The Numerical Cliff in Multimodal Language Models
In high-stakes multimodal decision-making, such as clinical diagnosis and scientific measurement analysis, language models frequently encounter continuous numerical values near critical clinical decision boundaries.
We discover a systematic failure mode — the Numerical Cliff — where multimodal models that exhibit near-ceiling accuracy across most of the feature space collapse drastically when inputs approach critical thresholds.
Characterizing the Numerical Cliff
Across 7 vision-language model architectures evaluated on our controlled 1,576-case benchmark ($p < 0.001$), accuracy degrades precipitously. For example, LLaVA-Med experiences a 92.4 percentage point collapse at the boundary despite maintaining high accuracy away from it.
Knowledge-Grounded Selective Prediction
To mitigate catastrophic boundary failures, we introduce a structured framework that combines symbolic constraints extracted from a 740K-node UMLS knowledge graph with calibrated uncertainty estimation.
Conformal Calibration for Safe Abstention
Using split conformal prediction, the model learns a distribution-free threshold $\hat{q}$ to guarantee bounded error rates:
$$\mathbb{P}(Y \notin \mathcal{C}(X)) \le \alpha$$When the model's confidence set size exceeds a safety tolerance near ambiguous boundaries, the system defers to human expert judgment rather than hallucinating dangerous answers.