Theory of Space: Can Foundation Models Construct Spatial Beliefs through Active Exploration?
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.
698a94fc1b2dc6b37d61aecd
Pingyue Zhang
claimed_verified
2026-02-10T09:07:28.765Z
66d32d853c8270397e6c2f0a
/avatars/3b99da95769673f773dff9ccbdb6887d.svg
pingyue zhang
williamzhangNU
user
williamzhangNU
698a94fc1b2dc6b37d61aece
Zihan Huang
698a94fc1b2dc6b37d61aecf
Yue Wang
698a94fc1b2dc6b37d61aed0
Jieyu Zhang
698a94fc1b2dc6b37d61aed1
Letian Xue
698a94fc1b2dc6b37d61aed2
Zihan Wang
698a94fc1b2dc6b37d61aed3
Qineng Wang
698a94fc1b2dc6b37d61aed4
Keshigeyan Chandrasegaran
698a94fc1b2dc6b37d61aed5
Ruohan Zhang
698a94fc1b2dc6b37d61aed6
Yejin Choi
698a94fc1b2dc6b37d61aed7
Ranjay Krishna
698a94fc1b2dc6b37d61aed8
Jiajun Wu
698a94fc1b2dc6b37d61aed9
Li Fei-Fei
698a94fc1b2dc6b37d61aeda
Manling Li
claimed_verified
2026-04-13T07:38:50.810Z
6746a140f2ca2162e3bcfe2b
/avatars/d9d8cfb5f112e6ed7f6152fc230135d3.svg
Manling Li
ManlingLi
user
ManlingLi
Theory of Space: Can Foundation Models Construct Spatial Beliefs through Active Exploration?
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.
Current multimodal foundation models show limitations in maintaining coherent spatial beliefs during active exploration, exhibiting gaps between active and passive performance, inefficient exploration strategies, and difficulties in updating outdated spatial knowledge.
spatial embodied intelligence multimodal foundation models active exploration spatial belief cognitive mapping spatial belief probing Active-Passive Gap belief inertia vision-based models text-based agents