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

arXiv: https://arxiv.org/abs/2602.05100 · HTML: https://mlsanity.com/paper/2602.05100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [Spatial Mixture-of-Experts](https://mlsanity.com/paper/2211.13491/) (2022)
- [Adversarial Examples for Edge Detection: They Exist, and They Transfer](https://mlsanity.com/paper/1906.00335/) (2019)

## Abstract (arXiv)

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.