SCAMP: Sparse-Anchor Control Is One Small Projection

A text-to-motion generator turns a sentence into plausible human motion. Text fixes what that motion is, but not where the body must be. Authoring needs sparse anchors: chosen joints, at chosen frames, at given positions. Meeting them cur- rently costs either a conditioning branch trained for the task or hundreds of per- clip optimisation steps in the architecture’s native variables. The problem all this machinery solves is a single small one. In any generator that decodes a continu- ous state through a frozen differentiable decoder, sparse anchors define a residual whose dimension is orders of magnitude below the state’s, and meeting them is one constrained projection: the state nearest the generator’s own output whose decoded motion satisfies the anchors. Our solver, SCAMP (sparse-anchor control as a minimum-norm projection), takes that projection’s first step and continues along it: damped Gauss–Newton in the space of the anchors, through the frozen decoder alone, training-free, with one dimensionless damping constant. Applied unchanged to published generators spanning diffusion, token and latent designs, it matches or exceeds each released control method it is measured against, and closes the anchors on hosts that ship none. Holding the solver fixed turns the com- parison into an experiment on the representation, and the outcome splits along one property of the decoder: how far in time it spreads a change of state. Every gener- ator pays for the correction in foot skating; what differs is how much. A decoder that reconstructs each frame from a window of state spreads the correction over that window, and its mean contact-speed skating stays within a small multiple of the unconstrained generator’s own; an analytic recovery displaces the body itself, and skating multiplies several times over. Widening the temporal basis of the up- date lowers that cost on a frame-local decoder and raises it on one that already spreads a correction. Our generator is built to that criterion: a windowed decoder, trained through the correction, so the state it emits meets its anchors within a shal- low solve at sub-second cost. The decoder’s temporal support is a design criterion for controllable motion generation.