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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.14514 |
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| _version_ | 1866913801033482240 |
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| author | Cheng, Daizhan |
| author_facet | Cheng, Daizhan |
| contents | The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using projection. Its properties and calculating formulas are obtained. Using projection-based transformation of hypervector (PBTH), the framework of dimension-free transformer (DFT) is proposed by verifying each linear transformation in a transformer and replacing it by a proper PBTH, which allows the inputs and outputs being of arbitrary dimensions. Using balanced information about all entries, DFT must be more efficient in dealing with signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Dimension-Free Transformer: An Application of STP to AI Cheng, Daizhan Machine Learning Artificial Intelligence Systems and Control The matrix expressions for every parts of a transformer are firstly described. Based on semi-tensor product (STP) of matrices the hypervectors are reconsidered and the linear transformation over hypervectors is constructed by using projection. Its properties and calculating formulas are obtained. Using projection-based transformation of hypervector (PBTH), the framework of dimension-free transformer (DFT) is proposed by verifying each linear transformation in a transformer and replacing it by a proper PBTH, which allows the inputs and outputs being of arbitrary dimensions. Using balanced information about all entries, DFT must be more efficient in dealing with signals. |
| title | On Dimension-Free Transformer: An Application of STP to AI |
| topic | Machine Learning Artificial Intelligence Systems and Control |
| url | https://arxiv.org/abs/2504.14514 |