Convergence with misspecified ICA nonlinearities

Characterize the convergence behavior of the equivariant online ICA algorithm and its population mean dynamics when the model scores η_j differ from the unknown true source scores, beyond the local stability conditions established for separating equilibria.

Background

The paper proves that correctly specified scores make separating solutions locally stable under suitable regularity assumptions, while also exhibiting stable non-separating equilibria. In practical ICA, however, the true source densities and therefore their scores are unknown, so the algorithm uses chosen model scores instead.

The paper states that the remaining issue is the behavior when the chosen model scores are misspecified. Its local theorem supplies sufficient conditions in some cases but does not resolve the broader convergence question, especially the possibility of convergence to separating versus non-separating equilibria from general initializations.