Exact capacity of the \emph{wide} hidden layer treelike neural networks with generic activations

Recent progress in studying \emph{treelike committee machines} (TCM) neural networks (NN) in \cite{Stojnictcmspnncaprdt23,Stojnictcmspnncapliftedrdt23,Stojnictcmspnncapdiffactrdt23} showed that the Random Duality Theory (RDT) and its a \emph{partially lifted}(pl RDT) variant are powerful tools that can be used for very precise networks capacity analysis. Here, we consider \emph{wide} hidden layer networks and uncover that certain aspects of numerical difficulties faced in \cite{Stojnictcmspnncapdiffactrdt23} miraculously disappear. In particular, we employ recently developed \emph{fully lifted} (fl) RDT to characterize the \emph{wide} ($d\rightarrow \infty$) TCM nets capacity. We …

analysis capacity cond-mat.dis-nn cs.it cs.lg hidden layer machines math.it math.pr networks neural networks progress random stat.ml studying theory tools