While recent audio-visual models have demonstrated impressive performance, their robustness to distributional shifts at test-time remains not fully understood. Existing robustness benchmarks mainly focus on single modalities, making them insufficient for thoroughly assessing the robustness of audio-visual models. Motivated by real-world scenarios where shifts can occur $\textit{simultaneously}$ in both audio and visual modalities, we introduce $\texttt{AVROBUSTBENCH}$, a comprehensive benchmark designed to evaluate the test-time robustness of audio-visual recognition models. $\texttt{AVROBUSTBENCH}$ comprises four audio-visual benchmark datasets, $\texttt{AUDIOSET-2C}$, $\texttt{VGGSOUND-2C}$, $\texttt{KINETICS-2C}$, and $\texttt{EPICKITCHENS-2C}$, each incorporating 75 bimodal audio-visual corruptions that are $\textit{co-occurring}$ and $\textit{correlated}$. Through extensive evaluations, we observe that state-of-the-art supervised and self-supervised audio-visual models exhibit declining robustness as corruption severity increases. Furthermore, online test-time adaptation (TTA) methods, on $\texttt{VGGSOUND-2C}$ and $\texttt{KINETICS-2C}$, offer minimal improvements in performance under bimodal corruptions. We further propose $\texttt{AV2C}$, a simple TTA approach enabling on-the-fly cross-modal fusion by penalizing high-entropy samples, which achieves improvements on $\texttt{VGGSOUND-2C}$. We hope that $\texttt{AVROBUSTBENCH}$ will steer the development of more effective and robust audio-visual TTA approaches. Our code is available $\href{https://github.com/sarthaxxxxx/AV-C-Robustness-Benchmark}{here}$.

Convolutional neural networks (CNNs) have become widely adopted in gravitational wave (GW) detection pipelines due to their ability to automatically learn hierarchical features from raw strain data. However, the physical meaning of these learned features remains underexplored, limiting the interpretability of such models. In this work, we propose a hybrid architecture that combines a CNN-based feature extractor with a random forest (RF) classifier to improve both detection performance and interpretability. Unlike prior approaches that directly connect classifiers to CNN outputs, our method introduces four physically interpretable metrics - variance, signal-to-noise ratio (SNR), waveform overlap, and peak amplitude - computed from the final convolutional layer. These are jointly used with the CNN output in the RF classifier to enable more informed decision boundaries. Tested on long-duration strain datasets, our hybrid model outperforms a baseline CNN model, achieving a relative improvement of 21\% in sensitivity at a fixed false alarm rate of 10 events per month. Notably, it also shows improved detection of low-SNR signals (SNR $\le$ 10), which are especially vulnerable to misclassification in noisy environments. Feature attribution via the RF model reveals that both CNN-extracted and handcrafted features contribute significantly to classification decisions, with learned variance and CNN outputs ranked among the most informative. These findings suggest that physically motivated post-processing of CNN feature maps can serve as a valuable tool for interpretable and efficient GW detection, bridging the gap between deep learning and domain knowledge.

The growing adoption of spectrum-aware matrix-valued optimizers such as Muon and Shampoo in deep learning motivates a systematic study of their generalization properties and, in particular, when they might outperform competitive algorithms. We approach this question by introducing appropriate simplifying abstractions as follows: First, we use imbalanced data as a testbed. Second, we study the canonical form of such optimizers, which is Spectral Gradient Descent (SpecGD) -- each update step is $UV^T$ where $UΣV^T$ is the truncated SVD of the gradient. Third, within this framework we identify a canonical setting for which we precisely quantify when SpecGD outperforms vanilla Euclidean GD. For a Gaussian mixture data model and both linear and bilinear models, we show that unlike GD, which prioritizes learning dominant principal components of the data first, SpecGD learns all principal components of the data at equal rates. We demonstrate how this translates to a growing gap in balanced accuracy favoring SpecGD early in training and further show that the gap remains consistent even when the GD counterpart uses adaptive step-sizes via normalization. By extending the analysis to deep linear models, we show that depth amplifies these effects. We empirically verify our theoretical findings on a variety of imbalanced datasets. Our experiments compare practical variants of spectral methods, like Muon and Shampoo, against their Euclidean counterparts and Adam. The results validate our findings that these spectral optimizers achieve superior generalization by promoting a more balanced learning of the data's underlying components.

Physics-informed statistical learning (PISL) integrates empirical data with physical knowledge to enhance the statistical performance of estimators. While PISL methods are widely used in practice, a comprehensive theoretical understanding of how informed regularization affects statistical properties is still missing. Specifically, two fundamental questions have yet to be fully addressed: (1) what is the trade-off between considering soft penalties versus hard constraints, and (2) what is the statistical gain of incorporating physical knowledge compared to purely data-driven empirical error minimisation. In this paper, we address these questions for PISL in convex classes of functions under physical knowledge expressed as linear equations by developing appropriate complexity dependent error rates based on the small-ball method. We show that, under suitable assumptions, (1) the error rates of physics-informed estimators are comparable to those of hard constrained empirical error minimisers, differing only by constant terms, and that (2) informed penalization can effectively reduce model complexity, akin to dimensionality reduction, thereby improving learning performance. This work establishes a theoretical framework for evaluating the statistical properties of physics-informed estimators in convex classes of functions, contributing to closing the gap between statistical theory and practical PISL, with potential applications to cases not yet explored in the literature.

Centered kernel alignment (CKA) is a popular metric for comparing representations, determining equivalence of networks, and neuroscience research. However, CKA does not account for the underlying manifold and relies on numerous heuristics that cause it to behave differently at different scales of data. In this work, we propose Manifold approximated Kernel Alignment (MKA), which incorporates manifold geometry into the alignment task. We derive a theoretical framework for MKA. We perform empirical evaluations on synthetic datasets and real-world examples to characterize and compare MKA to its contemporaries. Our findings suggest that manifold-aware kernel alignment provides a more robust foundation for measuring representations, with potential applications in representation learning.

We investigate the role of network architecture in shaping the inductive biases of modern score-based generative models. To this end, we introduce the Score Anisotropy Directions (SADs), architecture-dependent directions that reveal how different networks preferentially capture data structure. Our analysis shows that SADs form adaptive bases aligned with the architecture's output geometry, providing a principled way to predict generalization ability in score models prior to training. Through both synthetic data and standard image benchmarks, we demonstrate that SADs reliably capture fine-grained model behavior and correlate with downstream performance, as measured by Wasserstein metrics. Our work offers a new lens for explaining and predicting directional biases of generative models. The only difference is the choice of subspace: the left "sphere" lies in a subspace aligned with the network's geometry, G Despite identical setups, their quality differs consistently across repeated trials, suggesting that alignment with architectural geometry controls generalization. Neural networks generalize through inductive biases, i.e., biases that guide learning beyond training data (Goyal & Bengio, 2020; Wilson & Izmailov, 2020).

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

The Hierarchical Reasoning Model (HRM) has impressive reasoning abilities given its small size, but has only been applied to supervised, static, fully-observable problems. One of HRM's strengths is its ability to adapt its computational effort to the difficulty of the problem. However, in its current form it cannot integrate and reuse computation from previous time-steps if the problem is dynamic, uncertain or partially observable, or be applied where the correct action is undefined, characteristics of many real-world problems. This paper presents HRM-Agent, a variant of HRM trained using only reinforcement learning. We show that HRM can learn to navigate to goals in dynamic and uncertain maze environments. Recent work suggests that HRM's reasoning abilities stem from its recurrent inference process. We explore the dynamics of the recurrent inference process and find evidence that it is successfully reusing computation from earlier environment time-steps.

Recent interpretability work on large language models (LLMs) has been increasingly dominated by a feature-discovery approach with the help of proxy modules. Then, the quality of features learned by, e.g., sparse auto-encoders (SAEs), is evaluated. This paradigm naturally raises a critical question: do such learned features have better properties than those already represented within the original model parameters, and unfortunately, only a few studies have made such comparisons systematically so far. In this work, we revisit the interpretability of feature vectors stored in feed-forward (FF) layers, given the perspective of FF as key-value memories, with modern interpretability benchmarks. Our extensive evaluation revealed that SAE and FFs exhibits a similar range of interpretability, although SAEs displayed an observable but minimal improvement in some aspects. Furthermore, in certain aspects, surprisingly, even vanilla FFs yielded better interpretability than the SAEs, and features discovered in SAEs and FFs diverged. These bring questions about the advantage of SAEs from both perspectives of feature quality and faithfulness, compared to directly interpreting FF feature vectors, and FF key-value parameters serve as a strong baseline in modern interpretability research.

Coordinate denoising has emerged as a promising method for 3D molecular pretraining due to its theoretical connection to learning molecular force field. However, existing denoising methods rely on oversimplied molecular dynamics that assume atomic motions to be isotropic and homoscedastic. To address these limitations, we propose a novel denoising framework AniDS: Anisotropic Variational Autoencoder for 3D Molecular Denoising. AniDS introduces a structure-aware anisotropic noise generator that can produce atom-specific, full covariance matrices for Gaussian noise distributions to better reflect directional and structural variability in molecular systems. These covariances are derived from pairwise atomic interactions as anisotropic corrections to an isotropic base. Our design ensures that the resulting covariance matrices are symmetric, positive semi-definite, and SO(3)-equivariant, while providing greater capacity to model complex molecular dynamics. Extensive experiments show that AniDS outperforms prior isotropic and homoscedastic denoising models and other leading methods on the MD17 and OC22 benchmarks, achieving average relative improvements of 8.9% and 6.2% in force prediction accuracy. Our case study on a crystal and molecule structure shows that AniDS adaptively suppresses noise along the bonding direction, consistent with physicochemical principles. Our code is available at https://github.com/ZeroKnighting/AniDS.