R4: Retrieval-Augmented Reasoning for Vision-Language Models in 4D Spatio-Temporal Space

Humans perceive and reason about their surroundings in four dimensions-three spatial and one temporal axis-by building persistent, structured internal representations that encode semantic meaning, spatial layout, and temporal dynamics. These multimodal memories enable them to recall past events, infer unobserved states, and integrate new information into context-dependent reasoning. Inspired by this capability, we introduce R4, a training-free framework for retrieval-augmented reasoning in 4D spatio-temporal space that equips vision-language models (VLMs) with structured, lifelong memory. R4 continuously constructs a 4D knowledge database by anchoring object-level semantic descriptions in metric space and time, yielding a persistent world model that can be shared across agents. At inference, natural language queries are decomposed into semantic, spatial, and temporal keys to retrieve relevant observations, which are integrated into the VLM's reasoning through an iterative retrieval-reasoning loop. Unlike classical retrieval-augmented generation methods, retrieval in R4 operates directly in structured 4D space, enabling episodic and collaborative reasoning without training. Experiments on embodied question answering and navigation benchmarks demonstrate that R4 substantially improves retrieval and reasoning over spatio-temporal information compared to baselines, advancing a new paradigm for embodied 4D reasoning in dynamic environments.