Optimized memory usage and management is crucial to the overall performance of a neural network (NN) or deep neural network (DNN) computing environment. Using various characteristics of the input data dimension, an apportionment sequence is calculated for the input data to be processed by the NN or DNN that optimizes the efficient use of the local and external memory components. The apportionment sequence can describe how to parcel the input data (and its associated processing parameters—e.g., processing weights) into one or more portions as well as how such portions of input data (and its associated processing parameters) are passed between the local memory, external memory, and processing unit components of the NN or DNN. Additionally, the apportionment sequence can include instructions to store generated output data in the local and/or external memory components so as to optimize the efficient use of the local and/or external memory components.