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Upcoming measurements of the high-redshift 21 cm signal from the Epoch ofReionization (EoR) are a promising probe of the astrophysics of the firstgalaxies and of cosmological parameters. In particular, the optical depth$\tau$ to the last scattering surface of the cosmic microwave background (CMB)should be tightly constrained by direct measurements of the neutral hydrogenstate at high redshift. A robust measurement of $\tau$ from 21 cm data wouldhelp eliminate it as a nuisance parameter from CMB estimates of cosmologicalparameters. Previous proposals for extracting $\tau$ from future 21 cm datasetshave typically used the 21 cm power spectra generated by semi-numerical modelsto reconstruct the reionization history. We present here a different approachwhich uses convolution neural networks (CNNs) trained on mock images of the 21cm EoR signal to extract $\tau$. We construct a CNN that improves upon onpreviously proposed architectures, and perform an automated hyperparameteroptimization. We show that well-trained CNNs are able to accurately predict$\tau$, even when removing Fourier modes that are expected to be corrupted bybright foreground contamination of the 21 cm signal. Typical random errors foran optimized network are less than $3.06\%$, with biases factors of severalsmaller. While preliminary, this approach could yield constraints on $\tau$that improve upon sample-variance limited measurements of the low-$\ell$ EEobservations of the CMB, making this approach a valuable complement to moretraditional methods of inferring $\tau$.

Extracting the Optical Depth to Reionization $\tau$ from 21 cm Data Using Machine Learning Techniques