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

First, the matrix expressions for each part of a transformer are described. Based on the semi-tensor product (STP) of matrices, the hypervectors are reconsidered, and a linear transformation over hypervectors is constructed using projection. The properties and calculation formulas are then obtained. The framework of a dimension-free transformer (DFT) is proposed using the projection-based transformation of hypervectors (PBTH) by verifying each linear transformation in a transformer and replacing it with a proper PBTH. This allows the inputs and outputs to be of arbitrary dimensions. Due to balanced information about all entries, the DFT is expected to be more efficient in processing signals.