Sequential Training of Neural Networks with Gradient Boosting

This paper presents a novel technique based on gradient boosting to train a shallow neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive model where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in $T$ steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of $J$ neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the $T$ partial models and bias are integrated as a single NN with $T \times J$ neurons in the hidden layer. Extensive experiments in classification and regression tasks are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS and SGD. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.