Conclusion

Numerical stability is part of model behavior.

You have seen the main deep-learning failure modes and fixes:

• dtype choice affects range, precision, memory, and speed
• FP16 and BF16 are useful but require care
• overflow and underflow come from values outside representable ranges
• log-sum-exp and stable softmax avoid dangerous exponentials
• epsilons guard small denominators
• NaN and infinity are alarms
• mixed precision trades memory and speed against stability

The next chapter introduces a framework only after these moves are visible. At that point, framework code should feel like compression of known ideas: tensors, gradients, modules, losses, optimizers, and data loading.