The Spiraling Intelligence Thesis: Intelligence as a Bounded Non-Convergent Trajectory

Most deployed AI systems follow a Train-Freeze-Deploy lifecycle: parameters are optimized offline and then served as a static checkpoint until a new training cycle produces a replacement. This design assumes intelligence can be captured as a fixed point in parameter space, making continual adaptation brittle under distribution shift. This paper advances a different thesis: intelligence is better modeled as a bounded trajectory than as a convergent point. The central object is not a final parameter vector W∗ but an evolving state W(t) whose identity is its history. This study proposes the Spiraling Intelligence Architecture (SIA) as a concrete instantiation, grounded in the Infinite Transformation Principle (ITP): irreversible, history-dependent evolution with recurrent revisitation and self-maintenance. The core mechanism combines (i) Rotational Hebbian Learning (RHL), a drift-inducing complex-valued plasticity rule that separates memories by phase, and (ii) an Autopoietic Sleep Cycle that reorganizes the internal structure without external labels. Through a minimal, reproducible toy simulation, the paper demonstrates the qualitative signature implied by the thesis: under distribution switching, a spiraling learner exhibits bounded non-convergence and recurrent re-alignment peaks for an earlier task, exceeding a convergent baseline that relaxes to a static compromise. The empirical scope is intentionally modest; the contribution is a falsifiable theoretical framing and a minimal mechanism that exhibits the predicted qualitative behaviour.