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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| 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 |
| 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 |
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