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TFM_Garrido_Garcia_Diego.pdf (609.36 KB)

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Master thesis

Publication date

2025-06-13

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cc by-nc-nd (c) Diego Garrido Garcia, 2025
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228161

An approach to topos theory related to neural networks

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Abstract

This work describes an application of topos theory and stacks to the semantic modeling of deep neural networks. Following the work of by Jean-Claude Belfiore and Daniel Bennequin, we present tools from topos theory to capture the learning process and semantic diffusion in a deep neural network architecture. We introduce the concepts of Grothendieck topoi, stacks and classifying topoi. Within this framework we establish conditions under which the semantic flow of information in a network can be transported across its layers.

Description

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Carles Casacuberta

Subject

Topos (Matemàtica), Xarxes neuronals (Informàtica), Aprenentatge automàtic, Lògica matemàtica, Diego Garrido Garcia, Treballs de fi de màster

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Toposes, Neural networks (Computer science), Machine learning, Mathematical logic, Master's thesis

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Màster Oficial - Matemàtica Avançada

Citation

GARRIDO GARCIA, Diego. An approach to topos theory related to neural networks. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/228161

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