About this module
Our final module makes the implementation trustworthy enough to inspect.
Floating-point limits, online state, random seeds, shape alignment, and train-only preprocessing can change an answer without changing the displayed formula.
We finish by testing properties and preserving an audit trail, not by assuming that runnable code is correct code.
Lessons
- Lesson 111
Floating-Point Representation, Overflow, and Underflow
Why a familiar decimal can fail exact equality
2:47 - Lesson 112
Stable Summation and Mean Calculation
Recovering low-order contributions during accumulation
2:37 - Lesson 113
Stable Online Variance and Welford’s Algorithm
Updating variance as records arrive without unstable raw subtraction
2:38 - Lesson 114
Batch, Rolling, and Streaming Statistic Equivalence
Making different execution styles compute the same statistic
2:41 - Lesson 115
Missing, Infinite, Invalid, and Unsupported-State Policies
Refusing to make invalid inputs look like calm markets
2:36 - Lesson 116
Pseudorandom Numbers, Seeds, and Reproducibility
Replaying a simulation without confusing reproducibility with security
2:33 - Lesson 117
Vectorization, Index Alignment, and Shape Safety
Preventing a dimensionally valid but semantically wrong dot product
2:27 - Lesson 118
Leakage-Free Fitting, Scaling, and Preprocessing
Fitting a scaler without teaching it the test distribution
2:37 - Lesson 119
Fixtures, Numerical Tolerances, and Property Tests
Testing mathematical behavior, not just one screenshot
2:43 - Lesson 120
Reproducible Analysis, Metadata, and Audit Trails
Making a result reproducible without confusing metadata with truth
2:57