High-dimensional Neural Feature Design for Layer-wise Reduction of Training Cost
This work addresses training efficiency for neural network practitioners, offering an incremental improvement by reducing computational overhead through analytical regularization.
The paper tackles the problem of high training costs in multilayer neural networks by designing a ReLU-based architecture that maps features to higher dimensions in each layer, analytically deriving regularization hyperparameters to guarantee monotonic cost reduction and eliminate cross-validation, achieving lower training costs with convex minimization.
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.