QKAN-LSTM：量子启发的科尔莫戈罗夫-阿诺德长短期记忆网络
QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory
December 4, 2025
作者: Yu-Chao Hsu, Jiun-Cheng Jiang, Chun-Hua Lin, Kuo-Chung Peng, Nan-Yow Chen, Samuel Yen-Chi Chen, En-Jui Kuo, Hsi-Sheng Goan
cs.AI
摘要
长短期记忆（LSTM）模型作为循环神经网络（RNN）的特殊变体，在城域通信预测等时序建模任务中具有核心地位，这类任务主要受时间相关性和非线性依赖关系支配。然而传统LSTM存在参数冗余度高和非线性表达能力有限的问题。本研究提出量子启发式柯尔莫哥洛夫-阿诺德长短期记忆模型（QKAN-LSTM），通过将数据重上传激活（DARUAN）模块集成至LSTM的门控结构中，每个DARUAN模块作为量子变分激活函数（QVAF），在无需多量子比特纠缠的情况下增强频率自适应能力，实现指数级丰富的光谱表征。该架构在保持量子级表达能力的同时，仍可完全在经典硬件上运行。在阻尼简谐运动、贝塞尔函数和城域通信三个数据集上的实证评估表明，QKAN-LSTM相比经典LSTM可减少79%可训练参数，同时获得更优的预测精度与泛化能力。我们将该框架扩展至江-黄-陈-吴网络（JHCG Net），将KAN推广至编码器-解码器结构，进而利用QKAN实现潜在KAN，最终构建用于分层表征学习的混合QKAN（HQKAN）。所提出的HQKAN-LSTM由此为现实数据环境中的量子启发性时序建模提供了可扩展且可解释的实现路径。
English
Long short-term memory (LSTM) models are a particular type of recurrent neural networks (RNNs) that are central to sequential modeling tasks in domains such as urban telecommunication forecasting, where temporal correlations and nonlinear dependencies dominate. However, conventional LSTMs suffer from high parameter redundancy and limited nonlinear expressivity. In this work, we propose the Quantum-inspired Kolmogorov-Arnold Long Short-Term Memory (QKAN-LSTM), which integrates Data Re-Uploading Activation (DARUAN) modules into the gating structure of LSTMs. Each DARUAN acts as a quantum variational activation function (QVAF), enhancing frequency adaptability and enabling an exponentially enriched spectral representation without multi-qubit entanglement. The resulting architecture preserves quantum-level expressivity while remaining fully executable on classical hardware. Empirical evaluations on three datasets, Damped Simple Harmonic Motion, Bessel Function, and Urban Telecommunication, demonstrate that QKAN-LSTM achieves superior predictive accuracy and generalization with a 79% reduction in trainable parameters compared to classical LSTMs. We extend the framework to the Jiang-Huang-Chen-Goan Network (JHCG Net), which generalizes KAN to encoder-decoder structures, and then further use QKAN to realize the latent KAN, thereby creating a Hybrid QKAN (HQKAN) for hierarchical representation learning. The proposed HQKAN-LSTM thus provides a scalable and interpretable pathway toward quantum-inspired sequential modeling in real-world data environments.