Scale-Equivariant Generative Forecasting: Weight-Tied Dilated Convolutions, Wavelet Scattering Inputs, and Spectral-Consistency Training for Self-Similar Time Series

ArXi:2605.17582v1 Announce Type: new Many natural and engineered time series -- equity returns, climate anomalies, turbulent velocities, neural recordings, packet-level network traffic -- are approximately self-similar: their horizon-$T$ distribution is tied to the horizon-$1$ distribution by one scaling exponent $H$. Standard deep generative sequence models (transformers, dilated TCNs, the WaveNet family) ignore this. Their receptive fields are wide, but kernel parameters live independently at every dilation level, yielding a multi-scale architecture, not a scale-equivariant one.