BLM${}_1$: A Boundless Large Model for Cross-Space, Cross-Task, and Cross-Embodiment Learning

Multimodal large language models (MLLMs) have advanced vision-language reasoning and are increasingly deployed in embodied agents. However, significant limitations remain: MLLMs generalize poorly across digital-physical spaces and embodiments; vision-language-action models (VLAs) produce low-level actions yet lack robust high-level embodied reasoning; and most embodied large language models (ELLMs) are constrained to digital-space with poor generalization to the physical world. Thus, unified models that operate seamlessly across digital and physical spaces while generalizing across embodiments and tasks remain absent. We introduce the $\mathbf{\text{Boundless}}\mathbf{\text{Large}}\mathbf{\text{Model}}\mathbf{\text{(BLM}}{}_1\mathbf{\text{)}}$, a multimodal spatial foundation model that preserves instruction following and reasoning, incorporates embodied knowledge, and supports robust cross-embodiment control. BLM${}_1$ integrates three key capabilities – $\mathit{\text{cross-space}}\mathit{\text{transfer,}}\mathit{\text{cross-task}}\mathit{\text{learning,}}\mathit{\text{and}}\mathit{\text{cross-embodiment}}\mathit{\text{generalization}}$ – via a two-stage training paradigm. Stage I injects embodied knowledge into the MLLM through curated digital corpora while maintaining language competence. Stage II trains a policy module through an intent-bridging interface that extracts high-level semantics from the MLLM to guide control, without fine-tuning the MLLM backbone. This process is supported by a self-collected cross-embodiment demonstration suite spanning four robot embodiments and six progressively challenging tasks. Evaluations across digital and physical benchmarks show that a single BLM${}_1$ instance outperforms four model families – MLLMs, ELLMs, VLAs, and GMLMs – achieving \sim\!\textbf{6%} gains in digital tasks and \sim\!\textbf{3%} in physical tasks.