A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schrödinger Equations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912831848316928 |
|---|---|
| author | Cole, Frank Lu, Yulong Sehgal, Shaurya |
| author_facet | Cole, Frank Lu, Yulong Sehgal, Shaurya |
| contents | We address the following question: given a collection $\{\mathbf{A}^{(1)}, \dots, \mathbf{A}^{(N)}\}$ of independent $d \times d$ random matrices drawn from a common distribution $\mathbb{P}$, what is the probability that the centralizer of $\{\mathbf{A}^{(1)}, \dots, \mathbf{A}^{(N)}\}$ is trivial? We provide lower bounds on this probability in terms of the sample size $N$ and the dimension $d$ for several families of random matrices which arise from the discretization of linear Schrödinger operators with random potentials. When combined with recent work on machine learning theory, our results provide guarantees on the generalization ability of transformer-based neural networks for in-context learning of Schrödinger equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12587 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schrödinger Equations Cole, Frank Lu, Yulong Sehgal, Shaurya Machine Learning We address the following question: given a collection $\{\mathbf{A}^{(1)}, \dots, \mathbf{A}^{(N)}\}$ of independent $d \times d$ random matrices drawn from a common distribution $\mathbb{P}$, what is the probability that the centralizer of $\{\mathbf{A}^{(1)}, \dots, \mathbf{A}^{(N)}\}$ is trivial? We provide lower bounds on this probability in terms of the sample size $N$ and the dimension $d$ for several families of random matrices which arise from the discretization of linear Schrödinger operators with random potentials. When combined with recent work on machine learning theory, our results provide guarantees on the generalization ability of transformer-based neural networks for in-context learning of Schrödinger equations. |
| title | A Theory of Diversity for Random Matrices with Applications to In-Context Learning of Schrödinger Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.12587 |