# An Algorithm for Training Polynomial Networks

arXiv: https://arxiv.org/abs/1304.7045 · HTML: https://mlsanity.com/paper/1304.7045/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [Decoupled Vertical Federated Learning for Practical Training on Vertically Partitioned Data](https://mlsanity.com/paper/2403.03871/) (2024)
- [Tensor-based framework for training flexible neural networks](https://mlsanity.com/paper/2106.13542/) (2021)

## Abstract (arXiv)

We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the Basis Learner. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.