Math behind
the Machine
Exploring machine learning, optimization, and the deep structures underneath — through proofs, code, and visual intuition.
Matt Jacob — MA Statistics, incoming PhD Mathematics.
Latest Posts
NMF on Immune Cells: What Chemo-Immunotherapy Does to Your T-Cell Army
We applied Non-negative Matrix Factorization to single-cell immune data from a lung cancer patient. The algorithm independently rediscovered when treatment-responsive T cells peak.
The Bias-Variance Tradeoff: It Holds Until It Doesn't
The textbook says more training means more overfitting — until a researcher went on vacation and came back to find the opposite was true.
Gradient Descent: The Blind Man Who Finds the Valley
The algorithm behind all of deep learning is a blind man walking downhill. The strange part is why he almost never gets stuck.
The Strange Simplicity of Machine Learning
Most of machine learning comes down to one elegant idea from 1958 — finding a line between points.
Projects
MTG Hand Evaluator: ML Model Comparison on Opening Hands
Predicting opening hand win rates in Magic: The Gathering Limited using five ML models — from logistic regression to card embeddings — with an interactive Streamlit dashboard.
NMF: Derivation of Update Rules & Convergence Proof
A self-contained derivation of Lee & Seung's multiplicative update rules for Non-Negative Matrix Factorization, with full convergence proofs for both the Euclidean and divergence objectives.
TR-NMF: Temporally-Regularized Non-Negative Matrix Factorization
A research roadmap for developing a novel NMF variant that exploits temporal ordering in longitudinal data — objectives, reading list, and key gaps in the literature.
Videos
Mathematical animations and visual explanations built with Manim.
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