Related papers: Fast and Complete: Enabling Complete Neural Networ…

As neural networks become more integrated into the systems that we depend on for transportation, medicine, and security, it becomes increasingly important that we develop methods to analyze their behavior to ensure that they are safe to use…

The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a…

Solving mixed-integer nonlinear programs (MINLPs) typically relies on constructing relaxations that are easier to tackle than the original problem. Recently, global parabolic (PARA) relaxations were introduced, featuring separable quadratic…

Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations.…

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs)…

Until recently, LP relaxations have played a limited role in the design of approximation algorithms for the Steiner tree problem. In 2010, Byrka et al. presented a ln(4)+epsilon approximation based on a hypergraphic LP relaxation, but…

Implicit neural representations have become pivotal in robotic perception, enabling robots to comprehend 3D environments from 2D images. Given a set of camera poses and associated images, the models can be trained to synthesize novel,…

The next release problem (NRP) aims to effectively select software requirements in order to acquire maximum customer profits. As an NP-hard problem in software requirement engineering, NRP lacks efficient approximate algorithms for large…

Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification problem seeks to determine whether a small perturbation of a…

Motivated by the philosophy and phenomenal success of compressed sensing, the problem of reconstructing a matrix from a sampling of its entries has attracted much attention recently. Such a problem can be viewed as an information-theoretic…

As a new programming paradigm, deep neural networks (DNNs) have been increasingly deployed in practice, but the lack of robustness hinders their applications in safety-critical domains. While there are techniques for verifying DNNs with…

Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Modern neural network training relies on piece-wise (sub-)differentiable functions in order to use backpropagation to update model parameters. In this work, we introduce a novel method to allow simple non-differentiable functions at…

Recently, cutting-plane methods such as GCP-CROWN have been explored to enhance neural network verifiers and made significant advances. However, GCP-CROWN currently relies on generic cutting planes (cuts) generated from external mixed…

Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…

Traditional logic programming relies on symbolic computation on the CPU, which can limit performance for large-scale inference tasks. Recent advances in GPU hardware enable high-throughput matrix operations, motivating a shift toward…

Deep neural networks are increasingly being used as controllers for safety-critical systems. Because neural networks are opaque, certifying their correctness is a significant challenge. To address this issue, several neural network…

LLM training is scaled up to 10Ks of GPUs by a mix of data-(DP) and model-parallel (MP) execution. Critical to achieving efficiency is tensor-parallel (TP; a form of MP) execution within tightly-coupled subsets of GPUs, referred to as a…

Neural networks have demonstrated considerable success on a wide variety of real-world problems. However, networks trained only to optimize for training accuracy can often be fooled by adversarial examples - slightly perturbed inputs that…