The linear algebra and calculus behind every model

8 hours ago

Every machine learning model relies on three pillars: linear algebra, calculus, and convex optimization.
The MNIST dataset is treated as a matrix of 70,000 rows (images) and 784 columns (pixels) after flattening.
Data exploration shows balanced classes, no missing values, and a bimodal pixel intensity distribution.
Vectors have L1 and L2 norms; dot products measure similarity between images.
Matrix multiplication forms a Gram matrix of pairwise similarities.
Broadcasting allows adding a scalar bias to tensors without explicit loops.
Projections decompose images into components along and perpendicular to the mean image direction.
The Singular Value Decomposition (SVD) factors the centered data matrix and reveals 626 significant singular values out of 784.

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