SP

Notes and articles

Deep dive explanation

Computational Geometry of Delaunay Triangulations for Spanning Tree Optimization

1/8/2026

Demonstrates a high-performance Minimum Spanning Tree (MST) implementation. By recognizing that every edge of an MST is a subset of the Delaunay triangulation, the complexity is reduced bypassing the inefficiencies of naive approaches.

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Markov Chains and Principal Eigenvectors in Network Centrality: PageRank

10/3/2025

A mathematical derivation of node-level feature engineering in GNNs, focusing on the spectral properties of Markov Chains and the convergence of the PageRank principal eigenvector.

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Stochastic Gradient Descent & The Error Backpropagation Calculus

1/8/2025

An analytical derivation of the backpropagation algorithm, examining the application of the multivariable chain rule to gradient-based optimization. This essay bridges the gap between the calculus of sensitivity analysis and its high-performance implementation in deep learning architectures.

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