gatehorizon

the question

Can a bfloat16-stored decay gate represent slow-forgetting memory half-lives?

what came out

In bfloat16 near 1 the gate spacing is 2^-8, so any target decay below 2^-9 snaps to exactly 1.0 (never forgets) and the longest finite half-life is about 177 steps (177.1 exactly; ln2*2^8 = 177.4 to first order). Longer finite half-lives are unreachable, and targets between 177 and 355 collapse to it. Absent in fp32.

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