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Electron-Proton Dynamics in Deep Learning (arxiv.org)
1 point by EvgeniyZh on Feb 4, 2017 | hide | past | pdf | discuss on HN

In plain words: Training a two-layer network with gradient descent acts like charged particles settling into matched pairs, with the data and each node's shaping rule setting the forces. With one chosen shaping rule, gradient descent learns one hidden node at a time until the target is recovered.

Abstract · Convergence Results for Neural Networks via Electrodynamics

We study whether a depth two neural network can learn another depth two network using gradient descent. Assuming a linear output node, we show that the question of whether gradient descent converges to the target function is equivalent to the following question in electrodynamics: Given $k$ fixed protons in $\mathbb{R}^d,$ and $k$ electrons, each moving due to the attractive force from the protons and repulsive force from the remaining electrons, whether at equilibrium all the electrons will be matched up with the protons, up to a permutation. Under the standard electrical force, this follows from the classic Earnshaw's theorem. In our setting, the force is determined by the activation function and the input distribution. Building on this equivalence, we prove the existence of an activation function such that gradient descent learns at least one of the hidden nodes in the target network. Iterating, we show that gradient descent can be used to learn the entire network one node at a time.

Rina Panigrahy, Sushant Sachdeva, Qiuyi Zhang
arXiv:1702.00458 · cs.DS, cs.LG, physics.data-an · submitted Feb 1, 2017 · updated Dec 4, 2018
abstract · pdf · html · in ITCS 2018

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