Related papers: Bounding the Complexity of Formally Verifying Neur…

Recent theoretical works on over-parameterized neural nets have focused on two aspects: optimization and generalization. Many existing works that study optimization and generalization together are based on neural tangent kernel and require…

Deep Neural Networks (DNN) have emerged as an effective approach to tackling real-world problems. However, like human-written software, DNNs are susceptible to bugs and attacks. This has generated significant interests in developing…

We point out that (continuous or discontinuous) piecewise linear functions on a convex polytope mesh can be represented by two-hidden-layer ReLU neural networks in a weak sense. In addition, the numbers of neurons of the two hidden layers…

The problem of verifying multi-threaded execution against the memory consistency model of a processor is known to be an NP hard problem. However polynomial time algorithms exist that detect almost all failures in such execution. These are…

We describe a method for verifying the output of a deep neural network for medical image segmentation that is robust to several classes of random as well as worst-case perturbations i.e. adversarial attacks. This method is based on a…

A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU networks, which reduces…

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…

The superior performance of Deep Neural Networks (DNNs) has led to their application in various aspects of human life. Safety-critical applications are no exception and impose rigorous reliability requirements on DNNs. Quantized Neural…

Graph neural networks (GNNs) are the predominant architecture for learning over graphs. As with any machine learning model, an important issue is the detection of attacks, where an adversary can change the output with a small perturbation…

Neural networks (NNs) have been extremely successful across many tasks in machine learning. Quantization of NN weights has become an important topic due to its impact on their energy efficiency, inference time and deployment on hardware.…

Neural networks are ubiquitous. However, they are often sensitive to small input changes. Hence, to prevent unexpected behavior in safety-critical applications, their formal verification -- a notoriously hard problem -- is necessary. Many…

Theorem proving is fundamental to program verification, where the automated proof of Verification Conditions (VCs) remains a primary bottleneck. Real-world program verification frequently encounters hard VCs that existing Automated Theorem…

Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN…

Formal verification has emerged as a powerful approach to ensure the safety and reliability of deep neural networks. However, current verification tools are limited to only a handful of properties that can be expressed as first-order…

Training deep neural networks is a challenging non-convex optimization problem. Recent work has proven that the strong duality holds (which means zero duality gap) for regularized finite-width two-layer ReLU networks and consequently…

Verifiable computing (VC) has gained prominence in decentralized machine learning systems, where resource-intensive tasks like deep neural network (DNN) inference are offloaded to external participants due to blockchain limitations. This…

Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying…

Formal certification of Neural Networks (NNs) is crucial for ensuring their safety, fairness, and robustness. Unfortunately, on the one hand, sound and complete certification algorithms of ReLU-based NNs do not scale to large-scale NNs. On…

We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized…

We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions. Additionally, as in…