相关论文: Globally Injective ReLU Networks

We study finite sample expressivity, i.e., memorization power of ReLU networks. Recent results require $N$ hidden nodes to memorize/interpolate arbitrary $N$ data points. In contrast, by exploiting depth, we show that 3-layer ReLU networks…

Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…

We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…

Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is…

We study the problem of training deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

In recent years, inductive graph embedding models, \emph{viz.}, graph neural networks (GNNs) have become increasingly accurate at link prediction (LP) in online social networks. The performance of such networks depends strongly on the input…

We prove that the set of functions representable by ReLU neural networks with integer weights strictly increases with the network depth while allowing arbitrary width. More precisely, we show that $\lceil\log_2(n)\rceil$ hidden layers are…

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…

We present the first acquisition-agnostic diffusion generative model for Magnetic Resonance Imaging (MRI) in the neonatal intensive care unit (NICU) to solve a range of inverse problems for shortening scan time and improving motion…

We study the least-square regression problem with a two-layer fully-connected neural network, with ReLU activation function, trained by gradient flow. Our first result is a generalization result, that requires no assumptions on the…

It is a significant challenge to predict the network topology from a small amount of dynamical observations. Different from the usual framework of the node-based reconstruction, two optimization approaches (i.e., the global and partitioned…

A common method in training neural networks is to initialize all the weights to be independent Gaussian vectors. We observe that by instead initializing the weights into independent pairs, where each pair consists of two identical Gaussian…

Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However,…

For artificial deep neural networks, we prove expression rates for analytic functions $f:\mathbb{R}^d\to\mathbb{R}$ in the norm of $L^2(\mathbb{R}^d,\gamma_d)$ where $d\in {\mathbb{N}}\cup\{ \infty \}$. Here $\gamma_d$ denotes the Gaussian…

We formalize and interpret the geometric structure of $d$-dimensional fully connected ReLU layers in neural networks. The parameters of a ReLU layer induce a natural partition of the input domain, such that the ReLU layer can be…

Estimating causal effects from observational network data is a significant but challenging problem. Existing works in causal inference for observational network data lack an analysis of the generalization bound, which can theoretically…

Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions…

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…

We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…

The training of neural networks requires tedious and often manual tuning of the network architecture. We propose a systematic approach to inserting new layers during the training process. Our method eliminates the need to choose a fixed…