Related papers: On Optimizing Back-Substitution Methods for Neural…

Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…

Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…

Application of deep neural networks to medical imaging tasks has in some sense become commonplace. Still, a "thorn in the side" of the deep learning movement is the argument that deep networks are prone to overfitting and are thus unable to…

Branch-and-bound with preactivation splitting has been shown highly effective for deterministic verification of neural networks. In this paper, we extend this framework to the probabilistic setting. We propose BaB-prob that iteratively…

Pruning neural networks has proven to be a successful approach to increase the efficiency and reduce the memory storage of deep learning models without compromising performance. Previous literature has shown that it is possible to achieve a…

Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions…

Neural network verification mainly focuses on local robustness properties, which can be checked by bounding the image (set of outputs) of a given input set. However, often it is important to know whether a given property holds globally for…

Deep neural networks are known to be overconfident when applied to out-of-distribution (OOD) inputs which clearly do not belong to any class. This is a problem in safety-critical applications since a reliable assessment of the uncertainty…

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 aims to enhance the computational efficiency of safety verification of neural network control systems by developing a guaranteed neural network model reduction method. First, a concept of model reduction precision is proposed to…

We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. These…

Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…

The increasing size of recently proposed Neural Networks makes it hard to implement them on embedded devices, where memory, battery and computational power are a non-trivial bottleneck. For this reason during the last years network…

This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…

This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded…

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,…

Backpropagation through nonlinear neurons is an outstanding challenge to the field of optical neural networks and the major conceptual barrier to all-optical training schemes. Each neuron is required to exhibit a directionally dependent…

"To Appear in Theory and Practice of Logic Programming (TPLP)" This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the…

Training neural networks with verifiable robustness guarantees is challenging. Several existing approaches utilize linear relaxation based neural network output bounds under perturbation, but they can slow down training by a factor of…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…