# Applying the maximum entropy principle to neural networks enhances multi-species distribution models

arXiv: https://arxiv.org/abs/2412.19217 · HTML: https://mlsanity.com/paper/2412.19217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 66 references that are in the map.
- First posted on arXiv 26 Dec 2024.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Do Deep Nets Really Need to be Deep?](https://mlsanity.com/paper/1312.6184/) (2013)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Spatial Implicit Neural Representations for Global-Scale Species Mapping](https://mlsanity.com/paper/2306.02564/) (2023)
- [Deep Multi-Species Embedding](https://mlsanity.com/paper/1609.09353/) (2016)
- [GeoPlant: Spatial Plant Species Prediction Dataset](https://mlsanity.com/paper/2408.13928/) (2024)
- [On the selection and effectiveness of pseudo-absences for species distribution modeling with deep learning](https://mlsanity.com/paper/2401.02989/) (2024)
- [On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models](https://mlsanity.com/paper/1707.08538/) (2017)
- [Modelling Species Distributions with Deep Learning to Predict Plant Extinction Risk and Assess Climate Change Impacts](https://mlsanity.com/paper/2401.05470/) (2024)
- [Cumulant-based approximation for fast and efficient prediction for species distribution](https://mlsanity.com/paper/2405.14456/) (2024)

## Abstract (arXiv)

The rapid expansion of citizen science initiatives has led to a significant growth of biodiversity databases, and particularly presence-only (PO) observations. PO data are invaluable for understanding species distributions and their dynamics, but their use in a Species Distribution Model (SDM) is curtailed by sampling biases and the lack of information on absences. Poisson point processes are widely used for SDMs, with Maxent being one of the most popular methods. Maxent maximises the entropy of a probability distribution across sites as a function of predefined transformations of variables, called features. In contrast, neural networks and deep learning have emerged as a promising technique for automatic feature extraction from complex input variables. Arbitrarily complex transformations of input variables can be learned from the data efficiently through backpropagation and stochastic gradient descent (SGD). In this paper, we propose DeepMaxent, which harnesses neural networks to automatically learn shared features among species, using the maximum entropy principle. To do so, it employs a normalised Poisson loss where for each species, presence probabilities across sites are modelled by a neural network. We evaluate DeepMaxent on a benchmark dataset known for its spatial sampling biases, using PO data for calibration and presence-absence (PA) data for validation across six regions with different biological groups and covariates. Our results indicate that DeepMaxent performs better than Maxent and other leading SDMs across all regions and taxonomic groups. The method performs particularly well in regions of uneven sampling, demonstrating substantial potential to increase SDM performances. In particular, our approach yields more accurate predictions than traditional single-species models, which opens up new possibilities for methodological enhancement.