Related papers: Bounding the Complexity of Formally Verifying Neur…
The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…
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,…
Inspired by recent successes with parallel optimization techniques for solving Boolean satisfiability, we investigate a set of strategies and heuristics that aim to leverage parallel computing to improve the scalability of neural network…
Formal verification of transformers has become increasingly important due to their widespread deployment in safety-critical applications. Compared to classic neural networks, the inferences of transformers involve highly complex…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for…
Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a…
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…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
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,…
Large language models (LLMs) facilitate the development of autonomous agents. As a core component of such agents, task planning aims to decompose complex natural language requests into concrete, solvable sub-tasks. Since LLM-generated plans…
Theoretical analyses of Empirical Risk Minimization (ERM) are standardly framed within the Real-RAM model of computation. In this setting, training even simple neural networks is known to be $\exists \mathbb{R}$-complete -- a complexity…
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)…
Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus,…
In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear programming (LP) and semidefinite programming (SDP)…
A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these…
Neural networks can learn complex, non-convex functions, and it is challenging to guarantee their correct behavior in safety-critical contexts. Many approaches exist to find failures in networks (e.g., adversarial examples), but these…
Consider the following fundamental learning problem: given input examples $x \in \mathbb{R}^d$ and their vector-valued labels, as defined by an underlying generative neural network, recover the weight matrices of this network. We consider…
Neural networks have emerged as essential components in safety-critical applications -- these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is…
Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting…