Complex-Valued Unitary Representations as Classification Heads for Improved Uncertainty Quantification in Deep Neural Networks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915801420791808 |
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| author | Jafari, Akbar Anbar Ozcinar, Cagri Anbarjafari, Gholamreza |
| author_facet | Jafari, Akbar Anbar Ozcinar, Cagri Anbarjafari, Gholamreza |
| contents | Modern deep neural networks achieve high predictive accuracy but remain poorly calibrated: their confidence scores do not reliably reflect the true probability of correctness. We propose a quantum-inspired classification head architecture that projects backbone features into a complex-valued Hilbert space and evolves them under a learned unitary transformation parameterised via the Cayley map. Through a controlled hybrid experimental design - training a single shared backbone and comparing lightweight interchangeable heads - we isolate the effect of complex-valued unitary representations on calibration. Our ablation study on CIFAR-10 reveals that the unitary magnitude head (complex features evolved under a Cayley unitary, read out via magnitude and softmax) achieves an Expected Calibration Error (ECE) of 0.0146, representing a 2.4x improvement over a standard softmax head (0.0355) and a 3.5x improvement over temperature scaling (0.0510). Surprisingly, replacing the softmax readout with a Born rule measurement layer - the quantum-mechanically motivated approach - degrades calibration to an ECE of 0.0819. On the CIFAR-10H human-uncertainty benchmark, the wave function head achieves the lowest KL-divergence (0.336) to human soft labels among all compared methods, indicating that complex-valued representations better capture the structure of human perceptual ambiguity. We provide theoretical analysis connecting norm-preserving unitary dynamics to calibration through feature-space geometry, report negative results on out-of-distribution detection and sentiment analysis to delineate the method's scope, and discuss practical implications for safety-critical applications. Code is publicly available. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complex-Valued Unitary Representations as Classification Heads for Improved Uncertainty Quantification in Deep Neural Networks Jafari, Akbar Anbar Ozcinar, Cagri Anbarjafari, Gholamreza Machine Learning Artificial Intelligence Modern deep neural networks achieve high predictive accuracy but remain poorly calibrated: their confidence scores do not reliably reflect the true probability of correctness. We propose a quantum-inspired classification head architecture that projects backbone features into a complex-valued Hilbert space and evolves them under a learned unitary transformation parameterised via the Cayley map. Through a controlled hybrid experimental design - training a single shared backbone and comparing lightweight interchangeable heads - we isolate the effect of complex-valued unitary representations on calibration. Our ablation study on CIFAR-10 reveals that the unitary magnitude head (complex features evolved under a Cayley unitary, read out via magnitude and softmax) achieves an Expected Calibration Error (ECE) of 0.0146, representing a 2.4x improvement over a standard softmax head (0.0355) and a 3.5x improvement over temperature scaling (0.0510). Surprisingly, replacing the softmax readout with a Born rule measurement layer - the quantum-mechanically motivated approach - degrades calibration to an ECE of 0.0819. On the CIFAR-10H human-uncertainty benchmark, the wave function head achieves the lowest KL-divergence (0.336) to human soft labels among all compared methods, indicating that complex-valued representations better capture the structure of human perceptual ambiguity. We provide theoretical analysis connecting norm-preserving unitary dynamics to calibration through feature-space geometry, report negative results on out-of-distribution detection and sentiment analysis to delineate the method's scope, and discuss practical implications for safety-critical applications. Code is publicly available. |
| title | Complex-Valued Unitary Representations as Classification Heads for Improved Uncertainty Quantification in Deep Neural Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.15283 |