  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.
