CAW-KAN: Context-Aware Dual-Grid Wavelet KAN with Low-Rank Edge-Function Mixing for Long-Horizon Forecasting

Time series are rarely governed by a single simple relationship: once a variable is embedded into a latent representation, its future behavior depends on nonlinear interactions among the resulting latent coordinates. Kolmogorov-Arnold Networks (KANs) can model such interactions with learnable nonlinear edge functions, but giving every latent edge its own basis expansion requires a three-way coefficient tensor of size $d_{\text{in}}\cdot d_{\text{out}}\cdot N$, which erodes efficiency as latent width or dictionary size grows. We present CAW-KAN, a channel-independent forecaster that separates temporal context extraction from nonlinear mixing in value space. For each observed variable, reversible instance normalization and a value embedding produce a $d_{\text{model}}$ -dimensional latent sequence, then a dense temporal convolution mixes across neighboring time steps and latent dimensions. A token-wise Wavelet-KAN evaluates a shared dictionary, built from two offset grids for complementary coverage of latent-value space, on the resulting scalar values; the grid centers and scales are currently fixed after initialization, with only the CP-factorized coefficients learned. To retain cross-feature edge functions without materializing the full coefficient tensor, CAW-KAN learns a low-rank CP factorization of these coefficients. Across 12 datasets and four forecast horizons, CAW-KAN attains the lowest error or ties for it in 59 of 96 MSE/MAE cells. Resource measurements show that CAW-KAN operates with significantly fewer parameters than other state-of-the-art models. Here, "context-aware" refers only to the local temporal representation fed into the Wavelet-KAN, not to a context gate or a temporal wavelet transform. The source code and implementation details are publicly available at https://github.com/tftpbe/CAW-KAN.