Improving neural networks using topological data analysis
| Autor: | Ballester Bautista, Rubén |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Pfeifle, Julián |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
55 Algebraic topology::55U Applied homological algebra and category theory [Classificació AMS]
Topological data analysis Àlgebra homològica Deep learning TDA Topology Regularisation Correlation Distances Training algorithms Persistence diagrams Categories (Matemàtica) Differential calculus Machine learning Aprenentatge automàtic Loss functions Persistent homology Categories (Mathematics) Metric Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC] Neural networks Algebra Homological |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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