AI Math Foundations — Personal Reference¶

Quick-access index. All content lives in four nav pages below.

What each page is¶

Page	What it covers
Modules 01–12	All 12 lesson pages — token → logit → probability → entropy → variance → regression → guardrails → evaluation
Reference	All formulas, code explanations, and distribution guide in one place
Ops Cheatsheet	Routing policy, rollout gates, audit fields, review checklist, and self-check questions
Notebook Labs	Links to all 13 Jupyter notebooks with lab descriptions

Ticket text is tokenized — budget determines how much history you can keep.
Model outputs logits — raw preference scores per intent.
Softmax converts logits to probabilities — normalized confidence values.
Entropy measures how spread-out those probabilities are — high entropy → escalate.
Temperature / top-p / top-k control how stochastic the sampling is.
Variance and std dev catch run-to-run instability across repeated prompts.
Regression predicts numeric outcomes like resolution hours from token count.
Classification + calibration tunes thresholds so auto-routing is trustworthy.
Correlation ≠ causation — segment before making policy changes.
Guardrail thresholds map confidence to auto / review / abstain actions.
Weighted KPI gates rollout decisions: go / hold / rollback.

What you observe	Distribution
Single routing decision (right/wrong)	Bernoulli
Correct routes out of N tickets	Binomial
Average quality score across many runs	Normal (bell curve)
Time between ticket arrivals	Exponential
Incident count per hour	Poisson
Token selection at high temperature	Approaches Uniform

Sprint 1 (M1–M4): tokens → probabilities → softmax → entropy.

Sprint 2 (M5–M8): stability → determinism → regression → calibration.

Sprint 3 (M9–M12): causation → sampling controls → guardrails → production evaluation.