相关论文: Network size and weights size for memorization wit…

We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a…

Rectified Linear Units (ReLUs) have been shown to ameliorate the vanishing gradient problem, allow for efficient backpropagation, and empirically promote sparsity in the learned parameters. They have led to state-of-the-art results in a…

Modern machine learning models often employ a huge number of parameters and are typically optimized to have zero training loss; yet surprisingly, they possess near-optimal prediction performance, contradicting classical learning theory. We…

In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to…

Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a…

It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…

Over the past few years, there has been a significant amount of research focused on studying the ReLU activation function, with the aim of achieving neural network convergence through over-parametrization. However, recent developments in…

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by…

Layer normalization (LN) is a ubiquitous technique in deep learning but our theoretical understanding to it remains elusive. This paper investigates a new theoretical direction for LN, regarding to its nonlinearity and representation…

For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit…

We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based…

Benign overfitting refers to how over-parameterized neural networks can fit training data perfectly and generalize well to unseen data. While this has been widely investigated theoretically, existing works are limited to two-layer networks…

We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting models are typically equivalent to networks whose nonzero weights are also $\pm 1$. The method…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

This study explores the number of neurons required for a Rectified Linear Unit (ReLU) neural network to approximate multivariate monomials. We establish an exponential lower bound on the complexity of any shallow network approximating the…

We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory…

A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…

The paper presents Multi-layer Auto Resonance Networks (ARN), a new neural model, for image recognition. Neurons in ARN, called Nodes, latch on to an incoming pattern and resonate when the input is within its 'coverage.' Resonance allows…

We construct pairs of distributions $\mu_d, \nu_d$ on $\mathbb{R}^d$ such that the quantity $|\mathbb{E}_{x \sim \mu_d} [F(x)] - \mathbb{E}_{x \sim \nu_d} [F(x)]|$ decreases as $\Omega(1/d^2)$ for some three-layer ReLU network $F$ with…