Reinforcement learning (RL) is one of the most vibrant research frontiers in machine
learning and has been recently applied to solve a number of challenging problems. In this …

Diffusion models achieve state-of-the-art performance in various generation tasks. However,
their theoretical foundations fall far behind. This paper studies score approximation …

While efficient distribution learning is no doubt behind the groundbreaking success of
diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the …

We study the first gradient descent step on the first-layer parameters $\boldsymbol {W} $ in a
two-layer neural network: $ f (\boldsymbol {x})=\frac {1}{\sqrt {N}}\boldsymbol {a}^\top\sigma …

Neural networks have achieved remarkable performance across various problem domains,
but their widespread applicability is hindered by inherent limitations such as overconfidence …

Despite the great empirical success of deep reinforcement learning, its theoretical
foundation is less well understood. In this work, we make the first attempt to theoretically …

Physics-informed neural networks (PINNs)[31] use automatic differentiation to solve partial
differential equations (PDEs) by penalizing the PDE in the loss function at a random set of …

Recent results in nonparametric regression show that deep learning, that is, neural network
estimates with many hidden layers, are able to circumvent the so-called curse of …

This paper establishes the optimal approximation error characterization of deep rectified
linear unit (ReLU) networks for smooth functions in terms of both width and depth …

As AI model size grows, neural scaling laws have become a crucial tool to predict the
improvements of large models when increasing capacity and the size of original (human or …