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 …

Recent works have demonstrated that the sample complexity of gradient-based learning of
single index models, ie functions that depend on a 1-dimensional projection of the input …

Existing analyses of neural network training often operate under the unrealistic assumption
of an extremely small learning rate. This lies in stark contrast to practical wisdom and …

Neural network in the mean-field regime is known to be capable of\textit {feature learning},
unlike the kernel (NTK) counterpart. Recent works have shown that mean-field neural …

As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics
recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide …

We study the problem of training a two-layer neural network (NN) of arbitrary width using
stochastic gradient descent (SGD) where the input $\boldsymbol {x}\in\mathbb {R}^ d $ is …

The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin
dynamics that incorporates a distribution-dependent drift, and it naturally arises from the …

We study the complexity of sampling from the stationary distribution of a mean-field SDE, or
equivalently, the complexity of minimizing a functional over the space of probability …

Finding the mixed Nash equilibria (MNE) of a two-player zero sum continuous game is an
important and challenging problem in machine learning. A canonical algorithm to finding the …

In the theory of lossy compression, the rate-distortion (RD) function $ R (D) $ describes how
much a data source can be compressed (in bit-rate) at any given level of fidelity (distortion) …