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Generalized Gradient Descent is a Hypergraph Functor
Tyler Hanks, Matthew Klawonn, James Fairbanks
https://arxiv.org/abs/2403.19845 https://

Generalized Gradient Descent is a Hypergraph Functor
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…

Generalized Gradient Descent is a Hypergraph Functor
Tyler Hanks, Matthew Klawonn, James Fairbanks
https://arxiv.org/abs/2403.19845 https://

Generalized Gradient Descent is a Hypergraph Functor
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…

This https://arxiv.org/abs/2308.16546 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

Inference of dynamic hypergraph representations in temporal interaction data
A range of systems across the social and natural sciences generate datasets consisting of interactions between two distinct categories of items at various instances in time. Online shopping, for example, generates purchasing events of the form (user, product, time of purchase), and mutualistic interactions in plant-pollinator systems generate pollination events of the form (insect, plant, time of pollination). These data sets can be meaningfully modeled as temporal hypergraph snapshots in which…

Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
Will Grilliette
https://arxiv.org/abs/2403.13165

Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
By applying simplification operations to categories of multigraphs, several natural graph operations are shown to demonstrate categorical issues. The replacement of an undirected edge with a directed cycle for digraphs admits both a left and a right adjoint, while the analogous operation for quivers only admits a left adjoint. The clique-replacement graph, intersection graph, and dual hypergraph fail to be functorial with traditional graph homomorphisms. The three failures are remedied by consi…

This https://arxiv.org/abs/2308.16546 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

Inference of dynamic hypergraph representations in temporal interaction data
A range of systems across the social and natural sciences generate datasets consisting of interactions between two distinct categories of items at various instances in time. Online shopping, for example, generates purchasing events of the form (user, product, time of purchase), and mutualistic interactions in plant-pollinator systems generate pollination events of the form (insect, plant, time of pollination). These data sets can be meaningfully modeled as temporal hypergraph snapshots in which…

Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
Will Grilliette
https://arxiv.org/abs/2403.13165

Simplification & Incidence: How an Incidence-focused Perspective Patches Category-theoretic Problems in Graph Theory
By applying simplification operations to categories of multigraphs, several natural graph operations are shown to demonstrate categorical issues. The replacement of an undirected edge with a directed cycle for digraphs admits both a left and a right adjoint, while the analogous operation for quivers only admits a left adjoint. The clique-replacement graph, intersection graph, and dual hypergraph fail to be functorial with traditional graph homomorphisms. The three failures are remedied by consi…