VAMPS: Visual-Assisted Mathematical Problem Solving Benchmark

Multimodal large language models are increasingly capable of complex reasoning, yet their performance often degrades when they must externalize a problem through a tool and then reason over the tool's output, specifically when they rely on visual aids. This gap is especially important because real engineering and scientific workflows often rely on visualization tools for analysis, validation, and decision-making. To study this discrepancy, we introduce VAMPS (Visual-Assisted Mathematical Problem Solving), a benchmark for graph-assisted mathematics. VAMPS contains 1,168 multimodal, bilingual multiple-choice question-answer pairs drawn from Iranian University Entrance Exam algebra and calculus problems and expanded with human-reviewed LLM-generated synthetic variants, all selected so that plotting provides a natural solution strategy by revealing intersections, extrema, asymptotes, etc. Designed for both benchmarking and diagnosis, VAMPS goes beyond prior multimodal benchmarks that primarily evaluate reasoning over fixed visual inputs by testing whether a model can benefit from constructing a useful graph and grounding its answer in the resulting visualization. Overall, we found that across a diverse set of models, direct analytical solving surprisingly outperforms tool-enabled visual solving, even on problems where plotting is a natural strategy.

Modeling Access Differences to Reduce Disparity in Resource Allocation

Motivated by COVID-19 vaccine allocation, where vulnerable subpopulations are simultaneously more impacted in terms of health and more disadvantaged in terms of access to the vaccine, we formalize and study the problem of resource allocation when there are inherent access differences that correlate with advantage and disadvantage. We identify reducing resource disparity as a key goal in this context and show its role as a proxy to more nuanced downstream impacts. We develop a concrete access model that helps quantify how a given allocation translates to resource flow for the advantaged vs. the disadvantaged, based on the access gap between them. We then provide a methodology for access-aware allocation. Intuitively, the resulting allocation leverages more vaccines in locations with higher vulnerable populations to mitigate the access gap and reduce overall disparity. Surprisingly, knowledge of the access gap is often not needed to perform access-aware allocation. To support this formalism, we provide empirical evidence for our access model and show that access-aware allocation can significantly reduce resource disparity and thus improve downstream outcomes. We demonstrate this at various scales, including at county, state, national, and global levels.