data visualization engineers

Abstract: Legends are fundamental to chart understanding, as reliable interpretation requires correctly binding legend entries to corresponding visual marks. While vision-language models (VLMs) are increasingly applied to chart understanding, their legend understanding is poorly diagnosed by aggregate accuracy, which can be satisfied by superficial shortcuts and confound legend-specific errors with other reasoning failures. To enable fine-grained diagnosis and controlled testing, we introduce LegendBench, a parametric benchmark and generation pipeline that produces targeted legend-centric test cases. LegendBench contributes (1) a capability-task taxonomy spanning legend parsing, legend grounding, legend-conditioned reasoning, and legend-aware abstention to localize failures, and (2) counterfactual group generation, where each base chart yields multiple variants under controlled legend interventions to probe model invariance and sensitivity. Using LegendBench, we evaluate both general-purpose VLMs and specialized chart models and generate their capability profiles, revealing persistent bottlenecks in reliable legend-to-mark binding and counterfactual consistency. We then use these capability profiles to guide targeted fine-tuning, demonstrating that bottleneck-specific interventions can effectively close the localized capability gaps and generalize to unseen data. We further leverage our counterfactual design to conduct fine-grained diagnostic experiments, analyzing encoding-channel effects, legend-order shortcuts, and abstention under varying visibility.

Abstract: A point set is universal for planar graphs on $n$ vertices if every such graph has a straight-line drawing without crossings whose vertices belong to the set. We construct universal point sets of size $n^{1+o(1)}$, improving the previous quadratic upper bound. Our construction uses the reduction of Bannister, Cheng, Devanny, and Eppstein from universal point sets to superpatterns for $213$-avoiding permutations. We represent these permutations by ordered rooted forests and construct a small family of intervals containing every such forest. The result follows from a straightforward bound on the size of the family of intervals. GPT-6 Astra assisted in developing the construction and proof.

Abstract: Charts are structured visual compositions whose elements have distinct functional roles, semantic correspondences, and visibility relations. This structural view motivates evaluating whether models can understand and manipulate charts at the layer level. Existing chart benchmarks, however, primarily assess the correctness or fidelity of final outputs and do not directly evaluate these layer-wise behaviors. We present LayerWiseBench, a benchmark organized around three core concepts, layer attribution, layer binding, and visibility ordering, that structure its chart-understanding and chart-editing evaluations. Generated from executable chart programs, LayerWiseBench pairs each rendered chart with spatially aligned per-layer RGBA assets and construction-derived labels for functional roles, semantic bindings, and visibility relations. From this layer-wise representation, we derive controlled understanding questions, editing targets, reference images, and evaluation regions. It contains 2,800 source charts across 14 chart paradigms, from which we derive 7,329 layer-wise understanding questions and 53,791 instruction-guided editing variants. Among the evaluated VLMs, Qwen3.5-27B, which achieves the highest QA macro-average, obtains 93.04% accuracy on layer attribution and 97.46% on layer binding, but only 61.46% on visibility ordering. Across the four evaluated image editors, overall mIoU ranges from 1.49% to 4.93%, and visibility-constrained edits have the lowest mIoU for every editor, ranging from 0.37% to 2.00%. Taken together, these results identify tasks involving front-to-back relations between overlapping components as a recurring challenge across understanding and editing, motivating more explicit modeling of component identity and visibility relations.