# Effective Dimension Governs Generalization in Quantum Kernel Vision Models

arXiv: https://arxiv.org/abs/2606.20183 · HTML: https://mlsanity.com/paper/2606.20183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum Vision Transformers](https://mlsanity.com/paper/2209.08167/) (2022)
- [HQViT: Hybrid Quantum Vision Transformer for Image Classification](https://mlsanity.com/paper/2504.02730/) (2025)
- [Efficient Quantum Convolutional Neural Networks for Image Classification: Overcoming Hardware Constraints](https://mlsanity.com/paper/2505.05957/) (2025)

## Abstract (arXiv)

Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it. These observations are currently treated as curiosities, discovered by grid search and explained, if at all, by hand. We show that both are manifestations of a single, measurable quantity: the effective dimension drm eff of the (noise-shaped) quantum feature kernel. Working primarily with quantum-kernel vision models-a quantum feature map read out by a kernel classifier-we give a spectral account in which entanglement structure and quantum noise are two knobs that move drm eff; in an overfitting regime, contracting drm eff acts as ridge-like regularization. We analyze the mechanism: an exact decomposition of the depolarized kernel Kp=(1-p)2K+tfracp(2-p)D11^top with drm eff(Kp)→1, a contraction result (and its boundary) for amplitude damping, a kernel-machine capacity bound, and a capacity/alignment risk decomposition; the monotone contraction operative in our entangled experiments is verified empirically, not proven in general. Along the one-parameter depolarizing family the collapse is instead exact by construction; we use it only to confirm the kernel decomposition to machine precision and at up to 12 qubits, not as evidence for drm eff. Amplitude damping contracts drm eff and lifts test accuracy by up to +13% along an inverted-U sweet spot; the effect's sign flips between the over- and under-fitting regimes; noise injection matches an explicit spectral-filtering frontier. Our results organize two reported anecdotes into a single measurable principle for designing quantum-vision models.