MPD$^2$-Router: Mask-aware Multi-expert Prior-regularized Dual-head Deferral Router in Glaucoma Screening and Diagnosis

Medical image interpretation is high-volume and time-consuming, and while AI interpretation can reduce workload, fully autonomous deployment carries potential safety concerns and low specificity may in practice lead to increased clinician workload. Learning to Defer (L2D) addresses this by selectively routing cases between autonomous prediction and human experts by learning from input features and AI model and human performance. While theoretical guarantees have been proven for L2D, its performance has not been validated on real-world medical datasets with human reader annotations. We evaluate the predictor-rejector formulation of two-stage L2D, where the AI predictor model is fixed and separate from the trainable routing or rejector model, on Collab-CXR, a multilabel chest X-ray dataset with multiple human annotations per case. This is the first work to look at L2D in the context of real-world medical imaging data with human annotations. We further introduce a new setup, L2D with Guidance, where the decision space is extended to three choices: predict autonomously, defer to a human expert, or defer to a human expert and provide AI guidance. We compare multiple rejector architectures and loss functions, and different input feature availabilities. This is reproduced on two larger datasets, VinDr-CXR and CheXpert. Our results show that two-stage L2D with Guidance outperforms classic two-stage learning to defer, as well as human-alone, AI-alone and AI-guided human baselines. Notably, this performance is achieved with simpler loss functions compared to formally defined L2D surrogate loss functions in current literature.

Retinal fundus images frequently exhibit multiple co-occurring pathologies, yet standard deep learning classifiers apply static, identical computation to every image regardless of the underlying disease distribution. We propose a novel architecture that resolves this via sparse conditional computation, pairing a Guided Context Gating (GCG) spatial attention front-end with a sparsely-routed Mixture-of-Experts (MoE) block operating over feature tokens. Crucially, this routing yields an interpretable, data-driven decomposition. Expert allocation is significantly disease-dependent (p < 0.001), with the healthy Normal state and morphologically distinct pathologies (e.g., ERM, AMD) isolating to dedicated experts. On a five-class, patient-disjoint 5-fold cross-validation benchmark, our model achieves 0.912 +/- 0.008 macro AUC and 0.653 +/- 0.014 macro F1. Furthermore, Grad-CAM++ and post-MoE t-SNE visualizations confirm that expert routing aligns with localized lesions and geometrically maps co-occurring cases between their constituent clusters, positioning sparse MoE as an interpretable approach to multi-disease retinal screening.

Learning algorithms can be significantly improved by routing complex or uncertain inputs to specialized experts, balancing accuracy with computational cost. This approach, known as learning to defer, is essential in domains like natural language generation, medical diagnosis, and computer vision, where an effective deferral can reduce errors at low extra resource consumption. However, the two-stage learning to defer setting, which leverages existing predictors such as a collection of LLMs or other classifiers, often faces challenges due to an expert imbalance problem. This imbalance can lead to suboptimal performance, with deferral algorithms favoring the majority expert. We present a comprehensive study of two-stage learning to defer in expert imbalance settings. We cast the deferral loss optimization as a novel cost-sensitive learning problem over the input-expert domain. We derive new margin-based loss functions and guarantees tailored to this setting, and develop novel algorithms for cost-sensitive learning. Leveraging these results, we design principled deferral algorithms, MILD (Margin-based Imbalanced Learning to Defer), specifically suited for expert imbalance settings. Extensive experiments demonstrate the effectiveness of our approach, showing clear improvements over existing baselines on both image classification and real-world Large Language Model (LLM) routing tasks.