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We introduce a framework for robust uncertainty quantification in situations where labeled training data are corrupted, through noisy or missing labels. We build on conformal prediction, a statistical tool for generating prediction sets…

Conformal Prediction (CP) is a popular uncertainty quantification method that provides distribution-free, statistically valid prediction sets, assuming that training and test data are exchangeable. In such a case, CP's prediction sets are…

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…

We consider the stochastic optimization problem with smooth but not necessarily convex objectives in the heavy-tailed noise regime, where the stochastic gradient's noise is assumed to have bounded $p$th moment ($p\in(1,2]$). Zhang et al.…

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence,…

Robustness and counterfactual bias are usually evaluated on a test dataset. However, are these evaluations robust? If the test dataset is perturbed slightly, will the evaluation results keep the same? In this paper, we propose a "double…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

This paper presents four theoretical contributions that improve the usability of risk certificates for neural networks based on PAC-Bayes bounds. First, two bounds on the KL divergence between Bernoulli distributions enable the derivation…

In this work, we propose a new bounded arithmetic theory, denoted $APX_1$, designed to formalize a broad class of probabilistic arguments commonly used in theoretical computer science. Under plausible assumptions, $APX_1$ is strictly weaker…

Formal verification of neural networks is essential before their deployment in safety-critical applications. However, existing methods for formally verifying neural networks are not yet scalable enough to handle practical problems under…

Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…

Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often…

Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…

Formal verification provides critical security assurances for neural networks, yet its practical application suffers from the long verification time. This work introduces a novel method for training verification-friendly neural networks,…

This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability…

We motivate weakly supervised learning as an effective learning paradigm for problems where curating perfectly annotated datasets is expensive and may require domain expertise such as fine-grained classification. We focus on Partial Label…

Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper…

This short study presents an opportunistic approach to a (more) reliable validation method for prediction uncertainty average calibration. Considering that variance-based calibration metrics (ZMS, NLL, RCE...) are quite sensitive to the…

Reinforcement Learning (RL) for Large Language Models (LLMs) faces a fundamental tension: the numerical divergence between high-throughput inference engines and numerically precise training engines. Although these systems share the same…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…