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TKAN: Temporal Kolmogorov-Arnold Networks

Remi Genet, Hugo Inzirillo

TL;DR

The paper introduces Temporal Kolmogorov-Arnold Networks (TKANs), a hybrid architecture that blends Recurring Kolmogorov-Arnold Networks (RKAN) with LSTM-like gating to address long-range temporal dependencies in time-series forecasting. By embedding an external memory and leveraging B-spline activations within KAN layers, TKAN aims to outperform traditional RNNs (GRU/LSTM) in multi-step ahead predictions. The authors validate the approach on notional BTC trading data from Binance, showing TKAN achieves higher accuracy and greater training stability, particularly for longer forecast horizons. This work suggests a promising direction for robust, multi-step temporal modeling that combines interpretable KAN representations with memory-based dynamics.

Abstract

Recurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies in sequential data. Inspired by the Kolmogorov-Arnold Networks (KANs) a promising alternatives to Multi-Layer Perceptrons (MLPs), we proposed a new neural networks architecture inspired by KAN and the LSTM, the Temporal Kolomogorov-Arnold Networks (TKANs). TKANs combined the strenght of both networks, it is composed of Recurring Kolmogorov-Arnold Networks (RKANs) Layers embedding memory management. This innovation enables us to perform multi-step time series forecasting with enhanced accuracy and efficiency. By addressing the limitations of traditional models in handling complex sequential patterns, the TKAN architecture offers significant potential for advancements in fields requiring more than one step ahead forecasting.

TKAN: Temporal Kolmogorov-Arnold Networks

TL;DR

The paper introduces Temporal Kolmogorov-Arnold Networks (TKANs), a hybrid architecture that blends Recurring Kolmogorov-Arnold Networks (RKAN) with LSTM-like gating to address long-range temporal dependencies in time-series forecasting. By embedding an external memory and leveraging B-spline activations within KAN layers, TKAN aims to outperform traditional RNNs (GRU/LSTM) in multi-step ahead predictions. The authors validate the approach on notional BTC trading data from Binance, showing TKAN achieves higher accuracy and greater training stability, particularly for longer forecast horizons. This work suggests a promising direction for robust, multi-step temporal modeling that combines interpretable KAN representations with memory-based dynamics.

Abstract

Recurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies in sequential data. Inspired by the Kolmogorov-Arnold Networks (KANs) a promising alternatives to Multi-Layer Perceptrons (MLPs), we proposed a new neural networks architecture inspired by KAN and the LSTM, the Temporal Kolomogorov-Arnold Networks (TKANs). TKANs combined the strenght of both networks, it is composed of Recurring Kolmogorov-Arnold Networks (RKANs) Layers embedding memory management. This innovation enables us to perform multi-step time series forecasting with enhanced accuracy and efficiency. By addressing the limitations of traditional models in handling complex sequential patterns, the TKAN architecture offers significant potential for advancements in fields requiring more than one step ahead forecasting.
Paper Structure (16 sections, 18 equations, 5 figures, 2 tables)

This paper contains 16 sections, 18 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Kolmogorov-Arnold Networks (KANs)
  3. Temporal Kolmogorov-Arnold Networks (TKANs)
  4. Recurring Kolmogorov-Arnold Networks (RKAN)
  5. TKAN Architecture
  6. Learning task
  7. Task Definition and Dataset
  8. Preprocessing
  9. Loss Function for Model Training
  10. Benchmarks
  11. Model Architectures
  12. Note on training details
  13. Results
  14. Performance Metrics Summary
  15. Training Dynamics and Model Stability
  16. ...and 1 more sections

Figures (5)

  • Figure 2: Temporal Kolmogorov-Arnold Networks (TKAN)
  • Figure 3: A three layers Temporal Kolmogorov-Arnold Networks (TKAN) Block
  • Figure 4: TKAN training and validation loss over epochs
  • Figure 5: GRU training and validation loss over epochs
  • Figure 6: LSTM training and validation loss over epochs