Theory of Space: Can Foundation Models Construct Spatial Beliefs through Active Exploration?

2026-02-04

AI Summary

This work addresses the challenge that foundation models face in constructing, updating, and maintaining coherent spatial beliefs in partially observable environments. We propose a “Theory of Space” framework that systematically evaluates agents’ ability to build cognitive maps and form revisable spatial beliefs from sequences of local observations through curiosity-driven active exploration tasks. By introducing a spatial belief probing mechanism—integrating cognitive mapping benchmarks, false-belief paradigms, and comparisons with procedural agents—we uncover critical limitations in current models, including a performance gap between active and passive settings, inefficient exploration, unstable beliefs, and belief inertia. Our experiments demonstrate that foundation models suffer significant performance degradation during active exploration and that vision-based models exhibit greater difficulty than text-based models in revising outdated spatial beliefs.

Technology Category

• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

Problem

• spatial belief
• active exploration
• foundation models
• partial observability
• belief updating

Innovation

• Theory of Space
• spatial belief probing
• active exploration
• belief inertia
• cognitive map