In these Lecture Notes, we provide a comprehensive introduction to the most recent
advances in the application of machine learning methods in quantum sciences. We cover …

In typical artificial neural networks, neurons adjust according to global calculations of a
central processor, but in the brain, neurons and synapses self-adjust based on local …

In this paper, we study the implicit regularization of stochastic gradient descent (SGD)
through the lens of dynamical stability (Wu et al., 2018). We start by revising existing stability …

This article introduces a special issue on the interaction between the rapidly expanding field
of machine learning and ongoing research in physics. The first half of the papers in this …

The training process of ReLU neural networks often exhibits complicated nonlinear
phenomena. The nonlinearity of models and non-convexity of loss pose significant …

The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a
critical role in understanding the implicit regularization of SGD. In this paper, we provide an …

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine
learning. The noise encountered in these applications is different from that in many …

The multiplicative structure of parameters and input data in the first layer of neural networks
is explored to build connection between the landscape of the loss function with respect to …

Modern deep networks are trained with stochastic gradient descent (SGD) whose key
hyperparameters are the number of data considered at each step or batch size B, and the …

Stochastic gradient descent (SGD) is the workhorse algorithm of deep learning technology.
At each step of the training phase, a mini batch of samples is drawn from the training dataset …