We use a convolutional neural network (CNN) to study cosmic string detection in cosmic microwave background (CMB) flat sky maps with Nambu-Goto strings. On noiseless maps we can measure string tensions down to order $10^{-9}$, however when noise is included we are unable to measure string tensions below.

$10^{-7}$. Motivated by this impasse, we derive an information theoretic bound on the detection of the cosmic string tension $Gμ$ from CMB maps. In particular we bound the information entropy of the posterior distribution of.

$Gμ$ in terms of the resolution, noise level and total survey area of the CMB.