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All You Need Is Non-Commutative Words

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

We represent lexical tokens as unitary matrices and encode each sentence as their ordered product. The noncommutativity of matrix product captures word order without positional encodings (PEs). The same algebra yields several capabilities, including antisymmetric self-attention with no query, key, or value projections, and parallel composition of variable-length text chunks at a reduced attention cost. Furthermore, it provides a canonical-coset readout layer that encodes all true unitary degrees of freedom compactly, while supporting continual learning through nested group extensions that enla

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