This repository is a curated collection of resources on the theoretical underpinnings of deep learning, targeting researchers and engineers interested in the mathematical foundations of AI. It aims to consolidate and organize academic papers, lecture notes, and discussions covering topics from approximation theory and optimization to geometric deep learning and the interplay between deep learning and physics.

How It Works

The repository organizes resources into thematic categories, including approximation theory, optimization dynamics, geometric interpretations of data and optimization, network architectures, and theoretical analyses of generalization. It highlights key papers and concepts, such as the Kolmogorov-Arnold Networks (KANs) and their connection to the Kolmogorov-Arnold representation theorem, as well as the theoretical implications of over-parameterization and the geometry of loss landscapes.

Quick Start & Requirements

• Access: Primarily through browsing the README and linked external resources (papers, GitHub repositories, lecture notes).
• Requirements: A strong background in mathematics (calculus, linear algebra, probability, information theory) and machine learning theory is beneficial for understanding the content.

Highlighted Details

• Extensive coverage of geometric deep learning, including graph neural networks and manifold-based approaches.
• Detailed exploration of optimization theory, from SGD dynamics to stochastic differential equations and landscape geometry.
• Inclusion of cutting-edge research like Kolmogorov-Arnold Networks (KANs) and their potential for interpretability and accuracy.
• Links to numerous academic papers, lecture series, and discussions from leading researchers and institutions.

Maintenance & Community

The repository appears to be a personal curation rather than a community-driven project, with content spanning from 2019 to 2025 (projected). It aggregates work from various sources, including prominent researchers and institutions like MIT, TTIC, and DeepMind.

Licensing & Compatibility

The repository itself does not host code or papers directly but links to external resources. The licensing and compatibility of the linked materials would vary by their original source.

Limitations & Caveats

This is a collection of links and summaries, not a runnable codebase. The depth and breadth of coverage vary, and some linked resources may be behind paywalls or require specific academic access. The "2025" dates indicate future or ongoing research rather than completed projects.