A Hitchhiker's Guide to Poisson Gradient Estimation
This provides practical guidance for computational neuroscience practitioners working with Poisson latent variable models, though it is incremental as it builds on existing methods.
The paper tackled the challenge of gradient estimation in Poisson-distributed latent variable models by systematically comparing Exponential Arrival Time (EAT) simulation and Gumbel-SoftMax relaxation, and introduced a modified EAT method that improved performance across metrics, often matching exact gradients.
Poisson-distributed latent variable models are widely used in computational neuroscience, but differentiating through discrete stochastic samples remains challenging. Two approaches address this: Exponential Arrival Time (EAT) simulation and Gumbel-SoftMax (GSM) relaxation. We provide the first systematic comparison of these methods, along with practical guidance for practitioners. Our main technical contribution is a modification to the EAT method that theoretically guarantees an unbiased first moment (exactly matching the firing rate), and reduces second-moment bias. We evaluate these methods on their distributional fidelity, gradient quality, and performance on two tasks: (1) variational autoencoders with Poisson latents, and (2) partially observable generalized linear models, where latent neural connectivity must be inferred from observed spike trains. Across all metrics, our modified EAT method exhibits better overall performance (often comparable to exact gradients), and substantially higher robustness to hyperparameter choices. Together, our results clarify the trade-offs between these methods and offer concrete recommendations for practitioners working with Poisson latent variable models.