Analytic Network Learning
arXiv:1811.08227
Abstract
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of the multilayer network can be derived. By exploiting into the vast number of feasible solutions of these interdependent weight matrices, the learning can be performed analytically layer by layer without needing of gradient computation after an initialization. Possible initialization schemes include utilizing the data matrix as initial weights and random initialization. The study is followed by an investigation into the representation capability and the output variance of the learning scheme. An extensive experimentation on synthetic and real-world data sets validates its numerical feasibility.
arXiv commentSome of the preliminary ideas of this work has been presented in the IEEE/ACIS 17th International Conference on Computer and Information Science: "Learning from the kernel and the range space" (ICIS 2018)
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