提出考虑时间依赖的有效样本量评估方法，提升时序模型泛化分析准确性。
Effective Sample Size and Generalization Bounds for Temporal Networks
- 用有效样本量替代序列长度控制实验，结合分块耦合技术提取独立锚点
- 证明TCN在β-混合序列上泛化误差随有效样本量呈约N_eff^{-1.0}的快速下降
- 适用于关注时序建模泛化性、需公平比较不同依赖强度模型的研究者
从时间序列学习本质上不同于独立同分布数据：时间依赖会使长序列实际信息稀疏，而现有评估协议却将序列长度与统计信息混为一谈。本文提出一种依赖感知的评估方法，以有效样本量 $N_{\text{eff}}$ 而非原始长度 $N$ 为控制变量，并为时序卷积网络（TCNs）在 $β$-混合序列上提供端到端泛化保证。分析结合了分块/耦合降维技术，提取出 $B = Θ(N/\log N)$ 个近似独立的锚点，以及针对 $\ell_{2,1}$-范数受控卷积网络的结构感知Rademacher界，得到深度 $D$ 和核大小 $p$ 的复杂度为 $O(\sqrt{D\log p / B})$。实验发现，在控制 $N_{\text{eff}}$ 的条件下，更强的时间依赖反而能减小泛化差距，这与固定 $N$ 评估下的结论相反，观测到的衰减速率为 $N_{\text{eff}}^{-0.9}$ 至 $N_{\text{eff}}^{-1.2}$，显著快于最坏情况下的 $O(N^{-1/2})$ 混合预测速率。结果表明，依赖感知评估应成为时序深度学习基准的标准做法。
原文摘要 · Abstract (English)
Learning from time series is fundamentally different from learning from i.i.d.\ data: temporal dependence can make long sequences effectively information-poor, yet standard evaluation protocols conflate sequence length with statistical information. We propose a dependence-aware evaluation methodology that controls for effective sample size $N_{\text{eff}}$ rather than raw length $N$, and provide end-to-end generalization guarantees for Temporal Convolutional Networks (TCNs) on $β$-mixing sequences. Our analysis combines a blocking/coupling reduction that extracts $B = Θ(N/\log N)$ approximately independent anchors with an architecture-aware Rademacher bound for $\ell_{2,1}$-norm-controlled convolutional networks, yielding $O(\sqrt{D\log p / B})$ complexity scaling in depth $D$ and kernel size $p$. Empirically, we find that stronger temporal dependence can \emph{reduce} generalization gaps when comparisons control for $N_{\text{eff}}$ - a conclusion that reverses under standard fixed-$N$ evaluation, with observed rates of $N_{\text{eff}}^{-0.9}$ to $N_{\text{eff}}^{-1.2}$ substantially faster than the worst-case $O(N^{-1/2})$ mixing-based prediction. Our results suggest that dependence-aware evaluation should become standard practice in temporal deep learning benchmarks.
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