Consistent submodular maximization aims to maintain a high-utility subset of size at most $k$ as new elements arrive one by one, while changing only a limited number of elements per update. Previously, [DFL+25](STOC '25) established an information-theoretic bound of $2/3$ and gave the first polynomial-time randomized algorithm with a $0.51$-approximation guarantee. However, a fundamental question remained open: Is it possible to design an efficient algorithm for consistent submodular maximization that matches the classical offline $(1-1/e)$-approximation? In this paper, we answer this question in the negative by proving that the sharp approximation threshold achievable with polynomially many value queries and worst-case constant recourse is \[β:=2-\sqrt{2}\approx0.5858<1-1/e.\] Specifically, we develop an improved poly-time randomized algorithm, which can attain a $(β-\varepsilon)$-approximation in expectation at each fixed time with $O(\varepsilon^{-2})$ worst-case recourse. The cornerstone of this algorithm is a novel anchored sampling scheme, which uses only value queries on subsets of the elements seen so far to construct a solution that remains competitive under unknown future arrivals. Conversely, we establish a matching lower bound by showing that any fixed improvement over $β$ requires either exponentially many value queries or $Ω(k)$ changes per update. Furthermore, we characterize the impact of curvature by establishing a sharp threshold of $1-(\sqrt{2}-1)\vartheta$ for consistent submodular maximization, where $\vartheta\in[0,1]$ denotes the total curvature. Surprisingly, for weighted coverage objectives, we devise a poly-time randomized algorithm that can match the optimal $(1-1/e-\varepsilon)$-approximation with $O(\varepsilon^{-1})$ worst-case recourse, thereby separating coverage maximization from general submodular maximization in the consistent settings.
Multicalibration requires predicted scores to agree with label probabilities across rich families of subgroups and score-dependent tests, but existing methods require clean input-label pairs for evaluation and post-processing. This assumption fails in weakly supervised learning (WSL) regimes -- including positive-unlabeled, unlabeled-unlabeled, and positive-confidence learning -- where clean labels are costly or unavailable even though reliable uncertainty estimates may be crucial. We address this gap by developing estimators of multicalibration error and post-hoc correction methods for WSL settings in which clean input-label pairs are unavailable. We propose a unified framework for estimating and correcting multicalibration under weak supervision by combining contamination-matrix risk rewrites with witness-based calibration constraints, yielding corrected multicalibration moments with finite-sample guarantees. We further propose weak-label multicalibration boost (WLMC), a generic post-hoc recalibration algorithm under weak supervision. Finally, we conduct experiments across multiple weak-supervision settings to evaluate multicalibration behavior and offer empirical insight into uncertainty estimation under weak supervision.
Jin Liu, Yunpeng Liu, Keyi Wang, Jie Shi Fudan University, Xiao Xu, Wenkang Huang Ant Group, Xingzhong Xu Ant Group, Xin Liang Alibaba Group 等 9 位作者
Insurance claims adjudication demands not only accurate decisions but also interpretable reasoning grounded in policy clauses. However, existing benchmarks are limited to information retrieval or simple multiple-choice setups, which fail to require step-by-step inferences from facts to conclusions. To address this gap, we introduce InsLogicBench, a benchmark providing complete reasoning traces that link factual inputs, relevant policy clauses, and final verdicts. We construct the dataset using a controllable synthesis framework based on the Nested Toulmin Model. By capturing the defeasible logic of insurance policies through hierarchical truth assignment and enforcing validity via consistency verification, we ensure interpretability and logical rigor across generated examples. We evaluate eight Large Language Models (LLMs) on InsLogicBench. Results show significant difficulties in handling exception clauses and verifying missing conditions. Notably, models often produce correct final decisions but fail to provide precise justifications, highlighting a critical discrepancy between their decision accuracy and logical reasoning capabilities.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表