Robust neural determination of the source-count distribution of the <i>Fermi</i> -LAT sky at high latitudes

Over the past 16 years, the Large Area Telescope (LAT) has significantly advanced our view of the GeV gamma-ray sky, yet several key questions remain—such as the composition of the isotropic gamma-ray background, the origin of the Bubbles, or the potential presence of signatures from exotic physics like dark matter. Addressing these challenges requires sophisticated astrophysical modeling and robust statistical methods capable of handling high-dimensional parameter spaces. In this work, we analyze 14 years of high-latitude ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">|</a:mo> <a:mi>b</a:mi> <a:mo stretchy="false">|</a:mo> <a:mo>≥</a:mo> <a:mn>3</a:mn> <a:mn>0</a:mn> <a:mi>°</a:mi> </a:math> ) -LAT data in the range from 1 to 10 GeV using simulation-based inference (SBI) via neural ratio estimation. This approach allows us to detect individual gamma-ray sources and derive a list of significant gamma-ray emitters containing more than 98% of all sources listed in the -LAT Fourth Source Catalog (4FGL) with a flux <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>S</e:mi> <e:mo>&gt;</e:mo> <e:mn>3</e:mn> <e:mo>×</e:mo> <e:msup> <e:mn>10</e:mn> <e:mrow> <e:mo>−</e:mo> <e:mn>10</e:mn> </e:mrow> </e:msup> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:msup> <e:mrow> <e:mi>cm</e:mi> </e:mrow> <e:mrow> <e:mo>−</e:mo> <e:mn>2</e:mn> </e:mrow> </e:msup> <e:mtext> </e:mtext> <e:msup> <e:mi mathvariant="normal">s</e:mi> <e:mrow> <e:mo>−</e:mo> <e:mn>1</e:mn> </e:mrow> </e:msup> </e:math> (about a factor of 3 larger than the flux above which 4FGL is nearly complete), without any non-4FGL source detected in that flux range. Additionally, we reconstruct the source-count distribution in both parametric and nonparametric forms, achieving large agreement with previous literature results as well as those sources detected by our SBI pipeline. We also quantitatively validate our gamma-ray emission simulator via an anomaly detection technique, demonstrating that the synthetic data closely reproduce the complexity of the real observations.