Prof.  Hengjin  Cai
Wuhan University,  China

Title: Mechanics of Structural Evolution

Abstract:

The engineering ambition of AGI, and beyond it ASI, has outrun its theoretical foundation. We know how to scale models, distribute computation, and optimize losses; we do not yet have a mathematics of what it means for a system to hold structure—to build internal organization out of noise and drive, to defend it against disturbance, to revise it when demand changes, and to do all of this with a standard that is internal to the system rather than supplied by an external objective. Without such a mathematics, “intelligence” remains a performance score, and the safety, stability, and interpretability of increasingly capable systems rest on empirical caution rather than on constraints we can state and verify. This keynote presents a candidate for that missing foundation: a deductive theory of structural evolution, developed in two books—Mathematical Foundations of Canxian Mechanics and The Observer–Observed Dyad—in which the formation of structure is computed from a single object, the Freidlin–Wentzell large-deviation rate functional of the underlying stochastic dynamics,

I_cx^[0,T][γ] = (1/4ε) ∫_0^T ‖ γ̇_t − b(γ_t) ‖² dt

the cost every adaptive system implicitly assigns to every path it could take.

The theoretical construction is complete in the following sense. First, the functional is not one of many descriptions but the common source of five bodies of theory that live apart in the literature—the Girsanov density (path-level surprise), damage registration (fidelity of internal recording), the c-theorem (monotone relative-entropy decay), the Landauer bound (thermodynamic floor of erasure), and the instanton (most probable transition path)—proven, by the Five-Face Theorem, to be five contractions of one object. Second, the framework is erected on a three-tier ladder of dynamics—continuous diffusion, discrete jump processes, and piecewise-deterministic Markov processes—joined by explicit limits, and docked onto the Hodgkin–Huxley neuron natively at the PDMP rung, with 44 reproducible numerical projects, fixed seeds, and a tagging discipline in which every claim is labeled proved, assumed, conjectured, or named, and every conjecture carries a pre-registered Kill condition. Third, the same machinery is turned from the system to the observer: the object of the theory becomes the observer–observed dyad, carried by six phenomenological equations, in which privacy is quantified as a positive geometric dimension (the degrees of freedom observation leaves behind), subjectivity follows from an orthogonal decomposition rather than from information loss, and the normative standard of the system is set by its own escape history in a closed loop of pressure, learning, fatigue, and standards.

What emerges is a checkable statement of the price of structure: what any finite observer—a cortical circuit or a trained model—can and cannot read is quantifiable, the structure it keeps is the structure it can defend against its own noise, and the mechanics of paying that price, continuously, is the mechanics of structural evolution that an engineered intelligence must implement by design rather than acquire by accident.

Keywords: AGI theory; large deviations; rate functionals; structure formation; observer–observed dyad; compression; reproducibility.

Biography: