Author: Gabriel Jacob Perin
Supervisor: Prof. Dr. Nina S. T. Hirata
Degree: Bachelor of Computer Science
Institution: Institute of Mathematics, Statistics and Computer Science, University of São Paulo
Year: 2025
Deep Learning has become a dominant paradigm in modern artificial intelligence, achieving impressive results across many domains, yet much of its development remains empirical rather than theoretically grounded. Geometric Deep Learning (GDL) offers a principled framework to understand and design neural architectures through symmetries.
This work aims to make GDL accessible at the undergraduate level by simplifying its theoretical foundations and focusing on three core geometric domains: Sets, Graphs, and Grids. Rather than presenting an exhaustive survey, the text emphasizes intuition, essential mathematical tools, and clear examples that connect geometric structure to neural network design.
The reader is introduced to foundational concepts in Machine Learning, the role of geometric priors, and the GDL blueprint, before exploring how canonical architectures such as DeepSets, Graph Neural Networks, and Convolutional Neural Networks naturally emerge from these principles. Finally, the thesis presents experiments comparing symmetry-aware models with universal approximators, highlighting the impact of geometric inductive biases on model behavior and performance.
📄 Thesis (PDF):
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💻 Code Repository:
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🪧 Poster (PDF):
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