How informative are summaries of the cosmic 21 cm signal?

The cosmic 21 cm signal will bring data-driven advances to studies of Cosmic Dawn (CD) and the Epoch of Reionization (EoR). Radio telescopes such as the Square Kilometre Array (SKA) will eventually map the HI fluctuations over the first billion years - the majority of our observable Universe. With such large data volumes, it becomes increasingly important to develop "optimal"summary statistics, which will allow us to learn as much as possible about the CD and EoR. In this work we compare the astrophysical parameter constraining power of several 21 cm summary statistics, using the determinant of the Fisher information matrix, detF. Since we do not have an established "fiducial"model for the astrophysics of the first galaxies, we computed for each summary the distribution of detF across the prior volume. Using a large database of cosmic 21 cm light cones that include realizations of telescope noise, we compared the following summaries: (i) the spherically averaged power spectrum (1DPS), (ii) the cylindrically averaged power spectrum (2DPS), (iii) the 2D wavelet scattering transform (WST), (iv) a recurrent neural network (RNN) trained as a regressor; (v) an information-maximizing neural network (IMNN); and (vi) the combination of 2DPS and IMNN. Our best performing individual summary is the 2DPS, which provides relatively high Fisher information throughout the parameter space. Although capable of achieving the highest Fisher information for some parameter choices, the IMNN does not generalize well, resulting in a broad distribution across the prior volume. Our best results are achieved with the concatenation of the 2DPS and IMNN. The combination of only these two complimentary summaries reduces the recovered parameter variances on average by factors of ~6.5- 9.5, compared with using each summary independently. Finally, we point out that that the common assumption of a constant covariance matrix when doing Fisher forecasts using 21 cm summaries can significantly underestimate parameter constraints.