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.