Related papers: Random weights of DNNs and emergence of fixed poin…
Training strategies for modern deep neural networks (NNs) tend to induce a heavy-tailed (HT) empirical spectral density (ESD) in the layer weights. While previous efforts have shown that the HT phenomenon correlates with good generalization…
Neural networks have been used successfully in a variety of fields, which has led to a great deal of interest in developing a theoretical understanding of how they store the information needed to perform a particular task. We study the…
Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…
In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples. More specifically we…
There is a growing literature on the study of large-width properties of deep Gaussian neural networks (NNs), i.e. deep NNs with Gaussian-distributed parameters or weights, and Gaussian stochastic processes. Motivated by some empirical and…
Deep neural networks (DNNs) have emerged as a popular mathematical tool for function approximation due to their capability of modelling highly nonlinear functions. Their applications range from image classification and natural language…
Safe use of Deep Neural Networks (DNNs) requires careful testing. However, deployed models are often trained further to improve in performance. As rigorous testing and evaluation is expensive, triggers are in need to determine the degree of…
Fixed-point optimization of deep neural networks plays an important role in hardware based design and low-power implementations. Many deep neural networks show fairly good performance even with 2- or 3-bit precision when quantized weights…
Developing strong AI signifies the arrival of technological singularity, contributing greatly to advancing human civilization and resolving social issues. Neural networks (NNs) and deep learning, which utilize NNs, are expected to lead to…
Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…
Deep neural networks (DNNs), are widely used in many industries such as image recognition, supply chain, medical diagnosis, and autonomous driving. However, prior work has shown the high accuracy of a DNN model does not imply high…
Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be…
In modern deep learning, there is a recent and growing literature on the interplay between large-width asymptotic properties of deep Gaussian neural networks (NNs), i.e. deep NNs with Gaussian-distributed weights, and Gaussian stochastic…
Deep neural network (DNN) quantization for fast, efficient inference has been an important tool in limiting the cost of machine learning (ML) model inference. Quantization-specific model development techniques such as regularization,…
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…
During training, the weights of a Deep Neural Network (DNN) are optimized from a random initialization towards a nearly optimum value minimizing a loss function. Only this final state of the weights is typically kept for testing, while the…
Much research effort has been devoted to explaining the success of deep learning. Random Matrix Theory (RMT) provides an emerging way to this end: spectral analysis of large random matrices involved in a trained deep neural network (DNN)…
Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the…
Deep neural networks (DNNs) are often coupled with physics-based models or data-driven surrogate models to perform fault detection and health monitoring of systems in the low data regime. These models serve as digital twins to generate…
Deep neural networks are typically initialized with random weights, with variances chosen to facilitate signal propagation and stable gradients. It is also believed that diversity of features is an important property of these…