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

Kuo-Chung Peng; Jiun-Cheng Jiang; Chun-Hua Lin; Tai-Yue Li; Nan-Yow Chen; Samuel Yen-Chi Chen

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

Kuo-Chung Peng, Jiun-Cheng Jiang, Chun-Hua Lin, Tai-Yue Li, Nan-Yow Chen, Samuel Yen-Chi Chen

arXiv:2606.27821v1Jun 26, 2026quant-phcs.AIcs.LG

TL;DR

Whole-matrix traffic forecasting must capture temporal and cross-channel dependencies under online control constraints. This paper benchmarks compact quantum-inspired fast-weight recurrent models for direct multi-step Abilene forecasting and finds that G-QKANFWP delivers the best pooled RMSE among evaluated recurrent models using 22.4% of the larger LSTM’s parameters.

Problem
Whole-matrix traffic forecasting must preserve temporal and cross-channel dependencies while operating within constrained memory, compute, update, and training budgets.
Method
The paper adapts gated quantum-inspired Kolmogorov–Arnold network fast-weight programmers to direct multi-step Abilene traffic-matrix forecasting and benchmarks variants against recurrent baselines.
Results
0.06897±0.00030 pooled RMSE: G-QKANFWP achieves the best result among evaluated recurrent models using only 22.4% of the larger LSTM-L’s parameters.
Takeaways & Limitations
G-QKANFWP is a strong compact recurrent candidate for traffic-matrix forecasting when model size and training budget matter.

Abstract

from arXiv · show

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.

I. INTRODUCTION

The introduction frames whole-matrix traffic-matrix forecasting as a structured problem requiring temporal modeling and cross-channel dependency preservation under resource-conscious operational constraints. It presents compact quantum-inspired recurrent models as a candidate approach and reports G-QKANFWP’s accuracy-efficiency advantage over recurrent baselines.

Motivation: Traffic matrices require forecasting methods that model temporal dynamics while preserving cross-channel dependencies for network operations.These dependencies support capacity planning, congestion mitigation, routing, failure response, and resource scheduling.
Approach: Compact quantum-inspired recurrent models are evaluated for direct multi-step Abilene traffic-matrix forecasting under a resource-conscious setting.The study adapts the gated quantum-inspired Kolmogorov–Arnold network fast-weight programmer (QKAN-FWP) family.
Evaluation: The benchmark compares three gated QKAN-FWP variants with matched-size and larger LSTM networks plus a classical G-FWP baseline.All models are evaluated on a multi-channel traffic-matrix forecasting task.
Results: G-QKANFWP achieves the best pooled RMSE, outperforms LSTM-S and classical G-FWP, and slightly improves over LSTM-L using only 22.4% of LSTM-L’s parameters.This result identifies an accuracy-efficiency advantage for the quantum-inspired variant relative to the evaluated recurrent baselines.
Results: All quantum-inspired variants achieve lower validation-loss AULC than LSTM-S and G-FWP under the fixed epoch budget.The convergence analysis complements aggregate forecasting accuracy with learning-curve behavior.

II. RELATED WORK

Related work spans traffic-matrix and spatio-temporal forecasting, compact recurrent sequence models, fast-weight programmers, and quantum-inspired sequence learning. The proposed architecture follows this trajectory by pairing a classical slow programmer with an HQKAN fast programmer.

Traffic-matrix and spatio-temporal forecasting: Traffic-matrix forecasting extends OD-demand estimation from current or historical states to future network states, including neural approaches for dynamic traffic engineering and SDN prediction.The literature connects classical partial-measurement and link-load estimation with subsequent forecasting methods.
Compact sequence models: LSTMs support streaming prediction through incremental sequence processing, while fast-weight programmers store temporal information in dynamically updated parameters.These approaches provide compact recurrent alternatives to relying only on hidden states.
Compact sequence models: G-QKANFWP combines a classical slow programmer that dynamically generates the parameters of an HQKAN fast programmer.This architecture is presented as a quantum-inspired fast-weight programming design.

III. MODEL ARCHITECTURES AND BASELINES

The study compares three gated quantum-inspired fast-weight programmer placements with classical fast-weight and LSTM baselines. The variants differ in whether HQKAN appears in the fast readout, slow programmer, both, or neither.

Fast-weight framework: Gated fast-weight programmers use a slow pathway to update compact fast parameters, a fast pathway to generate outputs, and a scalar gate to stabilize evolution.The gate interpolates between previous fast parameters and the new proposal.
Quantum-inspired variants: G-QKANFWP places HQKAN in the fast readout while retaining a classical slow programmer.This tests whether a quantum-inspired fast programmer helps when the update generator remains simple.
Quantum-inspired variants: GQKAN-FWP places HQKAN in the slow programmer and uses a classical linear fast programmer.This tests whether HQKAN is more useful before fast-memory generation than inside the fast readout.
Quantum-inspired variants: GQKAN-QKANFWP uses HQKAN on both slow and fast sides and is the smallest model in the comparison.It tests whether greater compression can preserve whole-matrix forecasting accuracy.
Baselines: The comparison includes classical G-FWP without HQKAN, matched-size LSTM-S, and larger LSTM-L baselines.G-FWP isolates the gated fast-weight framework from the quantum-inspired components.

IV. DATA AND EXPERIMENTAL PROTOCOL

The experiments use frame-normalized Abilene traffic matrices represented as 144-dimensional OD vectors and evaluate direct 20-step forecasts from two-hour histories. Models are compared under a fixed chronological split and training budget using pooled horizon errors, OD-channel wins, and validation-loss AULC.

Dataset: 48,384 five-minute frames from 24 weekly Abilene files are represented as 144-dimensional origin-destination vectors.Each original row contains 720 values organized as 144 OD pairs, with the 12 × 12 matrix form used only for visualization.
Preprocessing: Frame-normalized traffic matrices retain values in [0, 1], and all losses and reported errors are computed in FN-TM space.Normalization is performed over the 144 OD entries within each frame; larger FN-TM values indicate lower relative raw traffic because of the inversion.
Forecasting protocol: Each model directly predicts 20 future five-minute frames from 24 historical frames, corresponding to 100 minutes ahead without autoregressive roll-outs.RMSE@1, RMSE@10, and RMSE@20 represent 5, 50, and 100 minutes ahead, respectively.
Training protocol: 70/15/15 chronological splits and 50-epoch training with MSE loss, learning rate 10^-3, and five random seeds define the shared evaluation budget.The same direct-forecast setup is applied across training, validation, and test windows.
Evaluation metrics: OD-channel wins and normalized Val-loss AULC complement pooled RMSE by summarizing localized performance and convergence within the fixed training budget.Channel wins use seed-averaged per-channel RMSE, while lower AULC indicates lower validation loss during training and is not a test-set accuracy metric.

V. RESULTS AND ANALYSIS · A. Aggregate Accuracy and Parameter Efficiency

G-QKANFWP delivers the best pooled RMSE among the evaluated recurrent models while using a small fraction of the larger LSTM’s parameters. Horizon-level results support an accuracy–parameter trade-off rather than universal dominance, with matrix diagnostics serving as qualitative supplementary evidence.

A. Aggregate Accuracy and Parameter Efficiency: 0.06897±0.00030 pooled RMSE is achieved by G-QKANFWP with 8,189 parameters, outperforming the matched-size LSTM-S.LSTM-S reaches 0.07155 ± 0.00053 pooled RMSE with slightly more parameters.
A. Aggregate Accuracy and Parameter Efficiency: 22.4% of LSTM-L’s parameter count is used by G-QKANFWP while achieving slightly lower pooled RMSE than LSTM-L.G-QKANFWP reaches 0.06897±0.00030 pooled RMSE, versus 0.06920±0.00019 for LSTM-L.
A. Aggregate Accuracy and Parameter Efficiency: All three quantum-inspired variants improve over LSTM-S in pooled RMSE, although the other two trail both G-QKANFWP and LSTM-L.This comparison places G-QKANFWP as the strongest quantum-inspired variant in the aggregate results.
A. Aggregate Accuracy and Parameter Efficiency: 0.07038 ± 0.00057 pooled RMSE is obtained by G-FWP, so G-QKANFWP’s improvement is not explained by the gated fast-weight framework alone.G-FWP retains the gated fast-weight framework but removes the HQKAN components.
A. Aggregate Accuracy and Parameter Efficiency: H = 1 and H = 20 are won by G-QKANFWP, while LSTM-L remains slightly better at H = 10.At H = 1, G-QKANFWP improves over LSTM-S by about 7.4% relative and over LSTM-L by about 2.9% relative.
A. Aggregate Accuracy and Parameter Efficiency: About 7.4% relative improvement over LSTM-S and about 2.9% over LSTM-L are observed for G-QKANFWP at H = 1.At H = 20, the advantage over LSTM-L is much smaller but still favors G-QKANFWP.
A. Aggregate Accuracy and Parameter Efficiency: Figure 2 offers a qualitative H = 20 FN-TM matrix diagnostic for assessing whether low scalar error corresponds to coherent matrix-level structure.The primary evidence remains the five-seed aggregate results in Table I.

B. Validation Convergence and OD-Channel Wins

Quantum-inspired variants converge more favorably under the fixed-budget protocol and deliver substantial OD-channel gains. G-QKANFWP is the strongest compact recurrent model, while LSTM-L remains the leading large baseline overall.

Validation convergence: 0.00298±0.00001: G-QKANFWP records the lowest Val-loss AULC, essentially tied with LSTM-L at 0.00299 ± 0.00001.All three quantum-inspired variants have lower val-loss AULC than LSTM-S and G-FWP.
OD-channel wins: 52 of 144: LSTM-L wins the most OD channels, while GQKAN-FWP and G-QKANFWP win 39 and 33, respectively, versus 8 each for LSTM-S and G-FWP.An OD-channel win is based on the lowest pooled per-channel RMSE.
OD-channel wins: GQKAN-FWP wins more channels than G-QKANFWP despite weaker pooled RMSE, indicating broader lower-impact flow gains for GQKAN-FWP and stronger aggregate-error reduction for G-QKANFWP.The channel-wise pattern shows that quantum-inspired models improve localized performance, not merely a small set of high-variance channels.
OD-channel wins: Figure 3 uses H = 20 sliding test-window traces on selected OD channels to diagnose localized improvements over the strongest classical comparator.The traces are intended to be interpreted alongside aggregate metrics rather than as standalone evidence.
Overall comparison: Under common-learning-rate fixed-budget training for spatially coupled Abilene channels, G-QKANFWP beats LSTM-S and G-FWP, slightly leads LSTM-L in pooled RMSE, and matches it in Val-loss AULC.The fully HQKAN-based compressed variant remains competitive with LSTM-S, despite differing from its ordering in heterogeneous prior tasks.

VI. CONCLUSION

G-QKANFWP provides the strongest accuracy–efficiency result among the evaluated recurrent models, achieving the best pooled RMSE with substantially fewer parameters than LSTM-L. The study also identifies spatial-module integration and further hyperparameter analysis as next steps.

Main findings: 22.4%: G-QKANFWP uses only 22.4% of LSTM-L’s parameters while achieving the best pooled RMSE among evaluated models.All three quantum-inspired variants also outperform LSTM-S in pooled RMSE and have lower validation-loss AULC than LSTM-S and G-FWP.
Accuracy–efficiency trade-off: G-QKANFWP leads LSTM-L in pooled RMSE, matches its validation-loss AULC, and requires far fewer parameters, although LSTM-L is slightly better at H = 10 and wins the most OD channels.The conclusion frames this as an accuracy–efficiency trade-off under model-size and training-budget constraints.
Future work: Future work should combine G-QKANFWP with graph, diffusion, or topology-aware modules and study hyperparameter sensitivity, especially learning-rate effects across the gated QKAN-FWP family.The current study intentionally isolates the recurrent temporal model and does not add a dedicated spatial module.