Learnable wavelet neural networks for cosmological inference

TL;DR

This paper introduces learnable wavelet-based scattering networks for cosmological inference, demonstrating they outperform traditional CNNs especially with limited training data and offering improved interpretability.

Contribution

It presents novel scattering transform models with trainable wavelets for cosmology, outperforming CNNs and enhancing interpretability in the field.

Findings

Scattering networks outperform CNNs with small training datasets.

Lightweight scattering network offers high interpretability.

Models effectively marginalize over astrophysical effects.

Abstract

Convolutional neural networks (CNNs) have been shown to both extract more information than the traditional two-point statistics from cosmological fields, and marginalise over astrophysical effects extremely well. However, CNNs require large amounts of training data, which is potentially problematic in the domain of expensive cosmological simulations, and it is difficult to interpret the network. In this work we apply the learnable scattering transform, a kind of convolutional neural network that uses trainable wavelets as filters, to the problem of cosmological inference and marginalisation over astrophysical effects. We present two models based on the scattering transform, one constructed for performance, and one constructed for interpretability, and perform a comparison with a CNN. We find that scattering architectures are able to outperform a CNN, significantly in the case of small training data samples. Additionally we present a lightweight scattering network that is highly interpretable.