无需梯度的持续学习方法，可实现低遗忘、高效率的模型更新。
Gradient-Free Warm-Start Library Recovery: an Amortized-Regret Separation
- 通过解耦识别与估计，实现不依赖梯度的局部在线学习。
- 在高维数据下，相比传统方法降低恢复成本达$O((R-K)D/\varepsilon^2)$。
- 适用于边缘计算和流式数据场景，适合无记忆、零遗忘需求的部署。
针对边缘与流式部署中无需梯度、局部、在线且追加式的持续学习，本文在循环模式流上给出了可证明的分析。给定分段信息，热启动库学习者在恢复成本上达到 $O\!ig(KD/\varepsilon^2 + (R-K)\log K/\Delta^2\big)$，优于无记忆重估器的 $Θ(RD/\varepsilon^2)$，优势为 $(R-K)\,Θ(D/\varepsilon^2)$，随维度 $D$ 与重复密度增长。其机制在于解耦：识别 $K$ 个已见模式的活跃状态成本为 $O(\log K/\Delta^2)$，独立于 $D$；而估计一个模式的成本为 $Θ(D/\varepsilon^2)$。我们证明该界紧致：匹配下界表明识别与无记忆类下界分别为 $Θ(\log K/\Delta^2)$ 与 $Ω(RD/\varepsilon^2)$，每项均为极小极大最优（联合结论条件成立）。该优势为固有免疫型（无记忆学习者无优势），且处于范式级——与公平的贝叶斯基线持平但无需端到端反向传播与遗忘。计数校准变体将基线主导常数绑定至一个有界、非负的每循环超调量，无需超参且无每步超越函数。我们界定范围：可识别模式数受单纯形打包限制（墙为 $e^{Θ(D)}$）；自主分段在打包墙处不可能（探测器无法逃离误报/延迟前沿，当模式重叠时优势消失）。维度相关分离在合成流与真实 $k$-mer 基因组分布上得到验证（无记忆成本 $\propto D^{1.04}$，识别成本 $D$-无关）；一实序列流位于 $D=1$ 的近零区域。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。