# HQFNN: A Compact Quantum-Fuzzy Neural Network for Accurate Image Classification

arXiv: https://arxiv.org/abs/2506.11146 · HTML: https://mlsanity.com/paper/2506.11146/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 61 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Can AI help in screening Viral and COVID-19 pneumonia?](https://mlsanity.com/paper/2003.13145/) (2020)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [q-means: A quantum algorithm for unsupervised machine learning](https://mlsanity.com/paper/1812.03584/) (2018)
- ["Excavating AI" Re-excavated: Debunking a Fallacious Account of the JAFFE Dataset](https://mlsanity.com/paper/2107.13998/) (2021)
- [Towards Certification of Uncertainty Calibration under Adversarial Attacks](https://mlsanity.com/paper/2405.13922/) (2024)
- [A Deep Neuro-Fuzzy Network for Image Classification](https://mlsanity.com/paper/2001.01686/) (2019)
- [A Hierarchical Fused Quantum Fuzzy Neural Network for Image Classification](https://mlsanity.com/paper/2403.09318/) (2024)

## Abstract (arXiv)

Deep learning vision systems excel at pattern recognition yet falter when inputs are noisy or the model must explain its own confidence. Fuzzy inference, with its graded memberships and rule transparency, offers a remedy, while parameterized quantum circuits can embed features in richly entangled Hilbert spaces with striking parameter efficiency. Bridging these ideas, this study introduces a innovative Highly Quantized Fuzzy Neural Network (HQFNN) that realises the entire fuzzy pipeline inside a shallow quantum circuit and couples the resulting quantum signal to a lightweight CNN feature extractor. Each image feature is first mapped to a single qubit membership state through repeated angle reuploading. Then a compact rule layer refines these amplitudes, and a clustered CNOT defuzzifier collapses them into one crisp value that is fused with classical features before classification. Evaluated on standard image benchmarks, HQFNN consistently surpasses classical, fuzzy enhanced and quantum only baselines while using several orders of magnitude fewer trainable weights, and its accuracy degrades only marginally under simulated depolarizing and amplitude damping noise, evidence of intrinsic robustness. Gate count analysis further shows that circuit depth grows sublinearly with input dimension, confirming the model's practicality for larger images. These results position the model as a compact, interpretable and noise tolerant alternative to conventional vision backbones and provide a template for future quantum native fuzzy learning frameworks.