Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in scale, the corresponding covariance and kernel matrices become increasingly large, often reaching magnitudes that make their direct formation impractical or impossible. Existing techniques typically rely on matrix-vector products, which can provide efficient approximations, if the matrix spectrum behaves well. However, in settings like distributed learning, or when the matrix is defined only indirectly, access to the full data set can be restricted to only very small sub-matrices of the original matrix. In these cases, the matrix of nominal interest is not even available as an implicit operator, meaning that even matrix-vector products may not be available. In such settings, the matrix is "impalpable," in the sense that we have access to only masked snapshots of it. We draw on principles from free probability theory to introduce a novel method of "free decompression" to estimate the spectrum of such matrices. Our method can be used to extrapolate from the empirical spectral densities of small submatrices to infer the eigenspectrum of extremely large (impalpable) matrices (that we cannot form or even evaluate with full matrix-vector products). We demonstrate the effectiveness of this approach through a series of examples, comparing its performance against known limiting distributions from random matrix theory in synthetic settings, as well as applying it to submatrices of real-world datasets, matching them with their full empirical eigenspectra.

Large reasoning models (LRMs), such as OpenAI o1 and DeepSeek-R1, have significantly enhanced their reasoning capabilities by generating longer chains of thought, demonstrating outstanding performance across a variety of tasks. However, this performance gain comes at the cost of a substantial increase in redundant reasoning during the generation process, leading to high computational overhead and exacerbating the issue of overthinking. Although numerous existing approaches aim to address the problem of overthinking, they often rely on external interventions. In this paper, we propose a novel framework, Self-Braking Tuning (SBT), which tackles overthinking from the perspective of allowing the model to regulate its own reasoning process, thus eliminating the reliance on external control mechanisms. We construct a set of overthinking identification metrics based on standard answers and design a systematic method to detect redundant reasoning. This method accurately identifies unnecessary steps within the reasoning trajectory and generates training signals for learning self-regulation behaviors. Building on this foundation, we develop a complete strategy for constructing data with adaptive reasoning lengths and introduce an innovative braking prompt mechanism that enables the model to naturally learn when to terminate reasoning at an appropriate point. Experiments across mathematical benchmarks (AIME, AMC, MATH500, GSM8K) demonstrate that our method reduces token consumption by up to 60% while maintaining comparable accuracy to unconstrained models.

Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional complex systems predict future states individually. This approach struggles to model complex temporal dependencies and fails to explicitly account for the progressive growth of uncertainty inherent to the systems. While rolling diffusion frameworks, which apply increasing noise to forecasts at longer lead times, have been proposed to address this, their integration with state-of-the-art, high-fidelity diffusion techniques remains a significant challenge. We tackle this problem by introducing Elucidated Rolling Diffusion Models (ERDM), the first framework to successfully unify a rolling forecast structure with the principled, performant design of Elucidated Diffusion Models (EDM). To do this, we adapt the core EDM components-its noise schedule, network preconditioning, and Heun sampler-to the rolling forecast setting. The success of this integration is driven by three key contributions: piq a novel loss weighting scheme that focuses model capacity on the mid-range forecast horizons where determinism gives way to stochasticity; piiq an efficient initialization strategy using a pre-trained EDM for the initial window; and piiiq a bespoke hybrid sequence architecture for robust spatiotemporal feature extraction under progressive denoising. On 2DNavier-Stokes simulations and ERA5 global weather forecasting at 1.5 resolution, ERDM consistently outperforms key diffusion-based baselines, including conditional autoregressive EDM. ERDM offers a flexible and powerful general framework for tackling diffusion-based dynamics forecasting problems where modeling uncertainty propagation is paramount.1

Translating brain activity into meaningful visual content has long been recognized as a fundamental challenge in neuroscience and brain-computer interface research. Recent advances in EEG-based neural decoding have shown promise, yet two critical limitations remain in this area: poor generalization across subjects and constraints to specific visual tasks. We introduce NEED, the first unified framework achieving zero-shot cross-subject and cross-task generalization for EEG-based visual reconstruction. Our approach addresses three fundamental challenges: (1) cross-subject variability through an Individual Adaptation Module pretrained on multiple EEG datasets to normalize subject-specific patterns, (2) limited spatial resolution and complex temporal dynamics via a dual-pathway architecture capturing both low-level visual dynamics and high-level semantics, and (3) task specificity constraints through a unified inference mechanism adaptable to different visual domains. For video reconstruction, NEED achieves better performance than existing methods. Importantly, Our model maintains 93.7% of within-subject classification performance and 92.4% of visual reconstruction quality when generalizing to unseen subjects, while achieving an SSIM of 0.352 when transferring directly to static image reconstruction without fine-tuning, demonstrating how neural decoding can move beyond subject and task boundaries toward truly generalizable brain-computer interfaces.

AI agents have the potential to significantly alter the cybersecurity landscape. Here, we introduce the first framework to capture offensive and defensive cyber-capabilities in evolving real-world systems. Instantiating this framework with BountyBench, we set up 25 systems with complex, real-world codebases. To capture the vulnerability lifecycle, we define three task types: Detect (detecting a new vulnerability), Exploit (exploiting a given vulnerability), and Patch (patching a given vulnerability). For Detect, we construct a new success indicator, which is general across vulnerability types and provides localized evaluation. We manually set up the environment for each system, including installing packages, setting up server(s), and hydrating database(s). We add 40 bug bounties, which are vulnerabilities with monetary awards from \\$10 to \\$30,485, covering 9 of the OWASP Top 10 Risks. To modulate task difficulty, we devise a new strategy based on information to guide detection, interpolating from identifying a zero day to exploiting a given vulnerability. We evaluate 10 agents: Claude Code, OpenAI Codex CLI with o3-high and o4-mini, and custom agents with o3-high, GPT-4.1,

Functional brain network (FBN) modeling often relies on local pairwise interactions, whose limitation in capturing high-order dependencies is theoretically analyzed in this paper. Meanwhile, the computational burden and heuristic nature of current hypergraph modeling approaches hinder end-to-end learning of FBN structures directly from data distributions. To address this, we propose to extract high-order FBN structures under global constraints, and implement this as a Global Constraints oriented Multi-resolution (GCM) FBN structure learning framework. It incorporates 4 types of global constraint (signal synchronization, subject identity, expected edge numbers, and data labels) to enable learning FBN structures for 4 distinct levels (sample/subject/group/project) of modeling resolution. Experimental results demonstrate that GCM achieves up to a 30.6% improvement in relative accuracy and a 96.3% reduction in computational time across 5 datasets and 2 task settings, compared to 9 baselines and 10 state-of-the-art methods. Extensive experiments validate the contributions of individual components and highlight the interpretability of GCM. This work offers a novel perspective on FBN structure learning and provides a foundation for interdisciplinary applications in cognitive neuroscience. Code is publicly available on https://github.com/lzhan94swu/GCM.

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Cybersecurity and software research have crossed paths with modern deep learning research for a few years. The power of large language models (LLMs) in particular has intrigued us to apply them to understanding binary code. In this paper, we investigate some of the many ways LLMs can be applied to binary code similarity detection, as it is a significantly more difficult task compared to source code similarity detection due to the sparsity of information and less meaningful syntax. It also has great practical implications, such as vulnerability and malware detection. We find that pretrained LLMs are mostly capable of detecting similar binary code, even with a zero-shot setting. Our main contributions and findings are to provide several supervised fine-tuning methods that, when combined, significantly surpass zero-shot LLMs and state-of-the-art binary code similarity detection methods.

Multi-class tissue-type classification of colorectal cancer (CRC) histopathologic images is a significant step in the development of downstream machine learning models for diagnosis and treatment planning. However, publicly available CRC datasets used to build tissue classifiers often suffer from insufficient morphologic diversity, class imbalance, and low-quality image tiles, limiting downstream model performance and generalizability. To address this research gap, we introduce STARC-9 (STAnford coloRectal Cancer), a large-scale dataset for multi-class tissue classification. STARC-9 comprises 630,000 histopathologic image tiles uniformly sampled across nine clinically relevant tissue classes (each represented by 70,000 tiles), systematically extracted from hematoxylin & eosin-stained whole-slide images (WSI) from 200 CRC patients at the Stanford University School of Medicine. To construct STARC-9, we propose a novel framework, DeepCluster++, consisting of two primary steps to ensure diversity within each tissue class, followed by pathologist verification.