Nonlinear shape–colour resonance as the mechanism limiting global linearisation

Determine whether shape–colour resonance, rather than orbit curvature or non-sharing, is the mechanism that prevents global linearisation of neural colour representations, particularly as phase organisation destabilises in deeper layers.

Background

The paper finds that local, phase-conditioned transporters substantially outperform global operator families on colour orbits. A leave-one-shape-out experiment succeeds at a mid-level site but fails at a deeper site, where phase organisation is less stable. These observations are consistent with a resonance-based explanation in which the interaction between shape and colour makes a single global operator inadequate.

However, the authors explicitly label this interpretation as a hypothesis rather than an established result. The unresolved issue is therefore whether the depth-dependent failure of global linearisation is specifically caused by shape–colour resonance, as opposed to curvature, loss of cross-shape sharing, or another source of representational variation.