PIN Architecture v2 - A Geometric Framework for Model Compression via Co-Designed Quotient Structure

PIN describes a family of neural architectures in which a model's weights are tied across the orbits of a finite group G, so that the deployed model is a compact quotient B rather than the full parameter set A. Version 1.1 presented PIN primarily as a compression technique applied to existing models, supported by a geometric argument for constant-time inference. This revision reverses that emphasis. Empirical testing shows that retrofitting a fold onto a conventionally trained network is lossy and inferior, while co-designing the network around a chosen G (the alternative proposed in v1.1 §7.2 as an aside) is both more accurate and cheaper to produce. The constant-depth inference claim is withdrawn in its original form: the geometric argument supporting it contains a codimension error, and every mechanism derived from it fails under direct measurement. A corrected form survives and is stronger: constraining the activation space to k spectral components makes traversal depth ≤ k by construction, with no reliance on high-dimensional concentration.