# Learning in Gated Neural Networks

## TL;DR

This paper analyzes the optimization landscape of gated neural networks, showing that with specially designed loss functions, gradient descent can accurately recover parameters, supported by new sample complexity results and improved numerical performance.

## Contribution

It introduces two distinct loss functions for better parameter recovery in mixture-of-experts models and provides the first sample complexity analysis for this problem.

## Key findings

- Gradient descent can learn parameters accurately with proper loss functions.
- Two specialized loss functions improve parameter recovery.
- First sample complexity results for mixture-of-experts models.

## Abstract

Gating is a key feature in modern neural networks including LSTMs, GRUs and sparsely-gated deep neural networks. The backbone of such gated networks is a mixture-of-experts layer, where several experts make regression decisions and gating controls how to weigh the decisions in an input-dependent manner. Despite having such a prominent role in both modern and classical machine learning, very little is understood about parameter recovery of mixture-of-experts since gradient descent and EM algorithms are known to be stuck in local optima in such models. In this paper, we perform a careful analysis of the optimization landscape and show that with appropriately designed loss functions, gradient descent can indeed learn the parameters accurately. A key idea underpinning our results is the design of two {\em distinct} loss functions, one for recovering the expert parameters and another for recovering the gating parameters. We demonstrate the first sample complexity results for parameter recovery in this model for any algorithm and demonstrate significant performance gains over standard loss functions in numerical experiments.