Inverting toeplitz matrices for convolutional neural networks

The thesis focuses on finding new methods for inverting image convolution. It starts with the idea that matrix convolution can be transformed into matrix multiplication using some special matrix related with tridiagonal toeplitz matrices. An algorithm for its inversion is given and we also discover...

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Detalles Bibliográficos
Autor: Segura Montero, Oier
Tipo de recurso: tesis de maestría
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/415748
Acceso en línea:https://hdl.handle.net/2117/415748
Access Level:acceso abierto
Palabra clave:Neural networks (Computer science)
Toeplitz
tridiagonal
convolution
inversion
determinant
neural network.
Xarxes neuronals (Informàtica)
Classificació AMS::68 Computer science::68T Artificial intelligence
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:The thesis focuses on finding new methods for inverting image convolution. It starts with the idea that matrix convolution can be transformed into matrix multiplication using some special matrix related with tridiagonal toeplitz matrices. An algorithm for its inversion is given and we also discover how deeply related the inverse is with the determinant of a general tridiagonal toeplitz matrix. So we also find a general formula for those. Experiments and implementations are given