An optimal control approach for neural network architecture adaptation with a posteriori error estimation

2026-07-08 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, quick

Summary

This work introduces a novel method for adapting neural network architecture depth using a posteriori error estimation. It frames neural network training as a continuous-time optimal control problem, yielding rigorous error estimates that detail error distribution across network layers. This error decomposition guides a principled depth adaptation strategy, inserting new layers where estimated error is highest to efficiently capture complex, nonlinear variations. The framework employs a novel architecture where weights and biases are piecewise linear functions across layers, with an error estimator bounding the discrete representation's discrepancy from the continuous optimal control solution. Leveraging dual weighted residual methodology, the approach provides explicit error bounds for targeted refinement. Demonstrated on scientific datasets, including the Navier-Stokes equation, the method consistently surpasses existing architecture adaptation techniques in generalization performance.

Key takeaway

For Research Scientists developing advanced neural network architectures, this method offers a principled way to optimize network depth. By leveraging a posteriori error estimation, you can precisely identify and address approximation errors, leading to improved generalization performance. Consider integrating this optimal control framework to dynamically adapt your models, potentially reducing manual architecture tuning and enhancing model robustness on complex scientific problems.

Key insights

Neural network depth can be optimally adapted by inserting layers where a posteriori error is highest.

Principles

• NN training can be modeled as continuous optimal control.
• Error estimation can guide architecture adaptation.
• Dual weighted residual improves error bounds.

Method

Formulate NN training as continuous-time optimal control. Derive error estimates across layers. Insert new layers at maximum estimated error locations. Use dual weighted residual for error bounds.

In practice

• Apply to scientific datasets like Navier-Stokes.
• Improve generalization performance in NNs.

Topics

• Neural Network Architecture
• Optimal Control
• Error Estimation
• Depth Adaptation
• Navier-Stokes Equation
• Generalization Performance

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.