Nan Hu

Hongru Wang, Wenyu Huang, Yufei Wang et al.

Existing benchmarks that assess Language Models (LMs) as Language Agents (LAs) for tool use primarily focus on stateless, single-turn interactions or partial evaluations, such as tool selection in a single turn, overlooking the inherent stateful nature of interactions in multi-turn applications. To fulfill this gap, we propose \texttt{DialogTool}, a multi-turn dialogue dataset with stateful tool interactions considering the whole life cycle of tool use, across six key tasks in three stages: 1) \textit{tool creation}; 2) \textit{tool utilization}: tool awareness, tool selection, tool execution; and 3) \textit{role-consistent response}: response generation and role play. Furthermore, we build \texttt{VirtualMobile} -- an embodied virtual mobile evaluation environment to simulate API calls and assess the robustness of the created APIs\footnote{We will use tools and APIs alternatively, there are no significant differences between them in this paper.}. Taking advantage of these artifacts, we conduct comprehensive evaluation on 13 distinct open- and closed-source LLMs and provide detailed analysis at each stage, revealing that the existing state-of-the-art LLMs still cannot perform well to use tools over long horizons.

Nan Hu, Raif M. Rustamov, Leonidas Guibas

In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the Laplacian family signature (LFS) on the nodes, and the pairwise heat kernel map on the edges. In this paper, without assuming an explicit form of parametric dependence nor a distance metric between node signatures, we formulate an optimization problem which incorporates the knowledge of anchor nodes. Solving this problem gives us an optimized proximity measure specific to the graphs under consideration. Using this as a first order compatibility term, we then set up an integer quadratic program (IQP) to solve for a near optimal graph matching. Our experiments demonstrate the superior performance of our approach on randomly generated graphs and on two widely-used image sequences, when compared with other existing signature and adjacency matrix based graph matching methods.

Nan Hu, Qixing Huang, Boris Thibert et al.

In this paper we propose an optimization-based framework to multiple object matching. The framework takes maps computed between pairs of objects as input, and outputs maps that are consistent among all pairs of objects. The central idea of our approach is to divide the input object collection into overlapping sub-collections and enforce map consistency among each sub-collection. This leads to a distributed formulation, which is scalable to large-scale datasets. We also present an equivalence condition between this decoupled scheme and the original scheme. Experiments on both synthetic and real-world datasets show that our framework is competitive against state-of-the-art multi-object matching techniques.

Nan Hu, Raif M. Rustamov, Leonidas Guibas

In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our approach relies on a rigorous analysis of stability of spectral signatures based on the graph Laplacian. In the case of the first order term, we derive an objective function that measures both the stability and informativeness of a given spectral signature. By optimizing this objective, we design new spectral node signatures tuned to a specific graph to be matched. We also introduce the pairwise heat kernel distance as a stable second order compatibility term; we justify its plausibility by showing that in a certain limiting case it converges to the classical adjacency matrix-based second order compatibility function. We have tested our approach on a set of synthetic graphs, the widely-used CMU house sequence, and a set of real images. These experiments show the superior performance of our first and second order compatibility terms as compared with the commonly used ones.