← Back to all news
arXiv Machine Learning By Madison Cooley, Shandian Zhe, Robert M. Kirby, Varun Shankar

Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation

Read the original on arXiv Machine Learning →

Polynomial-Augmented Neural Networks (PANNs) merge deep neural networks with polynomial expansions to leverage the flexibility of DNNs and the rapid convergence of polynomials. The architecture introduces orthogonality constraints, basis pruning, and polynomial preconditioning to stabilize training and improve accuracy across diverse problems. Experiments show that PANNs outperform both pure DNNs and polynomial methods in approximating smooth and limited‑smoothness functions, as well as in solving partial differential equations.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Aug 28

Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks

The paper proposes a conjecture that composing a fixed number of distinct nonconstant polynomials with a generic high‑degree polynomial produces linearly independent polynomials, extending Newman–Slater’s theorem. The authors prove the conjecture for two polynomials and for any number when the degrees are bounded, and they show how these results explain the parameter symmetries of deep fully connected neural networks with generic polynomial activations. In particular, for architectures with layer‑specific activations of increasing degree, the conjecture’s proven cases fully characterize the parameter sets that yield the same end‑to‑end network function, and it also resolves the identifiability of shallow polynomial networks.

By Kathl\'en Kohn, Giovanni Luca Marchetti, Alex Massarenti, Massimiliano Mella
More like this →
arXiv AI
Jul 13

All you need is SAMPAT

arXiv:2607. 09235v1 Announce Type: cross Abstract: The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability.

By Jayadeva, Madhur Aswani
benchmarkssafety
More like this →