# Exponential Machines

arXiv: https://arxiv.org/abs/1605.03795 · HTML: https://mlsanity.com/paper/1605.03795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2016.

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

- [No-Free-Lunch Theories for Tensor-Network Machine Learning Models](https://mlsanity.com/paper/2412.05674/) (2024)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models all interactions of every order. The key idea is to represent an exponentially large tensor of parameters in a factorized format called Tensor Train (TT). The Tensor Train format regularizes the model and lets you control the number of underlying parameters. To train the model, we develop a stochastic Riemannian optimization procedure, which allows us to fit tensors with 2^160 entries. We show that the model achieves state-of-the-art performance on synthetic data with high-order interactions and that it works on par with high-order factorization machines on a recommender system dataset MovieLens 100K.