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Towards Foundations of Categorical Cybernetics

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arxiv 2105.06332 v2 pith:RLUCBX6L submitted 2021-05-13 math.CT

Matteo Capucci , Bruno Gavranović , Jules Hedges , Eigil Fjeldgren Rischel This is my paper · ORCID
classification math.CT
keywords controllercategoricalframeworkopenprocessesagentsapproachappropriate
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We propose a categorical framework for processes which interact bidirectionally with both an environment and a 'controller'. Examples include open learners, in which the controller is an optimiser such as gradient descent, and an approach to compositional game theory closely related to open games, in which the controller is a composite of game-theoretic agents. We believe that 'cybernetic' is an appropriate name for the processes that can be described in this framework.

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Cited by 1 Pith paper

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  1. Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures

    cs.LG 2025-01 reject novelty 3.0 of 10

    The paper claims that linear self-attention defines a parametric endofunctor whose layered stacking is the free monad, but the construction is mostly restatement and has serious technical flaws.

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