High-dimensional Neural Feature Design for Layer-wise Reduction of Training Cost

• URL: http://arxiv.org/abs/2003.13058v2
• Date: Fri, 21 Aug 2020 21:16:00 GMT
• Title: High-dimensional Neural Feature Design for Layer-wise Reduction of Training Cost
• Authors: Alireza M. Javid, Arun Venkitaraman, Mikael Skoglund, and Saikat Chatterjee
• Abstract summary: We design a ReLU-based multilayer neural network by mapping the feature vectors to a higher dimensional space in every layer. We show that the proposed architecture is norm-preserving and provides an invertible feature vector.
• Score: 47.34374677507664
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We design a ReLU-based multilayer neural network by mapping the feature vectors to a higher dimensional space in every layer. We design the weight matrices in every layer to ensure a reduction of the training cost as the number of layers increases. Linear projection to the target in the higher dimensional space leads to a lower training cost if a convex cost is minimized. An $\ell_2$-norm convex constraint is used in the minimization to reduce the generalization error and avoid overfitting. The regularization hyperparameters of the network are derived analytically to guarantee a monotonic decrement of the training cost, and therefore, it eliminates the need for cross-validation to find the regularization hyperparameter in each layer. We show that the proposed architecture is norm-preserving and provides an invertible feature vector, and therefore, can be used to reduce the training cost of any other learning method which employs linear projection to estimate the target.

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