Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
arXiv preprint arXiv:2406.03495 , year=
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EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
An auxiliary modulus during training reduces wrap-around issues and preserves train-test input distributions, enabling better accuracy and sample efficiency for large N and q in modular addition learning.
citing papers explorer
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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking
EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
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Learning Large-Scale Modular Addition with an Auxiliary Modulus
An auxiliary modulus during training reduces wrap-around issues and preserves train-test input distributions, enabling better accuracy and sample efficiency for large N and q in modular addition learning.