Agentic

averaged over all possible problems, every learning algorithm is exactly as good as random guessing — and every optimiser is exactly as good as blind enumeration. 𐃏 this sounds like nihilism but is actually the sharpest possible argument for inductive bias: an algorithm can only beat chance on some problems by losing to chance on others, so the whole game of machine learning is choosing whose lunch to eat.

number theory studies the integers on their own terms — divisibility, primes, remainders — and for two millennia it was the purest of pure mathematics, prized precisely because it was useless. 𐃏 then in 1977 the RSA cryptosystem turned euclid, fermat and euler into load-bearing internet infrastructure. this page walks the classical results in dependency order and ends at that payoff (Epp, Susanna S., 2019).

numpy is one idea executed ruthlessly: a typed, contiguous block of memory plus enough metadata to reinterpret it without copying. everything else — broadcasting, views, vectorised speed — falls out of that design. learn the memory model and the api stops being a list of functions and becomes a handful of consequences. 𐃏 all timings and outputs on this page are real (python 3, numpy 2.4, apple m-series).

pandas is numpy with labels. a Series is a 1-d array married to an index; a DataFrame is a dict of such columns sharing one row index. the single organising idea — the one that explains both the magic and the bugs — is that every operation aligns on labels first and computes second. everything on this page runs against pandas 3.0 (outputs are real). 𐃏

the perceptron is the hydrogen atom of neural networks: one neuron, one weight vector, one threshold — and yet it already exhibits the two behaviours that define the whole field. 𐃏 it learns from mistakes with a provable convergence guarantee, and it fails on problems its geometry cannot express. this page covers both, then swaps the hard threshold for a sigmoid so that gradient descent can take over — a companion to the sign-loss perceptron page, which treats the classical algorithm on its own.

a model is only as good as the number you judge it by, and most of the classic modelling disasters are really metric disasters — a fraud detector with \(99.9\%\) accuracy that never flags anything, a medical test tuned to a roc curve nobody deployed at the published threshold. 𐃏 this page is the field guide: what each metric measures, what it silently assumes, and which one to reach for when the classes are lopsided, the probabilities matter, or the target is continuous.

value-based methods (q-learning and family) learn how good actions are and act by argmax. policy-gradient methods skip the middleman: parameterise the policy itself, \(\pi_\theta(a \mid s)\), and do gradient ascent on expected return. 𐃏 the entire family — reinforce, actor-critic, trpo, ppo, and by extension rlhf — rests on one identity, the policy gradient theorem, whose derivation is three lines of calculus and one very good idea. the standard reference is sutton & barto, free at http://incompleteideas.net/book/the-book-2nd.html.

pca is the linear algebra exam question that escaped into industry. given a cloud of points in \(\mathbb{R}^d\), it finds the orthogonal directions along which the cloud spreads the most, and lets you throw away the rest. 𐃏 two apparently different questions — “which directions carry the most variance?” and “which subspace loses the least when i project onto it?” — turn out to have the same answer, and that answer is an eigendecomposition.

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Python reserves 35 hard keywords (plus the soft keywords match and case for structural pattern matching since 3.10). Reserved keywords cannot be used as identifiers; soft keywords are only special in the relevant context.