相关论文: Robust Implicit Networks via Non-Euclidean Contrac…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of…

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can…

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…

Deep networks should be robust to rare events if they are to be successfully deployed in high-stakes real-world applications (e.g., self-driving cars). Here we study the capability of deep networks to recognize objects in unusual poses. We…

Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…

We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by…

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also…

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal…

Deep predictive models of neuronal activity have recently enabled several new discoveries about the selectivity and invariance of neurons in the visual cortex. These models learn a shared set of nonlinear basis functions, which are linearly…

Deep Equilibrium Models (DEQs) are an interesting class of implicit model where the model output is implicitly defined as the fixed point of a learned function. These models have been shown to outperform explicit (fixed-depth) models in…

The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like…

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…