Exploiting Spline Models for the Training of Fully Connected Layers in Neural Network

The fully connected (FC) layer, one of the most fundamental modules in artificial neural networks (ANN), is often considered difficult and inefficient to train due to issues including the risk of overfitting caused by its large amount of parameters. Based on previous work studying ANN from linear spline perspectives, we propose a spline-based approach that eases the difficulty of training FC layers. Given some dataset, we first obtain a continuous piece-wise linear (CPWL) fit through spline methods such as multivariate adaptive regression spline (MARS). Next, we construct an ANN model from the linear spline model and continue to train the ANN model on the dataset using gradient descent optimization algorithms. Our experimental results and theoretical analysis show that our approach reduces the computational cost, accelerates the convergence of FC layers, and significantly increases the interpretability of the resulting model (FC layers) compared with standard ANN training with random parameter initialization followed by gradient descent optimizations.