用于流量矩阵预测的参数高效量子启发式快速权重编程器

摘要

流量矩阵（TMs）捕获了全网范围内的起点-终点需求，是流量工程的核心。然而，当预测必须在在线网络控制的内存、更新和训练预算约束下进行时，准确的全矩阵预测仍然具有挑战性。本文研究了紧凑型量子启发循环模型能否在无需依赖专用图、Transformer或扩散模块的情况下提供有效的TM预测。我们将门控量子启发Kolmogorov-Arnold网络快速权重编程器（QKAN-FWPs）适配于直接多步Abilene TM预测，其中每个模型从两小时的历史数据中预测包含144个起点-终点（OD）通道的矩阵中接下来的20个五分钟帧。我们在共享固定预算训练协议下，将三种QKAN放置变体与等规模长短期记忆（LSTM）网络、更大的LSTM网络以及经典门控快速权重编程器进行了基准测试。在所评估的循环模型中，G-QKANFWP实现了最低的池化均方根误差（RMSE），同时仅使用了更大LSTM网络的22.4%的资源。它还优于等规模LSTM和经典G-FWP基线，表明这一增益并非仅来自门控快速权重框架。收敛性和通道分析进一步表明，量子启发变体比等规模循环基线获得了更低的验证损失学习曲线下面积（AULC），而G-QKANFWP和GQKAN-FWP在更多的OD通道上取得了显著优势。这些结果表明，经典慢编程器与量子启发快编程器的组合是一种有前景的精度-效率设计，适用于资源受限的网络流量矩阵预测。

English

Traffic matrices (TMs) capture network-wide origin-destination demand and are central to traffic engineering, yet accurate whole-matrix forecasting remains challenging when prediction must be performed under the memory, update, and training-budget constraints of online network control. This paper investigates whether compact quantum-inspired recurrent models can provide effective TM forecasts without relying on dedicated graph, transformer, or diffusion modules. We adapt gated quantum-inspired Kolmogorov-Arnold network fast-weight programmers (QKAN-FWPs) to direct multi-step Abilene TM forecasting, where each model predicts the next 20 five-minute frames of a 144-channel origin-destination (OD) matrix from a two-hour history. We benchmark three QKAN placement variants against a matched-size long short-term memory (LSTM) network, a larger LSTM, and a classical gated fast-weight programmer under a shared fixed-budget training protocol. Among the evaluated recurrent models, G-QKANFWP achieves the best pooled root-mean-square error (RMSE), while using only 22.4% of the larger LSTM. It also outperforms both the matched-size LSTM and the classical G-FWP baseline, indicating that the gain is not due to gated fast-weight framework alone. Convergence and channel-wise analyses further show that the quantum-inspired variants obtain lower validation-loss area under the learning curve (AULC) than matched-size recurrent baselines, while G-QKANFWP and GQKAN-FWP achieve substantially more OD-channel wins. These results identify a classical slow programmer with a quantum-inspired fast programmer as a promising accuracy-efficiency design for resource-conscious network traffic-matrix forecasting.