# Parametric Matrix Models

arXiv: https://arxiv.org/abs/2401.11694 · HTML: https://mlsanity.com/paper/2401.11694/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 123 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://mlsanity.com/paper/2107.01188/) (2021)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [SpinalNet: Deep Neural Network with Gradual Input](https://mlsanity.com/paper/2007.03347/) (2020)
- [The Convolutional Tsetlin Machine](https://mlsanity.com/paper/1905.09688/) (2019)
- [Hybrid Macro/Micro Level Backpropagation for Training Deep Spiking Neural Networks](https://mlsanity.com/paper/1805.07866/) (2018)
- [Fenchel Lifted Networks: A Lagrange Relaxation of Neural Network Training](https://mlsanity.com/paper/1811.08039/) (2018)
- [Fine-Tuning DARTS for Image Classification](https://mlsanity.com/paper/2006.09042/) (2020)
- [Equilibrated Recurrent Neural Network: Neuronal Time-Delayed Self-Feedback Improves Accuracy and Stability](https://mlsanity.com/paper/1903.00755/) (2019)
- [RNNs Evolving on an Equilibrium Manifold: A Panacea for Vanishing and Exploding Gradients?](https://mlsanity.com/paper/1908.08574/) (2019)

## Built on by (most cited first, 1 of 1)

- [The Spectral Neuron](https://mlsanity.com/paper/2608.08003/) (2026)

## Abstract (arXiv)

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate physical systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation.