Summary of Polynomial-augmented Neural Networks (panns) with Weak Orthogonality Constraints For Enhanced Function and Pde Approximation, by Madison Cooley et al.
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
by Madison Cooley, Shandian Zhe, Robert M. Kirby, Varun Shankar
First submitted to arxiv on: 4 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary We introduce Polynomial-Augmented Neural Networks (PANNs), a novel architecture combining deep neural networks (DNNs) and polynomial approximation. PANNs leverage the strengths of both components, offering flexibility and efficiency in higher-dimensional approximation, along with rapid convergence rates for smooth functions. To ensure stable training and enhanced accuracy, we propose orthogonality constraints, basis pruning, and polynomial preconditioning strategies. We experimentally demonstrate PANNs’ superior approximation properties over DNNs for regression and partial differential equations (PDEs) solution, as well as improved accuracy over both polynomial and DNN-based regression when regressing functions with limited smoothness. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary We created a new way to make neural networks better at solving problems. We combined two ideas: deep neural networks (good for complex tasks) and polynomials (fast and simple). Our new architecture, called Polynomial-Augmented Neural Networks (PANNs), does this combination in a clever way. This helps it solve some problems more accurately than just using one or the other alone. We tested PANNs on different types of problems and showed that it’s better at solving certain kinds of equations and functions. |
Keywords
» Artificial intelligence » Pruning » Regression
