Improving neural networks using topological data analysis
Generalisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only the training set are candidates to be used as loss regularisation terms to imp...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2022 |
| 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:2117/373847 |
| Acceso en línea: | https://hdl.handle.net/2117/373847 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebra, Homological Categories (Mathematics) Machine learning TDA Topological data analysis Topology Metric Distances Differential calculus Persistent homology Persistence diagrams Correlation Deep learning Neural networks Regularisation Loss functions Training algorithms Àlgebra homològica Categories (Matemàtica) Aprenentatge automàtic Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
| Sumario: | Generalisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only the training set are candidates to be used as loss regularisation terms to improve neural network training processes. Recently, persistent homology has been used to build robust generalisation measures of this kind by means of persistence diagrams. However, some of these measures involve non-standard distances, and thus the usual stability and differentiability results are not valid. In this thesis, we prove more general stability and differentiability results that fit the conditions required by the previous topological measures. Also, we define a new measure called topological redundancy that we use together with one of the previous topological terms to improve accuracies of networks with respect to usual training without topological regularisation terms. |
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