Convergence Analysis of Two-Layer Neural Networks under Gaussian Input Masking

TL;DR

This paper analyzes the convergence of two-layer neural networks trained with Gaussian masked inputs, showing linear convergence up to an error bound related to the mask's variance, using NTK analysis.

Contribution

It introduces a novel NTK-based analysis for neural networks with Gaussian input masking, addressing the randomness in non-linear activations.

Findings

Achieves linear convergence with Gaussian masked inputs

Error region proportional to mask variance

Addresses randomness in non-linear activation functions

Abstract

We investigate the convergence guarantee of two-layer neural network training with Gaussian randomly masked inputs. This scenario corresponds to Gaussian dropout at the input level, or noisy input training common in sensor networks, privacy-preserving training, and federated learning, where each user may have access to partial or corrupted features. Using a Neural Tangent Kernel (NTK) analysis, we demonstrate that training a two-layer ReLU network with Gaussian randomly masked inputs achieves linear convergence up to an error region proportional to the mask's variance. A key technical contribution is resolving the randomness within the non-linear activation, a problem of independent interest.