Search Results for author: Kangjie Zhou

Found 5 papers, 0 papers with code

Sharp Analysis of Power Iteration for Tensor PCA

no code implementations2 Jan 2024 Yuchen Wu, Kangjie Zhou

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

Learning time-scales in two-layers neural networks

no code implementations28 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).

Vocal Bursts Valence Prediction

Lower Bounds for the Convergence of Tensor Power Iteration on Random Overcomplete Models

no code implementations7 Nov 2022 Yuchen Wu, Kangjie Zhou

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

LEMMA Tensor Decomposition

Overparametrized linear dimensionality reductions: From projection pursuit to two-layer neural networks

no code implementations14 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 $\mathscr{F}_{m, \alpha}$.

Tractability from overparametrization: The example of the negative perceptron

no code implementations28 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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