用於交通矩陣預測的參數高效量子啟發快速權重編程器

摘要

流量矩陣（TMs）捕捉了網路端到端的起訖需求，是流量管理中的核心要素。然而，當預測必須在線上網路控制的記憶體、更新與訓練預算限制下進行時，準確的矩陣級預測仍是一大挑戰。本研究探討是否緊湊的量子啟發式遞迴模型能夠在無需依賴專用圖神經網路、Transformer或擴散模組的情況下，提供有效的流量矩陣預測。我們將門控量子啟發式柯爾莫哥洛夫-阿諾德網路快速權重程式設計器（QKAN-FWPs）改編應用於Abilene流量矩陣的直接多步預測任務，其中每個模型根據兩小時的歷史資料，預測一個144通道起訖（OD）矩陣的接下來20個五分鐘框架。我們將三種QKAN安置變體與規模匹配的長短期記憶網路（LSTM）、較大的LSTM，以及一個經典門控快速權重程式設計器進行基準比較，所有模型均在共享固定預算訓練協議下進行評估。在所評估的遞迴模型中，G-QKANFWP在合併均方根誤差（RMSE）上表現最佳，且其參數量僅為較大LSTM的22.4%。它同時優於規模匹配的LSTM與經典G-FWP基線，顯示此優勢並非單純來自門控快速權重框架。收斂性分析與通道分析進一步顯示，量子啟發式變體的驗證損失下之學習曲線面積（AULC）低於規模匹配的遞迴基線，而G-QKANFWP與GQKAN-FWP則獲得顯著更多的OD通道勝出。這些結果指出，經典慢速程式設計器搭配量子啟發式快速程式設計器，是一種適用於資源受限網路流量矩陣預測、兼具準確性與效率的設計方向。

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.