auto-fpt: Automating Free Probability Theory Calculations for Machine Learning Theory
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908320131973120 |
|---|---|
| author | Subramonian, Arjun Dohmatob, Elvis |
| author_facet | Subramonian, Arjun Dohmatob, Elvis |
| contents | A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability theory, we introduce auto-fpt, a lightweight Python and SymPy-based tool that can automatically produce a reduced system of fixed-point equations which can be solved for the quantities of interest, and effectively constitutes a theory. We overview the algorithmic ideas underlying auto-fpt and its applications to various interesting problems, such as the high-dimensional error of linearized feed-forward neural networks, recovering well-known results. We hope that auto-fpt streamlines the majority of calculations involved in high-dimensional analysis, while helping the machine learning community reproduce known and uncover new phenomena. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | auto-fpt: Automating Free Probability Theory Calculations for Machine Learning Theory Subramonian, Arjun Dohmatob, Elvis Machine Learning Mathematical Software A large part of modern machine learning theory often involves computing the high-dimensional expected trace of a rational expression of large rectangular random matrices. To symbolically compute such quantities using free probability theory, we introduce auto-fpt, a lightweight Python and SymPy-based tool that can automatically produce a reduced system of fixed-point equations which can be solved for the quantities of interest, and effectively constitutes a theory. We overview the algorithmic ideas underlying auto-fpt and its applications to various interesting problems, such as the high-dimensional error of linearized feed-forward neural networks, recovering well-known results. We hope that auto-fpt streamlines the majority of calculations involved in high-dimensional analysis, while helping the machine learning community reproduce known and uncover new phenomena. |
| title | auto-fpt: Automating Free Probability Theory Calculations for Machine Learning Theory |
| topic | Machine Learning Mathematical Software |
| url | https://arxiv.org/abs/2504.10754 |