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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 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.…
Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…
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…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…
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…
Recent works have shown that interval bound propagation (IBP) can be used to train verifiably robust neural networks. Reseachers observe an intriguing phenomenon on these IBP trained networks: CROWN, a bounding method based on tight linear…
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN…
Quantizing the weights of a neural network has two steps: (1) Finding a good low bit-complexity representation for weights (which we call the quantization grid) and (2) Rounding the original weights to values in the quantization grid. In…
Neural networks have become critical components of reactive systems in various domains within computer science. Despite their excellent performance, using neural networks entails numerous risks that stem from our lack of ability to…
Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before deployment, which are…
Formal verification of neural networks is essential before their deployment in safety-critical applications. However, existing methods for formally verifying neural networks are not yet scalable enough to handle practical problems under…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike…
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…
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…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
We present two improved randomized neural network methods, namely RNN-Scaling and RNN-Boundary-Processing (RNN-BP) methods, for solving elliptic equations such as the Poisson equation and the biharmonic equation. The RNN-Scaling method…
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…