The "weight smoothing" regularization of MLP for Jacobian stabilization
1Laboratoire de Meteorologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France.
IEEE Transactions on Neural Networks
|February 7, 2008
Summary
Neural networks often require smooth Jacobians for accurate approximation, especially in complex problems like atmospheric radiative transfer. This study introduces "weight smoothing" to regularize Jacobian profiles, improving approximation stability and enabling better inversion processes.
Area of Science:
- Computational Science
- Applied Mathematics
- Atmospheric Science
Background:
- Low root mean square (rms) error in neural network approximations is insufficient when Jacobian derivatives are critical.
- The compensation phenomenon in functional approximation leads to irregular neural Jacobian profiles, causing ill-posed problems.
- Accurate Jacobian derivatives are essential for inverse problems and understanding model behavior.
Purpose of the Study:
- To address the limitations of standard error criteria in neural network approximation.
- To introduce a quality criterion for Jacobian profiles during the neural network learning phase.
- To improve the stability and accuracy of approximating functionals, particularly in the presence of compensation phenomena.
Main Methods:
- Proposed a regularization technique by introducing Jacobian profile smoothness as a priori information.
- Developed a novel and efficient learning algorithm named "weight smoothing."
- Assessed the algorithm's robustness on the neural approximation of the radiative transfer equation's forward model in meteorology.
Main Results:
- The "weight smoothing" algorithm effectively stabilizes Jacobian profiles, mitigating irregularities caused by compensation phenomena.
- Demonstrated improved Jacobian quality in a complex meteorological application (radiative transfer equation).
- Stabilized Jacobians facilitated a more robust inversion process, showcasing practical benefits.
Conclusions:
- Jacobian profile smoothness is a crucial, often overlooked, criterion for reliable neural network approximation.
- The "weight smoothing" algorithm provides an effective solution for ill-posed approximation problems by regularizing Jacobians.
- This approach enhances the utility of neural networks in scientific domains requiring accurate derivative information, such as atmospheric modeling.
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