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We demonstrate that a very deep ResNet with stacked modules with one neuron per hidden layer and ReLU activation functions can uniformly approximate any Lebesgue integrable function in $d$ dimensions, i.e. $\ell_1(\mathbb{R}^d)$. Because of…

Network pruning is widely used to lighten and accelerate neural network models. Structured network pruning discards the whole neuron or filter, leading to accuracy loss. In this work, we propose a novel concept of neuron merging applicable…

Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…

We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization using networks of a…

Neural Representations have recently been shown to effectively reconstruct a wide range of signals from 3D meshes and shapes to images and videos. We show that, when adapted correctly, neural representations can be used to directly…

In the presence of noisy or incorrect labels, neural networks have the undesirable tendency to memorize information about the noise. Standard regularization techniques such as dropout, weight decay or data augmentation sometimes help, but…

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…

We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set $s_1, \dots, s_n \in \mathbb{R}^p$ with corresponding responses $t_1,\dots,t_n \in \mathbb{R}^q$, fitting a…

Neuron death is a complex phenomenon with implications for model trainability: the deeper the network, the lower the probability of finding a valid initialization. In this work, we derive both upper and lower bounds on the probability that…

Given a length $n$ sample from $\mathbb{R}^d$ and a neural network with a fixed architecture with $W$ weights, $k$ neurons, linear threshold activation functions, and binary outputs on each neuron, we study the problem of uniformly sampling…

An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong…

Substantial experiments have validated the success of Batch Normalization (BN) Layer in benefiting convergence and generalization. However, BN requires extra memory and float-point calculation. Moreover, BN would be inaccurate on…

We initiate the study of the inherent tradeoffs between the size of a neural network and its robustness, as measured by its Lipschitz constant. We make a precise conjecture that, for any Lipschitz activation function and for most datasets,…

Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, it acts as a sophisticated designer of task-based neurons. In this study, we address the following question: since the…

Adversarial reprogramming, introduced by Elsayed, Goodfellow, and Sohl-Dickstein, seeks to repurpose a neural network to perform a different task, by manipulating its input without modifying its weights. We prove that two-layer ReLU neural…

Recent advances in machine learning have led to a surge in adoption of neural networks for various tasks, but lack of interpretability remains an issue for many others in which an understanding of the features influencing the prediction is…

Deep learning typically requires training a very capable architecture using large datasets. However, many important learning problems demand an ability to draw valid inferences from small size datasets, and such problems pose a particular…

As modern deep learning architectures grow in complexity, representational ambiguity emerges as a critical barrier to their interpretability and reliable merging. For ReLU networks, identical functional mappings can be achieved through…

Deep neural networks are highly expressive machine learning models with the ability to interpolate arbitrary datasets. Deep nets are typically optimized via first-order methods and the optimization process crucially depends on the…