DINO as a von Mises-Fisher mixture model
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929347182460928 |
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| author | Govindarajan, Hariprasath Sidén, Per Roll, Jacob Lindsten, Fredrik |
| author_facet | Govindarajan, Hariprasath Sidén, Per Roll, Jacob Lindsten, Fredrik |
| contents | Self-distillation methods using Siamese networks are popular for self-supervised pre-training. DINO is one such method based on a cross-entropy loss between $K$-dimensional probability vectors, obtained by applying a softmax function to the dot product between representations and learnt prototypes. Given the fact that the learned representations are $L^2$-normalized, we show that DINO and its derivatives, such as iBOT, can be interpreted as a mixture model of von Mises-Fisher components. With this interpretation, DINO assumes equal precision for all components when the prototypes are also $L^2$-normalized. Using this insight we propose DINO-vMF, that adds appropriate normalization constants when computing the cluster assignment probabilities. Unlike DINO, DINO-vMF is stable also for the larger ViT-Base model with unnormalized prototypes. We show that the added flexibility of the mixture model is beneficial in terms of better image representations. The DINO-vMF pre-trained model consistently performs better than DINO on a range of downstream tasks. We obtain similar improvements for iBOT-vMF vs iBOT and thereby show the relevance of our proposed modification also for other methods derived from DINO. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DINO as a von Mises-Fisher mixture model Govindarajan, Hariprasath Sidén, Per Roll, Jacob Lindsten, Fredrik Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition Self-distillation methods using Siamese networks are popular for self-supervised pre-training. DINO is one such method based on a cross-entropy loss between $K$-dimensional probability vectors, obtained by applying a softmax function to the dot product between representations and learnt prototypes. Given the fact that the learned representations are $L^2$-normalized, we show that DINO and its derivatives, such as iBOT, can be interpreted as a mixture model of von Mises-Fisher components. With this interpretation, DINO assumes equal precision for all components when the prototypes are also $L^2$-normalized. Using this insight we propose DINO-vMF, that adds appropriate normalization constants when computing the cluster assignment probabilities. Unlike DINO, DINO-vMF is stable also for the larger ViT-Base model with unnormalized prototypes. We show that the added flexibility of the mixture model is beneficial in terms of better image representations. The DINO-vMF pre-trained model consistently performs better than DINO on a range of downstream tasks. We obtain similar improvements for iBOT-vMF vs iBOT and thereby show the relevance of our proposed modification also for other methods derived from DINO. |
| title | DINO as a von Mises-Fisher mixture model |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2405.10939 |