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KAN vs LSTM Performance in Time Series Forecasting

Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova, Federico Frascoli

TL;DR

This work addresses forecasting non-deterministic stock prices by comparing Kolmogorov-Arnold Networks (KAN) and Long Short-Term Memory (LSTM) models, focusing on the accuracy-interpretability trade-off via RMSE. It empirically demonstrates that LSTM substantially outperforms standard KAN across short-, medium-, and long-horizon forecasts, with RMSE improvements roughly in the range of $6.5$–$10$×, while KAN offers theoretical interpretability and faster training (about $2.1\times$) and remains viable for extended horizons (up to 200+ days) in resource-constrained settings. The findings advocate LSTM as the practical default for accuracy-critical financial forecasting, while suggesting specialized KAN variants and hybrid models as promising directions to balance interpretability and scalability. The study also highlights key architectural insights, such as the effectiveness of shallower LSTMs and moderate spline degrees in KAN, and points to open mathematical challenges around free-knot spline optimization that will influence future KAN viability.

Abstract

This paper compares Kolmogorov-Arnold Networks (KAN) and Long Short-Term Memory networks (LSTM) for forecasting non-deterministic stock price data, evaluating predictive accuracy versus interpretability trade-offs using Root Mean Square Error (RMSE).LSTM demonstrates substantial superiority across all tested prediction horizons, confirming their established effectiveness for sequential data modelling. Standard KAN, while offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits significantly higher error rates and limited practical applicability for time series forecasting. The results confirm LSTM dominance in accuracy-critical time series applications while identifying computational efficiency as KANs' primary advantage in resource-constrained scenarios where accuracy requirements are less stringent. The findings support LSTM adoption for practical financial forecasting while suggesting that continued research into specialised KAN architectures may yield future improvements.

KAN vs LSTM Performance in Time Series Forecasting

TL;DR

This work addresses forecasting non-deterministic stock prices by comparing Kolmogorov-Arnold Networks (KAN) and Long Short-Term Memory (LSTM) models, focusing on the accuracy-interpretability trade-off via RMSE. It empirically demonstrates that LSTM substantially outperforms standard KAN across short-, medium-, and long-horizon forecasts, with RMSE improvements roughly in the range of –×, while KAN offers theoretical interpretability and faster training (about ) and remains viable for extended horizons (up to 200+ days) in resource-constrained settings. The findings advocate LSTM as the practical default for accuracy-critical financial forecasting, while suggesting specialized KAN variants and hybrid models as promising directions to balance interpretability and scalability. The study also highlights key architectural insights, such as the effectiveness of shallower LSTMs and moderate spline degrees in KAN, and points to open mathematical challenges around free-knot spline optimization that will influence future KAN viability.

Abstract

This paper compares Kolmogorov-Arnold Networks (KAN) and Long Short-Term Memory networks (LSTM) for forecasting non-deterministic stock price data, evaluating predictive accuracy versus interpretability trade-offs using Root Mean Square Error (RMSE).LSTM demonstrates substantial superiority across all tested prediction horizons, confirming their established effectiveness for sequential data modelling. Standard KAN, while offering theoretical interpretability through the Kolmogorov-Arnold representation theorem, exhibits significantly higher error rates and limited practical applicability for time series forecasting. The results confirm LSTM dominance in accuracy-critical time series applications while identifying computational efficiency as KANs' primary advantage in resource-constrained scenarios where accuracy requirements are less stringent. The findings support LSTM adoption for practical financial forecasting while suggesting that continued research into specialised KAN architectures may yield future improvements.

Paper Structure

This paper contains 27 sections, 1 theorem, 6 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Artificial Neural Networks
  4. Deep Learning Models for Stock Market Prediction
  5. Recurrent Neural Networks (RNN)
  6. Long Short-Term Memory (LSTM)
  7. Long Short-Term Memory (LSTM)
  8. Kolmogorov-Arnold Networks
  9. Kolmogorov-Arnold Representation Theorem
  10. Architecture
  11. Evaluation and Research Challenges
  12. Methodology
  13. Problem Formulation
  14. Data Collection and Preparation
  15. Model Implementation
  16. ...and 12 more sections

Key Result

Theorem 2.1

Let $f: [0,1]^n \to \mathbb{R}$ be a continuous function. Then, there exist continuous univariate functions $\Phi_q: \mathbb{R} \to \mathbb{R}$ and $\varphi_{q,p}: \mathbb{R} \to \mathbb{R}$ such that: for all $\mathbf{x} = (x_1, \dots, x_n) \in [0,1]^n$, where $\Phi_q$ are outer functions and $\varphi_{q,p}$ are inner univariate functions kolmogorov1957representation.

Figures (8)

  • Figure 1: LSTM representation goodfellow2016deep
  • Figure 2: Train and Test RMSE for Different LSTM Model Configurations
  • Figure 3: Train and Test Loss for Different KAN Configurations
  • Figure 4: KAN vs LSTM Performance Comparison: 1-Day and 100-Day Forecast Horizons
  • Figure 5: KAN vs LSTM Performance Comparison: 2-Day and 200-Day Forecast Horizons
  • ...and 3 more figures

Theorems & Definitions (1)

  • Theorem 2.1: Kolmogorov-Arnold Representation Theorem