Decay & the forgetting curve

In the brain

Memories weaken with time unless they’re renewed. Ebbinghaus measured it on himself in 1885 — a steep initial drop that flattens into a long tail^{Ebbinghaus 1885}. Forgetting isn’t simply failure: it clears capacity and keeps one-off events from overwriting durable knowledge.

Whether the trace physically fades or is just crowded out by competitors is a century-old open question⚖.

The model

The forgetting curve. Retention falls off as an exponential or, better-fitting, a power-law function of elapsed time^{Wickelgren 1974}, modulated by how strongly it was encoded and flattened each time it’s retrieved — the mathematics behind spaced repetition.

In AI

The most-copied idea in AI memory. MemoryBank applies Ebbinghaus directly; a granted EMC/Dell patent decays relevance by linear, exponential, or step functions; DeWix claims R = e^(−a·x). Counterparts computes strength on read from salience, access history, and elapsed time rather than storing a stale number. Most systems still decay linearly, which doesn’t match the brain’s power-law shape.