Related papers: Why Smooth Stability Assumptions Fail for ReLU Lea…

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence.…

The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural…

Machine learning from explanations (MLX) is an approach to learning that uses human-provided explanations of relevant or irrelevant features for each input to ensure that model predictions are right for the right reasons. Existing MLX…

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…

Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…

Despite a great deal of research, it is still not well-understood why trained neural networks are highly vulnerable to adversarial examples. In this work we focus on two-layer neural networks trained using data which lie on a low…

Linear classifiers and leaky ReLU networks trained by gradient flow on the logistic loss have an implicit bias towards solutions which satisfy the Karush--Kuhn--Tucker (KKT) conditions for margin maximization. In this work we establish a…

Explanation methods for machine learning models tend not to provide any formal guarantees and may not reflect the underlying decision-making process. In this work, we analyze stability as a property for reliable feature attribution methods.…

Large language models (LLMs) are increasingly deployed with hierarchical instruction schemes, where certain instructions (e.g., system-level directives) are expected to take precedence over others (e.g., user messages). Yet, we lack a…

It is widely recognized that reinforcement learning (RL) fine-tuning of large language models often leads to diversity collapse, where outputs lack variety. Prior work has proposed a range of heuristics to counteract this effect, but these…

We address hallucination detection in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) by framing the problem through the lens of dynamical systems stability theory. Rather than treating hallucination as a…

The topic of nonparametric estimation of smooth boundaries is extensively studied in the conventional setting where pairs of single covariate and response variable are observed. However, this traditional setting often suffers from the cost…

Since statistical guarantees for neural networks are usually restricted to global optima of intricate objective functions, it is unclear whether these theories explain the performances of actual outputs of neural network pipelines. The goal…

We study the loss surface of a feed-forward neural network with ReLU non-linearities, regularized with weight decay. We show that the regularized loss function is piecewise strongly convex on an important open set which contains, under some…

Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…

This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…

Deep neural networks are vulnerable to adversarial attacks. Recent studies about adversarial robustness focus on the loss landscape in the parameter space since it is related to optimization and generalization performance. These studies…