The recently proposed optimization algorithm for deep neural networks Sharpness Aware Minimization (SAM) suggests perturbing parameters before gradient calculation by a gradient ascent step to guide the optimization into parameter space regions of flat loss. While significant generalization improvements and thus reduction of overfitting could be demonstrated, the computational costs are doubled due to the additionally needed gradient calculation, making SAM unfeasible in case of limited computationally capacities. Motivated by Nesterov Accelerated Gradient (NAG) we propose Momentum-SAM (MSAM), which perturbs parameters in the direction of the accumulated momentum vector to achieve low sharpness without significant computational overhead or memory demands over SGD or Adam. We evaluate MSAM in detail and reveal insights on separable mechanisms of NAG, SAM and MSAM regarding training optimization and generalization.

We introduce PurpCode, the first post-training recipe for training safe code reasoning models towards generating secure code and defending against malicious cyberactivities. PurpCode trains a reasoning model in two stages: (i) Rule Learning, which explicitly teaches the model to reference cybersafety rules to generate vulnerabilityfree code and to avoid facilitating malicious cyberactivities; and (ii) Reinforcement Learning, which optimizes model safety and preserves model utility through diverse, multi-objective reward mechanisms. To empower the training pipelines with comprehensive cybersafety data, we conduct internal red-teaming to synthesize comprehensive and high-coverage prompts based on real-world tasks for inducing unsafe cyberactivities in the model. Based on PurpCode, we develop a reasoning-based coding model, namely PurpCode-32B, which demonstrates state-of-the-art cybersafety, outperforming various frontier models. Moreover, our alignment method decreases the model overrefusal rates in both general and cybersafety-specific scenarios, while preserving model utility in both code generation and common security knowledge.

A major problem of kernel-based methods (e.g., least squares support vector machines, LS-SVMs) for solving linear/nonlinear ordinary differential equations (ODEs) is the prohibitive O(an3) (a = 1 for linear ODEs and 27 for nonlinear ODEs) part of their computational complexity with increasing temporal discretization points n. We propose a novel Nyström-accelerated LS-SVMs framework that breaks this bottleneck by reformulating ODEs as primal-space constraints. Specifically, we derive for the first time an explicit Nyström-based mapping and its derivatives from one-dimensional temporal discretization points to a higher m-dimensional feature space (1 < m n), enabling the learning process to solve linear/nonlinear equation systems with m-dependent complexity. Numerical experiments on sixteen benchmark ODEs demonstrate: 1) 10 6000 times faster computation than classical LS-SVMs and physics-informed neural networks (PINNs), 2) comparable accuracy to LS-SVMs (< 0.13% relative MAE, RMSE, and y ˆy difference) while maximum surpassing PINNs by 72% in RMSE, and 3) scalability to n = 104 time steps with m = 50features. This work establishes a new paradigm for efficient kernel-based ODEs learning without significantly sacrificing the accuracy of the solution.

One way to address the known limitations of backpropagation through time is to directly adjust neural activities during the learning process. However, it remains unclear how to effectively use feedback to shape RNN dynamics. Here, we introduce error forcing (EF), where the network activity is guided orthogonally toward the zero-error manifold during learning. This method contrasts with alternatives like teaching forcing, which impose stronger constraints on neural activity and thus induce larger feedback influence on circuit dynamics. Furthermore, EF can be understood from a Bayesian perspective as a form of approximate dynamic inference. Empirically, EF consistently outperforms other learning algorithms across several tasks and its benefits persist when additional biological constraints are taken into account. Overall, EF is a powerful temporal credit assignment mechanism and a promising candidate model for learning in biological systems.

Reasoning segmentation aims to segment target objects in complex scenes based on human intent and spatial reasoning. While recent multimodal large language models (MLLMs) have demonstrated impressive 2D image reasoning segmentation, adapting these capabilities to 3D scenes remains underexplored. In this paper, we introduce MLLM-For3D, a simple yet effective framework that transfers knowledge from 2DMLLMs to 3D scene understanding. Specifically, we utilize MLLMs to generate multi-view pseudo-segmentation masks and corresponding text embeddings, then unproject 2D masks into 3D space and align them with the text embeddings. The primary challenge lies in the absence of 3D context and spatial consistency across multiple views, causing the model to hallucinate objects that do not exist and fail to target objects consistently.

Image classifiers play a critical role in detecting diseases in medical imaging and identifying anomalies in manufacturing processes. However, their predefined behaviors after extensive training make post hoc model editing difficult, especially when it comes to forgetting specific classes or adapting to distribution shifts. Existing classifier editing methods either focus narrowly on correcting errors or incur extensive retraining costs, creating a bottleneck for flexible editing. Moreover, such editing has seen limited investigation in image classification. To overcome these challenges, we introduce Class Vectors, which capture class-specific representation adjustments during fine-tuning.

Video generation models have rapidly progressed, positioning themselves as video world models capable of supporting decision-making applications like robotics and autonomous driving. However, current benchmarks fail to rigorously evaluate these claims, focusing only on general video quality, ignoring important factors to world models such as physics adherence. To bridge this gap, we propose WorldModelBench, a benchmark designed to evaluate the world modeling capabilities of video generation models in application-driven domains. WorldModelBench offers two key advantages: (1) Against to nuanced world modeling violations: By incorporating instruction-following and physics-adherence dimensions, WorldModelBench detects subtle violations, such as irregular changes in object size that breach the mass conservation law--issues overlooked by prior benchmarks.

Explaining black-box models for time series data is critical for the wide-scale adoption of deep learning techniques across domains such as healthcare. Recently, explainability methods for deep time series models have seen significant progress by adopting saliency methods that perturb masked segments of time series to uncover their importance towards the prediction of black-box models. Thus far, such methods have been largely restricted to regular time series. Irregular time series, however, sampled at irregular time intervals and potentially with missing values, are the dominant form of time series in various critical domains (e.g., hospital records). In this paper, we conduct the first evaluation of saliency methods for the interpretation of irregular time series models.

Recent studies have shown LLMs possess some ability to improve their responses when given external feedback. However, it remains unclear how effectively and thoroughly these models can incorporate extrinsic feedback. In an ideal scenario, if LLMs receive near-perfect and complete feedback, we would expect them to fully integrate the feedback and reach correct solutions. In this paper, we systematically investigate LLMs' ability to incorporate feedback by designing a controlled experimental environment. For each problem, a solver model attempts a solution, then a feedback generator with access to near-complete ground-truth answers produces targeted feedback, after which the solver tries again. We evaluate this pipeline across a diverse range of tasks, including math reasoning, knowledge reasoning, scientific reasoning, and general multi-domain evaluations with state-of-the-art language models including Claude 3.7 with extended thinking.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (αReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.