Quantum Self-Attention (QSA): Complex Projective Attention with Constructive and Destructive Interference v2
Authors/Creators
Description
Quantum Self-Attention (QSA) is a drop-in replacement for softmax attention that lifts the real probability simplex into complex projective space CP^{n-1}. By preserving phase information, QSA enables constructive and destructive interference, native subtractive logic, and antisymmetric relational encoding—capabilities impossible for softmax.
This paper presents the full mathematical derivation, production-ready PyTorch implementations, and empirical benchmarks including:
- 99.83% accuracy on harmonic interference (vs 97.80% softmax)
- Stable training on causal arithmetic where softmax crashes
- First large-scale graft of QSA into a frozen 1.3B model (DeepSeek-Coder) using NecroGraft, reducing training loss from 70.4 to 2.06
The architecture is strictly more expressive than affine-softmax models (Ω(N²) separation).
Files
Files
(337.7 kB)
| Name | Size | |
|---|---|---|
|
md5:519cb2297f2d7584b9921ed1f9193484
|
337.7 kB | Download |
Additional details
Related works
- Cites
- Working paper: 10.5281/zenodo.21811634 (DOI)
Dates
- Created
-
2026-09-02
Software
- Repository URL
- https://github.com/ElBalor/QSA.git
- Programming language
- Python
- Development Status
- Active
References
- [1] Nebli et al. (2026). Born-rule readout separates expressive power from affine-softmax models. arXiv preprint. [2] PRISM (2025). Phase coherence in word embeddings. Computational Linguistics, 31(2), 112–128. [3] QCSAM (2025). Complex weights vs real in attention. https://arxiv.org/abs/2503.19002 [4] Holographic Transformer (2025). Coherent superposition for robustness. IEEE Transactions on Neural Networks, 36(4), 890–901. [5] QISA (2026). 38(1), 45–67. [6] Phasor Memory Networks (2026). Stable phase dynamics via unitary constraints. Machine Learning Journal, 52(3), 201–220. [7] Yaka, H. (2026). QSA Harmonic and Symbolic Causal Stress-Tests — internal verification logs. Technical Report, Elbàlor Research. [8] Yaka, H. (2026). Pure W-Expansion: Full-Rank Weight Growth for Zero-Forgetting Model Adaptation. Zenodo. https://zenodo.org/records/21811634