Halo assembly bias from a deep learning model of halo formation

ABSTRACT We build a deep learning framework that connects the local formation process of dark matter haloes to the halo bias. We train a convolutional neural network (CNN) to predict the final mass and concentration of dark matter haloes from the initial conditions. The CNN is then used as a surrogate model to derive the response of the haloes’ mass and concentration to long-wavelength perturbations in the initial conditions, and consequently the halo bias parameters following the ‘response bias’ definition. The CNN correctly predicts how the local properties of dark matter haloes respond to changes in the large-scale environment, despite no explicit knowledge of halo bias being provided during training. We show that the CNN recovers the known trends for the linear and second-order density bias parameters b1 and b2, as well as for the local primordial non-Gaussianity linear bias parameter bϕ. The expected secondary assembly bias dependence on halo concentration is also recovered by the CNN: at fixed mass, halo concentration has only a mild impact on b1, but a strong impact on bϕ. Our framework opens a new window for discovering which physical aspects of the halo’s Lagrangian patch determine assembly bias, which in turn can inform physical models of halo formation and bias.