Complex-Valued Phase-Coherent Transformer
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916000146915328 |
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| author | Hioki, Leona |
| author_facet | Hioki, Leona |
| contents | Complex-valued Transformers have largely inherited softmax attention from real-valued architectures. However, row-normalised token competition is not necessarily aligned with phase-preserving computation. In this paper, we introduce the Phase-Coherent Transformer (PCT), which applies a real-valued, element-independent, smooth gate to L2-normalised complex query-key similarities. PCT replaces token competition with token-non-competing attention and is designed to preserve phase information across layers.
Across mid-scale benchmarks spanning long-range memory, hierarchical long-range reasoning, positional retrieval, phase-based memory and superposition, and image classification, PCT shows strong generalisation across task categories. Under parameter-fair comparison, PCT consistently outperforms both the standard softmax Transformer and its direct complex-valued counterpart. Moreover, even on tasks traditionally considered difficult for complex-valued neural networks, such as NIAH and LRA-Text, PCT remains competitive with Multiscreen, the strongest real-valued NN baseline in our comparison. Experiments introducing gates that deliberately violate the PCT conditions show that the design is not incidental: smooth gates that preserve negatively aligned phase components remain strong, whereas gates that delete such components collapse on long-range retrieval, and gates whose outputs become excessively large suffer clear performance degradation. PCT also shows no depth-related accuracy collapse across the tested depth range. These results support introducing multi-layer phase-coherent structure into attention as a promising design principle for achieving generalisation in complex-valued Transformers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10123 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complex-Valued Phase-Coherent Transformer Hioki, Leona Machine Learning 68T07, 68V20, 60J10 I.2.6; I.5.1; I.2.7 Complex-valued Transformers have largely inherited softmax attention from real-valued architectures. However, row-normalised token competition is not necessarily aligned with phase-preserving computation. In this paper, we introduce the Phase-Coherent Transformer (PCT), which applies a real-valued, element-independent, smooth gate to L2-normalised complex query-key similarities. PCT replaces token competition with token-non-competing attention and is designed to preserve phase information across layers. Across mid-scale benchmarks spanning long-range memory, hierarchical long-range reasoning, positional retrieval, phase-based memory and superposition, and image classification, PCT shows strong generalisation across task categories. Under parameter-fair comparison, PCT consistently outperforms both the standard softmax Transformer and its direct complex-valued counterpart. Moreover, even on tasks traditionally considered difficult for complex-valued neural networks, such as NIAH and LRA-Text, PCT remains competitive with Multiscreen, the strongest real-valued NN baseline in our comparison. Experiments introducing gates that deliberately violate the PCT conditions show that the design is not incidental: smooth gates that preserve negatively aligned phase components remain strong, whereas gates that delete such components collapse on long-range retrieval, and gates whose outputs become excessively large suffer clear performance degradation. PCT also shows no depth-related accuracy collapse across the tested depth range. These results support introducing multi-layer phase-coherent structure into attention as a promising design principle for achieving generalisation in complex-valued Transformers. |
| title | Complex-Valued Phase-Coherent Transformer |
| topic | Machine Learning 68T07, 68V20, 60J10 I.2.6; I.5.1; I.2.7 |
| url | https://arxiv.org/abs/2605.10123 |