  This paper presents a storage-efficient learning model titled Recursive
Binary Neural Networks for sensing devices having a limited amount of on-chip
data storage such as < 100's kilo-Bytes. The main idea of the proposed model is
to recursively recycle data storage of synaptic weights (parameters) during
training. This enables a device with a given storage constraint to train and
instantiate a neural network classifier with a larger number of weights on a
chip and with a less number of off-chip storage accesses. This enables higher
classification accuracy, shorter training time, less energy dissipation, and
less on-chip storage requirement. We verified the training model with deep
neural network classifiers and the permutation-invariant MNIST benchmark. Our
model uses only 2.28 bits/weight while for the same data storage constraint
achieving ~1% lower classification error as compared to the conventional
binary-weight learning model which yet has to use 8 to 16 bit storage per
weight. To achieve the similar classification error, the conventional binary
model requires ~4x more data storage for weights than the proposed model.
