This article shows how to solve linear programs of the form min Ax= b, x≥ 0 c⊤ x with n
variables in time O*((n ω+ n 2.5− α/2+ n 2+ 1/6) log (n/δ)), where ω is the exponent of matrix …

Large language models (LLMs) have made transformed changes for human society. One of
the key computation in LLMs is the softmax unit. This operation is important in LLMs …

Operator learning techniques have recently emerged as a powerful tool for learning maps
between infinite-dimensional Banach spaces. Trained under appropriate constraints, they …

The softmax operator is a crucial component of large language models (LLMs), which have
played a transformative role in computer research. Due to the centrality of the softmax …

Overparameterized neural networks generalize well but are expensive to train. Ideally, one
would like to reduce their computational cost while retaining their generalization benefits …

Over the last decade, deep neural networks have transformed our society, and they are
already widely applied in various machine learning applications. State-of-the-art deep …

Deep neural networks have achieved impressive performance in many areas. Designing a
fast and provable method for training neural networks is a fundamental question in machine …

We consider the problem of training a multi-layer over-parametrized neural network to
minimize the empirical risk induced by a loss function. In the typical setting of over …

Deep networks are often considered to be more expressive than shallow ones in terms of
approximation. Indeed, certain functions can be approximated by deep networks provably …

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 …