Multi-Scaling Laws for Embodied Intelligence: A Conjecture on Nested Power-Law Relationships in Dexterous Manipulation

We propose the Multi-Scaling Law conjecture: performance in dexterous manipulation follows nested power-law relationships (N −α) β rather than simple scaling N −α. This arises from (1) exponential contact mode growth, (2) hierarchical skill compounding, and (3) multimodal super-linear synergies. Preliminary VLA training shows multiplicative interactions and task-dependent exponents supporting this hypothesis. If confirmed, multi-scaling laws would reshape data collection, compute allocation, and architecture design for robotic foundation models.