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Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation…
Robust learning is an important issue in Scientific Machine Learning (SciML). There are several works in the literature addressing this topic. However, there is an increasing demand for methods that can simultaneously consider all the…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
It is well-known that classifiers are vulnerable to adversarial perturbations. To defend against adversarial perturbations, various certified robustness results have been derived. However, existing certified robustnesses are limited to…
Machine learning-based static malware detectors remain vulnerable to adversarial evasion techniques, such as metamorphic engine mutations. To address this vulnerability, we propose a certifiably robust malware detection framework based on…
While deep learning has significantly advanced accident anticipation, the robustness of these safety-critical systems against real-world perturbations remains a major challenge. We reveal that state-of-the-art models like CRASH, despite…
Generations from large language models (LLMs) can be improved by sampling and scoring multiple solutions to select a final answer. Current "sample and select" methods such as self-consistency (SC) rely on majority voting to score answers.…
A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…
Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional setting, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates…
Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is…
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…
This paper considers smooth strongly convex and strongly concave (SC-SC) stochastic saddle point (SSP) problems. Suppose there is an arbitrary oracle that in expectation returns an $\epsilon$-solution in the sense of certain gaps, which can…
Stable distributions provide a flexible framework for modeling heavy-tailed and skewed data, with the stability index $\alpha$ quantifying tail heaviness. We propose a new semiparametric estimator for $\alpha$ that leverages the two-sum…
Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…
Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the…
Certifying the robustness of a graph-based machine learning model poses a critical challenge for safety. Current robustness certificates for graph classifiers guarantee output invariance with respect to the total number of node pair flips…
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Feature attribution methods (FAs) are popular approaches for providing insights into the model reasoning process of making predictions. The more faithful a FA is, the more accurately it reflects which parts of the input are more important…
Neural cellular automata (NCA) provide a lightweight alternative to encoder-decoder segmentation networks. However, it can be difficult to decide when a prediction should be trusted. Here, we study uncertainty estimation for NCA-based…