Six key factors needed to model cosmic microwave background spectra
OCCAMS: A Multi-Task Learning-Based Investigation of the CMB Power Spectra
Machine Learning
Summary
This study asks how many hidden factors a neural network needs to describe the cosmic microwave background (CMB) data without relying on known physics models. The researchers trained their models to find that six hidden factors best explain the detailed temperature and polarization patterns seen in the CMB. These six factors closely match the six standard parameters that cosmologists usually use, even though the model didn’t start with those assumptions. The study shows that machine learning can find a simple and data-driven way to describe the universe’s early light.
What this means in practice
- •For astrophysics data analysts: Use a deep learning model with six latent variables to compactly represent and analyze CMB spectra without assuming cosmological models in advance.
- •For machine learning engineers in physics: Develop interpretable multi-task neural networks with uncertainty weighting to disentangle complex scientific data into meaningful factors.
Authors
Ankit Mandal, Rahul Shah, Md. Wali Hossain, Somasri Sen, Anjan A Sen, Supratik Pal
Abstract
How many latent variables are needed to fit the cosmic microwave background (CMB) temperature and polarisation power spectra when a neural network is given no cosmological model, and to what extent do they map onto the standard cosmological parameters? We use multi-task learning with variational autoencoders trained on CLASS-generated spectra (TT, TE, EE) over $2\le\ell\le2500$. No cosmological model is built into the network, and the number of latent variables, $L$, is varied over $L=5$, $6$ and $7$. Their fits are compared to the Planck 2018 data using $\hatχ^2$, AIC, BIC and Bayesian evidence. Their correspondence with cosmological parameters is measured with normalised mutual information post-training. The loss weights are set within a single training run by uncertainty weighting, with the weight of the disentanglement term either fixed (semi-automated, SA) or learned (completely automated, CA). The reconstruction loss is split over multipole ranges in three configurations that separate the roles of temperature and polarisation and of the low- and high-$\ell$ ranges. In four of the six combinations of configuration and strategy, the fit improves from $L=5$ to $L=6$ and not beyond, and $L=6$ is the best, or close to the best, in five of the six cases. So, six latent variables are needed, as many as the free parameters of the standard, model-dependent approach. SA gives clearer disentanglement, while CA needs no a priori choice of the disentanglement weight and has the higher evidence at $L=5$ and $6$: the two strategies are points on a trade-off between interpretability and fit to the data. Notably, the latent variables for $τ$ and $A_s$ share almost no information in any model, consistent with large-scale polarisation separating the two, as in standard analyses. A deep-learning approach can thus give a compact, data-driven parametrisation of the CMB spectra.