arXiv subjects

Yihang Sun

Publications and source records attributed to Yihang Sun.

27 records · Page 2Linked to original sources

arXiv2025

On the number of modes of Gaussian kernel density estimators

We consider the Gaussian kernel density estimator with bandwidth $β^{-\frac12}$ of $n$ iid Gaussian samples. Using the Kac-Rice formula and an Edgeworth expansion, we prove that the expected number of modes on the real line scales as $Θ(\sqrt{β\logβ})$ as $β,n\to\infty$ provided $n^c\lesssim β\lesssim n^{2-c}$ for some constant $c>0$. An impetus behind this investigation is to determine the number of clusters to which Transformers are drawn in a metastable state.

math.ST↗

arXiv2025

Interleave-VLA: Enhancing Robot Manipulation with Interleaved Image-Text Instructions

The rise of foundation models paves the way for generalist robot policies in the physical world. Existing methods relying on text-only instructions often struggle to generalize to unseen scenarios. We argue that interleaved image-text inputs offer richer and less biased context and enable robots to better handle unseen tasks with more versatile human-robot interaction. Building on this insight, Interleave-VLA, the first robot learning paradigm capable of comprehending interleaved image-text instructions and directly generating continuous action sequences in the physical world, is introduced. It offers a natural, flexible, and model-agnostic paradigm that extends state-of-the-art vision-language-action (VLA) models with minimal modifications while achieving strong zero-shot generalization. Interleave-VLA also includes an automatic pipeline that converts text instructions from Open X-Embodiment into interleaved image-text instructions, resulting in a large-scale real-world interleaved embodied dataset with 210k episodes. Comprehensive evaluation in simulation and the real world shows that Interleave-VLA offers two major benefits: (1) improves out-of-domain generalization to unseen objects by 2x compared to text input baselines, (2) supports flexible task interfaces and diverse instructions in a zero-shot manner, such as hand-drawn sketches. We attribute Interleave-VLA's strong zero-shot capability to the use of instruction images, which effectively mitigate hallucinations, and the inclusion of heterogeneous multimodal datasets, enriched with Internet-sourced images, offering potential for scalability. More information is available at https://interleave-vla.github.io/Interleave-VLA-Anonymous/

cs.RO↗

arXiv2025

Computation of Approximately Stable Committees in Approval-based Elections

Approval-based committee selection is a model of significant interest in social choice theory. In this model, we have a set of voters $\mathcal{V}$, a set of candidates $\mathcal{C}$, and each voter has a set $A_v \subset \mathcal{C}$ of approved candidates. For any committee size $K$, the goal is to choose $K$ candidates to represent the voters' preferences. We study a criterion known as \emph{approximate stability}, where a committee is $λ$-approximately-stable if there is no other committee $T$ preferred by at least $\frac{λ|T|}{k} |\mathcal{V}| $ voters. We prove that a $3.65$-approximately stable committee always exists and can be computed algorithmically in this setting. Our approach is based on finding a Lindahl equilibrium and sampling from a strongly Rayleigh distribution associated with it.

cs.GT↗

arXiv2025

GraphEval: A Lightweight Graph-Based LLM Framework for Idea Evaluation

The powerful capabilities of Large Language Models (LLMs) have led to their growing use in evaluating human-generated content, particularly in evaluating research ideas within academic settings. Existing solutions primarily rely on prompt-based LLM methods or fine-tuned lightweight language models for idea evaluation. However, these methods are often unstable and struggle to comprehend the complex semantic information embedded in the ideas, impeding their ability to perform high-quality evaluations. To address the above challenges, we propose GraphEval, a lightweight graph-based LLM framework for idea evaluation. Our insight is that a complex idea can be broken down into comprehensible viewpoint nodes using prompts from small LLMs. These viewpoint nodes can then be linked together through edges created from LLM-based relation extraction and/or BERT similarity scores. The created viewpoint-graph can be used to conveniently propagate scores across view-nodes to improve the robustness of the idea evaluations. In particular, we propose two lightweight graph-based methods for idea evaluation: (1) GraphEval-LP: a training-free label propagation algorithm that propagates evaluation scores from known view-nodes to unknown nodes; (2) GraphEval-GNN: a Graph Neural Networks (GNN) that is trained to predict the evaluation scores given the observed graph with minimal computation resources. Moreover, to overcome LLM's limitation in objectively assessing the novelty of ideas, we further propose a novelty detection model to GraphEval-GNN to enhance its capability in judging idea novelty. Experiments on two datasets show GraphEval improves F1 scores by at least 14% with low computation and API costs. Additionally, GraphEval can effectively detect plagiarized ideas.

cs.LG↗

arXiv2024

Rainbow common graphs must be forests

We study the rainbow version of the graph commonness property: a graph $H$ is $r$-rainbow common if the number of rainbow copies of $H$ (where all edges have distinct colors) in an $r$-coloring of edges of $K_n$ is maximized asymptotically by independently coloring each edge uniformly at random. $H$ is \emph{$r$-rainbow uncommon} otherwise. We show that if $H$ has a cycle, then it is $r$-rainbow uncommon for every $r$ at least the number of edges of $H$. This generalizes a result of Erdős and Hajnal, and proves a conjecture of De Silva, Si, Tait, Tunçbilek, Yang, and Young.

math.CO↗

arXiv2024

ProAgent: Building Proactive Cooperative Agents with Large Language Models

Building agents with adaptive behavior in cooperative tasks stands as a paramount goal in the realm of multi-agent systems. Current approaches to developing cooperative agents rely primarily on learning-based methods, whose policy generalization depends heavily on the diversity of teammates they interact with during the training phase. Such reliance, however, constrains the agents' capacity for strategic adaptation when cooperating with unfamiliar teammates, which becomes a significant challenge in zero-shot coordination scenarios. To address this challenge, we propose ProAgent, a novel framework that harnesses large language models (LLMs) to create proactive agents capable of dynamically adapting their behavior to enhance cooperation with teammates. ProAgent can analyze the present state, and infer the intentions of teammates from observations. It then updates its beliefs in alignment with the teammates' subsequent actual behaviors. Moreover, ProAgent exhibits a high degree of modularity and interpretability, making it easily integrated into various of coordination scenarios. Experimental evaluations conducted within the Overcooked-AI environment unveil the remarkable performance superiority of ProAgent, outperforming five methods based on self-play and population-based training when cooperating with AI agents. Furthermore, in partnered with human proxy models, its performance exhibits an average improvement exceeding 10% compared to the current state-of-the-art method. For more information about our project, please visit~\url{https://pku-proagent.github.io}.

cs.AI↗

arXiv2023

Tetrahedra tiling problem

Kedlaya, Kolpakov, Poonen, and Rubinstein classified tetrahedra all of whose dihedral angles are rational multiples of $π$ into two one-parameter families (a Hill family and a new family) and $59$ sporadic tetrahedra. In this paper, we consider which of them tile space; we show that every member of the Hill family, exactly one member of the new family, and at most $40$ sporadic tetrahedra tile space. As a corollary, we disprove the converse of Debrunner's theorem, showing that not all Dehn invariant zero tetrahedra tile space.

math.MG↗

arXiv2023

Dehn invariant zero tetrahedra

We survey literature on all known families and examples of Dehn invariant zero tetrahedra. We also contribute two previously unknown families of Dehn invariant zero tetrahedra. Following a suggestion of Dill and Habegger, we show that there are finitely many Dehn invariant zero tetrahedra whose dihedral angles have a five-dimensional span over $\mathbb{Q}$, a first step towards classifying all Dehn invariant zero tetrahedra.

math.MG↗

arXiv2023

Randomly Initialized One-Layer Neural Networks Make Data Linearly Separable

Recently, neural networks have demonstrated remarkable capabilities in mapping two arbitrary sets to two linearly separable sets. The prospect of achieving this with randomly initialized neural networks is particularly appealing due to the computational efficiency compared to fully trained networks. This paper contributes by establishing that, given sufficient width, a randomly initialized one-layer neural network can, with high probability, transform two sets into two linearly separable sets without any training. Moreover, we furnish precise bounds on the necessary width of the neural network for this phenomenon to occur. Our initial bound exhibits exponential dependence on the input dimension while maintaining polynomial dependence on all other parameters. In contrast, our second bound is independent of input dimension, effectively surmounting the curse of dimensionality. The main tools used in our proof heavily relies on a fusion of geometric principles and concentration of random matrices.

cs.LG↗