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This research proposes a novel matrix-based representation for lexical tokens where the non-commutative product of unitary matrices inherently captures word order, eliminating the need for traditional positional encodings. The approach significantly reduces parameter count by replacing high-dimensional vocabulary spaces with compact real-valued encodings while enabling efficient parallel composition of text chunks and robust continual learning. By demonstrating competitive performance on standard classification benchmarks, this work highlights a promising direction for improving the expressive efficiency and architectural simplicity of next-generation language models.
All You Need Is Non-Commutative Words
arXiv:2608.29314v1 Announce Type: new Abstract: 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 enlarge the operator space with each new task preserving prior representations exactly. Across standard text-classification benchmarks, the method matches or exceeds bag-of-words baselines. Achieving higher accuracy on IMDB and comparable performance on AG News. Notably, this is accomplished by replacing the conventional $\sim$30,000-dimensional vocabulary space with a dense, 64-parameter real-valued encoding, highlighting the expressive efficiency of our parameterization.
Abstract: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 enlarge the operator space with each new task preserving prior representations exactly. Across standard text-classification benchmarks, the method matches or exceeds bag-of-words baselines. Achieving higher accuracy on IMDB and comparable performance on AG News. Notably, this is accomplished by replacing the conventional $\sim$30,000-dimensional vocabulary space with a dense, 64-parameter real-valued encoding, highlighting the expressive efficiency of our parameterization.
Computation and Language (cs.CL)
arXiv:2608.29314 [cs.CL]
(or arXiv:2608.29314v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2608.29314 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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