  The success of deep neural networks has inspired many to wonder whether other
learners could benefit from deep, layered architectures. We present a general
framework called forward thinking for deep learning that generalizes the
architectural flexibility and sophistication of deep neural networks while also
allowing for (i) different types of learning functions in the network, other
than neurons, and (ii) the ability to adaptively deepen the network as needed
to improve results. This is done by training one layer at a time, and once a
layer is trained, the input data are mapped forward through the layer to create
a new learning problem. The process is then repeated, transforming the data
through multiple layers, one at a time, rendering a new dataset, which is
expected to be better behaved, and on which a final output layer can achieve
good performance. In the case where the neurons of deep neural nets are
replaced with decision trees, we call the result a Forward Thinking Deep Random
Forest (FTDRF). We demonstrate a proof of concept by applying FTDRF on the
MNIST dataset. We also provide a general mathematical formulation that allows
for other types of deep learning problems to be considered.
