SNN-FRFT: ADAPTIVE FRACTIONAL REPRESENTATIONS FOR EFFICIENT SPIKING FORECASTING

A fixed orthogonal Fourier basis spreads chirp-like signals across coefficients, limiting sparse spiking forecasting. We introduce a spiking neural network with an adaptive fractional Fourier transform (SNN-FrFT). A spiking selector estimates the order from the observed history; the forecasting head predicts residual dynamics, and the same order reconstructs the future phase. Signed Dual-Region Log-Temporal Coding (DR-LTC) covers strong coefficients logarithmically and maps sufficiently weak coefficients to zero-event states. The compact head projects once and reuses current across leaky integrate-and-fire steps. On a three-seed repartitioned NeLoRa benchmark, SNN-FrFT achieves 79.28% spectral peak agreement at spreading factor 10 versus 73.67% for Spiking Fourier Network (SpikF), with 97.23% fewer core multiply-accumulate operations. Synthetic factorization connects the prediction gain to pairing the adaptive input representation with fu￾ture reconstruction. A matched three-epoch coding study improves NeLoRa peak agreement over linear time-to-first-spike coding while leaving 74.06% of terminal rails silent. On the same HM100, the compiled width-256 cached head uses 38.3% less mean board-level dynamic energy than SpikF’s decoder.