# Provable Training of a ReLU Gate with an Iterative Non-Gradient Algorithm

arXiv: https://arxiv.org/abs/2005.04211 · HTML: https://mlsanity.com/paper/2005.04211/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2020.

## Built on by (most cited first, 3 of 3)

- [Robustly Learning a Single Neuron via Sharpness](https://mlsanity.com/paper/2306.07892/) (2023)
- [Dynamics of Local Elasticity During Training of Neural Nets](https://mlsanity.com/paper/2111.01166/) (2021)
- [An Empirical Study of the Occurrence of Heavy-Tails in Training a ReLU Gate](https://mlsanity.com/paper/2204.12554/) (2022)

## Abstract (arXiv)

In this work, we demonstrate provable guarantees on the training of a single ReLU gate in hitherto unexplored regimes. We give a simple iterative stochastic algorithm that can train a ReLU gate in the realizable setting in linear time while using significantly milder conditions on the data distribution than previous such results. Leveraging certain additional moment assumptions, we also show a first-of-its-kind approximate recovery of the true label generating parameters under an (online) data-poisoning attack on the true labels, while training a ReLU gate by the same algorithm. Our guarantee is shown to be nearly optimal in the worst case and its accuracy of recovering the true weight degrades gracefully with increasing probability of attack and its magnitude. For both the realizable and the non-realizable cases as outlined above, our analysis allows for mini-batching and computes how the convergence time scales with the mini-batch size. We corroborate our theorems with simulation results which also bring to light a striking similarity in trajectories between our algorithm and the popular S.G.D. algorithm - for which similar guarantees as here are still unknown.