Weixuan Yuan

Maximilian Probst Gutenberg, Rasmus Kyng, Weixuan Yuan et al.

Given an undirected graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree on $V$ that preserves all-pairs mincuts of $G$ exactly. We present a simple, efficient reduction from Gomory-Hu trees to polylog maxflow computations. On unweighted graphs, our reduction reduces to maxflow computations on graphs of total instance size $\tilde{O}(m)$ and the algorithm requires only $\tilde{O}(m)$ additional time. Our reduction is the first that is tight up to polylog factors. The reduction also seamlessly extends to weighted graphs, however, instance sizes and runtime increase to $\tilde{O}(n^2)$. Finally, we show how to extend our reduction to reduce Gomory-Hu trees for unweighted hypergraphs to maxflow in hypergraphs. Again, our reduction is the first that is tight up to polylog factors.

Maximilian Probst Gutenberg, Weixuan Yuan

Given an undirected graph $G=(V,E,w)$, a Gomory-Hu tree $T$ (Gomory and Hu, 1961) is a tree on $V$ that preserves all-pairs mincuts of $G$ exactly. We present a simple and efficient randomized reduction from Gomory-Hu trees to polylog maxflow computations. On unweighted graphs, our reduction reduces to maxflow computations on graphs of total instance size $\tilde{O}(m)$ and the algorithm requires only $\tilde{O}(m)$ additional time. Our reduction is the first that is tight up to polylog factors. The reduction also seamlessly extends to weighted graphs, however, instance sizes and runtime increase to $\tilde{O}(n^2)$. Finally, we show how to extend our reduction to reduce Gomory-Hu trees for unweighted hypergraphs to maxflow in hypergraphs. Again, our reduction is the first that is tight up to polylog factors.

Ming Ding, Rasmus Kyng, Federico Solda et al.

As large language models (LLMs) advance, their role in higher education, particularly in free-response problem-solving, requires careful examination. This study assesses the performance of GPT-4o and o1-preview under realistic educational conditions in an undergraduate algorithms course. Anonymous GPT-generated solutions to take-home exams were graded by teaching assistants unaware of their origin. Our analysis examines both coarse-grained performance (scores) and fine-grained reasoning quality (error patterns). Results show that GPT-4o consistently struggles, failing to reach the passing threshold, while o1-preview performs significantly better, surpassing the passing score and even exceeding the student median in certain exercises. However, both models exhibit issues with unjustified claims and misleading arguments. These findings highlight the need for robust assessment strategies and AI-aware grading policies in education.

Tobias Preintner, Weixuan Yuan, Adrian König et al.

Combining large language models with evolutionary computation algorithms represents a promising research direction leveraging the remarkable generative and in-context learning capabilities of LLMs with the strengths of evolutionary algorithms. In this work, we present EvoCAD, a method for generating computer-aided design (CAD) objects through their symbolic representations using vision language models and evolutionary optimization. Our method samples multiple CAD objects, which are then optimized using an evolutionary approach with vision language and reasoning language models. We assess our method using GPT-4V and GPT-4o, evaluating it on the CADPrompt benchmark dataset and comparing it to prior methods. Additionally, we introduce two new metrics based on topological properties defined by the Euler characteristic, which capture a form of semantic similarity between 3D objects. Our results demonstrate that EvoCAD outperforms previous approaches on multiple metrics, particularly in generating topologically correct objects, which can be efficiently evaluated using our two novel metrics that complement existing spatial metrics.

Tobias Preintner, Weixuan Yuan, Qi Huang et al.

Combining natural language and geometric shapes is an emerging research area with multiple applications in robotics and language-assisted design. A crucial task in this domain is object referent identification, which involves selecting a 3D object given a textual description of the target. Variability in language descriptions and spatial relationships of 3D objects makes this a complex task, increasing the need to better understand the behavior of neural network models in this domain. However, limited research has been conducted in this area. Specifically, when a model makes an incorrect prediction despite being provided with a seemingly correct object description, practitioners are left wondering: "Why is the model wrong?". In this work, we present a method answering this question by generating counterfactual examples. Our method takes a misclassified sample, which includes two objects and a text description, and generates an alternative yet similar formulation that would have resulted in a correct prediction by the model. We have evaluated our approach with data from the ShapeTalk dataset along with three distinct models. Our counterfactual examples maintain the structure of the original description, are semantically similar and meaningful. They reveal weaknesses in the description, model bias and enhance the understanding of the models behavior. Theses insights help practitioners to better interact with systems as well as engineers to improve models.