Md. Asif Uddin

    Chapter 6 IV.6

    Prompting and In-Context Learning

    In-context learning is task inference at run time, and calling it learning obscures that nothing is updated.

    Task inference at run time, not learning: the parameters do not move.

    How this chapter is built

    M1Definitional

    Mathematics defines, and stops there. At most three displayed equations, no derivations.

    basics2/6what the words mean
    concept2/2what to picture
    theory0/1why it works, and when it does not
    mathematics0/4derive it, then compute it
    practice0/5build it, break it, read the papers

    Five strands, not one. Mathematics is the spine; the other four are the body. A chapter cannot pay its way out of teaching with problems, nor out of problems with teaching.

    Before you start

    The problem

    A model that has never been trained on a task can perform it from three examples in its context. Whatever is happening, it is not gradient descent, and the distinction matters for what can and cannot be relied on.

    Context length against output resolutionTwo axes: sequence context and output resolution. Earlier models occupy one corner or the other — fine resolution over a short window, or a long window with binned outputs. AlphaGenome occupies the corner that was assumed unreachable.contextresolution ↑ · context →SpliceAI, BPNet10kb, base resolutionEnformer, Borzoi200–500kb, 32–128bp binsAlphaGenome1Mb, base resolutionthe corner nobody hadThe constraint was computational rather than conceptual. Eleven output modalities at once, from one sequence.
    Fig. 6 — Context against output resolution. Every earlier model sits on one edge or the other; the claim is that the corner between them was an engineering limit rather than a law.

    What this chapter covers

    • Zero-shot
    • Few-shot
    • Chain-of-thought
    • Structured prompting
    • Tool use
    • Reasoning prompts

    Apparatus

    The mathematics this chapter leans on, held in Book 0 so it can be assumed here without being taught here. Not a gate — follow a link when a step stops making sense.

    Bayes' rule 0.PR.04

    Notation

    • TSequence length in tokens
    • 𝔼Expectation

    Propositions

    Not yet written. The topics above are the plan for this chapter; each will become a proposition with its own figure.

    Worked problems

    0/1 problems0/1 variants0/3 exercisesowes 4 more

    Not yet written. At M1 this chapter owes 1 worked problems across 1 distinct variants, and 3 exercises, every one with a published solution. The build enforces that from the day the chapter is marked published.