CONGR-WAM: DIAGNOSING LOCAL CONFLICTS FOR SPARSE GRADIENT ROUTING IN WORLD ACTION MODELS

Joint World Action Models learn visual dynamics and robot control together, yet global gradient alignment can conceal local conflicts between the two objectives. An analysis of video K/V parameters reveals a stable spatial pattern of conflict across training checkpoints and task suites, while conflict within a given subspace varies across optimizer steps. ConGR-WAM uses this structure to guide sparse gradient routing, separating where to intervene from when to intervene. Offline diagnosis constructs a conflict topology over block-pair subspaces with equal parameter budgets, yielding a sparse intervention subspace selected from gradient evidence through a tail-robust maximin criterion. During training, symmetric projection is applied only when the video and action gradients conflict within the selected subspace. Routing preserves the original gradient sum elsewhere and on nonconflicting steps. Controlled ablations show that routing in the diagnosed subspace outperforms random sparse and dense conditional alternatives, and that conditional activation improves over unconditional projection. On LIBERO and RoboTwin 2.0, ConGR-WAM achieves state-of-the-art performance among comparable World Action Models across single-arm and bimanual manipulation settings. Our project page is available at https://congr-wam-review.pages.dev/