Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.27626

TriGeoBench: A Multimodal Mathematical Geometry Benchmark with Figures and TikZ

Jing Wang·Yitong Yang·Hao Dou·Yaomin Wu·Shuting He·Tingfei Shen·Jia Wu·Jiaqi Li·Yinglin Wang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Multimodal Large Language Models show strong vision-language capabilities, yet their geometry-centric reasoning remains insufficiently understood. Existing mathematical benchmarks typically rely on rasterized figures and cover limited geometric knowledge areas and response formats, making it difficult to assess whether models reason over geometric structures or exploit superficial visual patterns. We introduce TriGeoBench, a geometry-centric multimodal benchmark constructed from Chinese middle- and high-school mathematics examinations. TriGeoBench contains 7,000 question-answer pairs and 12,235 geometric figures with TikZ code, spanning plane geometry, solid geometry, analytic geometry, function, and vector geometry across diverse response formats. Each instance forms a {question-answer pair, image, TikZ} triplet: question-answer pairs are stored in LaTeX, images as RGB figures, and TikZ preserves geometric topology, symbolic annotations, and relational structure. We evaluate representative open- and closed-source MLLMs through image-to-TikZ and multimodal reasoning probes. Results reveal persistent fine-grained structure and image-text alignment challenges. Oracle experiments with human-curated reference TikZ suggest that accurate executable representations provide complementary geometric cues; they do not evaluate an end-to-end conversion pipeline. TriGeoBench offers a testbed for structure-aware mathematical reasoning.

Explore related subjects

cs.AIcs.DB

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jing Wang, Yitong Yang, Hao Dou, Yaomin Wu, Shuting He, Tingfei Shen, Jia Wu, Jiaqi Li, Yinglin Wang. 2026-10-20. TriGeoBench: A Multimodal Mathematical Geometry Benchmark with Figures and TikZ. https://arxiv.org/abs/2610.27626

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Adaptive auditing of AI systems with anytime-valid guarantees

A major bottleneck in characterizing the failure modes of generative AI systems is the cost and time of annotation and evaluation. Consequently, adaptive testing paradigms have gained popularity, where one opportunistically decides which cases and how many to annotate based on past results. While this framework is highly practical, its extreme flexibility makes it difficult to draw statistically rigorous conclusions, as it violates classical assumptions: the number of observations is typically limited (often 10 to 50 cases) and decisions regarding sampling and stopping are made in the midst of data collection rather than based a pre-specified rule. To characterize what statistical inferences can be drawn from highly adaptive audits, we introduce a hypothesis testing framework from two "dueling" perspectives: (i) the model's null that asserts there is no failure mode with performance below a target threshold versus (ii) the auditor's null that asserts they have a sampling strategy that will uncover a failure mode. Leveraging Safe Anytime-Valid Inference (SAVI), we formalize the auditor as conducting "testing by betting," which translates into simultaneous e-processes for testing the dueling null hypotheses. Furthermore, if the auditor is sufficiently powerful, we prove that these two hypotheses are asymptotically inverses of each other, in that passage of such an audit certifies the AI system as being globally robust. Empirically, we demonstrate that our proposed testing procedures maintain anytime-valid Type-I error control, outperform pre-specified testing methods, and can reach statistically rigorous conclusions sometimes with as few as 20 observations.

cs.AI↗
arXiv2026

WindINR: Latent-State INR for Fast Local Wind Query and Correction in Complex Terrain

Many decisions in complex terrain require fast wind estimates at specific locations and heights rather than dense forecasts on fixed grids. We present WindINR, a latent-state implicit neural representation framework for continuous high-resolution local wind queries and correction using sparse observations. A latent-conditioned decoder maps terrain descriptors, a low-resolution background field, and continuous query coordinates to local wind estimates. WindINR separates reusable representation learning from sample-specific latent correction. During training, a privileged encoder infers reference latent states from high-resolution supervision, while a deployable predictor estimates initial states from inference-time inputs. Their discrepancies define a dataset-adaptive Gaussian prior over latent corrections. At inference time, network weights remain fixed, and only the latent state is updated through a regularized objective incorporating sparse observations and their uncertainty. We train WindINR on the large-scale FuXi-CFD dataset and evaluate it using controlled observing system simulation experiments, simulated helicopter trajectories, and real UAV measurements over Tromsø. Across these settings, sparse-observation assimilation consistently improves local wind predictions, with WindINR outperforming several baselines, including WindSeer. Updating only a low-dimensional latent state yields a 14-fold speedup over full-network fine-tuning while preserving continuous queries at arbitrary spatial coordinates. WindINR thus provides an efficient interface between kilometer-scale background products, sparse local observations, and local wind queries in complex terrain.

cs.AI↗
arXiv2026

DeepLook: Uncertainty-Guided Branching with Lookahead Confidence for Efficient Reasoning

Test-time scaling improves large language model reasoning, but spends compute uniformly along a reasoning trace, even in stretches that are already stable. Motivated by the observation that reasoning failures show an early onset of uncertainty, we introduce DeepLook, a training-free decoding framework that monitors segment-level confidence, branches only at uncertainty bottlenecks, and ranks candidate continuations by Average Lookahead Confidence (ALC)---their mean confidence over fixed-horizon rollouts---before completing and voting over a pruned subset. On four competition mathematics benchmarks across four open models, DeepLook matches or exceeds the accuracy of DeepConf-low in 12 of 16 settings while generating 87.3% fewer tokens, showing that a model's own confidence is informative enough to decide where extra decoding compute is worth spending. On knowledge-intensive GPQA-Diamond the accuracy advantage disappears even though the token saving does not: coherent hallucinations also receive high ALC, so internal confidence localizes instability, not falsehood. Code is available at https://github.com/txyang1/deeplook.

cs.AI↗