# Poisson Variational Autoencoder

arXiv: https://arxiv.org/abs/2405.14473 · HTML: https://mlsanity.com/paper/2405.14473/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 153 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [Semi-Amortized Variational Autoencoders](https://mlsanity.com/paper/1802.02550/) (2018)
- [Convolutional Neural Networks as a Model of the Visual System: Past, Present, and Future](https://mlsanity.com/paper/2001.07092/) (2020)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)

## Built on by (most cited first, 11 of 11)

- [Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalisation](https://mlsanity.com/paper/2603.28744/) (2026)
- [Negative Binomial Variational Autoencoders for Overdispersed Latent Modeling](https://mlsanity.com/paper/2508.05423/) (2025)
- [Inferring response times of perceptual decisions with Poisson variational autoencoders](https://mlsanity.com/paper/2511.11480/) (2025)
- [GraViti: Graph-Level Variational Autoencoders with Relaxed Permutation Invariance](https://mlsanity.com/paper/2605.16668/) (2026)
- [Zero-Variance Gradients for Variational Autoencoders](https://mlsanity.com/paper/2508.03587/) (2025)
- [A hitchhiker's guide to Poisson gradient estimation](https://mlsanity.com/paper/2602.03896/) (2026)
- [Pixel-Space Diffusion Transformers](https://mlsanity.com/paper/2607.17585/) (2026)
- [Likelihood-Free Variational Autoencoders](https://mlsanity.com/paper/2504.17622/) (2025)
- [Metabolic cost of information processing in Poisson variational autoencoders](https://mlsanity.com/paper/2602.13421/) (2026)
- [VAE-MS: An Asymmetric Variational Autoencoder for Mutational Signature Extraction](https://mlsanity.com/paper/2602.22239/) (2026)
- [Neighbor Embedding for High-Dimensional Sparse Poisson Data](https://mlsanity.com/paper/2604.16932/) (2026)

## Abstract (arXiv)

Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their success, traditional VAEs rely on continuous latent variables, which deviates sharply from the discrete nature of biological neurons. Here, we developed the Poisson VAE (P-VAE), a novel architecture that combines principles of predictive coding with a VAE that encodes inputs into discrete spike counts. Combining Poisson-distributed latent variables with predictive coding introduces a metabolic cost term in the model loss function, suggesting a relationship with sparse coding which we verify empirically. Additionally, we analyze the geometry of learned representations, contrasting the P-VAE to alternative VAE models. We find that the P-VAE encodes its inputs in relatively higher dimensions, facilitating linear separability of categories in a downstream classification task with a much better (5x) sample efficiency. Our work provides an interpretable computational framework to study brain-like sensory processing and paves the way for a deeper understanding of perception as an inferential process.