Parameter-Efficient Quantum-Inspired Fast Weight Programmers for Traffic-Matrix Forecasting

Technical Summary: Parameter-Efficient Quantum-Inspired Fast Weight Programmers for Traffic-Matrix Forecasting

Problem Statement
Traffic matrices (TMs) represent the origin–destination (OD) demand across a network and are critical for traffic engineering tasks such as capacity planning, congestion mitigation, and routing. While accurate whole-matrix forecasting is essential, it faces significant constraints in operational environments. In online network control loops, particularly within edge and cloud-edge settings, models must operate under strict memory, compute, and training-budget limitations. Moving fine-grained telemetry to remote clouds introduces latency and bandwidth costs, necessitating local prediction capabilities that are resource-efficient. Existing high-accuracy methods often rely on large-scale graph, transformer, or diffusion modules that may exceed these resource budgets. This paper investigates whether compact, quantum-inspired recurrent models can provide effective whole-matrix forecasts without relying on dedicated spatial encoders or large-capacity architectures.

Methodology
The authors adapt the Gated Quantum-Inspired Kolmogorov–Arnold Network Fast Weight Programmer (QKAN-FWP) architecture to the task of direct multi-step traffic-matrix forecasting. The study utilizes the Abilene backbone network dataset, processing 24 weekly files into 5-minute TM frames. Each frame consists of 144 OD pairs, converted into a frame-normalized TM (FN-TM) representation where values are inverted and scaled to [0, 1] to reflect relative traffic intensity.

The experimental protocol involves a direct multi-step forecasting approach: models ingest a 2-hour history (24 frames) and predict the subsequent 100 minutes (20 frames) in a single forward pass. The evaluation compares three variants of the QKAN-FWP family against three baselines under a shared fixed-budget training protocol (50 epochs, fixed learning rate, Adam optimizer):

1. G-QKANFWP: A classical slow programmer generates updates for a Hybrid QKAN (HQKAN) fast programmer (quantum-inspired nonlinearity in the fast readout).
2. GQKAN-FWP: The HQKAN module is placed in the slow programmer, with a classical linear fast programmer.
3. GQKAN-QKANFWP: HQKAN modules are used on both the slow and fast sides (the most compressed variant).
4. Baselines: A matched-size LSTM (LSTM-S), a larger LSTM (LSTM-L), and a classical Gated Fast Weight Programmer (G-FWP) without quantum-inspired components.

Performance is measured using pooled Root-Mean-Square Error (RMSE) across all test windows, horizons, and OD channels, as well as validation-loss Area Under the Learning Curve (AULC) and OD-channel win rates.

Key Contributions

1. Benchmarking: The study provides a rigorous comparison of gated QKAN-FWP variants against standard recurrent baselines (LSTMs) and a classical fast-weight baseline on a multi-channel TM forecasting task.
2. Architecture Analysis: It isolates the impact of quantum-inspired module placement within the fast-weight framework, testing whether the nonlinearity is more effective in the fast readout, the slow update generator, or both.
3. Efficiency-Accuracy Trade-off: The work demonstrates that a compact recurrent model can achieve competitive or superior accuracy to larger models while significantly reducing parameter counts, specifically validating the "accuracy–efficiency" design space for resource-conscious network control.

Results

• Aggregate Accuracy: The G-QKANFWP model achieved the best pooled RMSE (0.06897 ± 0.00030) among all evaluated models. It outperformed the matched-size LSTM-S (0.07155) and the classical G-FWP (0.07038). Notably, it slightly outperformed the significantly larger LSTM-L (0.06920) while using only 22.4% of LSTM-L's parameters (8,189 vs. 36,624 parameters).
• Horizon Performance: G-QKANFWP showed the strongest performance at short (H=1) and long (H=20) horizons, while LSTM-L remained slightly superior at the intermediate H=10 horizon.
• Convergence: All quantum-inspired variants demonstrated lower validation-loss AULC than the matched-size LSTM-S and the classical G-FWP, indicating faster and more sustained loss reduction within the fixed training budget. G-QKANFWP matched the convergence of the larger LSTM-L.
• Channel-Level Wins: While LSTM-L won the most individual OD channels (52/144), the quantum-inspired models (G-QKANFWP and GQKAN-FWP) won substantially more channels (33 and 39, respectively) than the matched-size baselines (8 each), suggesting localized improvements across the network topology.
• Ablation Insights: The comparison with G-FWP confirms that the performance gain is not solely due to the gated fast-weight framework but is significantly enhanced by the quantum-inspired fast readout. Placing HQKAN in the fast readout (G-QKANFWP) proved more effective than placing it in the slow programmer or on both sides for this specific task.

Significance and Claims
The paper claims that G-QKANFWP represents a promising "accuracy–efficiency" design for resource-conscious network traffic-matrix forecasting. The primary significance lies in demonstrating that a classical slow programmer combined with a quantum-inspired fast programmer can achieve state-of-the-art pooled accuracy with a fraction of the parameters required by larger recurrent baselines.

The authors modestly frame their contribution not as a replacement for high-capacity forecasters but as a validation of compact recurrent models for specific operational constraints. They emphasize that the results are specific to the Abilene dataset and the fixed-budget training protocol. The study intentionally isolates the temporal recurrent component, suggesting that future work should integrate these efficient recurrent modules with dedicated spatial encoders (e.g., graph or diffusion modules) to further leverage spatial dependencies. The findings support the viability of quantum-inspired fast-weight programming as a lightweight alternative for online network control where memory and training budgets are primary limitations.