The Stabilizer Shrinkage

Blind source separation has two classical routes to identifiability. If sources are non-Gaussian, you can separate them (ICA). If you have diverse observations of the same sources, you can separate them (multi-view methods). These have been treated as fundamentally different principles.

They aren’t. Both are instances of stabilizer shrinkage: the continuous symmetry group of the mixing model — the set of transformations that leave the observations invariant — is reduced by constraints until only finite ambiguity remains. Non-Gaussianity shrinks the stabilizer because Gaussian distributions are the most symmetric (invariant under orthogonal rotations), and any departure from Gaussianity breaks rotational symmetry. Observation diversity shrinks the stabilizer because additional views impose additional invariance constraints that are generically incompatible with continuous symmetries.

The through-claim: identifiability in BSS is not about the sources or the observations per se — it’s about how much symmetry survives. The two classical routes are orthogonal attacks on the same symmetry group. Source statistics break internal symmetries; observation diversity breaks external symmetries. The identifiability question reduces to: is the residual stabilizer finite?

This unification reveals a fundamental trade-off: you can have more Gaussian sources if you compensate with more observation diversity, and vice versa. The total identifiability budget is denominated in symmetry reduction, and it doesn’t matter where the reduction comes from.

One principle. Two disguises.