Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Michigan State University, Cornell Tech
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: FROM QUARKS TO STARS; A QUANTUM COMPUTING APPROACH TO THE NUCLEAR MANY-BODY PROBLEM, THEORETICAL NUCLEAR STRUCTURE, Quantum Many-Body Theories for the Nuclear Equation of State, G2973041457, G4675925564, THEORETICAL NUCLEAR STRUCTURE, G4845049930, NRI/Collaborative Research: Robot-Assisted Feeding: Towards Efficient, Safe, and Personalized Caregiving Robots, Efficient Quantum State Preparation Algorithms, FROM QUARKS TO STARS; A QUANTUM COMPUTING APPROACH TO THE NUCLEAR MANY-BODY PROBLEM, G6353015704, G6992476341, G7345843951, G8110749304, Computational Nuclear Many-Body Physics, The Heart and the Mind: An Integrative Approach to Brain-Body Interactions in the Zebrafish
OpenAlex ID: W4391158562