An End-to-End Quantum Interpretable Computer Vision Model Based on CNNs, FCMs, and Backpropagation

Abstract

Fuzzy Cognitive Maps (FCMs) were originally introduced as a framework for modeling complex systems and have since evolved into powerful pattern recognition models capable of capturing intricate causal relationships within data. Despite their potential, the application of FCMs in computer vision remains limited, primarily because they are not inherently designed to process high-dimensional visual representations and therefore rely on external feature extraction methods. In this work, we propose a quantum-enhanced architecture for image classification, termed QFCM-QCNN, in which a Quantum Convolutional Neural Network (QCNN) extracts compact feature representations that are subsequently processed by a Quantum Fuzzy Cognitive Map (QFCM) head for final prediction. To validate the proposed quantum approach, we also implement its classical counterpart, FCM-CNN, where a conventional CNN backbone feeds a differentiable FCM head. Both architectures are trained end-to-end via backpropagation through differentiable FCM and QFCM layers, enabling a unified learning framework that maps images directly to predictions. The proposed models are evaluated on ten medical imaging datasets using standard classification metrics as well as Degree of Confidence (DoC) prediction scores. Experimental results show that QFCM-QCNN achieves classification performance comparable to FCM-CNN-64D across most benchmarks while operating on only 8-dimensional feature representations instead of 64-dimensional ones, with 87.5% reduction in feature dimensionality. QFCM-QCNN produces the highest prediction confidence on seven out of the ten datasets.