Generalization error in the spherical perceptron*

The spherical perceptron is a simple linear classifier that can be mapped onto the sphere packing problem. Its analytical solvability has led to extensive research, including precise phase boundary calculations and detailed analyses of the solution space. However, the aspect of generalization error has been largely unexplored due to the absence of a method for incorporating generalizable features. In our research, we quantify the generalization error by directly modeling the data's noise statistics and linking them to the error. Our findings reveal the presence of the double descent phenomenon, which has received much attention lately. Notably, we find that this phenomenon only occurs when the system experiences a jamming transition that maintains replica symmetry. We present numerical and theoretical evidence supporting this observation.