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Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

Machine Learning · Computer Science 2023-10-26 Tsai Hor Chan , Kin Wai Lau , Jiajun Shen , Guosheng Yin , Lequan Yu

We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. First, we propose novel bounding algorithms based on Lagrangian Decomposition. Previous works have used…

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,…

Machine Learning · Computer Science 2024-12-31 Zongxin Liu , Zhe Zhao , Fu Song , Jun Sun , Pengfei Yang , Xiaowei Huang , Lijun Zhang

We study the problem of formal verification of Binarized Neural Networks (BNN), which have recently been proposed as a energy-efficient alternative to traditional learning networks. The verification of BNNs, using the reduction to hardware…

Software Engineering · Computer Science 2018-01-22 Chih-Hong Cheng , Georg Nührenberg , Chung-Hao Huang , Harald Ruess

The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…

Artificial Intelligence · Computer Science 2018-05-23 Rudy Bunel , Ilker Turkaslan , Philip H. S. Torr , Pushmeet Kohli , M. Pawan Kumar

Neural network verification aims to provide provable bounds for the output of a neural network for a given input range. Notable prior works in this domain have either generated bounds using abstract domains, which preserve some dependency…

Machine Learning · Computer Science 2022-10-18 Matt Jordan , Jonathan Hayase , Alexandros G. Dimakis , Sewoong Oh

Fairness is crucial for neural networks which are used in applications with important societal implication. Recently, there have been multiple attempts on improving fairness of neural networks, with a focus on fairness testing (e.g.,…

Machine Learning · Computer Science 2021-07-20 Bing Sun , Jun Sun , Ting Dai , Lijun Zhang

Robust machine learning models with accurately calibrated uncertainties are crucial for safety-critical applications. Probabilistic machine learning and especially the Bayesian formalism provide a systematic framework to incorporate…

Machine Learning · Computer Science 2022-10-11 Sumegha Premchandar , Sandeep Madireddy , Sanket Jantre , Prasanna Balaprakash

Bayesian neural networks and deep ensemble methods have been proposed for uncertainty quantification; however, they are computationally intensive and require large storage. By utilizing a single deterministic model, we can solve the above…

Machine Learning · Computer Science 2025-08-04 Yaxin Ma , Benjamin Colburn , Jose C. Principe

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…

Numerical Analysis · Computer Science 2013-03-19 Bojana V. Rosić , Anna Kučerová , Jan Sýkora , Oliver Pajonk , Alexander Litvinenko , Hermann G. Matthies

This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts,…

Machine Learning · Computer Science 2025-04-16 Jianting Yang , Srećko Ðurašinović , Jean-Bernard Lasserre , Victor Magron , Jun Zhao

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches…

Artificial Intelligence · Computer Science 2025-03-11 Souradeep Dutta , Michele Caprio , Vivian Lin , Matthew Cleaveland , Kuk Jin Jang , Ivan Ruchkin , Oleg Sokolsky , Insup Lee

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security,…

Machine Learning · Computer Science 2021-10-06 Aws Albarghouthi

Neural network verifiers aim to provide formal guarantees on model behavior, but existing verification benchmarks are fundamentally limited by their lack of ground-truth labels. As a result, verifier evaluation relies on indirect…

Machine Learning · Computer Science 2026-05-19 David Troxell , Yulia Alexandr , Sofia Hunt , Stephanie Lei , Guido Montúfar

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

Neural networks serve as effective controllers in a variety of complex settings due to their ability to represent expressive policies. The complex nature of neural networks, however, makes their output difficult to verify and predict, which…

Artificial Intelligence · Computer Science 2021-10-22 Sydney M. Katz , Kyle D. Julian , Christopher A. Strong , Mykel J. Kochenderfer

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Machine Learning · Computer Science 2025-09-30 Frederik Baymler Mathiesen , Nikolaus Vertovec , Francesco Fabiano , Luca Laurenti , Alessandro Abate

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii)…

Machine Learning · Computer Science 2022-03-09 Melih Kandemir , Abdullah Akgül , Manuel Haussmann , Gozde Unal

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the…

Machine Learning · Computer Science 2023-06-08 Victor Dheur , Souhaib Ben Taieb