AI Engineering/Phase 01/Lesson 13

Numerical Stability

Floating point is a leaky abstraction. It will bite you during training, and you will not see it coming.

Build 2 hr Python

Prerequisites: Phase 1, Lessons 01-04

#Learning Objectives

Implement numerically stable softmax and log-sum-exp using the max-subtraction trick
Identify overflow, underflow, and catastrophic cancellation in floating-point computations
Verify analytical gradients against numerical gradients using centered finite differences
Explain why bfloat16 is preferred over float16 for training and how loss scaling prevents gradient underflow

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The text and code of this lesson are based on AI Engineering from Scratch by Rohit Ghumare, MIT licensed.