# Extracting the gamma-ray source-count distribution below the Fermi-LAT detection limit with deep learning

arXiv: https://arxiv.org/abs/2302.01947 · HTML: https://mlsanity.com/paper/2302.01947/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 65 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 18 of 18)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [L2 Regularization versus Batch and Weight Normalization](https://mlsanity.com/paper/1706.05350/) (2017)
- [On Contrastive Learning for Likelihood-free Inference](https://mlsanity.com/paper/2002.03712/) (2020)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [Truncated Marginal Neural Ratio Estimation](https://mlsanity.com/paper/2107.01214/) (2021)
- [Learning Spherical Convolution for Fast Features from 360deg Imagery](https://mlsanity.com/paper/1708.00919/) (2017)
- [A neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess](https://mlsanity.com/paper/2110.06931/) (2021)
- [Dim but not entirely dark: Extracting the Galactic Center Excess' source-count distribution with neural nets](https://mlsanity.com/paper/2107.09070/) (2021)

## Built on by (most cited first, 1 of 1)

- [A deep learning framework for jointly extracting spectra and source-count distributions in astronomy](https://mlsanity.com/paper/2401.03336/) (2024)

## Abstract (arXiv)

We reconstruct the extra-galactic gamma-ray source-count distribution, or dN/dS, of resolved and unresolved sources by adopting machine learning techniques. Specifically, we train a convolutional neural network on synthetic 2-dimensional sky-maps, which are built by varying parameters of underlying source-counts models and incorporate the Fermi-LAT instrumental response functions. The trained neural network is then applied to the Fermi-LAT data, from which we estimate the source count distribution down to flux levels a factor of 50 below the Fermi-LAT threshold. We perform our analysis using 14 years of data collected in the (1,10) GeV energy range. The results we obtain show a source count distribution which, in the resolved regime, is in excellent agreement with the one derived from catalogued sources, and then extends as dN/dS ~ S-2 in the unresolved regime, down to fluxes of 5 · 10-12 cm-2 s-1. The neural network architecture and the devised methodology have the flexibility to enable future analyses to study the energy dependence of the source-count distribution.