The Singularity Space: A Generative Diffusion Framework for Signal Representation

What the math gives to ML

The paper replaces dense signal samples with a compact configuration of complex poles and residues, representing sharp transients as analytic structure rather than grid amplitudes. The transferable asset is a resolution-independent decoder: once pole locations and residues are predicted, the signal can be evaluated on arbitrary coordinates without interpolation or retraining. A practical neural adaptation is a set-valued latent diffusion model that predicts pole-residue tokens and reconstructs signals through a differentiable rational decoder, with multiresolution reconstruction and total-variation losses.