QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory
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
2025-12-05
Summary
This paper introduces a new type of LSTM, called QKAN-LSTM, which aims to improve how we predict things that happen in a sequence, like forecasting phone call traffic in a city.
What's the problem?
Traditional LSTMs, which are good at processing sequences of data, have a couple of drawbacks. They use a lot of unnecessary parameters, making them inefficient, and they aren't very good at capturing complex relationships within the data. Essentially, they can be bulky and not very flexible.
What's the solution?
The researchers came up with QKAN-LSTM, which borrows ideas from quantum computing – but importantly, it still runs on regular computers. They added special modules, called DARUANs, to the LSTM’s internal structure. These modules act like more powerful switches, allowing the model to adapt to different patterns in the data and represent information in a richer way without needing a huge number of settings to adjust. They also created a more advanced version called HQKAN-LSTM for even more complex data.
Why it matters?
This new approach is important because it can predict future events more accurately and efficiently than older methods. It also uses significantly fewer parameters, meaning it requires less computing power and can be scaled up more easily. This is particularly useful for real-world applications like predicting telecommunication needs in a city, where accurate forecasts can save money and improve service.
Abstract
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.