# Learning in Gated Neural Networks

arXiv: https://arxiv.org/abs/1906.02777 · HTML: https://mlsanity.com/paper/1906.02777/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- First posted on arXiv 6 Jun 2019.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Built on by (most cited first, 6 of 6)

- [Convergence Rates for Gaussian Mixtures of Experts](https://mlsanity.com/paper/1907.04377/) (2019)
- [Provably learning a multi-head attention layer](https://mlsanity.com/paper/2402.04084/) (2024)
- [Mixed Regression via Approximate Message Passing](https://mlsanity.com/paper/2304.02229/) (2023)
- [On Parameter Estimation in Deviated Gaussian Mixture of Experts](https://mlsanity.com/paper/2402.05220/) (2024)
- [Implicit Neural Representation For Accurate CFD Flow Field Prediction](https://mlsanity.com/paper/2408.06486/) (2024)
- [Soft-to-Hard Routing in Sparse Mixture-of-Experts Models](https://mlsanity.com/paper/2605.02124/) (2026)

## Abstract (arXiv)

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.