时间序列中自相关让KAN重陷频谱偏差，用DCT预处理可有效缓解。
Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting
- 用离散余弦变换（DCT）降低输入变量的自相关性。
- 自相关越强，KAN对低频信号的偏好越明显，预测性能下降。
- 适合做时间序列预测且输入具强自相关的研究者参考。
现有理论认为，柯尔莫哥洛夫-阿诺德网络（KANs）在输入统计独立时可克服神经网络常见的频谱偏差。然而，在时间序列预测（TSF）中，输入为滞后观测，具有强时间自相关性，该假设不成立。通过理论分析与实证验证，我们发现：时间自相关会重新引入频谱偏差，且偏差随自相关程度增强而加剧。这表明标准KAN在强自相关输入的时间序列预测中面临显著挑战。为此，我们引入离散余弦变换（DCT）以降低输入间的相关性。实验结果表明，经DCT预处理后，模型对低频成分的偏好显著减弱。该结果进一步证实：KAN在TSF任务中的频谱偏差由输入变量间的自相关引起。
原文摘要 · Abstract (English)
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.
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