Relative Representations: Topological and Geometric Perspectives
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908607918899200 |
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| author | García-Castellanos, Alejandro Marchetti, Giovanni Luca Kragic, Danica Scolamiero, Martina |
| author_facet | García-Castellanos, Alejandro Marchetti, Giovanni Luca Kragic, Danica Scolamiero, Martina |
| contents | Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose two improvements to relative representations. First, we introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. The latter coincides with the symmetries in parameter space induced by common activation functions. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes. We provide an empirical investigation on a natural language task, where both the proposed variations yield improved performance on zero-shot model stitching. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Representations: Topological and Geometric Perspectives García-Castellanos, Alejandro Marchetti, Giovanni Luca Kragic, Danica Scolamiero, Martina Machine Learning Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose two improvements to relative representations. First, we introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. The latter coincides with the symmetries in parameter space induced by common activation functions. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes. We provide an empirical investigation on a natural language task, where both the proposed variations yield improved performance on zero-shot model stitching. |
| title | Relative Representations: Topological and Geometric Perspectives |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2409.10967 |