The Forward/Inverse Duality of Controlled Emergence:A Computational Design Program from Explanation to Engineering

Hao Li, Minghui Ren, Shaowen Lu

The macroscopic capabilities of intelligent systems arise from the local interactions of many simple units. When such systems are deployed in the real world, their behaviour must nevertheless be constrained, leaving designers caught between releasing adaptability and preventing loss of control, yet without formal tools to resolve the dilemma. This paper proposes a unified research program for controlled emergence that restates this tension as a pair of dual problems: the forward problem explains macroscopic behaviour from local rules, and the inverse problem solves for controllable rules and readout mechanisms from a desired target. We take an augmented quintuple as the formal object shared by both ends, and decompose ``engineering'' into three independently measurable coordinates: controllability, reproducibility, and degree of formalizability. On this basis we give three testable working hypotheses (critical scale; the cooperation and trade-off between constraint and adaptability; minimal constraint) and one feasibility criterion, which reduce inverse design from unconstrained optimization to interval checking. The program takes explicit failure boundaries as its premise, does…