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Generalized Gradient Descent is a Hypergraph Functor
April 1, 2024, 4:42 a.m. | Tyler Hanks, Matthew Klawonn, James Fairbanks
cs.LG updates on arXiv.org arxiv.org
Abstract: Cartesian reverse derivative categories (CRDCs) provide an axiomatic generalization of the reverse derivative, which allows generalized analogues of classic optimization algorithms such as gradient descent to be applied to a broad class of problems. In this paper, we show that generalized gradient descent with respect to a given CRDC induces a hypergraph functor from a hypergraph category of optimization problems to a hypergraph category of dynamical systems. The domain of this functor consists of objective …
abstract algorithms arxiv class cs.lg generalized gradient hypergraph math.ct optimization paper show type
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