  We train neural networks to quickly generate redshift-space galaxy power
spectrum covariances from a given parameter set (cosmology and galaxy bias).
This covariance emulator utilizes a combination of traditional fully-connected
network layers and transformer architecture to accurately predict covariance
matrices for the high redshift, north galactic cap sample of the BOSS DR12
galaxy catalog. We run simulated likelihood analyses with emulated and
brute-force computed covariances, and we quantify the network's performance via
two different metrics: 1) difference in $\chi^2$ and 2) likelihood contours for
simulated BOSS DR 12 analyses. We find that the emulator returns excellent
results over a large parameter range. We then use our emulator to perform a
re-analysis of the BOSS HighZ NGC galaxy power spectrum, and find that varying
covariance with cosmology along with the model vector produces $\Omega_m =
0.276^{+0.013}_{-0.015}$, $H_0 = 70.2\pm 1.9$ km/s/Mpc, and $\sigma_8 =
0.674^{+0.058}_{-0.077}$. These constraints represent an average $0.46\sigma$
shift in best-fit values and a $5\%$ increase in constraining power compared to
fixing the covariance matrix ($\Omega_m = 0.293\pm 0.017$, $H_0 = 70.3\pm 2.0$
km/s/Mpc, $\sigma_8 = 0.702^{+0.063}_{-0.075}$). This work demonstrates that
emulators for more complex cosmological quantities than second-order statistics
can be trained over a wide parameter range at sufficiently high accuracy to be
implemented in realistic likelihood analyses.
