Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913713831804928 |
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| author | Basile, Lorenzo Acevedo, Santiago Bortolussi, Luca Anselmi, Fabio Rodriguez, Alex |
| author_facet | Basile, Lorenzo Acevedo, Santiago Bortolussi, Luca Anselmi, Fabio Rodriguez, Alex |
| contents | To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear nature, which makes them challenging to detect using standard methods. This paper exploits the entanglement between intrinsic dimensionality and correlation to propose a metric that quantifies the (potentially nonlinear) correlation between high-dimensional manifolds. We first validate our method on synthetic data in controlled environments, showcasing its advantages and drawbacks compared to existing techniques. Subsequently, we extend our analysis to large-scale applications in neural network representations. Specifically, we focus on latent representations of multimodal data, uncovering clear correlations between paired visual and textual embeddings, whereas existing methods struggle significantly in detecting similarity. Our results indicate the presence of highly nonlinear correlation patterns between latent manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations Basile, Lorenzo Acevedo, Santiago Bortolussi, Luca Anselmi, Fabio Rodriguez, Alex Machine Learning Computation and Language Computer Vision and Pattern Recognition To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear nature, which makes them challenging to detect using standard methods. This paper exploits the entanglement between intrinsic dimensionality and correlation to propose a metric that quantifies the (potentially nonlinear) correlation between high-dimensional manifolds. We first validate our method on synthetic data in controlled environments, showcasing its advantages and drawbacks compared to existing techniques. Subsequently, we extend our analysis to large-scale applications in neural network representations. Specifically, we focus on latent representations of multimodal data, uncovering clear correlations between paired visual and textual embeddings, whereas existing methods struggle significantly in detecting similarity. Our results indicate the presence of highly nonlinear correlation patterns between latent manifolds. |
| title | Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations |
| topic | Machine Learning Computation and Language Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2406.15812 |