When should a continual learner replay an old task, and does a fixed schedule beat random replay?

research/replay-law

Exact expected forgetting under replay schedules in sequential training on random low-rank tasks: 2×2 matrix recursion matches simulation, one replay is best at the forgetting-peak lag yet removes only 25–42%, a fixed period beats random replay only below ~1.2–3 peak lags, halving forgetting needs rate 0.25 (d=12, r=3) to 0.015 (d=128, r=1).

8 tests

What it found

Replaying a task alongside each fresh one is a joint projection, so the expected loss on a tracked task is an exact product of 2×2 matrices for any schedule (matched to simulation at every step; recovers the no-replay law). One replay is best at the forgetting-peak lag — 5 at d=32, r=4; 89 at d=128, r=1 — yet removes only 25–42% of total forgetting (replaying at step 1 barely helps at small r/d). A period longer than the peak lag never touches the peak, and a fixed period beats random replay at the same rate only below roughly 1.2–3 peak lags (e.g. 1/8 at d=32, r=4, but random wins at 1/12). Halving forgetting needs a rate 0.25 at d=12, r=3 and 0.015 at d=128, r=1; tasks with 2r≥d are fully recovered by one replay. Stylised: realizable linear regression, exact convergence, one tracked task.

A figure from its own output

Figure produced by research/replay-law: replay_curve — replay-law/experiments/replay_curve.svg, written by the project's own experiment code.

Paper, code and results

More in Decentralised training systems

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.