Two-stage sample robust optimization with linear decision rules is a standard data-driven approach to two-stage stochastic linear programs with unknown distributions. \cite{bertsimas2022two} established that this approach is asymptotically optimal under several conditions. Most are mild, but one is technical, and whether it follows from the others was left as an open question. We resolve this open question through a single geometric feature of the support set: simpleness, the property that every vertex is incident to exactly as many edges as the ambient dimension. When the support set is simple, the technical condition is automatic, and asymptotic optimality holds under the remaining standard assumptions. When the support set is not simple, there exists a problem instance on which the technical condition fails, and asymptotic optimality breaks down. This settles the open question in the negative and yields a sharp dichotomy. The dichotomy has direct practical consequences, since widely used support sets may not be simple. For such supports, we provide a polynomial-time algorithm that certifies the technical condition at any given vertex using only its incident edge directions. Our case study illustrates the effectiveness of our algorithm.
Multimodal large language models (MLLMs) make grounded predictions in real-world scenes by combining visual and textual cues, yet existing benchmarks rarely reveal how they arbitrate between these evidence sources when they conflict. We introduce SIGNPOST-Bench, a controlled counterfactual benchmark for evaluating text-vision conflict resolution. Each source image is transformed into a counterfactual quintuplet of Original, Blank, Similar, Random, and Adversarial variants. Synthetic, localized scene-text interventions are designed to preserve non-textual content, enabling paired measurements of changes in localization performance and directed shifts toward geographic targets introduced by conflicting text. SIGNPOST-Bench contains 5,111 counterfactual groups and 25,555 image variants from four datasets. We evaluate 20 MLLMs from seven providers. Compared with Original images, Adversarial variants raise median localization error from 282 km to 1,347 km, a 4.8-fold increase. Among geocodable adversarial samples, 6.5-20.1% of predictions lie less than 50 km from the injected target across models, and every evaluated model exhibits a positive mean paired reduction in target distance from Blank to Adversarial. Compatible, unrelated, and conflicting text replacements produce distinct effects on model predictions, while clean-input localization performance does not fully predict robustness to conflicting text. These results establish visual geolocation as a continuous diagnostic of scene-text arbitration and provide a controlled framework for evaluating how MLLMs resolve conflicting multimodal evidence.
Sirun Li, Minghao Liu, Ling Dai et al.· 0 citations
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