# Polynomial Networks and Factorization Machines: New Insights and Efficient Training Algorithms

arXiv: https://arxiv.org/abs/1607.08810 · HTML: https://mlsanity.com/paper/1607.08810/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2016.

## Built on by (most cited first, 11 of 11)

- [Improved Random Features for Dot Product Kernels](https://mlsanity.com/paper/2201.08712/) (2022)
- [Identifiability of Deep Polynomial Neural Networks](https://mlsanity.com/paper/2506.17093/) (2025)
- [Detecting Arbitrary Order Beneficial Feature Interactions for Recommender Systems](https://mlsanity.com/paper/2206.13764/) (2022)
- [Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations](https://mlsanity.com/paper/2108.08659/) (2021)
- [Ladder Polynomial Neural Networks](https://mlsanity.com/paper/2106.13834/) (2021)
- [xDeepInt: a hybrid architecture for modeling the vector-wise and bit-wise feature interactions](https://mlsanity.com/paper/2301.01089/) (2023)
- [Additive Higher-Order Factorization Machines](https://mlsanity.com/paper/2205.14515/) (2022)
- [SHORING: Design Provable Conditional High-Order Interaction Network via Symbolic Testing](https://mlsanity.com/paper/2107.01326/) (2021)
- [Constructing structured tensor priors for Bayesian inverse problems](https://mlsanity.com/paper/2406.17597/) (2024)
- [On subdifferential chain rule of matrix factorization and beyond](https://mlsanity.com/paper/2410.05022/) (2024)
- [tensorFM: Low-Rank Approximations of Cross-Order Feature Interactions](https://mlsanity.com/paper/2602.15229/) (2026)

## Abstract (arXiv)

Polynomial networks and factorization machines are two recently-proposed models that can efficiently use feature interactions in classification and regression tasks. In this paper, we revisit both models from a unified perspective. Based on this new view, we study the properties of both models and propose new efficient training algorithms. Key to our approach is to cast parameter learning as a low-rank symmetric tensor estimation problem, which we solve by multi-convex optimization. We demonstrate our approach on regression and recommender system tasks.