Rule-Based Spatial Mixture-of-Experts U-Net for Explainable Edge Detection

2026-02-04

AI Summary

This work proposes an interpretable edge detection framework to address the lack of transparency in existing deep learning approaches, which hinders their deployment in safety-critical applications requiring rigorous verification. The method integrates a spatially adaptive mixture-of-experts (sMoE) module with a Takagi–Sugeno–Kang fuzzy rule-based output head within a U-Net architecture, enabling pixel-level visualization of decision logic. By generating rule activation maps and strategy maps, the model explicitly reveals its reasoning process for edge prediction. Evaluated on the BSDS500 dataset, the approach achieves an ODS F-score of 0.7628—comparable to HED and superior to standard U-Net—demonstrating that high accuracy and interpretability can be jointly attained.

Technology Category

Machine Learning: Mixture of Experts (MoE)Computer Vision: Interpretability, Explainability, and TransparencyKnowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Deep learning models like U-Net and its variants, have established state-of-the-art performance in edge detection tasks and are used by Generative AI services world-wide for their image generation models. However, their decision-making processes remain opaque, operating as"black boxes"that obscure the rationale behind specific boundary predictions. This lack of transparency is a critical barrier in safety-critical applications where verification is mandatory. To bridge the gap between high-performance deep learning and interpretable logic, we propose the Rule-Based Spatial Mixture-of-Experts U-Net (sMoE U-Net). Our architecture introduces two key innovations: (1) Spatially-Adaptive Mixture-of-Experts (sMoE) blocks integrated into the decoder skip connections, which dynamically gate between"Context"(smooth) and"Boundary"(sharp) experts based on local feature statistics; and (2) a Takagi-Sugeno-Kang (TSK) Fuzzy Head that replaces the standard classification layer. This fuzzy head fuses deep semantic features with heuristic edge signals using explicit IF-THEN rules. We evaluate our method on the BSDS500 benchmark, achieving an Optimal Dataset Scale (ODS) F-score of 0.7628, effectively matching purely deep baselines like HED (0.7688) while outperforming the standard U-Net (0.7437). Crucially, our model provides pixel-level explainability through"Rule Firing Maps"and"Strategy Maps,"allowing users to visualize whether an edge was detected due to strong gradients, high semantic confidence, or specific logical rule combinations.

Problem

• edge detection
• explainability
• black-box models
• safety-critical applications
• interpretability

Innovation

• Spatial Mixture-of-Experts
• Explainable AI
• Fuzzy Logic
• Edge Detection
• Rule-Based Reasoning