Related papers: Dying ReLU and Initialization: Theory and Numerica…

This paper presents a novel framework for understanding trained ReLU networks as random, affine functions, where the randomness is induced by the distribution over the inputs. By characterizing the probability distribution of the network's…

Rectifier neuron units (ReLUs) have been widely used in deep convolutional networks. An ReLU converts negative values to zeros, and does not change positive values, which leads to a high sparsity of neurons. In this work, we first examine…

The large number of ReLU non-linearity operations in existing deep neural networks makes them ill-suited for latency-efficient private inference (PI). Existing techniques to reduce ReLU operations often involve manual effort and sacrifice…

ReLU activations are the main bottleneck in Private Inference that is based on ResNet networks. This is because they incur significant inference latency. Reducing ReLU count is a discrete optimization problem, and there are two common ways…

ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…

Re-initializing a neural network during training has been observed to improve generalization in recent works. Yet it is neither widely adopted in deep learning practice nor is it often used in state-of-the-art training protocols. This…

The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network…

This work proposes a novel solution to the problem of internal covariate shift and dying neurons using the concept of linked neurons. We define the neuron linkage in terms of two constraints: first, all neuron activations in the linkage…

In this work, we study the nonlinear dynamics of a shallow neural network trained with mean-squared loss and leaky ReLU activation. Under Gaussian inputs and equal layer width k, (1) we establish, based on the equivariant gradient degree, a…

We propose a novel network initialization method using Perlin noise for training image classification networks with a limited amount of data. Our main idea is to initialize the network parameters by solving an artificial noise…

Feed-forward ReLU neural networks partition their input domain into finitely many "affine regions" of constant neuron activation pattern and affine behaviour. We analyze their mathematical structure and provide algorithmic primitives for an…

A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural networks. So far, either theoretical or empirical studies on…

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number…

Prior work has demonstrated a consistent tendency in neural networks engaged in continual learning tasks, wherein intermediate task similarity results in the highest levels of catastrophic interference. This phenomenon is attributed to the…

Neural networks are usually over-parameterized with significant redundancy in the number of required neurons which results in unnecessary computation and memory usage at inference time. One common approach to address this issue is to prune…

Training a neural network (NN) depends on multiple factors, including but not limited to the initial weights. In this paper, we focus on initializing deep NN parameters such that it performs better, comparing to random or zero…

In this work, we provide a characterization of the feature-learning process in two-layer ReLU networks trained by gradient descent on the logistic loss following random initialization. We consider data with binary labels that are generated…

We revisit the problem of learning a single neuron with ReLU activation under Gaussian input with square loss. We particularly focus on the over-parameterization setting where the student network has $n\ge 2$ neurons. We prove the global…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…