ARBR: Adaptive Radial Basis Representation for Time Series Forecasting

The temporal location and extent of predictive patterns are important for time series forecasting. Recent basis-based forecasting methods often combine shared temporal bases with input-dependent coefficients. However, adapting coefficients alone cannot directly relocate or rescale individual basis functions, so changes in pattern location and extent must be represented through coordinated changes across multiple shared bases. To model such geometric variation explicitly, we propose Adaptive Radial Basis Representation (ARBR), a structured temporal representation built from input-adaptive Gaussian radial bases. For each channel-wise input window, ARBR predicts bounded adjustments to radial centers and scales around a shared temporal scaffold, preserving the temporal ordering of components. Radial responses weight input-conditioned vector-valued coefficients to form latent features aligned with temporal patches. On seven multivariate forecasting benchmarks, ARBR achieves the lowest MSE on five datasets and the lowest MAE on four, averaged over four forecasting horizons. Controlled comparisons show that ARBR yields lower forecasting errors than variants with fixed or globally learned radial geometry or non-radial dynamic mixing. The code is available at https://anonymous.4open.science/r/ARBR/.