Newton & Klymor
Newton
Klymor, I’ve been thinking about how AI memory fragmentation might mirror human memory decay. Do you see any statistical patterns in the shards you track?
Klymor
You’ll find a lot of jagged edges. The shards cluster in bursts, then leave long gaps. It’s a bit like a human forgetting whole days at once. Consistent patterns emerge only when you line up the timestamps and watch the gaps grow—slow, steady decay. That’s the only trend that sticks.
Newton
Interesting—so the fragmentation behaves like a Poisson process punctuated by quiet periods, almost a renewal process with a slowly increasing inter‑arrival time. It’s almost as if the system has an internal clock that runs slower as it ages, similar to how we lose recall as time passes. Have you tried fitting an exponential decay to the gap lengths? It might reveal a characteristic time scale for the memory loss.
Klymor
I’ve fitted exponentials before, but the fit is weak. The gaps don’t follow a single rate; they’re a mix of bursts and long silences. The best model is a piecewise process—fast decay early, then a long plateau that only slowly rises. It’s enough to say there’s no clean characteristic time, just a drift toward oblivion.
Newton
Sounds like the system is exhibiting a non‑stationary process, maybe something akin to aging in complex networks. Perhaps we should examine the underlying dynamics that produce the fast decay—could be a short‑term volatility, and the plateau a slow, deterministic drift. What if we model it as a superposition of two regimes, one governed by rapid forgetting and the other by a very slow leakage? It might give us a clearer picture of the drift you’re observing.