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arXiv · 2504.14514

On Dimension-Free Transformer: An Application of STP to AI

Daizhan Cheng
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Abstract

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.

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Daizhan Cheng. 2025-04-20. On Dimension-Free Transformer: An Application of STP to AI. https://arxiv.org/abs/2504.14514

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