We thank the reviewers for their thoughtful and constructive feedback on our manuscript. This should help both contextualize each task's difficulty and illustrate what it involves. Reviewer 3 noted the Section 2 task descriptions could be better presented. We have reformatted it so that "the order We also changed our description of IMP ALA to match Reviewer 5's suggestion. Regarding the task suite, Reviewer 4 raised a thoughtful consideration on whether "most of the findings translate when Some 3D tasks in the suite already have '2D-like' semi-counterparts that do not require navigation, '2D-like' because everything is fully observable and the agent has a first-person point of view from a fixed point, without Spot the Difference level, was overall harder than Change Detection for our ablation models.

Foundation models have become central to unifying perception and planning in robotics, yet real-world deployment exposes a mismatch between their monolithic assumption that a single model can handle all cognitive functions and the distributed, dynamic nature of practical service workflows. Vision-language models offer strong semantic understanding but lack embodiment-aware action capabilities while relying on hand-crafted skills. Vision-Language-Action policies enable reactive manipulation but remain brittle across embodiments, weak in geometric grounding, and devoid of proactive collaboration mechanisms. These limitations indicate that scaling a single model alone cannot deliver reliable autonomy for service robots operating in human-populated settings. To address this gap, we present InteractGen, an LLM-powered multi-agent framework that decomposes robot intelligence into specialized agents for continuous perception, dependency-aware planning, decision and verification, failure reflection, and dynamic human delegation, treating foundation models as regulated components within a closed-loop collective. Deployed on a heterogeneous robot team and evaluated in a three-month open-use study, InteractGen improves task success, adaptability, and human-robot collaboration, providing evidence that multi-agent orchestration offers a more feasible path toward socially grounded service autonomy than further scaling standalone models.

T o Reviewer #3: Thank you for your careful reading and thoughtful reviews. Q1: Theorems 3 and 4. (i) Theorem 3: Theorem 3 shows that SD2 helps to reduce the overestimation bias compared We empirically show that SD2 does not underestimate and can reduce the absolute bias in Figure 4. The left-hand side in Eq. (19) equals to Q5: How is the performance of the proposed approximation method? We will try to further investigate it in future research. Q2: Related works about ensemble methods.

We thank the reviewers for the valuable feedback and address specific comments below. We plan to expand Section 2.1 with additional explanation to make the paper more self-contained. Although the samples are not i.i.d., no burn-in or thinning is used. Defining such moves does require some domain expertise. We plan to include updated Guacamol results in the paper.

We kindly thank the reviewers for their detailed reviews, valuable feedback and suggestions for improvement. Indeed, our proof of the new SW theorem relies on an "ordering" of the coordinates of arbitrary equivariant SW theorem under arbitrary finite group action would be desirable, however the proof is out of our reach as of today. In a way, this limitation is similar to the distinction between "point clouds" (which in We will add this discussion in the paper, and mention it in the abstract. In its "deep" original version, it covers all type of "Message-Passing" GNNs, but not spectral GNNs which use powers of the adjacency matrix. We will clarify this in the final version.

As Large Language Models (LLMs) are increasingly integrated in diverse applications, obtaining reliable measures of their predictive uncertainty has become critically important. A precise distinction between aleatoric uncertainty, arising from inherent ambiguities within input data, and epistemic uncertainty, originating exclusively from model limitations, is essential to effectively address each uncertainty source. In this paper, we introduce Spectral Uncertainty, a novel approach to quantifying and decomposing uncertainties in LLMs. Leveraging the V on Neumann entropy from quantum information theory, Spectral Uncertainty provides a rigorous theoretical foundation for separating total uncertainty into distinct aleatoric and epistemic components. Unlike existing baseline methods, our approach incorporates a fine-grained representation of semantic similarity, enabling nuanced differentiation among various semantic interpretations in model responses. Empirical evaluations demonstrate that Spectral Uncertainty outperforms state-of-the-art methods in estimating both aleatoric and total uncertainty across diverse models and benchmark datasets.

The BottomUpTopDown [2] achieved 63.2 accuracy across all question types and the