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.

翻译：泊松分布潜变量模型在计算神经科学中应用广泛，但通过离散随机样本进行微分仍具挑战性。现有两种主要方法：指数到达时间模拟与Gumbel-SoftMax松弛技术。本研究首次系统比较了这两种方法，并为实践者提供实用指导。我们的主要技术贡献是对EAT方法的改进，该改进理论上保证了一阶矩的无偏性（精确匹配发放率），同时降低了二阶矩偏差。我们从分布保真度、梯度质量及两项任务表现评估这些方法：（1）具有泊松潜变量的变分自编码器；（2）部分可观测广义线性模型——需从观测到的脉冲序列推断潜在神经连接性。在所有评估指标中，改进的EAT方法展现出更优的综合性能（常与精确梯度相当），且对超参数选择具有显著更高的鲁棒性。本研究结果明确了这些方法间的权衡关系，并为泊松潜变量模型的实践者提供了具体建议。