用量子启发方法提升LSTM表达力,参数减少79%仍更准。
QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory
- 在LSTM门控中嵌入量子变分激活,增强频率适应性。
- 参数量降79%,在3个数据集上预测精度和泛化能力更优。
- 适合需要高效高表达的时序建模场景,如城市通信预测。
长短期记忆(LSTM)模型是处理序列任务的核心方法,广泛应用于城市通信预测等依赖时间相关性和非线性关系的领域。然而传统LSTM存在参数冗余高、非线性表达力有限的问题。本文提出量子启发的柯尔莫戈洛夫-阿诺德长短期记忆(QKAN-LSTM),将数据重加载激活(DARUAN)模块融入LSTM门控结构,每个DARUAN作为量子变分激活函数(QVAF),在不依赖多比特纠缠的情况下实现指数级丰富的频谱表示,保留量子级表达力的同时可在经典硬件上运行。在阻尼简谐运动、贝塞尔函数和城市通信三个数据集上的实证结果表明,相比传统LSTM,QKAN-LSTM在可训练参数减少79%的前提下,仍具备更优的预测准确率与泛化能力。研究进一步扩展至江-黄-陈-顾网络(JHCG Net),将KAN推广至编码器-解码器结构,并引入潜变量KAN构建混合量子-经典网络(HQKAN),为真实世界数据中的层次化表征学习提供可扩展且可解释的路径。
原文摘要 · Abstract (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.
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