Learning to Defer with Guidance on Real World Medical Data

Learning to Defer (L2D) enables a model to predict autonomously or defer to an expert, but prior work largely assumes flat label spaces. We study the first L2D setting with hierarchical multi-label decisions, motivated by medical-imaging workflows in which findings are organised by clinical taxonomies. In this setting, deferral is a delegation action rather than a label assignment, so treating it as an independent per-label decision can produce deferral incoherence, including taxonomic contradictions, delegation violations, and deferrals of labels already implied by the model's own assertions. We formalise coherent hierarchical deferral under a Selective-Exclusion handoff contract, characterise the Bayes-optimal coherent deferral rule, and show that even nodewise Bayes L2D can be action-incoherent. We then propose two remedies: exact coherent projection, a dynamic-programming decoder over the coherent action set, and Taxonomic Belief Propagation (TBP) with Recursive Policy Optimisation (RPO), a contract-aware joint action model trained through the same recursion used at inference. Across real-reader and controlled-expert medical-imaging benchmarks, naive binary-relevance L2D exhibits non-trivial incoherence. Projection removes it exactly, and fast TBP+RPO drives incoherence near zero while retaining strong utility.

Learning-to-defer (L2D) can make glaucoma screening safer by routing difficult/uncertain cases to humans, yet standard formulations overlook expert availability, heterogeneous readers behavior, workload imbalance, asymmetric diagnostic harm, case difficulty from morphology and deployment shift. We introduce MPD$^2$-Router, a mask-aware multi-expert deferral framework that recasts ophthalmic triage as constrained human--AI routing: whether to defer and to which available expert. It couples a dual-head deferral/allocation policy with mask-aware Gumbel--sigmoid gating that strictly enforces per-sample availability, and fuses uncertainty, morphology, image-quality, and OOD signals. Training uses an asymmetric cost-sensitive objective with an augmented-Lagrangian deferral budget, a group-specific distribution prior, and a rank-majorization JS regularizer that jointly prevent expert collapse without forcing uniform allocation. Across three cross-national glaucoma cohorts (REFUGE, CHAKSU, ORIGA) with a frozen REFUGE-trained backbone, MPD$^2$-Router substantially lowers clinical cost and improves MCC over AI-only at a moderate deferral rate. It is Pareto-optimal in F1--MCC--cost, robust under cross-domain shift, and yields balanced expert utilization.

Pulmonary nodule malignancy prediction typically depends on image-trained specialist deep learning (DL) models that require substantial annotated imaging data and task-specific training. We investigate whether a generalist large language model (LLM), reading only a faithful natural-language rendering of standard nodule attributes, can serve as a calibrated triage layer. We propose ConfTriage, a confidence-calibrated method built on three pillars: language as the modality, calibration as the safety mechanism, and a selective specialist DL backstop for low-confidence cases. We prove two guarantees: a finite-sample combined-error bound yielding an explicit per-threshold operational certificate, and an oracle inequality showing that excess risk over the Bayes-optimal deferral classifier is controlled by the L1 calibration error of the LLM probability. A controlled seven-way input ablation across five frontier LLMs on LIDC-IDRI shows that natural-language descriptions dominate the diagnostic signal, while low-level image statistics are essentially diagnostically vacuous. ConfTriage achieved an F1 score of 88.22% and an AUC of 0.92, resolving 76.5% of cases using zero-shot LLM inference alone and referring only uncertain cases to the specialist DL backstop. These results demonstrate that clinically meaningful diagnostic information can be captured through structured radiological descriptions and leveraged by calibrated LLMs for selective referral. The framework suggests a practical pathway for combining generalist LLM prediction with specialist AI models in medical decision-support systems. Source code is publicly available at https://github.com/rabiul-ai/ConfTriage.