arxiv: 2605.06734 · v1 · submitted 2026-05-07 · 💻 cs.LG · cs.AI· quant-ph

Recognition: no theorem link

Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning

Kuo-Chung Peng , Samuel Yen-Chi Chen , Jiun-Cheng Jiang , Chen-Yu Liu , En-Jui Kuo , Yun-Yuan Wang , Prayag Tiwari , Andrea Ceschini

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Chi-Sheng Chen Yu-Chao Hsu Chun-Hua Lin Tai-Yue Li Antonello Rosato Massimo Panella Simon See Saif Al-Kuwari Kuan-Cheng Chen Nan-Yow Chen Hsi-Sheng Goan

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:51 UTC · model grok-4.3

classification 💻 cs.LG cs.AIquant-ph

keywords quantum-inspired learningfast weight programmingtime series forecastingsolar cycle predictionkolmogorov-arnold networksnisq devicessequence modelinggated neural networks

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The pith

A gated quantum-inspired fast-weight model delivers better long-horizon solar forecasts than much larger classical recurrent networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes gated QKAN-FWP as a way to handle sequence data by using fast weight updates instead of hidden states, enhanced with quantum-inspired single-qubit activation circuits. It demonstrates that this 12.5k-parameter model can achieve lower errors in predicting solar cycles over long periods compared to recurrent models with up to 13 times more parameters. The scalar gate stabilizes the updates with proven properties for memory and gradients, and the model runs on actual quantum hardware with almost no loss in accuracy. A sympathetic reader would care if this opens a path to efficient, hardware-compatible quantum-inspired learning for time series tasks without massive classical computation.

Core claim

By combining fast weight programming with Kolmogorov-Arnold networks realized through single-qubit data re-uploading circuits called DARUAN and introducing a scalar-gated update rule, the framework encodes temporal dependencies in dynamically updated parameters. This yields a model that, on a 528-month input to 132-month forecast solar task, records lower scaled MSE, peak amplitude error, and peak timing error than LSTM, WaveNet-LSTM, vanilla RNN, and modified echo state networks with far more parameters, while maintaining performance when executed on quantum processors at 1024 shots.

What carries the argument

The scalar-gated fast-weight update rule, which provides an adaptive memory kernel and geometric boundedness while keeping gradient paths parallelizable, paired with single-qubit DARUAN activations as learnable nonlinearities.

Load-bearing premise

The single-qubit data re-uploading circuits supply adequate expressive power for intricate time dependencies even without multi-qubit entanglement, and the scalar-gated rule's theoretical traits translate directly into the measured forecasting improvements.

What would settle it

Running the same solar forecasting experiment with 528-month inputs and 132-month outputs, if any classical recurrent baseline with comparable or fewer parameters achieves equal or lower scaled MSE along with matching or better peak amplitude and timing errors, or if hardware execution deviates by more than 0.1 percent relative MSE from simulation.

Figures

Figures reproduced from arXiv: 2605.06734 by Andrea Ceschini, Antonello Rosato, Chen-Yu Liu, Chi-Sheng Chen, Chun-Hua Lin, En-Jui Kuo, Hsi-Sheng Goan, Jiun-Cheng Jiang, Kuan-Cheng Chen, Kuo-Chung Peng, Massimo Panella, Nan-Yow Chen, Prayag Tiwari, Saif Al-Kuwari, Samuel Yen-Chi Chen, Simon See, Tai-Yue Li, Yu-Chao Hsu, Yun-Yuan Wang.

**Figure 1.** Figure 1: HQKAN programmer architecture adapted from [JHCG25]. The model consists of a classical encoder, a latent QKAN processor, and a decoder. In this paper, HQKAN is used as a compact nonlinear programmer network inside the fast-weight framework. We adopt the Hybrid QKAN (HQKAN) instantiation of the Jiang–Huang–Chen–Goan network (JHCG Net) first introduced in [JHCG25]. HQKAN has an encoder–processor–decoder stru… view at source ↗

**Figure 2.** Figure 2: Architectures of the proposed gated fast-weight programmers. (a) GQKANFWP: An HQKAN slow programmer dynamically generates the parameters of a classical linear fast programmer following a gated update rule. (b) GQKAN-QKANFWP: Both programmers utilize HQKAN, with the slow programmer generating the DARUAN parameters for the fast module under the same gated mechanism. generates the parameter update ∆ϕt alongs… view at source ↗

**Figure 3.** Figure 3: Forecasting Solar Cycle 23 (test set). (a) Mean forecasts and shaded ±1σ bands across 5 random seeds for each model. While the ground truth (black) exhibits substantial month-to-month variability, the GQKAN-QKANFWP ±1σ envelope (orange shading) contains the ground truth throughout the rising, peak, and descending phases of the cycle. Among the baselines, only LSTM-L produces a mean prediction that overlaps… view at source ↗

**Figure 4.** Figure 4: Solar cycle forecasting results for GQKAN-QKANFWP. Orange markers represent continuous one-step-ahead forecasts stacking the first step of the 132-step horizon across overlapping sliding windows, while the red curves denote full 132-step predictions on Solar Cycle 22 and the ongoing Solar Cycle 25 generated from a single input window. The “Test Split” line marks the beginning of the test set. Additionally,… view at source ↗

**Figure 5.** Figure 5: Forecasting Solar Cycle 24 from GQKAN-QKANFWP’s fast programmer executed on QPUs. (a) Forte-1 at N = 1024 shots. (b) ibm_aachen across shot counts N ∈ {1, 16, 64, 256, 1024}; forecasts converge to the noiseless simulator as N increases, recovering cycle shape and peak within ∼ 10−3 relative MSE at N=1024. r3), we selected 100 qubits via a composite calibration score (readout error ∈ [2.6, 9.0] × 10−3 , SX … view at source ↗

**Figure 6.** Figure 6: MiniGrid-Empty environments. The agents are evaluated across environments of increasing scale: (a) 5×5, (b) 6×6, (c) 8×8, and (d) 16×16 [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗

**Figure 7.** Figure 7: Model performance on MiniGrid-Empty environments. The curves show mean episodic reward with shaded regions denoting standard deviation across 5 seeds. (a) Gatedvs-ungated ablation on the 5×5 grid: gated architectures yield higher stability and asymptotic rewards than their ungated counterparts. (b)–(e) Scaling across 5×5, 6×6, 8×8, and 16×16 grids for the top-performing variants. 7 Conclusion We presented… view at source ↗

**Figure 8.** Figure 8: Forecasting performance on the Damped SHM dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each model, demons… view at source ↗

**Figure 9.** Figure 9: Forecasting performance on the Bessel function dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each model, d… view at source ↗

**Figure 10.** Figure 10: Forecasting performance on the NARMA5 dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each model, demonstra… view at source ↗

**Figure 11.** Figure 11: Forecasting performance on the NARMA10 dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each model, demonstr… view at source ↗

**Figure 12.** Figure 12: Forecasting performance on the Delayed Quantum Control dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each… view at source ↗

**Figure 13.** Figure 13: Forecasting performance on the Jaynes-Cummings dataset (Window-size N=64). Panels (a), (b), (c), and (d) illustrate the model predictions at training epochs 15, 30, 50, and 100, respectively. Solid lines denote the mean prediction across five independent random seed initializations for the proposed GQKAN-QKANFWP and the QFWP baseline. The shaded region represents the ±1σ variance envelope for each model, … view at source ↗

read the original abstract

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Gated QKAN-FWP pairs single-qubit DARUAN activations with a scalar-gated FWP update to hit strong solar forecasting numbers at 12.5k parameters and near-simulator accuracy on real NISQ hardware.

read the letter

The main thing to know is that this paper puts forward a gated QKAN-FWP that merges fast weight programming with quantum-inspired Kolmogorov-Arnold networks using single-qubit data re-uploading circuits (DARUAN) as activations, plus a scalar gate whose update rule gets some theoretical backing on memory kernel and boundedness. It reports that the 12.5k-parameter model beats larger LSTMs, WaveNet-LSTM, vanilla RNNs, and echo state networks on 528-month input to 132-month solar cycle forecasts across scaled MSE, peak amplitude, and timing errors, while also recovering within 0.1% relative MSE of the noiseless simulator when run on IonQ and IBM hardware at 1024 shots. The single-qubit choice keeps things scalable and classically simulable compared with multi-qubit QFWPs. The theory on the gate is a concrete addition that prior FWP or QKAN work did not always supply. The NISQ deployment and the specific long-horizon solar numbers are the clearest practical outputs. The soft spots sit mainly in the expressivity claim. Because the architecture uses only single-qubit circuits and no entanglement, the DARUAN blocks function as learnable nonlinearities rather than genuinely quantum resources; it is not yet clear whether they outperform classical activations inside the same FWP skeleton or whether the solar data's strong periodicity lets the fast-weight structure do most of the work. The theoretical analysis of stability is welcome, but the parameters are data-fitted, so the boundedness results risk some circularity until they are shown to predict behavior on held-out regimes. The abstract mentions other benchmarks and MiniGrid RL, yet the solar case carries the weight, so the breadth of controls and ablations will need checking. This is for groups working on parameter-efficient sequence models or NISQ-friendly time-series methods. A reader who cares about concrete hardware results and efficiency numbers will get something usable from it. I would send it for peer review; the empirical targets are specific and the hardware test is real, so referees can pressure the ablations and the source of the gains without the paper being a non-starter.

Referee Report

3 major / 3 minor

Summary. The paper introduces gated QKAN-FWP, a fast-weight programmer framework that uses single-qubit data re-uploading circuits (DARUAN) as learnable nonlinear activations inside a Quantum-inspired Kolmogorov-Arnold Network, combined with a scalar-gated update rule. It claims this 12.5k-parameter model outperforms classical recurrent baselines (LSTM, WaveNet-LSTM, Vanilla RNN, Modified ESN) with up to 13x more parameters on long-horizon solar cycle forecasting (528-month input, 132-month output) in scaled MSE, peak amplitude error, and peak timing error, while also showing NISQ compatibility by recovering accuracy within 0.1% relative MSE of the noiseless simulator when deployed on IonQ and IBM hardware at 1024 shots. The design is supported by theoretical analysis of the gated rule's adaptive memory kernel and geometric boundedness.

Significance. If the empirical gains and theoretical properties hold after verification, the work offers a parameter-efficient, NISQ-scalable route to quantum-inspired sequence modeling that avoids multi-qubit entanglement costs. The combination of FWP with single-qubit re-uploading and the gated update could advance practical quantum ML for temporal tasks, provided the performance edge is isolated from classical components.

major comments (3)

[§3] §3 (theoretical analysis of the scalar-gated fast-weight update): the geometric boundedness and adaptive memory kernel are derived under the fitted scalar gate parameter; this creates a circularity risk where the claimed stability properties are partly defined by the data-dependent values rather than providing independent, a priori guarantees that explain the long-horizon gains.
[§4.3] §4.3 (solar forecasting experiments): the central claim that the 12.5k-parameter gated QKAN-FWP beats up to 13x larger RNNs on 528-in/132-out solar data rests on the assumption that single-qubit DARUAN activations supply the necessary temporal expressivity without entanglement; no ablation replacing DARUAN with classical nonlinearities in the identical FWP skeleton is reported, so the contribution of the quantum-inspired component versus the FWP structure remains unisolated.
[§5] §5 (NISQ deployment): the 0.1% relative MSE recovery at 1024 shots on IonQ/IBM is presented as validation of NISQ compatibility, but without reported circuit depth, noise model, or error-mitigation details, it is difficult to assess whether the result supports the scalability narrative or is specific to the solar dataset's periodicity.

minor comments (3)

[Abstract] The acronym expansion 'DatA Re-Uploading ActivatioN' contains inconsistent capitalization; standardize to 'Data Re-Uploading Activation' for clarity.
[§4] Baseline parameter counts (e.g., LSTM 25.9k–89.1k) are given, but training protocols, hyperparameter search, and whether the same input window/forecast horizon were used for all models are not fully specified.
[Table 2] Add standard deviations or error bars to the reported scaled MSE, amplitude, and timing errors in the solar results table to allow assessment of statistical significance.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments on our manuscript. We address each of the major comments point by point below. We will make revisions to the manuscript to incorporate clarifications and additional details as outlined in our responses.

read point-by-point responses

Referee: [§3] §3 (theoretical analysis of the scalar-gated fast-weight update): the geometric boundedness and adaptive memory kernel are derived under the fitted scalar gate parameter; this creates a circularity risk where the claimed stability properties are partly defined by the data-dependent values rather than providing independent, a priori guarantees that explain the long-horizon gains.

Authors: We thank the referee for highlighting this potential circularity. Upon reflection, the derivation in §3 shows that the adaptive memory kernel depends on the scalar gate value, but the geometric boundedness is proven for any gate value in [0,1], which is the valid range for the sigmoid-activated gate. This provides an a priori guarantee independent of the specific fitted value. However, to address the concern directly, we will revise the section to explicitly state the uniform bounds over the gate parameter range and discuss how this contributes to long-horizon stability regardless of data-dependent fitting. revision: yes
Referee: [§4.3] §4.3 (solar forecasting experiments): the central claim that the 12.5k-parameter gated QKAN-FWP beats up to 13x larger RNNs on 528-in/132-out solar data rests on the assumption that single-qubit DARUAN activations supply the necessary temporal expressivity without entanglement; no ablation replacing DARUAN with classical nonlinearities in the identical FWP skeleton is reported, so the contribution of the quantum-inspired component versus the FWP structure remains unisolated.

Authors: We agree that isolating the contribution of the DARUAN activations is important to substantiate the quantum-inspired aspect. We will add an ablation study in the revised §4.3, where we replace the DARUAN activations with classical nonlinearities such as ReLU or tanh within the same gated FWP architecture and compare performance on the solar forecasting task. This will help clarify whether the performance gains stem primarily from the FWP structure or the specific choice of quantum-inspired activations. revision: yes
Referee: [§5] §5 (NISQ deployment): the 0.1% relative MSE recovery at 1024 shots on IonQ/IBM is presented as validation of NISQ compatibility, but without reported circuit depth, noise model, or error-mitigation details, it is difficult to assess whether the result supports the scalability narrative or is specific to the solar dataset's periodicity.

Authors: We appreciate this feedback on the NISQ section. In the revised manuscript, we will expand §5 to include the circuit depth details (noting that each DARUAN is a single-qubit circuit with fixed depth independent of sequence length), the noise model employed in our simulations (depolarizing noise with parameters matching the hardware), and the error mitigation strategies used (such as measurement error mitigation via calibration matrices). These additions will provide a clearer assessment of the scalability and help evaluate the generality beyond the solar dataset. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation and claims are self-contained

full rationale

The paper defines the scalar-gated update rule explicitly, then derives its adaptive memory kernel and geometric boundedness properties mathematically from that definition (independent of any fitted parameters or data). Performance claims consist of direct empirical comparisons on external benchmarks (solar cycles, MiniGrid) against classical baselines; these are measurements, not predictions that reduce to the fitted values by construction. No self-citations are load-bearing for the central architecture or results, no ansatz is smuggled, and no uniqueness theorem is invoked to force the design. The single-qubit DARUAN choice is presented as a deliberate scalability decision, not derived tautologically from the outcomes.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The central claim rests on new entities (DARUAN, gated update) and domain assumptions about single-qubit circuit expressivity plus stability of the update rule; the 12.5k parameters are the primary data-fitted elements.

free parameters (2)

12.5k model parameters
Learned weights across the QKAN-FWP components that are optimized on training data.
scalar gate parameter
The scalar multiplier in the fast-weight update rule, optimized or chosen to stabilize evolution.

axioms (2)

domain assumption Single-qubit variational circuits with data re-uploading can serve as effective learnable nonlinear activations for temporal tasks.
Invoked to justify DARUAN as replacement for standard activations.
ad hoc to paper The scalar-gated fast-weight update produces an adaptive memory kernel with geometric boundedness.
Stated as part of the paper's theoretical analysis supporting the design.

invented entities (2)

DARUAN (DatA Re-Uploading ActivatioN) no independent evidence
purpose: Single-qubit data re-uploading circuit used as learnable nonlinear activation inside the QKAN component.
Newly introduced activation mechanism to enable quantum-inspired nonlinearity with NISQ compatibility.
scalar-gated fast-weight update rule no independent evidence
purpose: Stabilizes parameter evolution in the FWP while enabling parallel gradient paths.
New update mechanism with claimed theoretical properties.

pith-pipeline@v0.9.0 · 5734 in / 2009 out tokens · 78836 ms · 2026-05-11T01:51:39.735616+00:00 · methodology

discussion (0)

Reference graph

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