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Weight-sharing is one of the pillars behind Convolutional Neural Networks andtheir successes. However, in physical neural systems such as the brain,weight-sharing is implausible. This discrepancy raises the fundamental questionof whether weight-sharing is necessary. If so, to which degree of precision? Ifnot, what are the alternatives? The goal of this study is to investigate thesequestions, primarily through simulations where the weight-sharing assumption isrelaxed. Taking inspiration from neural circuitry, we explore the use of FreeConvolutional Networks and neurons with variable connection patterns. UsingFree Convolutional Networks, we show that while weight-sharing is a pragmaticoptimization approach, it is not a necessity in computer vision applications.Furthermore, Free Convolutional Networks match the performance observed instandard architectures when trained using properly translated data (akin tovideo). Under the assumption of translationally augmented data, FreeConvolutional Networks learn translationally invariant representations thatyield an approximate form of weight sharing.

Learning in the Machine: To Share or Not to Share?