Lemma
math, backwards
journey · 4 days · ml → finance
Finding the Minimum
The nouns change — loss, calibration error, portfolio risk. The shape is the same — choose a number to improve, move through choices, stop when improvement runs out. This path reads the optimization module first, then walks the three applications that already use it, with the same five-step skeleton in mind on every page.
Most of math that calls itself fitting, tuning, minimizing, or finding equilibrium is one procedure under different vocabularies. Read the skeleton once; the rest of the path is the same five steps with three different what to improve.
the path · 0/4 · 0%
- 1module·day 1·→ next/modules/optimizationRead the skeleton first. Five steps — objective, search space, move, step size, stopping — and the widget that walks them in 1D. Note what each step is *named* abstractly; the applications will rename them.open →
- 2application·day 2/ml/gradient-descentThe canonical example. Objective = loss. Search space = a parameter. Move = the derivative. Step size = the learning rate. Read with the five-step skeleton in mind — every word on the page lands on one of the five.open →
- 3application·day 3/ml/model-calibrationSame skeleton, one-dimensional search space. Objective = negative log-likelihood. Search space = a single scalar T. Move = the derivative of NLL with respect to T. *Two pages, identical procedure*; only the dimension differs.open →
- 4application·day 4/finance/portfolio-riskSame skeleton, finance vocabulary. Objective = portfolio variance. Search space = weights summing to 1. Move = the derivative of variance with respect to weight. For two assets the minimum is closed-form; in higher dimensions the same procedure iterates. *The skeleton crosses pillars without changing.*open →