  Relu Fully Connected Networks are ubiquitous but uninterpretable because they
fit piecewise linear functions emerging from multi-layered structures and
complex interactions of model weights. This paper takes a novel approach to
piecewise fits by using set operations on individual pieces(parts). This is
done by approximating canonical normal forms and using the resultant as a
model. This gives special advantages like (a)strong correspondence of
parameters to pieces of the fit function(High Interpretability); (b)ability to
fit any combination of continuous functions as pieces of the piecewise
function(Ease of Design); (c)ability to add new non-linearities in a targeted
region of the domain(Targeted Learning); (d)simplicity of an equation which
avoids layering. It can also be expressed in the general max-min representation
of piecewise linear functions which gives theoretical ease and credibility.
This architecture is tested on simulated regression and classification tasks
and benchmark datasets including UCI datasets, MNIST, FMNIST, and CIFAR 10.
This performance is on par with fully connected architectures. It can find a
variety of applications where fully connected layers must be replaced by
interpretable layers.
