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Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…
With the rapid development of deep learning, the sizes of neural networks become larger and larger so that the training and inference often overwhelm the hardware resources. Given the fact that neural networks are often over-parameterized,…
Although modern deep learning often relies on massive over-parameterized models, the fundamental interplay between capacity, sparsity, and robustness in low-capacity networks remains a vital area of study. We introduce a controlled…
Adversarial examples pose a security threat to many critical systems built on neural networks (such as face recognition systems, and self-driving cars). While many methods have been proposed to build robust models, how to build certifiably…
The Lipschitz constant of neural networks has been established as a key quantity to enforce the robustness to adversarial examples. In this paper, we tackle the problem of building $1$-Lipschitz Neural Networks. By studying Residual…
This work investigates a novel approach to boost adversarial robustness and generalization by incorporating structural prior into the design of deep learning models. Specifically, our study surprisingly reveals that existing dictionary…
Neural Ordinary Differential Equations (NODEs) are a novel neural architecture, built around initial value problems with learned dynamics which are solved during inference. Thought to be inherently more robust against adversarial…
Lipschitz bounded neural networks are certifiably robust and have a good trade-off between clean and certified accuracy. Existing Lipschitz bounding methods train from scratch and are limited to moderately sized networks (< 6M parameters).…
This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the…
Despite the efficacy on a variety of computer vision tasks, deep neural networks (DNNs) are vulnerable to adversarial attacks, limiting their applications in security-critical systems. Recent works have shown the possibility of generating…
Graph neural networks (GNNs) have recently gained much attention for node and graph classification tasks on graph-structured data. However, multiple recent works showed that an attacker can easily make GNNs predict incorrectly via…
Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high…
Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable…
We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$,…
The robustness of deep neural networks (DNNs) against adversarial attacks has been studied extensively in hopes of both better understanding how deep learning models converge and in order to ensure the security of these models in…
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…
Deep neural networks have achieved impressive performance in many applications but their large number of parameters lead to significant computational and storage overheads. Several recent works attempt to mitigate these overheads by…
Channel estimation is crucial in wireless communications. However, in many papers neural networks are frequently tested by training and testing on one example channel or similar channels. This is because data-driven methods often degrade on…
Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…
Deep neural networks have proven to be extremely powerful, however, they are also vulnerable to adversarial attacks which can cause hazardous incorrect predictions in safety-critical applications. Certified robustness via randomized…