Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing conditional validity is challenging, as standard stratification methods suffer from the curse of dimensionality. We propose Conformal Prediction Assessment (CPA), a framework that reframes the evaluation of conditional coverage as a supervised learning task by training a reliability estimator that predicts instance-level coverage probabilities. Building on this estimator, we introduce the Conditional Validity Index (CVI), which decomposes reliability into safety (undercoverage risk) and efficiency (overcoverage cost). We establish convergence rates for the reliability estimator and prove the consistency of CVI-based model selection. Extensive experiments on synthetic and real-world datasets demonstrate that CPA effectively diagnoses local failure modes and that CC-Select, our CVI-based model selection algorithm, consistently identifies predictors with superior conditional coverage performance.

Generating chemically valid 3D molecules is hindered by discrete bond topology: small local bond errors can cause global failures (valence violations, disconnections, implausible rings), especially for drug-like molecules with long-range constraints. Many unconditional 3D generators emphasize coordinates and then infer bonds or rely on post-processing, leaving topology feasibility weakly controlled. We propose Hierarchy-Guided Latent Topology Flow (HLTF), a planner-executor model that generates bond graphs with 3D coordinates, using a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures. On QM9, HLTF achieves 98.8% atom stability and 92.9% valid-and-unique, improving PoseBusters validity to 94.0% (+0.9 over the strongest reported baseline). On GEOM-DRUGS, HLTF attains 85.5%/85.0% validity/valid-unique-novel without post-processing and 92.2%/91.2% after standardized relaxation, within 0.9 points of the best post-processed baseline. Explicit topology generation also reduces "false-valid" samples that pass RDKit sanitization but fail stricter checks.

Large language models (LLMs) are increasingly used as decision-support tools in data-constrained scientific workflows, where correctness and validity are critical. However, evaluation practices often emphasize stability or reproducibility across repeated runs. While these properties are desirable, stability alone does not guar- antee agreement with statistical ground truth when such references are available. We introduce a controlled behavioral evaluation framework that explicitly sep- arates four dimensions of LLM decision-making: stability, correctness, prompt sensitivity, and output validity under fixed statistical inputs. We evaluate multi- ple LLMs using a statistical gene prioritization task derived from differential ex- pression analysis across prompt regimes involving strict and relaxed significance thresholds, borderline ranking scenarios, and minor wording variations. Our ex- periments show that LLMs can exhibit near-perfect run-to-run stability while sys- tematically diverging from statistical ground truth, over-selecting under relaxed thresholds, responding sharply to minor prompt wording changes, or producing syntactically plausible gene identifiers absent from the input table. Although sta- bility reflects robustness across repeated runs, it does not guarantee agreement with statistical ground truth in structured scientific decision tasks. These findings highlight the importance of explicit ground-truth validation and output validity checks when deploying LLMs in automated or semi-automated scientific work- flows.

In machine learning, model calibration and predictive inference are essential for producing reliable predictions and quantifying uncertainty to support decision-making.

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