Why ordinary recurrent networks forget, the one equation that fixes it, and how gates turn that fix into a trainable memory cell. From the vanishing-gradient analysis to the modern cell, with backpropagation derived, a worked example, and a reference implementation.
READ MOREEvery matrix is a rotation, a stretch, and another rotation. Starting from that geometry, rank, low-rank approximation, pseudoinverses, conditioning and PCA all turn out to be the same fact viewed from different angles.
Why one function is reflected, why the other is shifted, and why the product is integrated. A walk from the definition through smoothing, impulse responses, the convolution theorem, Green's functions, and the translation-invariance theorem that explains why convolution turns up everywhere.
A long read on grids, groups, graphs, geodesics and gauges: why most successful neural architectures follow from the symmetries of the data's domain, based on the 2021 book-length paper by Bronstein, Bruna, Cohen and Veličković.