To Retain or to Adapt? Generalizing Continual Learning — part 15/15

Cleaned-text code points [216996, 219757). Bibliography omitted here; source.md includes it.

Figure 25 is the trajectory-level analogue of the continuous-drift phase diagrams. At small drift, the history remains predictive of the current optimum, so JTL starts each task closer to a useful solution and the advantage is mostly positive. As drift increases, the same history becomes stale: the transient benefit remains visible near some task changes, but it is eventually outweighed by the stationary error of fitting too many past tasks jointly.

The supervised trajectories in Figure 26 make the same decomposition visible on real benchmarks. CLEAR is the closest empirical analogue of low drift: adjacent tasks share visual and semantic structure, so JTL can reuse previous training. MD5 and the synthetic CIFAR variants create sharper input or label shifts, making the historical data less aligned with the current task and increasing the Instability term.

Figure 27 highlights the contrast most directly. On CLEAR, the JTL trajectory tends to remain competitive or ahead because the stream changes gradually. On MD5, where each task corresponds to a more abrupt semantic change, JTL is frequently pulled toward earlier classes and ITL benefits from specializing to the current task. This is the empirical counterpart of the sign change in TE as Instability grows.

The window-agent zooms in Figure 28 illustrate why a finite memory can outperform both extremes. Early in training, the window and JTL agents are similar because little history exists. Later, the finite window discards obsolete tasks, retaining the transient benefit of recent replay while reducing the bias from distant tasks. This behavior matches the theoretical picture: the best history length grows when tasks are short or drift is slow, and shrinks when old tasks become poor predictors of the current optimum.

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