Neural networks can be viewed as sets of functions, and these sets contain natural submodels—for instance, versions of the network where some hidden neurons are switched off. The authors of a new arXiv preprint ask whether networks, during training, prefer to settle into such submodels. Their answer, based on geometric analysis, is mostly no.
For shallow multilayer perceptrons, they prove that local minimizers never lie in submodels with inactive hidden neurons. For deep MLPs, they give conditions that rule out such submodels as well. The picture is slightly more nuanced for a simplified self-attention architecture: lower-rank submodels are generally avoided, but the authors identify specific cases where they are preferred because those submodels sit on the boundary of the full model.
The paper concludes that, apart from these boundary exceptions, submodel preference cannot be explained purely by the geometry of the neural model. Instead, the effect must arise from other sources, such as the training dynamics themselves. That shifts the question from "where do minimizers live?" to "how does optimization steer networks toward simpler internal structures?"