Related papers: Branch and Bound for Piecewise Linear Neural Netwo…

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…

Formal verification of neural networks is essential for their deployment in safety-critical areas. Many available formal verification methods have been shown to be instances of a unified Branch and Bound (BaB) formulation. We propose a…

Branch-and-bound (BaB) is among the most effective techniques for neural network (NN) verification. However, existing works on BaB for NN verification have mostly focused on NNs with piecewise linear activations, especially ReLU networks.…

Many available formal verification methods have been shown to be instances of a unified Branch-and-Bound (BaB) formulation. We propose a novel machine learning framework that can be used for designing an effective branching strategy as well…

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…

Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…

Formal verification is a rigorous approach that can provably ensure the quality of neural networks, and to date, Branch and Bound (BaB) is the state-of-the-art that performs verification by splitting the problem as needed and applying…

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce…

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…

Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such…

Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world…

State-of-the-art neural network verifiers are fundamentally based on one of two paradigms: either encoding the whole verification problem via tight multi-neuron convex relaxations or applying a Branch-and-Bound (BaB) procedure leveraging…

Formal verification of neural networks (NNs) is a challenging and important problem. Existing efficient complete solvers typically require the branch-and-bound (BaB) process, which splits the problem domain into sub-domains and solves each…

In this paper, we consider the computational complexity of formally verifying the behavior of Rectified Linear Unit (ReLU) Neural Networks (NNs), where verification entails determining whether the NN satisfies convex polytopic…

The use of neural networks as function approximators has enabled many advances in reinforcement learning (RL). The generalization power of neural networks combined with advances in RL algorithms has reignited the field of artificial…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

Deep learning has emerged as an effective approach for creating modern software systems, with neural networks often surpassing hand-crafted systems. Unfortunately, neural networks are known to suffer from various safety and security issues.…

This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…

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…

The vulnerability of neural networks to adversarial perturbations has necessitated formal verification techniques that can rigorously certify the quality of neural networks. As the state-of-the-art, branch and bound (BaB) is a…