arXiv subjects

Julia Kuhn

Publications and source records attributed to Julia Kuhn.

2 recordsLinked to original sources

arXiv2026

Relational Scene Graphs for Object Grounding of Natural Language Commands

Robots are finding wider adoption in human environments, increasing the need for natural human-robot interaction. However, understanding a natural language command requires the robot to infer the intended task and how to decompose it into executable actions, and to ground those actions in the robot's knowledge of the environment, including relevant objects, agents, and locations. This challenge can be addressed by combining the capabilities of large language models (LLMs) to understand natural language with 3D scene graphs (3DSGs) for grounding inferred actions in a semantic representation of the environment. However, many 3DSGs lack explicit spatial relations between objects, even though humans often rely on these relations to describe an environment. This paper investigates whether incorporating open- or closed-vocabulary spatial relations into 3DSGs can improve the ability of LLMs to interpret natural language commands. To address this, we implement two pipelines using off-the-shelf models: an LLM-based pipeline for target object grounding from open-vocabulary language commands and a vision language model-based pipeline to add open-vocabulary spatial edges to 3DSGs from images captured while mapping. Finally, we evaluate two LLMs across 14 scenes using 905 natural language statements (786 procedurally-generated, 119 human-authored) to assess performance on the downstream task of target object grounding. Our study demonstrates that explicit spatial relations improve the ability of LLMs to ground objects, and while open-vocabulary relation generation with vision language models proves feasible from robot-captured images, our analysis did not yield evidence favoring either open- or closed-vocabulary relations.

cs.RO↗

arXiv2017

Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a< \frac{1}{3}$ and $a > 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable.

math.PR↗