When applied to the nonlinear matter distribution of the universe, neural networks have been shown to be very statistically sensitive probes of cosmological parameters, such as the linear perturbation amplitude ${\sigma }_8$. However, when used as a “black box,” neural networks are not robust to baryonic uncertainty. We propose a robust architecture for constraining primordial non-Gaussianity $f_{NL}$, by training a neural network to locally estimate ${\sigma }_8$, and correlating these local estimates with the large-scale density field. We apply our method to $N$-body simulations, and show that $\sigma (f_{NL})$ is 3.5 times better than the constraint obtained from a standard halo-based approach. We show that our method has the same robustness property as large-scale halo bias: baryonic physics can change the normalization of the estimated $f_{NL}$, but cannot change whether $f_{NL}$ is detected.

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• Cosmological parameters
• Inflation
• Large scale structure of the Universe