as a controlled setting, we design a noise injection experiment to evaluate the robustness difference between AdamW-trained transformers and high-entropy model sampled from Wang-Landau Molecular Dynamics with identical saturated performance. By forcing both models to fully remember new data with random labels, we find that AdamW-trained models suffer from catastrophic forgetting, with original task test accuracy dropping from 100% to below 75%, whereas the high-entropy models maintain approximately 95% test accuracy. We term this hidden fragility behind apparent generalization the "grokked illusion." Through singular value decomposition of the neural network weights, we discover that high-entropy neural networks possess significantly higher effective rank in attention and MLP layers both before and after noise injection, indicating richer feature representations can serve as a buffer against catastrophic forgetting. Our findings demonstrate that perfect generalization does not imply equal robustness, offering a new perspective on what makes a trained model robust to interference.

AdvancedMathBench: A Benchmark Suite for Advanced Mathematical Proof Generation and Verification

Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed. To bridge this gap, we introduce AdvancedMathBench, a benchmark suite designed to evaluate advanced mathematical reasoning capabilities. Its core proof-generation benchmark, ProverBench, contains 296 problems spanning undergraduate and doctoral qualifying-exam levels. To provide reliable evaluation of the proofs, we develop a dedicated automatic verification pipeline trained on large-scale expert annotations to produce both correctness verdicts and fine-grained assessments of proof errors, which exhibits strong agreement with human experts on held-out proof trajectories. We further introduce VerifierBench, consisting of 888 model-generated proof trajectories paired with expert ground truth, to evaluate whether models can correctly judge proof validity and provide sound verification rationales. Experiments show that AdvancedMathBench remains challenging for frontier models. On proof generation, the best-performing model, GPT-5.5-xhigh, achieves only 75.8 and 66.1 on the UGD and QE splits, respectively, indicating substantial room for improvement on advanced mathematical proof construction. On proof verification, the best model attains a Balanced F1 of only 65.1, and models generally exhibit low true negative rates, suggesting that critical error detection remains a major bottleneck.

ProLaViT: Learning Progressive Latent Visual Thoughts in Structured Latent Space

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but still struggle with complex visual reasoning tasks requiring multi-step perception and logical deduction. While explicit visual generation incurs prohibitive computational costs, existing latent approaches often rely on external experts or lack rigorous cognitive logic. In this paper, we introduce ProLaViT (Progressive Latent Visual Thought), a framework empowering MLLMs to perform structured visual derivation in the continuous latent space. Unlike works dependent on heterogeneous external models, ProLaViT leverages an endogenous self-distillation mechanism, utilizing the model's own visual encoder to supervise latent thoughts. To facilitate this, we construct a scalable programmatic synthesis pipeline enabling the model to internalize algorithmic precision without inference time tools. We design two reasoning paradigms: (1) Coarse-to-Fine Causal Chain for spatial tasks, guiding attention from global context to local targets. (2) Dialectical Reasoning Chain for logical tasks, incorporating counter-factual thinking for verification. Furthermore, we propose a Distance-Weighted Diversity Loss to impose topology-aware constraints, preventing feature degeneration by enforcing semantic distinctiveness. Extensive experiments demonstrate that ProLaViT outperforms baselines on vision-centric benchmarks, achieving superior accuracy and interpretability with high efficiency.

VideoWeaver: Evaluating and Evolving Skills for Agentic Long Video Generation

Recent agent frameworks such as Claude Code, Codex, and OpenClaw are strong at tool use and orchestration, but whether they can handle long video generation, a long-horizon multimodal task, remains underexplored. Unlike earlier video agents whose pipeline is handcrafted, these frameworks can build and refine their own workflows. We introduce VideoWeaver, an agent harness and benchmark that evaluates and evolves skills for long video generation, where an agent turns a single instruction into a long video by composing foundation skills into its own workflow rather than following a predefined pipeline. The benchmark has 16 task categories and 285 cases, with references spanning text, image, audio, video, and their combinations. Because errors can arise at any stage and not just in the final video, we propose an agent-as-judge that inspects both the execution trace and the final video, grounding its scores in evidence such as metadata and intermediate files. Using this feedback, we further design a skill evolution algorithm that refines and merges the agent's skills. Across multiple frameworks and models, we find that an explicit composition skill improves the generation process over using foundation skills alone, that skill evolution further improves output quality, and that performance varies notably across harness and model choices. The proposed agent-as-judge also aligns well with human judgments, especially on process metrics. Code and dataset is available at https://github.com/JianhuiWei7/VideoWeaver

Learning, locomotion, and navigation of soft synthetic snakes in three-dimensional, heterogeneous environments

Limbless terrestrial animals exhibit exceptional locomotor versatility and control, currently unmatched by engineered counterparts. Here, we introduce a computational framework that enables soft synthetic snakes to navigate unstructured, heterogeneous 3D terrains. Our approach is grounded in bio-inspired actuation and sensing models that reduce the control complexity inherent to high-degree-of-freedom, continuum bodies. These models are integrated into a reinforcement learning architecture to derive environment-traversing policies. Training first occurs in simplified, homogeneous terrains to learn locomotion primitives. These are then composed into adaptive strategies for complex landscapes. We demonstrate robustness by deploying a snake in high-fidelity 3D environments reconstructed from real-world imaging, achieving reliable navigation. Overall, this work provides a physically-realistic simulation platform and practical insights for the control of continuum systems in natural terrains.

How Far Are Video Models from True Multimodal Reasoning?

Despite remarkable progress toward general-purpose video models, a critical question remains unanswered: how far are these models from achieving true multimodal reasoning? Existing benchmarks fail to address this question rigorously, as they remain constrained by straightforward task designs and fragmented evaluation metrics that neglect complex multimodal reasoning. To bridge this gap, we introduce CLVG-Bench, an evaluation framework designed to probe video models' zero-shot reasoning capabilities via Context Learning in Video Generation. CLVG-Bench comprises more than 1,000 high-quality, manually annotated metadata across 6 categories and 47 subcategories, covering complex scenarios including physical simulation, logical reasoning, and interactive contexts. To enable rigorous and scalable assessment, we further propose an Adaptive Video Evaluator (AVE) that aligns with human expert perception using minimal annotations, delivering interpretable textual feedback across diverse video context tasks. Extensive experiments reveal a striking answer to our central question: while state-of-the-art (SOTA) video models, such as Seedance 2.0, demonstrate competence on certain understanding and reasoning subtasks, they fall substantially short with logically grounded and interactive generation tasks (achieving success rates <25% and ~0%, respectively), exposing multimodal reasoning and physical grounding as critical bottlenecks. By systematically quantifying these limitations, the proposed method provides actionable feedbacks and a clear roadmap toward truly robust, general-purpose video models. CLVG-Bench and code are released here.

AgentSwing: Adaptive Parallel Context Management Routing for Long-Horizon Web Agents

As large language models (LLMs) evolve into autonomous agents for long-horizon information-seeking, managing finite context capacity has become a critical bottleneck. Existing context management methods typically commit to a single fixed strategy throughout the entire trajectory. Such static designs may work well in some states, but they cannot adapt as the usefulness and reliability of the accumulated context evolve during long-horizon search. To formalize this challenge, we introduce a probabilistic framework that characterizes long-horizon success through two complementary dimensions: search efficiency and terminal precision. Building on this perspective, we propose AgentSwing, a state-aware adaptive parallel context management routing framework. At each trigger point, AgentSwing expands multiple context-managed branches in parallel and uses lookahead routing to select the most promising continuation. Experiments across diverse benchmarks and agent backbones show that AgentSwing consistently outperforms strong static context management methods, often matching or exceeding their performance with up to $3\times$ fewer interaction turns while also improving the ultimate performance ceiling of long-horizon web agents. Beyond the empirical gains, the proposed probabilistic framework provides a principled lens for analyzing and designing future context management strategies for long-horizon agents.

A Feature Shuffling and Restoration Strategy for Universal Unsupervised Anomaly Detection

Unsupervised anomaly detection is vital in industrial fields, with reconstruction-based methods favored for their simplicity and effectiveness. However, reconstruction methods often encounter an identical shortcut issue, where both normal and anomalous regions can be well reconstructed and fail to identify outliers. The severity of this problem increases with the complexity of the normal data distribution. Consequently, existing methods may exhibit excellent detection performance in a specific scenario, but their performance sharply declines when transferred to another scenario. This paper focuses on establishing a universal model applicable to anomaly detection tasks across different settings, termed as universal anomaly detection. In this work, we introduce a novel, straightforward yet efficient framework for universal anomaly detection: \uline{F}eature \uline{S}huffling and \uline{R}estoration (FSR), which can alleviate the identical shortcut issue across different settings. First and foremost, FSR employs multi-scale features with rich semantic information as reconstruction targets, rather than raw image pixels. Subsequently, these multi-scale features are partitioned into non-overlapping feature blocks, which are randomly shuffled and then restored to their original state using a restoration network. This simple paradigm encourages the model to focus more on global contextual information. Additionally, we introduce a novel concept, the shuffling rate, to regulate the complexity of the FSR task, thereby alleviating the identical shortcut across different settings. Furthermore, we provide theoretical explanations for the effectiveness of FSR framework from two perspectives: network structure and mutual information. Extensive experimental results validate the superiority and efficiency of the FSR framework across different settings.Code is available at https://github.com/luow23/FSR.

UniVBench: Towards Unified Evaluation for Video Foundation Models

Video foundation models aim to integrate video understanding, generation, editing, and instruction following within a single framework, making them a central direction for next-generation multimodal systems. However, existing evaluation benchmarks remain fragmented and limited in scope, as they each target a single task, rely on task-specific metrics, and typically use short or simple video clips. As a result, they do not capture the unified capabilities that these models are designed to deliver. To address this gap, we introduce UniVBench, a benchmark purpose-built for evaluating video foundation models across four core abilities: video understanding, video generation, video editing, and a newly proposed task, video reconstruction, which assesses how faithfully a model can reproduce video content it has encountered. Our benchmark substantially expands the complexity of evaluation by incorporating 200 high-quality, diverse and multi-shot videos, each paired with detailed captions, multi-format editing instructions, and reference images. All videos are human-created and carefully validated, offering richer cinematic information than prior benchmarks. In addition, we develop a unified agentic evaluation system (UniV-Eval) that standardizes prompting, instruction parsing, and scoring across all tasks, enabling fair, scalable, and reproducible comparisons of unified video models. By grounding evaluation in instruction-based multi-shot video tasks, UniVBench provides the first framework for measuring the integrated capabilities that video foundation models aim to achieve. Extensive human annotations ensure our evaluation aligns with human judgment, enabling rigorous assessment and accelerating progress toward robust video intelligence.