Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911653401985024 |
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| author | Atanasov, Alexander Bordelon, Blake Zavatone-Veth, Jacob A. Paquette, Courtney Pehlevan, Cengiz |
| author_facet | Atanasov, Alexander Bordelon, Blake Zavatone-Veth, Jacob A. Paquette, Courtney Pehlevan, Cengiz |
| contents | We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with stochastic gradient descent. This includes high-dimensional linear regression, kernel regression, and linear random feature models. Our results include previously known asymptotics as well as novel ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models Atanasov, Alexander Bordelon, Blake Zavatone-Veth, Jacob A. Paquette, Courtney Pehlevan, Cengiz Disordered Systems and Neural Networks Machine Learning We derive a novel deterministic equivalence for the two-point function of a random matrix resolvent. Using this result, we give a unified derivation of the performance of a wide variety of high-dimensional linear models trained with stochastic gradient descent. This includes high-dimensional linear regression, kernel regression, and linear random feature models. Our results include previously known asymptotics as well as novel ones. |
| title | Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models |
| topic | Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2502.05074 |