Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting

TL;DR

This paper reveals that autocorrelation in time series inputs reintroduces spectral bias in KANs, challenging prior assumptions, and proposes DCT preprocessing to mitigate this issue, improving forecasting performance.

Contribution

The study uncovers the impact of autocorrelation on spectral bias in KANs for TSF and introduces DCT preprocessing as an effective mitigation technique.

Findings

Autocorrelation reintroduces spectral bias in KANs for TSF.

DCT preprocessing reduces low-frequency bias in KANs.

Spectral bias in TSF is driven by input autocorrelation.

Abstract

Existing theory suggests that Kolmogorov-Arnold Networks (KANs) can overcome the spectral bias commonly observed in neural networks under the assumption that inputs are statistically independent. However, this assumption does not hold in time series forecasting (TSF), where inputs are lagged observations with strong temporal autocorrelation. Through theoretical analysis and empirical validation, we obtain an unexpected finding: temporal autocorrelation reintroduces spectral bias in KANs, and the bias becomes increasingly pronounced as the degree of autocorrelation increases. This suggests that standard KANs may face substantial difficulties in TSF with strongly autocorrelated inputs. To address this problem, we introduce the Discrete Cosine Transform (DCT) to reduce the correlations among the network inputs. As expected, experimental results reveal that DCT preprocessing substantially reduces the observed low-frequency preference in TSF. This result also corroborates that the spectral bias of KANs in TSF tasks is indeed induced by the autocorrelation among input variables.