World Action Models (WAMs) have recently emerged as a promising paradigm for robotic manipulation, endowing policies with strong capabilities for modeling temporal and physical dynamics. Existing WAMs, encompassing both video-first action prediction and joint video-action modeling, directly transfer global physical representations from world models to action generation. However, global scene representations may underemphasize local robot-object interactions, creating a mismatch between representations optimized for world evolution and those required for manipulation. To bridge this gap, we propose LaST0.5, a novel WAM that introduces an interaction-centric physical representation between world modeling and action generation. Specifically, LaST0.5 learns a compact interaction-centric latent space under the supervision of visual interaction cues between the robot and the environment. This reasoning space is instantiated as a latent expert that bridges the world expert and the action expert within a Mixture-of-Transformers architecture. Furthermore, LaST0.5 performs adaptive world-to-action transfer by jointly predicting future representations and progress values, using progress consistency to adjust action execution and trigger future resampling. Finally, we pretrain LaST0.5 on a large-scale robotic data corpus comprising over 14k hours of data, establishing interaction-centric physical reasoning as a scalable and effective paradigm. LaST0.5 achieves 99.5% on LIBERO, surpasses the previous state of the art on ten evaluated RLBench tasks, and demonstrates robust long-horizon execution and precise dexterous manipulation in real-world experiments.

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