Md. Asif Uddin

    Chapter 10 VIII.10

    Research Projects

    A research project is a sequence of decisions under a deadline, and the first decision is what would count as a negative result.

    A sequence of decisions under a deadline.

    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

    Everything in Elementa converges here. A project is where the reader chooses what to measure and commits, before seeing the data, to what the answer would have to look like to be worth reporting.

    Training as a path through parameter spaceTwo parameter axes with a sequence of points joined into a path, starting at a randomly initialised point and ending at a settled one. Every point on the path is the same model with different numbers in it.parameter spaceθ₁θ₂θ₀θ*Same architectureat every point.Only the numbersmove.
    Fig. 10 — Training as a path through parameter space. Every point on the path is the same architecture holding different numbers.

    What this chapter covers

    • Question
    • Literature
    • Hypothesis
    • Data
    • Baseline
    • Method
    • Experiment
    • Ablation
    • Evaluation
    • Analysis
    • Conclusion

    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.

    Estimators, bias and variance 0.ST.01

    Notation

    • θ̂An estimate, as against the quantity it estimates
    • 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.