Neural networks are trained using gradient descent where the estimate of the error used to update the weights is calculated based on a subset of the training dataset. The number of examples from the training dataset used in the estimate of the error gradient is called the batch size and is an important hyperparameter that […]
Batch normalization is a technique designed to automatically standardize the inputs to a layer in a deep learning neural network. Once implemented, batch normalization has the effect of dramatically accelerating the training process of a neural network, and in some cases improves the performance of the model via a modest regularization effect. In this tutorial, […]
Training deep neural networks with tens of layers is challenging as they can be sensitive to the initial random weights and configuration of the learning algorithm. One possible reason for this difficulty is the distribution of the inputs to layers deep in the network may change after each mini-batch when the weights are updated. This […]
Developing neural networks is often referred to as a dark art. The reason for this is that being skilled at developing neural network models comes from experience. There are no reliable methods to analytically calculate how to design a “good” or “best” model for your specific dataset. You must draw on experience and experiment in […]
The vanishing gradients problem is one example of unstable behavior that you may encounter when training a deep neural network. It describes the situation where a deep multilayer feed-forward network or a recurrent neural network is unable to propagate useful gradient information from the output end of the model back to the layers near the […]
In a neural network, the activation function is responsible for transforming the summed weighted input from the node into the activation of the node or output for that input. The rectified linear activation function or ReLU for short is a piecewise linear function that will output the input directly if it is positive, otherwise, it […]
The training process of neural networks is a challenging optimization process that can often fail to converge. This can mean that the model at the end of training may not be a stable or best-performing set of weights to use as a final model. One approach to address this problem is to use an average […]
Model ensembles can achieve lower generalization error than single models but are challenging to develop with deep learning neural networks given the computational cost of training each single model. An alternative is to train multiple model snapshots during a single training run and combine their predictions to make an ensemble prediction. A limitation of this […]
Supervised learning is challenging, although the depths of this challenge are often learned then forgotten or willfully ignored. This must be the case, because dwelling too long on this challenge may result in a pessimistic outlook. In spite of the challenge, we continue to wield supervised learning algorithms and they perform well in practice. Fundamental […]
Model averaging is an ensemble technique where multiple sub-models contribute equally to a combined prediction. Model averaging can be improved by weighting the contributions of each sub-model to the combined prediction by the expected performance of the submodel. This can be extended further by training an entirely new model to learn how to best combine […]
