Hindsight-Guided Rationale Distillation for Rare Disease Diagnosis

We study hindsight-guided distillation for rare disease diagnosis on ZebraMap: a 1.5B student is fine-tuned on chain-of-thought traces from a 8B teacher that observes the ground-truth diagnosis during generation. Absolute accuracy remains low for all models - the task is hard at this scale - but within this ceiling a filtered variant (StudentF) achieves a small, statistically significant accuracy advantage over the teacher (p < 0.001), concentrated in better-represented diseases. The unfiltered student does not significantly outperform the teacher (p = 0.129), establishing that contamination filtering - not hindsight distillation alone - drives the gain. The gap traces to an artifact we term GT hallucination. Label-visible generation causes the teacher to embed "ground truth is X" phrases in its reasoning chain; SFT copies the pattern. At inference, the unfiltered student reproduces the phrase in 33.9% of cases, with severe accuracy degradation when the hallucinated label is wrong. A regex filter removing these slots reduces contamination to near-zero, producing the observed gain - though the effect remains small. We precisely quantify this gain-cost tradeoff, document frequency-dependent knowledge transfer absent from the RL-trained teacher, and characterize a calibration gap that SFT does not close - identifying both as directions for future work.