The probabilistic feedforward neural network language model has been proposed. It consists of input, projection, hidden and output layers. At the input layer, N previous words are encoded using 1-of-V coding, where V is size of the vocabulary. The input layer is then projected to a projection layer P that has dimensionality ND, using a shared projection matrix. As only N inputs are active at any given time, composition of the projection layer is a relatively cheap operation. The NNLM architecture becomes complex for computation between the projection and the hidden layer, as values in the projection layer are dense. For a common choice of N = 10, the size of the projection layer (P) might be 500 to 2000, while the hidden layer size H is typically 500 to 1000 units. Moreover, the hidden layer is used to compute probability distribution over all the words in the vocabulary, resulting in an output layer with dimensionality V. Thus, the computational complexity per each training example is Q = ND + NDH + HV; where the dominating term is HV. However, several practical solutions were proposed for avoiding it; either using hierarchical versions of the softmax, or avoiding normalized models completely by using models that are not normalized during training. With binary tree representations of the vocabulary, the number of output units that need to be evaluated can go down to around log2(V). Thus, most of the complexity is caused by the term NDH. … Feedforward Neural Network Language Model (NNLM)

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