A Fuzzy Rule-based Neuro-Symbolic Approach for Pipe Severity Prediction in Sewer Networks

Automated classification of sewer defects is essential for infrastructure condition assessment and maintenance decision-making, but existing deep learning methods struggle to balance classification accuracy and computational complexity in large-scale multi-label scenarios. This study develops Sewer-Transformer-ML, a hierarchical vision Transformer with multi-level feature fusion, together with two lightweight architectures, Sewer-MobileNet-ML and Sewer-Mobile-TransNet, for resource-constrained inspection scenarios. On the Sewer-ML test set, Sewer-Transformer-ML-Base achieved an $F2_{\text{CIW}}$ of 65.68% and an $F1_{\text{Normal}}$ of 92.68%, ranking first on the public leaderboard and exceeding the second-ranked method by 7.6 percentage points in $F2_{\text{CIW}}$. Sewer-MobileNet-ML achieved an $F2_{\text{CIW}}$ of 65.73% with only 17 M parameters, representing an approximately 95% parameter reduction relative to the base model. Under the standard Sewer-Capsule data split, Sewer-Mobile-TransNet achieved 96.43% classification accuracy. When the training set was reduced to 1,177 images, pretraining on Sewer-ML consistently improved model performance. Ablation experiments further showed that direct concatenation was more effective for Transformer features, whereas attention-based fusion better supported multiscale CNN features. These findings provide a computational basis for automated sewer inspection, lightweight model design, and adaptation across civil infrastructure inspection platforms.

Deep neural networks achieve high accuracy on image classification tasks. Yet, they often produce overconfident predictions as which fail to express epistemic uncertainty, and frequently violate logical or structural constraints present in the data. These limitations are particularly pronounced in hierarchical classification, where predictions across fine and coarse levels must remain coherent. We propose, for the first time, a unified neurosymbolic and epistemic modelling framework that augments Swin Transformers with focal set reasoning and differentiable fuzzy logic. Rather than treating labels as isolated categories, our method induces data-driven focal sets within the learnt embedding space, which helps capture epistemic uncertainty over multiple plausible fine-grained classes. These focal sets form the basis of a belief-theoretic layer that uses fuzzy membership functions and t-norm conjunctions to encourage consistency between fine- and coarse-grained predictions. A learnable loss further balances calibration, mass regularisation, and logical consistency, allowing the model to adaptively trade off symbolic structure with data-driven evidence. In experiments on hierarchical image classification, our framework maintains accuracy on par with transformer baselines while providing more calibrated and interpretable predictions, reducing overconfidence and enforcing high logical consistency across hierarchical outputs. Our experimental results show that combining focal set reasoning with fuzzy logic provides a practical step toward deep learning models that are both accurate and epistemically aware.

Interpretability is essential for trustworthy medical image diagnosis. However, existing concept-driven interpretable methods have key limitations: Concept Bottleneck Models (CBMs) require scoring all predefined concepts at inference time and for manual intervention, imposing a substantial burden on clinicians, while rationale-based generative approaches often select concepts by class discriminability, which can drift from diagnostic ontologies. To address these issues, we propose Neuro-Symbolic Rule Distillation (NeRD), a framework that produces efficient, ontology-grounded reasoning chains that are sufficient yet non-redundant, without manually crafting diagnostic rules. Experiments on two skin datasets demonstrate strong diagnostic performance and interpretability, and blinded expert evaluation confirms the clinical plausibility of NeRD rationales. Our method further enables a first expert-in-the-loop study for Multimodal Chain-of-Thought-based diagnosis, achieving efficient and effective concept-level intervention.