no code implementations • 2 Jan 2024 • Yuchen Wu, Kangjie Zhou

We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014).

no code implementations • 28 Feb 2023 • Raphaël Berthier, Andrea Montanari, Kangjie Zhou

In this paper, we study the gradient flow dynamics of a wide two-layer neural network in high-dimension, when data are distributed according to a single-index model (i. e., the target function depends on a one-dimensional projection of the covariates).

no code implementations • 7 Nov 2022 • Yuchen Wu, Kangjie Zhou

In this paper, we analyze the dynamics of tensor power iteration from random initialization in the overcomplete regime.

no code implementations • 14 Jun 2022 • Andrea Montanari, Kangjie Zhou

Denoting by $\mathscr{F}_{m, \alpha}$ the set of probability distributions in $\mathbb{R}^m$ that arise as low-dimensional projections in this limit, we establish new inner and outer bounds on $\mathscr{F}_{m, \alpha}$.

no code implementations • 28 Oct 2021 • Andrea Montanari, Yiqiao Zhong, Kangjie Zhou

In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i, y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label.

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