Growing evidence suggests that synaptic weights in the brain follow heavy-tailed distributions, yet most theoretical analyses of recurrent neural networks (RNNs) assume Gaussian connectivity. We systematically study the activity of RNNs with random weights drawn from biologically plausible Lévy alpha-stable distributions. While mean-field theory for the infinite system predicts that the quiescent state is always unstable---implying ubiquitous chaos---our finite-size analysis reveals a sharp transition between quiescent and chaotic dynamics. We theoretically predict the gain at which the finite system transitions from quiescent to chaotic dynamics, and validate it through simulations. Compared to Gaussian networks, finite heavy-tailed RNNs exhibit a broader gain regime near the edge of chaos, namely, a slow transition to chaos. However, this robustness comes with a tradeoff: heavier tails reduce the Lyapunov dimension of the attractor, indicating lower effective dimensionality. Our results reveal a biologically aligned tradeoff between the robustness of dynamics near the edge of chaos and the richness of high-dimensional neural activity. By analytically characterizing the transition point in finite-size networks---where mean-field theory breaks down---we provide a tractable framework for understanding dynamics in realistically sized, heavy-tailed neural circuits.

Hybrid language models that combine Attention and State Space Models (SSMs) have been shown to achieve state-of-the-art accuracy and runtime performance. Recent work has also demonstrated that applying pruning and distillation to Attention-only models yields smaller, more accurate models at a fraction of the training cost. In this work, we explore the effectiveness of compressing Hybrid architectures. To this end, we introduce a novel group-aware pruning method for Mamba layers that preserves the structural integrity of SSM blocks and their sequence modeling capabilities. We combine this method with FFN, embedding dimension, and layer pruning, along with knowledge distillation-based retraining to obtain a unified compression recipe for hybrid models. Using this recipe, we compress the Nemotron-H 8B Hybrid model down to 4B parameters with up to $40\times$ fewer training tokens compared to similarly-sized models.

Multimodal hallucination in multimodal large language models (MLLMs) restricts the correctness of MLLMs. However, multimodal hallucinations are multi-sourced and arise from diverse causes. Existing benchmarks fail to adequately distinguish between perception-induced hallucinations and reasoning-induced hallucinations. This failure constitutes a significant issue and hinders the diagnosis of multimodal reasoning failures within MLLMs. To address this, we propose the MIRAGE benchmark, which isolates reasoning hallucinations by constructing questions where input images are correctly perceived by MLLMs yet reasoning errors persist.

Foundation models have enabled rapid progress across many specialized domains by leveraging large-scale pre-training on unlabeled data, demonstrating strong generalization to a variety of downstream tasks. While such models have gained significant attention in fields like Earth Observation, their application to Mars science remains limited. A key enabler of progress in other domains has been the availability of standardized benchmarks that support systematic evaluation. In contrast, Mars science lacks such benchmarks and standardized evaluation frameworks, which have limited progress toward developing foundation models for Martian tasks. To address this gap, we introduce Mars-Bench, the first benchmark designed to systematically evaluate models across a broad range of Mars-related tasks using both orbital and surface imagery.

Learning transferable data representations from abundant unlabeled data remains a central challenge in machine learning. Although numerous self-supervised learning methods have been proposed to address this challenge, a significant class of these approaches aligns the covariance or correlation matrix with the identity matrix. Despite impressive performance across various downstream tasks, these methods often suffer from biased sample risk, leading to substantial optimization shifts in mini-batch settings and complicating theoretical analysis. In this paper, we introduce a novel \underline{\bf Adv}ersarial \underline{\bf S}elf-\underline{\bf S}upervised Representation \underline{\bf L}earning (Adv-SSL) for unbiased transfer learning with no additional cost compared to its biased counterparts. Our approach not only outperforms the existing methods across multiple benchmark datasets but is also supported by comprehensive end-to-end theoretical guarantees. Our analysis reveals that the minimax optimization in Adv-SSL encourages representations to form well-separated clusters in the embedding space, provided there is sufficient upstream unlabeled data. As a result, our method achieves strong classification performance even with limited downstream labels, shedding new light on few-shot learning.

Extracting neural signals at the single motor neuron level provides an optimal control signal for neuroprosthetic applications. However, current algorithms to decompose motor units from high-density electromyography (HD-EMG) are time-consuming and inconsistent, limiting their application to controlled scenarios in a research setting. We introduce MUelim, an algorithm for efficient motor unit decomposition that uses approximate joint diagonalization with a subtractive approach to rapidly identify and refine candidate sources. The algorithm incorporates an extend-lag procedure to augment data for enhanced source separability prior to diagonalization. By systematically iterating and eliminating redundant or noisy sources, MUelim achieves high decomposition accuracy while significantly reducing computational complexity, making it well-suited for real-time applications.

Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A leading conjecture, based on the manifold hypothesis, attributes this success to their ability to adapt to low-dimensional geometric structure within the data. This work provides evidence for this conjecture, focusing on how such phenomena could result from the formulation of the learning problem through score matching. We inspect the role of implicit regularisation by investigating the effect of smoothing minimisers of the empirical score matching objective. Our theoretical and empirical results confirm that smoothing the score function--or equivalently, smoothing in the log-density domain--produces smoothing tangential to the data manifold. In addition, we show that the manifold along which the diffusion model generalises can be controlled by choosing an appropriate smoothing.

Chemical reaction prediction remains a fundamental challenge in organic chemistry, where existing machine learning models face two critical limitations: sensitivity to input permutations (molecule/atom orderings) and inadequate modeling of substructural interactions governing reactivity. These shortcomings lead to inconsistent predictions and poor generalization to real-world scenarios. To address these challenges, we propose ReaDISH, a novel reaction prediction model that learns permutation-invariant representations while incorporating interaction-aware features. It introduces two innovations: (1) symmetric difference shingle encoding, which extends the differential reaction fingerprint (DRFP) by representing shingles as continuous high-dimensional embeddings, capturing structural changes while eliminating order sensitivity; and (2) geometry-structure interaction attention, a mechanism that models intra-and inter-molecular interactions at the shingle level. Extensive experiments demonstrate that ReaDISH improves reaction prediction performance across diverse benchmarks. It shows enhanced robustness with an average improvement of 8.76\% on R$^2$ under permutation perturbations.

Recent advancements in text-to-video (T2V) diffusion models have enabled high-fidelity and realistic video synthesis. However, current T2V models often struggle to generate physically plausible content due to their limited inherent ability to accurately understand physics. We found that while the representations within T2V models possess some capacity for physics understanding, they lag significantly behind those from recent video self-supervised learning methods. To this end, we propose a novel framework called {VideoREPA}, which distills physics understanding capability from video understanding foundation models into T2V models by aligning token-level relations. This closes the physics understanding gap and enables more physics-plausible generation. Specifically, we introduce the {Token Relation Distillation (TRD) loss}, leveraging spatio-temporal alignment to provide soft guidance suitable for finetuning powerful pre-trained T2V models--a critical departure from prior representation alignment (REPA) methods. To our knowledge, VideoREPA is the first REPA method designed for finetuning T2V models and specifically for injecting physical knowledge. Empirical evaluations show that VideoREPA substantially enhances the physics commonsense of baseline method, CogVideoX, achieving significant improvement on relevant benchmarks and demonstrating a strong capacity for generating videos consistent with intuitive physics. Code and more video results are available at https://videorepa.github.io/.

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level representations. In this work, we shift the focus to links and provide the first comprehensive study of GNN expressiveness in link representation. We introduce a unifying framework, the $k_\phi$-$k_\rho$-$m$ framework, that subsumes existing message-passing link models and enables formal expressiveness comparisons. Using this framework, we derive a hierarchy of state-of-the-art methods and offer theoretical tools to analyze future architectures. To complement our analysis, we propose a synthetic evaluation protocol comprising the first benchmark specifically designed to assess link-level expressiveness. Finally, we ask: does expressiveness matter in practice? We use a graph symmetry metric that quantifies the difficulty of distinguishing links and show that while expressive models may underperform on standard benchmarks, they significantly outperform simpler ones as symmetry increases, highlighting the need for dataset-aware model selection.