Double-descent curves in neural networks: a new perspective using Gaussian processes
Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regim...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Association for the Advancement of Artificial Intelligence
2024
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| _version_ | 1826313663406931968 |
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| author | El Harzli, O Cuenca Grau, B Valle-Pérez, G Louis, AA |
| author_facet | El Harzli, O Cuenca Grau, B Valle-Pérez, G Louis, AA |
| author_sort | El Harzli, O |
| collection | OXFORD |
| description | Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regime. In this paper, we use techniques from random matrix theory to characterize the spectral distribution of the empirical feature covariance matrix as a width-dependent perturbation of the spectrum of the neural network Gaussian process (NNGP) kernel, thus establishing a novel connection between the NNGP literature and the random matrix theory literature in the context of neural networks. Our analytical expressions allow us to explore the generalisation behavior of the corresponding kernel and GP regression. Furthermore, they offer a new interpretation of double-descent in terms of the discrepancy between the width-dependent empirical kernel and the width-independent NNGP kernel. |
| first_indexed | 2024-09-25T04:20:12Z |
| format | Conference item |
| id | oxford-uuid:395bbccd-6fd3-40bf-8f58-f06b21ad8ec3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:20:12Z |
| publishDate | 2024 |
| publisher | Association for the Advancement of Artificial Intelligence |
| record_format | dspace |
| spelling | oxford-uuid:395bbccd-6fd3-40bf-8f58-f06b21ad8ec32024-08-01T15:08:25ZDouble-descent curves in neural networks: a new perspective using Gaussian processesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:395bbccd-6fd3-40bf-8f58-f06b21ad8ec3EnglishSymplectic ElementsAssociation for the Advancement of Artificial Intelligence2024El Harzli, OCuenca Grau, BValle-Pérez, GLouis, AADouble-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regime. In this paper, we use techniques from random matrix theory to characterize the spectral distribution of the empirical feature covariance matrix as a width-dependent perturbation of the spectrum of the neural network Gaussian process (NNGP) kernel, thus establishing a novel connection between the NNGP literature and the random matrix theory literature in the context of neural networks. Our analytical expressions allow us to explore the generalisation behavior of the corresponding kernel and GP regression. Furthermore, they offer a new interpretation of double-descent in terms of the discrepancy between the width-dependent empirical kernel and the width-independent NNGP kernel. |
| spellingShingle | El Harzli, O Cuenca Grau, B Valle-Pérez, G Louis, AA Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title | Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title_full | Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title_fullStr | Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title_full_unstemmed | Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title_short | Double-descent curves in neural networks: a new perspective using Gaussian processes |
| title_sort | double descent curves in neural networks a new perspective using gaussian processes |
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