Adaptive Depth Scaling for Interpretable Equation Learning.
[EN] Equation Learners (Martius, G., & Lampert, C. H., 2016) are a type of network architecture that can discover generalizable equations with low error for unseen data, outperforming classic neural networks in terms of interpretability and accuracy. These models rely on predefined pools of...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/225633 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/225633 |
| Access Level: | acceso abierto |
| Palabra clave: | Funciones matemáticas Aprendizaje de ecuaciones Aprendizaje Profundo Medida heurísticas Mathematical functions Equation learning Heuristic measure Deep learning Máster Universitario en Inteligencia Artificial, Reconocimiento de Formas e Imagen Digital-Màster Universitari en Intel·ligència Artificial, Reconeixement de Formes i Imatge Digital |
| Sumario: | [EN] Equation Learners (Martius, G., & Lampert, C. H., 2016) are a type of network architecture that can discover generalizable equations with low error for unseen data, outperforming classic neural networks in terms of interpretability and accuracy. These models rely on predefined pools of mathematical functions to generate a dense and explanatory representation of the set of points observed during training. However, due to limitations of the original architecture, selecting an appropriate network size is crucial for performance and training complexity, considering the relation between depth and how expressive the equation can be. Given the long training times these networks may need for obtaining a reduced and interpretable equation form, techniques that scale network size dynamically as deeper architectures become necessary are valuable. The contributions of this work are three-fold: (1) we explore architecture modifications with Skip/Concat connections to ensure the network is trainable when it is deeper than required; (2) a heuristic measure for estimating network learning capacity using gradient information is developed; and (3) a transfer mechanism for increasing network depth dynamically while maintaining knowledge from smaller network versions based on the heuristic metric is implemented. The proposed method achieves competitive results or improves with respect to extremely deep networks. |
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