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Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit
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Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit
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Paper
Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit
2023
Overview
Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for general optimizers as well, including Adam -- albeit with a nonlinear notion of \"kernel.\" We derive the corresponding \"neural tangent\" and \"maximal update\" limits for any architecture. Two foundational advances underlie the above results: 1) A new Tensor Program language, NEXORT, that can express how adaptive optimizers process gradients into updates. 2) The introduction of bra-ket notation to drastically simplify expressions and calculations in Tensor Programs. This work summarizes and generalizes all previous results in the Tensor Programs series of papers.
Publisher
Cornell University Library, arXiv.org
Subject
