Numbers in the Machine: Floating Point for Machine Learning
Why does 0.1 + 0.2 not equal 0.3? A silent, animated tour of how computers represent numbers — and why it matters when you train neural networks. Covered: • Integers: exact, but bounded • Floating point as scientific notation in binary • Why floats spread out — uneven spacing along the number line • Is floating point "broken"? (no — and why) • The ML number zoo: fp32, fp16, bf16, fp8 • Training in low precision, and the tricks that keep it stable • Underflow, overflow, NaNs, and numerically-stable softmax / log-sum-exp / loss scaling Built with Manim. No narration or music; everything is explained on screen.
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