We use a native-decoder intervention—a donor-swap at the velocity level—to characterize the generative roles of individual token positions. Under conditional annealing, token k is bound to flow stage k via suffix masking, so as flow matching refines the trajectory from high- to low-noise stages, each token is trained to contribute at a particular refinement stage. We examine whether the learned tokens acquire distinct, flow-stage-aligned effects and a coarse-to-fine functional progression in action space; here, “coarse-to-fine” denotes the granularity of learned control information along the refinement process, not a prescribed frequency or fixed-basis decomposition.

We use the trained CATok tokenizer checkpoint (K=32, codebook 4096, horizon 20), its MMDiT velocity network v_θ, and its ODE decoder D—the same modules used at inference, not a separately trained prefix decoder. We encode 128 held-out Franka action chunks (7-DoF + gripper) as Q = (q₁, …, q_K). For each token k, we replace its embedding with the same-position embedding from a donor chunk—keeping the intervention within the slot’s empirical distribution—while holding x_t, t, and the noise realization fixed, so the resulting change isolates token k’s effect on the velocity prediction. Because conditional annealing masks token k outside its active range, we normalize its effect within that range.

• Schedule-consistent support. Token k is visible only for t < (k+1)/K, consistent with the suffix-masking schedule κ(t) = tK.
• Stage-specific peaks. Each token’s peak influence occurs near its assigned stage t* ≈ k/K, with corr(k, t*) = 0.985 (0.995 after grouping). Early tokens peak at high-noise (coarse) stages and late tokens at low-noise (fine) stages, so token effects are distinct and aligned with their assigned flow stages rather than interchangeable.