Topology-Enhanced Deep Learning
[eng] This thesis presents a comprehensive examination of topological deep learning through two complementary approaches: utilizing topological tools to analyze and improve traditional neural networks, and testing and developing novel architectures for learning on high-order topological domains such...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:dnet:ubarcelona__::88bfe3b8246fdf77ff32c973ade99a14 |
| Acceso en línea: | https://hdl.handle.net/2445/228985 https://hdl.handle.net/10803/697251 |
| Access Level: | acceso abierto |
| Palabra clave: | Topologia Aprenentatge profund Topology Deep learning (Machine learning) |
| Sumario: | [eng] This thesis presents a comprehensive examination of topological deep learning through two complementary approaches: utilizing topological tools to analyze and improve traditional neural networks, and testing and developing novel architectures for learning on high-order topological domains such as simplicial or cellular complexes. The thesis is organized into three thematic blocks. First, we establish the theoretical foundations of TDA and TDL, providing a comprehensive literature review of existing methodologies. Second, we exploit persistent homology —a fundamental TDA tool that quantifies multi-scale topological features— to analyze neural network activations and their relationship to neural network performance and generalization. We use the differentiability theory of persistent homology to develop topological regularization methods that demonstrably improve neural network performance on selected problems. In the third block, we address the challenges of learning on high-order domains such as simplicial and cellular complexes. We introduce MANTRA, a novel topological dataset specifically designed to evaluate the capacity of TDL methods to leverage high-order structural information. Furthermore, we develop the Cellular Transformer, an adaptation of the transformer architecture to cellular complexes that addresses some of the limitations of message passing neural networks, such as their general inability to capture long-range interactions. This thesis advances both the theoretical understanding of neural networks through a topological lens and the practical capabilities of learning algorithms on topological structures. The empirical results obtained in this thesis demonstrate that topology provides valuable insights into the geometric processes underlying deep learning while enabling more effective feature extraction from complex data representations. Thus, the research presented here expands the state-of-the-art in topological deep learning, establishing a foundation for more interpretable, topologically-aware neural architectures while opening promising avenues for future research at the intersection of algebraic topology and deep learning. |
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