Standard quantization places levels on a uniform grid. ICRB-Q places them on geodesics of the Fisher-Rao statistical manifold — the Riemannian manifold (M, g_F) where the metric tensor is the Fisher information. This means:
High-Fisher-curvature regions (where small weight changes cause large output changes) get exponentially denser levels.
Low-curvature, "flat" regions (e.g. many heads in early transformer layers) get coarse 2-bit or 3-bit quantization automatically.
The codebook construction reduces to solving: place 2^b points in parameter space to minimize expected geodesic distance from any weight to its nearest level.
This strictly generalizes AWQ's per-channel scaling (which is a zero-order approximation to this manifold geometry) and GPTQ's second-order correction (which is a local linearization).
