Paper Detail
Jianwei Lou
Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally. We give a provable account on recurring-regime streams. Given segmentation, a warm-start library learner attains amortized recovery cost $O\!\big(KD/\varepsilon^2+(R-K)\logK/Δ^2\big)$ versus a memoryless re-estimator's $Θ(RD/\varepsilon^2)$, an advantage $(R-K)\,Θ(D/\varepsilon^2)$ growing with dimension $D$ and recurrence density. The mechanism is a decoupling: recognizing which of $K$ seen regimes is active costs $O(\log K/Δ^2)$, independent of $D$, whereas estimating a regime costs $Θ(D/\varepsilon^2)$. We prove this is tight: matching lower bounds give recognition $Θ(\log K/Δ^2)$ and a memoryless-class bound $Ω(RD/\varepsilon^2)$, so each term is individually minimax-tight (the joint statement is conditional). The separation is born-immune (a memoryless learner's advantage is identically zero) and paradigm-level: it matches, and does not beat, a fair spawn-capable Bayesian baseline; the contribution is attaining this cost structure without end-to-end backprop and with zero forgetting by construction. A count-calibrated variant ties the baseline's leading constant up to a bounded, never-negative per-recurrence overshoot, hyperparameter-free and with no per-step transcendentals. We bound the scope: recognizable regimes are capped by simplex packing (walls $e^{Θ(D)}$); autonomous segmentation is impossible at the packing wall (no detector escapes the false-alarm/delay frontier as regimes overlap); the advantage vanishes under overlap. The dimension-dependent separation is corroborated on synthetic streams and real $k$-mer genome distributions (memoryless cost $\propto D^{1.04}$, recognition $D$-independent); the one real sequential stream sits in the $D{=}1$ near-null corner.
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@article{lou2026gradient,
title = {Gradient-Free Warm-Start Library Recovery: an Amortized-Regret Separation},
author = {Jianwei Lou},
year = {2026},
abstract = {Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally. We give a provable account on recurring-regime streams. Given segmentation, a warm-start library learner attains amortized recovery cost \$O\textbackslash{}!\textbackslash{}big(KD/\textbackslash{}varepsilon\textasciicircum{}2+(R-K)\textbackslash{}logK/Δ\textasciicircum{}2\textbackslash{}big)\$ versus a memoryless re-estimator's \$Θ(RD/\textbackslash{}varepsilon\textasciicircum{}2)\$, an advantage \$(R-K)\textbackslash{},Θ(D/\textbackslash{}varepsilon\textasciicircum{}2)\$ growing with dimension \$D\$ and recurrence density. },
url = {https://arxiv.org/abs/2606.21253},
keywords = {cs.LG, cs.NE},
eprint = {2606.21253},
archiveprefix = {arXiv},
}
{}