Your question is not clear to me. However, I am jotting down a few papers referring to this function. Please check.

1. Lucas, A., Tomlinson, T., Rohani, N., Chowdhury, R. H., Solla, S. A., Katsaggelos, A. K., & Miller, L. E. (2019). Deep Neural Networks for Modeling Neural Spiking in S1 Cortex. Frontiers in systems neuroscience, 13, 13.

2. Zhang, H., Chi, Y., & Liang, Y. (2018). Median-truncated nonconvex approach for phase retrieval with outliers. IEEE Transactions on Information Theory, 64(11), 7287-7310.

3. Li, Z., Cai, J. F., & Wei, K. (2018). Towards the optimal construction of a loss function without spurious local minima for solving quadratic equations. arXiv preprint arXiv:1809.10520.

You may refer to:

• [Loss Functions in NNs] https://isaacchanghau.github.io/post/loss_functions/
• [Poisson Regression using Multilayer NNs] Fallah et al., " Nonlinear Poisson Regression using Neural Networks: a Simulation Study ", 2009 - https://www.mathstat.dal.ca/~hgu/Neural%20Comput%20&%20Applic.pdf
• [Kernel Poisson Regression] Jia et al., " Sparse Bayesian Learning-based Kernel Poisson Regression ", 2017 - https://booksc.org/book/68435219/ab1363
• [Kernel Poisson Regression] Lee et al., " On the “Poisson Trick” and its Extensions for Fitting Multinomial Regression Models ", 2017 - https://arxiv.org/pdf/1707.08538.pdf

For linking Kernel-based Poisson regression to Deep NN-based Poisson regression, check out:

• Belkin et al., " To Understand Deep Learning We Need to Understand Kernel Learning ", 2018 - http://proceedings.mlr.press/v80/belkin18a/belkin18a.pdf
• M. Unser, " A Representer Theorem for Deep Neural Networks ", 2019 - https://arxiv.org/pdf/1802.09210.pdf