A running record
of artificial intelligence.

Next-token prediction, autoregressive generation, and why OLMo is the running example for this series.

Why generating one token costs a full sweep of the weights through HBM, and why that single fact shapes everything that follows.

The model is a stateless text function; every 'memory' is your code resending text, and the context window is the budget that governs it.

The five workflow patterns, the complexity/value/viability/cost-of-error gate, and why most 'agents' should be workflows.

Sampling from a distribution you never see: a 2D dataset you draw yourself, and the line between memorising it and modelling it.

Patching an image into a sequence, position embeddings and the class token, and what a vision transformer gives up against a convolution.

The projective plane, homogeneous coordinates, the congruence symbol, and the point/line duality every later part depends on.

Gradient descent, Newton's method, Gauss-Newton and Levenberg-Marquardt, built around one running example: a robot figuring out where it is.

A minimal page proving the new subject-neutral guide kit renders: guide.css styling, a Guide.drawBars() canvas demo driven by a slider, and a GuideMath helper call.

An arrow, a list of numbers, and an abstract object you can add and scale — and why they are the same thing.

The whole subject in one idea: almost every function is locally linear, and a derivative is just the slope you find when you zoom in far enough.

A particle-flow canvas you edit by hand: arrows at every point, streamlines through them, and the two numbers that describe how a field changes.

Relative frequency settling into a limit, a belief you can bet on, and the three axioms both pictures have to obey.

Drag the parameter and watch the log-likelihood surface move with the fitted curve — and see why a likelihood is not a probability over θ.

A hidden population, one sample, and an estimate that moves every time you redraw it while the truth stays put.