WEBVTT

00:00:00.000 --> 00:00:07.827
A derivative near zero point two becomes exactly zero in reverse mode. This is an actual MLX CPU result.

00:00:07.827 --> 00:00:18.760
The function is one hundred million times exp minus one, evaluated at minus twenty. Forward mode gives approximately zero point two zero six one one five.

00:00:18.760 --> 00:00:27.827
The backward rule reconstructs the derivative from the rounded output plus one. Once the output rounds to minus one, the derivative disappears.

00:00:27.827 --> 00:00:39.694
Computing exp directly repairs the tested float thirty two cases. But float sixty four also needs the already reported exp correction; otherwise some cases regress.

00:00:39.694 --> 00:00:49.902
The combined change passes all two hundred sixteen native comparisons, including second and third derivatives. Tests and all four control variants are public.

00:00:49.902 --> 00:01:01.302
An analogous JAX report is credited. This is an MLX implementation audit, with no global priority claim. GPU behavior and performance remain untested.
