相关论文: Universal approximation property of invertible neu…

A challenging problem in many modern machine learning tasks is to process weight-space features, i.e., to transform or extract information from the weights and gradients of a neural network. Recent works have developed promising…

Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power…

In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…

Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…

Implicit Neural Representations (INRs) are a novel paradigm for signal representation that have attracted considerable interest for image compression. INRs offer unprecedented advantages in signal resolution and memory efficiency, enabling…

Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a…

We present Wasserstein introspective neural networks (WINN) that are both a generator and a discriminator within a single model. WINN provides a significant improvement over the recent introspective neural networks (INN) method by enhancing…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

Deep convolutional neural networks (DCNNs) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases. Their architecture is somewhat similar to that of the human…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

Implicit Neural Representations (INRs) have emerged in the last few years as a powerful tool to encode continuously a variety of different signals like images, videos, audio and 3D shapes. When applied to 3D shapes, INRs allow to overcome…

In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential…

Recently it has been shown that using diffusion models for inverse problems can lead to remarkable results. However, these approaches require a closed-form expression of the degradation model and can not support complex degradations. To…

Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional…

Graph neural networks (GNNs) have various practical applications, such as drug discovery, recommendation engines, and chip design. However, GNNs lack transparency as they cannot provide understandable explanations for their predictions. To…

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…