Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distribution free uncertainty quantification in neuroscience-inspired deep operators

Shailesh Garg, Souvik Chakraborty

TL;DR

The paper tackles uncertainty quantification for energy-efficient neuroscience-inspired neural operators by proposing CRP-O, a distribution-free framework that uses randomized priors and split conformal prediction to guarantee marginal coverage $\ge 1-\alpha$. It extends this framework with Gaussian Process regression to enable zero-shot super-resolution and integrates it with the Variable Spiking Wavelet Neural Operator (VSWNO) and Wavelet Neural Operator (WNO). The key contributions are (1) a RP-based initial uncertainty estimator, (2) a calibration procedure via SCP that achieves MCC, (3) a GP-driven method for super-resolution uncertainty transfer, and (4) extensive numerical demonstrations across Burgers, Darcy, and Helmholtz problems showing robust coverage and competitive accuracy compared to prior UQ methods. The results indicate practical benefits for uncertainty-aware deployment of energy-efficient neuroscience-inspired operators, particularly in edge computing contexts where reliable UQ is essential.

Abstract

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.

Distribution free uncertainty quantification in neuroscience-inspired deep operators

TL;DR

The paper tackles uncertainty quantification for energy-efficient neuroscience-inspired neural operators by proposing CRP-O, a distribution-free framework that uses randomized priors and split conformal prediction to guarantee marginal coverage . It extends this framework with Gaussian Process regression to enable zero-shot super-resolution and integrates it with the Variable Spiking Wavelet Neural Operator (VSWNO) and Wavelet Neural Operator (WNO). The key contributions are (1) a RP-based initial uncertainty estimator, (2) a calibration procedure via SCP that achieves MCC, (3) a GP-driven method for super-resolution uncertainty transfer, and (4) extensive numerical demonstrations across Burgers, Darcy, and Helmholtz problems showing robust coverage and competitive accuracy compared to prior UQ methods. The results indicate practical benefits for uncertainty-aware deployment of energy-efficient neuroscience-inspired operators, particularly in edge computing contexts where reliable UQ is essential.

Abstract

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.

Paper Structure

This paper contains 18 sections, 1 theorem, 44 equations, 7 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Conformal Quantile DeepONet Regression
  4. Risk-Controlling Quantile Neural Operator
  5. Proposed approach
  6. Variable spiking WNO (VSWNO)
  7. Conformalized RP operator (CRP-O)
  8. Proof:
  9. Super-resolution predictions
  10. Numerical Illustrations
  11. E-I, Burgers Equation
  12. E-II, Darcy Equation on Rectangular Domain
  13. E-III, Darcy on Triangular Domain with a Notch
  14. E-IV, Helmholtz Equation
  15. Conclusion
  16. ...and 3 more sections

Key Result

Lemma 1

The SCP algorithm provides calibrated prediction intervals such that for any arbitrary score function $e(\bm{u}, y)$ that correctly estimates the discrepancy between predictions and true values, the probability of the true output $y_t$ lying within the calibrated interval $\mathcal{C}_p(\bm{u}_t)$ s for $\alpha \geq \frac{1}{n+1}$, where $n$ is the size of the calibration dataset.

Figures (7)

  • Figure 1: Schematic for the overall framework.
  • Figure 2: Mean predictions for test inputs obtained using CRP-WNO and CRP-VSWNO compared against the ground truth in E-I. Calibrated confidence intervals obtained using the two networks are also plotted for different test samples.
  • Figure 3: Super-resolution results for E-I.
  • Figure 4: Mean predictions for test inputs obtained using CRP-WNO and CRP-VSWNO compared against the ground truth in E-II.
  • Figure 5: Super-resolution results for E-II.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Lemma 1