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Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of "Neural Collapse", where…

Artificial intelligence is revolutionizing our lives at an ever increasing pace. At the heart of this revolution is the recent advancements in deep neural networks (DNN), learning to perform sophisticated, high-level tasks. However,…

In this work, we investigate a particular implicit bias in gradient descent training, which we term "Feature Averaging," and argue that it is one of the principal factors contributing to the non-robustness of deep neural networks. We show…

We propose to address the issue of sample efficiency, in Deep Convolutional Neural Networks (DCNN), with a semi-supervised training strategy that combines Hebbian learning with gradient descent: all internal layers (both convolutional and…

Learning algorithms related to artificial neural networks and in particular for Deep Learning may seem to involve many bells and whistles, called hyper-parameters. This chapter is meant as a practical guide with recommendations for some of…

We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…

Feedback alignment algorithms are an alternative to backpropagation to train neural networks, whereby some of the partial derivatives that are required to compute the gradient are replaced by random terms. This essentially transforms the…

De novo molecular design attempts to search over the chemical space for molecules with the desired property. Recently, deep learning has gained considerable attention as a promising approach to solve the problem. In this paper, we propose…

We describe the neural-network training framework used in the Kaldi speech recognition toolkit, which is geared towards training DNNs with large amounts of training data using multiple GPU-equipped or multi-core machines. In order to be as…

Constructing transferable descriptors for conformation representation of molecular and biological systems finds numerous applications in drug discovery, learning-based molecular dynamics, and protein mechanism analysis. Geometric graph…

While Graph Neural Networks (GNNs) excel on graph-structured data, their performance is fundamentally limited by the quality of the observed graph, which often contains noise, missing links, or structural properties misaligned with GNNs'…

We investigate the inherent bias of Stochastic Gradient Descent (SGD) toward learning low-rank weight matrices during the training of deep neural networks. Our results demonstrate that training with mini-batch SGD and weight decay induces a…

Recent accelerated MRI reconstruction models have used Deep Neural Networks (DNNs) to reconstruct relatively high-quality images from highly undersampled k-space data, enabling much faster MRI scanning. However, these techniques sometimes…

Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…

Most existing Graph Neural Networks (GNNs) are proposed without considering the selection bias in data, i.e., the inconsistent distribution between the training set with test set. In reality, the test data is not even available during the…

Training Artificial Neural Networks poses a challenging and critical problem in machine learning. Despite the effectiveness of gradient-based learning methods, such as Stochastic Gradient Descent (SGD), in training neural networks, they do…

Gradient descent computed by backpropagation (BP) is a widely used learning method for training artificial neural networks but has several limitations: it is computationally demanding, requires frequent manual tuning of the network…

A Deep Neural Network (DNN) is a composite function of vector-valued functions, and in order to train a DNN, it is necessary to calculate the gradient of the loss function with respect to all parameters. This calculation can be a…

Backpropagation (BP) is the standard algorithm for training the deep neural networks that power modern artificial intelligence including large language models. However, BP is energy inefficient and unlikely to be implemented by the brain.…

The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…