Compromissos de estabilidade numérica

Lower-precision Tensor Core math is fast, but fewer bits mean rounding errors. Numerical stability is the art of keeping results trustworthy. ⚖️

Each low-precision value is rounded to the nearest representable number. That tiny rounding error is harmless once but can pile up over many steps.

FP16's narrow range lets small numbers fall to zero, called underflow. Gradients and tiny weights can simply disappear during training.

The same narrow range causes overflow: a large value becomes infinity. One bad sum can then poison everything downstream.

A common fix is loss scaling: multiply values up before FP16 math so they leave the underflow zone, then scale back down afterward.

Tensor Cores accumulate in FP32 for a reason. That wider accumulator stops thousands of small additions from drifting badly.

Because BF16 keeps FP32's exponent, it rarely overflows or underflows. Its weakness is lower precision, not a shrunken range.

Subtracting two close numbers wipes out leading digits, called cancellation. Low precision makes the surviving error far more visible.

A safe pattern is mixed precision: do bulk multiplies in FP16 or BF16 but keep sensitive sums, norms, and updates in FP32.

Never assume a fast kernel is correct. Compare against an FP32 reference and check the error stays within an acceptable tolerance.

A simple check is the absolute difference against a trusted result. Compare this error to a small threshold you choose.

Why do Tensor Cores accumulate partial sums in FP32 even with FP16 inputs?

You learned the precision tradeoffs: watch for FP16 overflow and underflow, use loss scaling and FP32 accumulation, and always validate against a reference. 🎯