Simulation-based inference with scattering representations: scattering is all you need

TL;DR

The paper tackles the challenge of information loss in compression for simulation-based inference on high-dimensional field-level cosmology data. It proposes wavelet scattering representations as a non-learned, interpretable summary that avoids training data and derivative simulations, and applies neural likelihood estimation to a 37-dimensional scattering vector, comparing against bandpowers. The results show that scattering alone provides substantially tighter constraints than bandpowers, with further gains when combined with bandpowers, while remaining robust to covariate shift and not requiring extra simulations for training. This work offers a scalable, interpretable SBI pipeline for field-level cosmology that preserves non-Gaussian information without additional simulation cost, with implications for future cosmological analyses.

Abstract

We demonstrate the successful use of scattering representations without further compression for simulation-based inference (SBI) with images (i.e. field-level), illustrated with a cosmological case study. Scattering representations provide a highly effective representational space for subsequent learning tasks, although the higher dimensional compressed space introduces challenges. We overcome these through spatial averaging, coupled with more expressive density estimators. Compared to alternative methods, such an approach does not require additional simulations for either training or computing derivatives, is interpretable, and resilient to covariate shift. As expected, we show that a scattering only approach extracts more information than traditional second order summary statistics.

Figures (1)

• Figure 1: Posterior constraints for different compressed representations. Scattering representations, without further neural compression, are highly effective when using more expressive density estimators.