Abstractive summarization models remain vulnerable to factual inconsistency, redundancy, and weak length control. We propose a modular generation-and-selection framework for sentence-budget-constrained summarization. A pretrained generator produces multiple candidate summaries, which are decomposed into sentence-level candidates. A combinatorial selector then constructs the final summary by balancing relevance, factuality, and redundancy under an explicit budget. The framework supports MMR, ILP, and a DPP-inspired log-determinant objective without retraining the generator. Experiments on CNN/DailyMail, Multi-News, FaithBench, and TofuEval show consistent improvements in factuality and source-grounding metrics, especially for multi-document summarization, at the cost of lower reference-overlap scores. Human evaluation further indicates higher perceived consistency, relevance, clarity, and conciseness, with a small reduction in coherence. These results show that decoupling generation from selection provides a model-agnostic mechanism for improving factual grounding. Code is available at https://anonymous.4open.science/r/bcfs-D05E/.
Yong Yi Bay, Kathleen A. Yearickcs.LG cs.AI cs.CL stat.ML
People overthink; language models over-sample, and the extra effort can talk both into a worse answer. Reasoning systems answer a hard question by sampling it many times (test-time scaling), and the more they draw, the more often a correct answer turns up somewhere, so coverage, the fraction of problems with at least one correct try, climbs and appears to be progress. But a deployed system must return one answer, and choosing it, not knowing which try is right, is selection; selection is capped, and past a point extra samples only make the model surer of a confident mistake, even as every draw adds cost. The gap between climbing coverage and stalled selection, the identifiability gap, is the answer a model can produce but not pick. So the real question is not whether to sample but how far, and the answer is: not far. For picking an answer, the vote has already settled within a few dozen draws, the modal ceiling; for scoring a benchmark, sooner still, the correlation ceiling. Beyond that, extra draws cost compute and add nothing, and can even make the answer worse. This paper turns the cutoff into a single number, the effective number of samples, that any sampling run already reveals. The bottleneck is recognizing a right answer, not generating one.
Conformal selection aims to identify test candidates whose unknown responses fall in a target region while controlling the false discovery rate. Existing methods often inherit prediction-oriented nonconformity scores, such as residual or clipped residual scores, from conformal prediction. We argue that the natural score for selection is instead the target-membership probability. This score directly addresses the binary event being selected, and any monotone transform of it gives the Neyman--Pearson oracle ranking at a fixed null selection level. This distinction is irrelevant for mean-monotone targets, where conventional scores induce essentially the same ranking, but becomes important for interval-valued, variance-driven, multimodal, or multi-condition targets, where prediction-oriented scores can be misaligned with selection power. We study membership-score-based conformal selection and isolate one conformal calibration route, Null-Calibrated Conformal Selection (NCCS), which ranks test scores against confirmed non-target calibration examples. Under null exchangeability, NCCS yields finite-sample valid null p-values, which can be combined with BY under arbitrary dependence or with BH under standard positive-dependence conditions. Experiments support the score principle: membership scores match conventional scores on mean-monotone targets, substantially improve over mean-score selection on variance-driven targets, and, when calibrated by NCCS, trade power for finite-sample null validity in rare-target regimes where direct empirical-FDP thresholding can be anti-conservative.