On Representational Alignment among Embodied Agents

2026-10-02

AI Summary

This study addresses the challenge that representational misalignment among embodied agents impedes sustained collaboration, necessitating a precise characterization of which discrepancies must be resolved to maintain interaction. To this end, it proposes a theoretical framework termed relational sufficiency, integrating relational evidence mapping, equivalence class analysis, and differential geometry to derive local first-order lower bounds, validated through simulations of asynchronous handover scenarios. Theoretically, this work establishes task-relative stopping conditions that do not require global alignment. Furthermore, it proves that in smooth systems, the number of required independent scalar anchors strictly equals the dimensionality of unobservable directions, thereby quantifying alignment necessity in specific contexts. These findings provide a rigorous theoretical foundation for local coordination in multi-agent systems.

Abstract

Embodied agents interacting with the same physical process may maintain heterogeneous, asynchronous, and observer-relative representations. Rather than assuming that such representations should always be globally aligned, we investigate which distinctions among them must actually be resolved for coherent interaction. We formalize this question through relational sufficiency: an interaction-specific relational-evidence map defines the representational ambiguity left unresolved by comparison, and sufficiency holds when each residual ambiguity fiber lies within an interaction-equivalence class. When this condition fails, additional sensorimotor anchors must separate precisely the ambiguities that can change the interaction-relevant outcome. For smooth systems, we derive a local first-order lower bound on the number of inde- pendent scalar anchors required, given by the dimension of directions that are invisible to relational evidence but visible to the interaction-relevant map. We instantiate the theory in two variants of an asynchronous hand-off scenario that share the same observer agents, representations, transports, and relational evidence. Relative synchronization requires no additional anchor, whereas hand-off at an absolute time requires exactly one. The analysis there- fore provides a task-relative stopping condition for representational alignment: residual disagreement need not be eliminated when it is invariant with respect to the interaction.

Problem

• Representational Alignment
• Embodied Agents
• Relational Sufficiency
• Sensorimotor Anchors
• Coherent Interaction

Innovation

• Representational Alignment
• Relational Sufficiency
• Embodied Agents
• Sensorimotor Anchors
• Asynchronous Interaction