Boolean deep-layered machines — networks where every node computes an arbitrary function of all nodes below it — exhibit an exponential bias toward simple outputs as depth increases. The distribution of input-output maps concentrates around low-complexity functions not because of any regularization or training objective, but because the combinatorial structure of deep composition naturally funnels the space of possible maps. More layers mean more ways for distinct inputs to collide into the same output, and simple outputs have astronomically more pre-images than complex ones.
This matters beyond the specific architecture. The finding reframes simplicity bias not as a training artifact or an inductive prior imposed by human engineers, but as a geometric property of depth itself. Any system that processes information through successive layers of nonlinear transformation will, by the statistics of composition, prefer outputs that can be described with fewer bits. The deeper the pipeline, the steeper the preference.
The structural principle is that depth functions as a natural Occam's razor — not by penalizing complexity, but by making it exponentially unlikely. Simplicity emerges not because it is selected for, but because the space of deep transformations is shaped so that complexity has almost nowhere to stand.
(arXiv:2603.01217)