High-dimensional neural feature design for layer-wise reduction of training cost

Alireza M. Javid, Arun Venkitaraman, Mikael Skoglund, and Saikat Chatterjee

Abstract: We design a rectified linear unit-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 ℓ2-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.