GridPE: Unifying Positional Encoding in Transformers with a Grid Cell-Inspired Framework
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909315867082752 |
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| author | Li, Boyang Wu, Yulin Huang, Nuoxian Zhang, Wenjia |
| author_facet | Li, Boyang Wu, Yulin Huang, Nuoxian Zhang, Wenjia |
| contents | Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have highlighted the role of grid cells as a fundamental neural component for spatial representation, including distance computation, path integration, and scale discernment. In this paper, we introduce a novel positional encoding scheme inspired by Fourier analysis and the latest findings in computational neuroscience regarding grid cells. Assuming that grid cells encode spatial position through a summation of Fourier basis functions, we demonstrate the translational invariance of the grid representation during inner product calculations. Additionally, we derive an optimal grid scale ratio for multi-dimensional Euclidean spaces based on principles of biological efficiency. Utilizing these computational principles, we have developed a Grid-cell inspired Positional Encoding technique, termed GridPE, for encoding locations within high-dimensional spaces. We integrated GridPE into the Pyramid Vision Transformer architecture. Our theoretical analysis shows that GridPE provides a unifying framework for positional encoding in arbitrary high-dimensional spaces. Experimental results demonstrate that GridPE significantly enhances the performance of transformers, underscoring the importance of incorporating neuroscientific insights into the design of artificial intelligence systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GridPE: Unifying Positional Encoding in Transformers with a Grid Cell-Inspired Framework Li, Boyang Wu, Yulin Huang, Nuoxian Zhang, Wenjia Neural and Evolutionary Computing Machine Learning Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have highlighted the role of grid cells as a fundamental neural component for spatial representation, including distance computation, path integration, and scale discernment. In this paper, we introduce a novel positional encoding scheme inspired by Fourier analysis and the latest findings in computational neuroscience regarding grid cells. Assuming that grid cells encode spatial position through a summation of Fourier basis functions, we demonstrate the translational invariance of the grid representation during inner product calculations. Additionally, we derive an optimal grid scale ratio for multi-dimensional Euclidean spaces based on principles of biological efficiency. Utilizing these computational principles, we have developed a Grid-cell inspired Positional Encoding technique, termed GridPE, for encoding locations within high-dimensional spaces. We integrated GridPE into the Pyramid Vision Transformer architecture. Our theoretical analysis shows that GridPE provides a unifying framework for positional encoding in arbitrary high-dimensional spaces. Experimental results demonstrate that GridPE significantly enhances the performance of transformers, underscoring the importance of incorporating neuroscientific insights into the design of artificial intelligence systems. |
| title | GridPE: Unifying Positional Encoding in Transformers with a Grid Cell-Inspired Framework |
| topic | Neural and Evolutionary Computing Machine Learning |
| url | https://arxiv.org/abs/2406.07049 |