SpatialPC: Deep Computation with Sublinear Local Credit Propagation

arXiv:2610.36139v1 Announce Type: new Abstract: On a chain of $N$ states, any local learning rule with bounded communication range needs $\Theta(N)$ rounds before the loss can influence the earliest parameters, and this latency is usually attributed to depth. We show that it is a property of the communication geometry rather than of depth. For $N=m^d$ states placed at constant density in $d$ dimensions, a light-cone argument gives an $\Omega(N^{1/d})$ lower bound on the number of bounded-range rounds that any local algorithm needs before its gradient estimates can be sign-correct at every parameter.