arXiv:2511.18613cs.LGcs.AI2025-11被引 1

LSTM在金融时间序列预测中显著优于基础KAN,尤其在准确性上。

KAN vs LSTM Performance in Time Series Forecasting

  • 对比基础KAN与LSTM在时序数据上的表现
  • LSTM在所有预测时长远超KAN,RMSE更低
  • 适合关注时序建模准确性的研究者参考

本研究通过PyKAN实现的基础科尔莫戈罗夫-阿诺德网络(KAN)与长短期记忆网络(LSTM)在随机非平稳金融时间序列预测任务中进行受控对比。评估指标包括预测精度、计算效率和可解释性,其中精度以归一化特征空间的均方根误差(RMSE)衡量。在直接多输出预测协议下,LSTM在所有测试预测时长远优于KAN,符合其对序列数据建模的公认优势。基础KAN虽理论上具备可解释性,但在标准形式下误差显著更高,实际应用受限。尽管部分时序增强型KAN变体(如时间KAN、时频KAN)已被提出以克服此问题,但不在本研究范围内。实验观察到基础KAN训练收敛更快,但运行时比较受方法论因素限制。结果支持在高精度要求的金融预测中采用LSTM,并为标准KAN在随机序列数据上的表现提供了实证基线,推动对时序感知型KAN架构的进一步研究。本研究仅比较基础KAN与基础LSTM,不适用于专为时序设计的KAN变体或更广泛的时序模型。

原文摘要 · Abstract (English)

This study presents a controlled comparison of baseline Kolmogorov-Arnold Networks (KAN), implemented via PyKAN, and Long Short-Term Memory (LSTM) networks for the forecasting of stochastic, non-stationary financial time series. The two architectures are assessed in terms of predictive accuracy, computational efficiency, and interpretability, with accuracy measured by the Root Mean Square Error (RMSE) in normalised feature space. Under a direct multi-output forecasting protocol, LSTM attains clearly superior accuracy across all tested prediction horizons, consistent with its well-established effectiveness for sequential data modelling. Baseline KAN, although offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits substantially higher error rates and limited practical applicability for time series forecasting in its standard form. Several specialised temporal variants -- including Temporal KAN and Time-Frequency KAN -- have since been proposed to address these sequential modelling limitations, but they lie outside the scope of the present study. KAN is observed to converge faster during training under the configurations tested, although direct runtime comparisons are constrained by methodological factors. These findings support the adoption of LSTM for accuracy-critical financial forecasting and establish an empirical baseline for standard KAN on stochastic sequential data, motivating further investigation of temporally-aware KAN architectures. The study benchmarks baseline KAN against baseline LSTM only; the results do not extend to specialised KAN variants designed for sequential data, nor to the broader family of temporal models.

时间序列LSTMKAN金融预测

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