Uncertainty estimation is a standard tool to quantify the reliability of modern deep learning models, and crucial for many real-world applications. However, efficient uncertainty estimation methods for spiking neural networks, particularly for regression models, have been lacking. Here, we introduce two methods that adapt the Average-Over-Time Spiking Neural Network (AOT-SNN) framework to regression tasks, enhancing uncertainty estimation in event-driven models. The first method uses the heteroscedastic Gaussian approach, where SNNs predict both the mean and variance at each time step, thereby generating a conditional probability distribution of the target variable. The second method leverages the Regression-as-Classification (RAC) approach, reformulating regression as a classification problem to facilitate uncertainty estimation. We evaluate our approaches on both a toy dataset and several benchmark datasets, demonstrating that the proposed AOT-SNN models achieve performance comparable to or better than state-of-the-art deep neural network methods, particularly in uncertainty estimation. Our findings highlight the potential of SNNs for uncertainty estimation in regression tasks, providing an efficient and biologically inspired alternative for applications requiring both accuracy and energy efficiency.

翻译：不确定性估计是量化现代深度学习模型可靠性的标准工具，对许多现实应用至关重要。然而，针对脉冲神经网络的高效不确定性估计方法，特别是针对回归模型的方法，一直较为缺乏。本文介绍了两种将平均时间脉冲神经网络框架应用于回归任务的方法，以增强事件驱动模型中的不确定性估计。第一种方法采用异方差高斯方法，其中脉冲神经网络在每个时间步同时预测均值和方差，从而生成目标变量的条件概率分布。第二种方法利用回归即分类方法，将回归问题重新表述为分类问题，以促进不确定性估计。我们在一个玩具数据集和多个基准数据集上评估了所提出的方法，结果表明，所提出的平均时间脉冲神经网络模型在性能上达到或优于最先进的深度神经网络方法，特别是在不确定性估计方面。我们的研究结果突显了脉冲神经网络在回归任务中进行不确定性估计的潜力，为需要兼具准确性和能效的应用提供了一种高效且受生物启发的替代方案。