Liwei Wang | Search arXiv

arXiv2026

Towards Solving the Gilbert-Pollak Conjecture via Large Language Models

The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times that of the Euclidean minimum spanning tree (the Steiner ratio). A sequence of improvements through the 1980s culminated in a lower bound of $0.824$, with no substantial progress reported over the past three decades. Recent advances in LLMs have demonstrated strong performance on contest-level mathematical problems, yet their potential for addressing open, research-level questions remains largely unexplored. In this work, we present a novel AI system for obtaining tighter lower bounds on the Steiner ratio. Rather than directly prompting LLMs to solve the conjecture, we task them with generating rule-constrained geometric lemmas implemented as executable code. These lemmas are then used to construct a collection of specialized functions, which we call verification functions, that yield theoretically certified lower bounds of the Steiner ratio. Through progressive lemma refinement driven by reflection, the system establishes a new certified lower bound of 0.8559 for the Steiner ratio. The entire research effort involves only thousands of LLM calls, demonstrating the strong potential of LLM-based systems for advanced mathematical research.

cs.DM↗

arXiv2026

SinkPruner: Sink-Free Visual Token Pruning for Multimodal Large Language Models

Despite their strong multimodal understanding ability, multimodal large language models (MLLMs) incur substantial computational overhead when processing long visual token sequences. To reduce inference costs, recent studies have explored visual token pruning through vision-centric or text-guided strategies. However, these methods often overlook high-norm outlier tokens, i.e., tokens with abnormally large feature norms, leading to suboptimal pruning decisions. In this work, we show that such high-norm outlier tokens are highly redundant in both feature and spatial dimensions, yet are often mistakenly preserved as informative cues by existing methods. Motivated by this observation, we propose SinkPruner, a training-free visual token pruning framework for efficient MLLM inference. SinkPruner follows a coarse-to-fine design with two key modules: a visual sanitizer that filters high-norm redundancies and alleviates attention sink and attention dispersion, and a text-guided pruner that further retains tokens semantically aligned with the text query. Extensive experiments on twelve image-language and four video-language benchmarks demonstrate the effectiveness, efficiency, and generalizability of our framework. Notably, SinkPruner preserves 96.5% (91.8%) of the original performance of LLaVA-1.5 (Qwen2.5-VL) under an 89% token reduction. Experiments further indicate that our visual sanitizer exhibits promising transferability in enhancing the performance of existing pruning methods. Our code is available at https://github.com/LaVi-Lab/SinkPruner.

cs.CV↗