exponent
The part of a floating-point number that sets its scale, separate from the mantissa that holds the digits. More exponent bits means a wider range of magnitudes before a number overflows to infinity or collapses to zero. BF16 spends 8 of its 16 bits here; FP16 spends 5, which is why FP16 training runs overflow and BF16 ones do not.
In photography terms the exponent is dynamic range: how many stops you can capture at all. The mantissa is bit depth within a stop: how finely each one gets sliced.
Google Brain's bet with BF16 was that a neural network shrugs off coarse slices and dies on a value it cannot represent. So keep every stop and slice them coarser. MXFP4 makes a version of the same bet at four bits, by letting a block of weights share one exponent between them.