Distribution free uncertainty quantification in neuroscience-inspired deep operators
This work addresses uncertainty quantification for neuroscience-inspired deep operators, which is crucial for practical applications where accuracy is sacrificed for energy efficiency, though it appears incremental as it builds on existing techniques like Randomized Prior networks and Split Conformal Prediction.
The paper tackles the problem of uncertainty quantification in energy-efficient spiking neural networks by introducing the Conformalized Randomized Prior Operator framework, which combines Randomized Prior networks with Split Conformal Prediction to produce calibrated uncertainty bounds that significantly outperform existing methods like vanilla RP-VSWNO, Q-WNO, and CQ-WNO.
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.