Dance motion combines slowly varying body configurations with rapid local movements. We investigate how explicit temporal-frequency decomposition can guide the temporal resolution and codebook capacity of discrete motion representations. We introduce frequency-factorized motion tokenization (FFMT), which separates root-relative motion into a low-frequency choreographic scaffold and a complementary high-frequency residual. FFMT uses a lower token rate and a smaller codebook for the low-frequency component, and a higher token rate and a larger codebook for the high-frequency residual. This representation further induces a plan-then-articulate autoregressive factorization: low-frequency tokens establish coarse choreography, while high-frequency tokens realize local motion details conditioned on the generated plan and music. Experiments on AIST++ and FineDance show strong distributional fidelity while preserving realistic diversity and music--motion synchronization. Ablations consistently support frequency factorization, asymmetric temporal allocation, and low-to-high conditioning.
Sampling and selection spend test-time compute inside a candidate pool, but they cannot recover a correct answer that never enters it. We introduce ValueFormation, a test-time policy that decides after each primary-model draw whether to stop, continue sampling, or acquire one proposal from a heterogeneous reasoning specialist. The three actions are compared on one cost-regularized value scale learned from vote-state features; the calibration is frozen across tasks and primary models, and acquired proposals are accepted only through a frozen posterior comparison. On held-out MATH-500, one Llama-fitted calibration improves over the strongest of eight identically evaluated baselines by more than fifteen points for each of three 8B primaries and transfers unchanged to Qwen3-14B. Removing acquisition lowers Llama MATH accuracy by 20.43 points, while same-trace and same-access replays attribute the gain to state-conditioned acquisition rather than specialist access alone. Where primary coverage is high, as on GSM8K, acquisition is rare and gains mainly come from cheaper allocation; on MBPP, a fixed code route attains the top accuracy at the lowest interaction cost. Varying the token price monotonically reduces calls without retraining.