# Parametric Matrix Models Source: [Parametric Matrix Models]() Collection index: [llms.txt]() Data updated: 2026-01-04T03:58:37.779Z Authors: Patrick Cook, Danny Jammooa, Morten Hjorth-Jensen, Daniel D. Lee, Dean Lee Published: 2024-01-22T05:26:18.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on EMNIST Balanced 69 (test)](): Image Classification; EMNIST Balanced 69 (test); Accuracy: 85.95. - [Image Classification on MNIST Digits 61 (test)](): Image Classification; MNIST Digits 61 (test); Accuracy: 99.1. - [Image Classification on Fashion MNIST 66 (test)](): Image Classification; Fashion MNIST 66 (test); Accuracy: 90.94. ## Original sources and implementation [Original paper]() [PDF]()