Geometry of Lightning Self-Attention: Identifiability and Dimension
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913697685831680 |
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| author | Henry, Nathan W. Marchetti, Giovanni Luca Kohn, Kathlén |
| author_facet | Henry, Nathan W. Marchetti, Giovanni Luca Kohn, Kathlén |
| contents | We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of Lightning Self-Attention: Identifiability and Dimension Henry, Nathan W. Marchetti, Giovanni Luca Kohn, Kathlén Machine Learning Algebraic Geometry We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case. |
| title | Geometry of Lightning Self-Attention: Identifiability and Dimension |
| topic | Machine Learning Algebraic Geometry |
| url | https://arxiv.org/abs/2408.17221 |