Random Projection in Deep Neural Networks

This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve deep models: training neural networks on high-dimensional data and initialization of network parameters. Training deep neural networks (DNNs) on sparse, high-dimensional data with no exploitable structure implies a network architecture with an input layer that has a huge number of weights, which often makes training infeasible. We show that this problem can be solved by prepending the network with an input layer whose weights are initialized with an RP matrix. We propose several modifications to the network architecture and training regime that makes it possible to efficiently train DNNs with learnable RP layer on data with as many as tens of millions of input features and training examples. In comparison to the state-of-the-art methods, neural networks with RP layer achieve competitive performance or improve the results on several extremely high-dimensional real-world datasets. The second area where the application of RP techniques can be beneficial for training deep models is weight initialization. Setting the initial weights in DNNs to elements of various RP matrices enabled us to train residual deep networks to higher levels of performance

Effects of Sparse Initialization in Deep Belief Networks

Deep neural networks are often trained in two phases: first hidden layers are pretrained in an unsupervised manner and then network is fine-tuned with error backpropagation. Pretraining is often carried out using Deep Belief Networks (DBNs), with initial weights set to small random values. However, recent results established that well-designed initialization schemes, e.g. Sparse Initialization (SI), can greatly improve performance of networks that do not use pretraining. An interesting question arising from these results is whether such initialization techniques wouldn't also improve pretrained networks? To shed light on this question, in this work we evaluate SI in DBNs that are used to pretrain discriminative networks. The motivation behind this research is our observation that SI has an impact on the features learned by a DBN during pretraining. Our results demonstrate that this improves network performance: when pretraining starts from sparsely initialized weight matrices networks achieve lower classification error after fine-tuning