用于储备池计算零展开超参数选择的自由概率核
Free-Probability Kernels for Zero-Rollout Hyperparameter Selection in Reservoir Computing
- Telenor Research & Innovation（挪威电信研究与创新中心）
- University of Pisa（比萨大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出基于自由概率核的零展开超参数选择方法，无需大量展开即可高效选择储备池计算的超参数，性能接近穷举搜索且成本大幅降低，在多个时间预测任务中表现优异。
AI中文摘要：
储备池计算（Reservoir Computing，RC）将固定的循环动力系统与经过训练的轻量级读出器相结合，但其效率在超参数选择过程中部分丧失：循环增益、输入尺度和泄漏率决定了储备池的稳定性和时间处理机制，通常需要通过多次展开（rollout）进行调优。我们针对带坐标-wise非线性特征的泄漏线性储备池，提出了一种确定性的、基于先导样本的选择器。自由概率可生成跨滞后传播系数，用于总结储备池混合过往输入的方式。在大宽度极限下，这些系数定义了一个确定性时间核，可近似有限储备池的特征几何结构。因此，对短标记先导序列进行核岭回归，无需实例化或展开储备池即可对候选操作机制进行排序，且所选配置可跨不同宽度迁移。在10个合成时间基准测试中，零展开选择的平均部署得分为0.772，而基于穷举模拟搜索的平均得分为0.774，同时避免了156600次选择展开。在少量展开预算下，所提排序方法在每个测试的预算下均达到最强平均性能，且仅用穷举搜索4.8%的展开成本即可达到其性能。在4个公开的电力变压器温度（Electricity-Transformer-Temperature，ETT）预测数据集上，5个保留的候选方案在3个数据集上恢复了穷举搜索的最优操作点。在多元蜂窝流量预测任务中，每个单元仅需15次展开即可达到462次展开的穷举搜索参考性能，且在低预算下优于随机搜索和贝叶斯优化。这些结果表明，当验证展开稀缺时，自由概率核可作为选择储备池操作机制的确定性替代工具。
英文摘要：
Reservoir computing (RC) couples a fixed recurrent dynamical system with a trained lightweight readout, but this efficiency is partly lost during hyperparameter selection: the recurrent gain, input scale, and leakage rate determine the reservoir's stability and temporal processing regime and are usually tuned through many rollouts. We introduce a deterministic, pilot-informed selector for leaky linear reservoirs followed by coordinate-wise nonlinear features. Free probability yields cross-lag propagation coefficients that summarize how the reservoir mixes past inputs. In the large-width limit, these coefficients define a deterministic temporal kernel that approximates the finite-reservoir feature geometry. Kernel ridge regression on a short labelled pilot sequence therefore ranks candidate operating regimes without instantiating or rolling out a reservoir, and the selected configuration transfers across widths. Across ten synthetic temporal benchmarks, zero-rollout selection obtains a mean deployment score of $0.772$, compared with $0.774$ for exhaustive simulation-based search, while avoiding $156\,600$ selection rollouts. With a small rollout budget, the proposed ranking provides the strongest mean performance at every tested budget and reaches the exhaustive reference using $4.8\%$ of its rollout cost. On four public electricity-transformer-temperature (ETT) forecasting datasets, five retained candidates recover the exhaustive operating point on three datasets. On multivariate cellular-traffic forecasting, 15 rollouts per cell reach the 462-rollout exhaustive reference and outperform random search and Bayesian optimization at low budgets. These results position free-probability kernels as deterministic surrogates for selecting reservoir operating regimes when validation rollouts are scarce.
