Energy-efficient deep learning algorithms are essential for a sustainable future and feasible edge computing setups. Spiking neural networks (SNNs), inspired from neuroscience, are a positive step in the direction of achieving the required energy efficiency. However, in a bid to lower the energy requirements, accuracy is marginally sacrificed. Hence, predictions of such deep learning algorithms require an uncertainty measure that can inform users regarding the bounds of a certain output. In this paper, we introduce the Conformalized Randomized Prior Operator (CRP-O) framework that leverages Randomized Prior (RP) networks and Split Conformal Prediction (SCP) to quantify uncertainty in both conventional and spiking neural operators. To further enable zero-shot super-resolution in UQ, we propose an extension incorporating Gaussian Process Regression. This enhanced super-resolution-enabled CRP-O framework is integrated with the recently developed Variable Spiking Wavelet Neural Operator (VSWNO). To test the performance of the obtained calibrated uncertainty bounds, we discuss four different examples covering both one-dimensional and two-dimensional partial differential equations. Results demonstrate that the uncertainty bounds produced by the conformalized RP-VSWNO significantly enhance UQ estimates compared to vanilla RP-VSWNO, Quantile WNO (Q-WNO), and Conformalized Quantile WNO (CQ-WNO). These findings underscore the potential of the proposed approach for practical applications.

翻译：节能深度学习算法对于可持续未来和可行的边缘计算设置至关重要。受神经科学启发的脉冲神经网络（SNNs）是实现所需能效的积极一步。然而，在降低能耗要求的同时，准确性会略有牺牲。因此，此类深度学习算法的预测需要一个不确定性度量，以告知用户特定输出的边界范围。本文介绍了共形化随机先验算子（CRP-O）框架，该框架利用随机先验（RP）网络和分割共形预测（SCP）来量化传统和脉冲神经算子的不确定性。为进一步实现不确定性量化中的零样本超分辨率，我们提出了一种结合高斯过程回归的扩展方法。这种增强的超分辨率支持CRP-O框架与最近开发的变量脉冲小波神经算子（VSWNO）相结合。为测试所得校准不确定性边界的性能，我们讨论了涵盖一维和二维偏微分方程的四个不同示例。结果表明，与原始RP-VSWNO、分位数WNO（Q-WNO）和共形化分位数WNO（CQ-WNO）相比，共形化RP-VSWNO产生的不确定性边界显著提升了不确定性量化估计。这些发现强调了所提方法在实际应用中的潜力。