Temporal Functional Circuits: From Spline Plots to Faithful Explanations in KAN Forecasting

Accurate time series forecasting in scientific domains such as climate modeling, physiological monitoring, and energy systems benefits from both competitive predictions and model transparency. This work proposes DecompKAN, a lightweight attention-free architecture that combines trend-residual decomposition, channel-wise patching, learned instance normalization, and B-spline Kolmogorov-Arnold Network (KAN) edge functions. Each KAN edge learns an explicit, inspectable 1D scalar function over learned patch-embedding coordinates that can be directly visualized. On standard benchmarks, DecompKAN achieves best or tied-best MSE on 15 of 32 dataset-horizon combinations among selected published baselines, and achieves best or tied-best MSE on 20 of 36 comparisons under a controlled same-recipe evaluation across 9 datasets including the physiological PPG-DaLiA benchmark. The architecture shows particular strength on datasets with smooth temporal dynamics (Solar -17%, ECL -10% vs. iTransformer, Weather) and physiological time series. Visualization of learned edge functions reveals qualitatively different latent nonlinearities across domains. Ablation analysis shows that the architectural pipeline (decomposition, patching, normalization) drives performance more than the choice of nonlinear layer, while the KAN formulation enables inspection of learned latent transformations.

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.

Accurate electricity load forecasting is a crucial prerequisite for stable power system operations. While prevalent deep learning models present competitive performance, they often operate as black boxes and lack interpretability. While the Kolmogorov-Arnold network (KAN) has emerged as a promising alternative because of its learnable activation function design, its direct application to time-series forecasting faces challenges in modeling complex temporal data patterns. Also, simple integration into existing architectures, such as serving as replacement of neural modules, cannot fully leverage KAN's interpretability strengths. To address these gaps, this study develops LoadKAN, a novel hybrid and interpretable framework for load forecasting that synergistically combines a specifically-designed feature-isolated temporal attention mechanism with a KAN module. The attention stage aims to extract temporal dynamics from each input feature independently, such as historical load and human mobility, providing distilled feature representations to the KAN module for interpretable predictions. When evaluated on datasets from three representative U.S. electricity markets, our LoadKAN remains highly competitive when compared to extensively-tuned, state-of-the-art, black-box deep learning benchmarks. More importantly, LoadKAN's interpretability enables a granular analysis of the learned non-linear relationships between six distinct mobility patterns and electricity load. Through KAN-learned activation functions, our quantitative sensitivity analyses on mobility features reveal complex and market-specific dependencies. These findings further demonstrate the ability of our LoadKAN to generate insights often obscured by opaque black-box neural forecasting models.