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Estimating uncertainty from feed-forward network based sensing using quasi-linear approximation.

Songhan Zhang¹, Matthew Singh², Delsin Menolascino³

¹Washington University in St. Louis, St. Louis, MO, USA.

Neural Networks : the Official Journal of the International Neural Network Society

|March 28, 2025

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This study introduces quasilinear approximation for quantifying uncertainty in feedforward neural networks. This analytical method offers an accurate alternative to Monte Carlo sampling for understanding uncertainty propagation.

Area of Science:

Artificial Intelligence
Machine Learning
Control Systems

Background:

Quantifying uncertainty in neural networks is critical for their integration into safety-critical engineered systems.
Traditional methods often rely on computationally intensive Monte Carlo sampling.
Understanding how input distribution moments change through network layers is a core challenge.

Purpose of the Study:

To develop a more analytical approach for estimating uncertainty in feedforward neural networks.
To address the mathematical challenges posed by nonlinearities in modern neural architectures.
To provide a rigorous method for uncertainty quantification.

Main Methods:

Utilizing quasilinear approximation, a technique from control systems engineering.

Keywords:

Kalman filter Neural networks Quasilinear approximation Stochastic linearization Uncertainty propagation

Related Experiment Videos

Linearizing nonlinearities based on the expectation of their input-output gain.

Deriving expectations for common nonlinearities assuming Gaussian inputs.

Main Results:

The quasilinear approximation demonstrates accuracy comparable to traditional linearization methods.
The derived method provides a formal framework for estimating uncertainty in latent variables.
A case study in target tracking validates the practical application of the approach.

Conclusions:

Quasilinear approximation offers an effective and analytical solution for uncertainty quantification in feedforward neural networks.
This method enhances the reliability of neural network outputs in decision-making systems.
The approach facilitates formal uncertainty estimation, crucial for robust AI applications.