Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting
For practitioners using KANs in time series forecasting, this identifies a critical limitation and provides a simple fix.
The paper shows that temporal autocorrelation in time series forecasting reintroduces spectral bias in Kolmogorov-Arnold Networks, which worsens with stronger autocorrelation. Applying Discrete Cosine Transform preprocessing reduces this bias, confirming the cause.
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.