相关论文: Expressivity of Quadratic Neural ODEs

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Early-exit neural networks enable adaptive computation by allowing confident predictions to exit at intermediate layers, achieving 2-8$\times$ inference speedup. Despite widespread deployment, their generalization properties lack…

Deep reinforcement learning techniques have demonstrated superior performance in a wide variety of environments. As improvements in training algorithms continue at a brisk pace, theoretical or empirical studies on understanding what these…

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models. It yields an optimistic sample size that quantifies the smallest possible sample size to fit/recover a target function using a…

Neural Network Pruning has been established as driving force in the exploration of memory and energy efficient solutions with high throughput both during training and at test time. In this paper, we introduce a novel criterion for model…

Ordinary differential equations (ODEs) are widely used to model complex dynamics that arises in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally very difficult. In…

Derivative training is an established method that can significantly increase the accuracy of neural networks in certain low-dimensional tasks. In this paper, we extend this improvement to an illustrative image analysis problem:…

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…

Mathematical expressions (MEs) have complex two-dimensional structures in which symbols can be present at any nested depth like superscripts, subscripts, above, below etc. As MEs are represented using LaTeX format, several text retrieval…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…

Quantum neural networks (QNNs) require an efficient training algorithm to achieve practical quantum advantages. A promising approach is gradient-based optimization, where gradients are estimated by quantum measurements. However, QNNs…

The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. Under a signal processing perspective, in this paper we…

A deep equilibrium model uses implicit layers, which are implicitly defined through an equilibrium point of an infinite sequence of computation. It avoids any explicit computation of the infinite sequence by finding an equilibrium point…

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…

Quantized deep neural networks (QDNNs) are necessary for low-power, high throughput, and embedded applications. Previous studies mostly focused on developing optimization methods for the quantization of given models. However, quantization…

Neural networks trained with standard objectives exhibit behaviors characteristic of probabilistic inference: soft clustering, prototype specialization, and Bayesian uncertainty tracking. These phenomena appear across architectures -- in…

Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…