by Prof. Saurabh · ZC416 · BITS Pilani WILP
All 16 sessions of MFML, rebuilt as interactive lessons: every idea told as a story first, every slide example worked in full, every concept something you can drag, zoom, and break. Read the intuition, play the widget, then pass the inline checks.
A matrix is a machine that moves space. Three windows on Ax = b, the three fates, and elimination — the algorithm that never lies.
The universe where vectors live: groups, subspaces, span, independence, basis, dimension — the architecture of ML math.
The board gets its ruler: norms, inner products, angles, orthogonality — and Gram–Schmidt, the cleanest grid a geometry can have.
A matrix's fingerprints: the numbers and directions that survive the transformation.
Take one complicated matrix apart into simple honest pieces — the ladder from spectral to SVD to low-rank.
Derivatives from scalars to tensors — the language of "which way is down?"
The chain rule, industrialized: how a network computes a million derivatives for the price of two forward passes.
Polynomial impostors: approximating any function — and knowing exactly how big the lie (the remainder) is.
Walk downhill in thick fog: steps, step sizes, and why a little noise helps you scale.
Nonlinear optimization and the minutiae that make or break gradient methods.
Momentum, AdaGrad, RMSProp, Adam — and the cliffs and valleys that defeat naive descent.
Compress a thousand dimensions without losing the story: variance, projections, eigenvectors.
Principal components at work — linear algebra earning its keep on real data.
Lagrange multipliers, KKT conditions, duality, and the kernel trick — the math that draws the widest possible line.
From primal to dual to solution — and soft margins for a messy world.
Awaiting slides — drop Lecture_16.pdf into the MFML folder and this unit joins the queue.