Abstract: "The Evidence Lower Bound (ELBO) is a widely used objective for training deep generative models, such as Variational Autoencoders (VAEs). In the neuroscience literature, an identical objective is known as the variational free energy, hinting at a potential unified framework for brain function and machine learning. Despite its utility in interpreting generative models, including diffusion models, ELBO maximization is often seen as too broad to offer prescriptive guidance for specific architectures in neuroscience or machine learning. In this work, we show that maximizing ELBO under Poisson assumptions for general sequence data leads to a spiking neural network that performs Bayesian posterior inference through its membrane potential dynamics. The resulting model, the iterative Poisson VAE (iP-VAE), has a closer connection to biological neurons than previous brain-inspired predictive coding models based on Gaussian assumptions. Compared to amortized and iterative VAEs, iP-VAElearns sparser representations and exhibits superior generalization to out-of-distribution samples. These findings suggest that optimizing ELBO, combined with Poisson assumptions, provides a solid foundation for developing prescriptive theories in NeuroAI."