  Dense nets are an integral part of any classification and regression problem.
Recently, these networks have found a new application as solvers for known
representations in various domains. However, one crucial issue with dense nets
is it's feature interpretation and lack of reproducibility over multiple
training runs. In this work, we identify a basis collapse issue as a primary
cause and propose a modified loss function that circumvents this problem. We
also provide a few general guidelines relating the choice of activations to
loss surface roughness and appropriate scaling for designing low-weight dense
nets. We demonstrate through carefully chosen numerical experiments that the
basis collapse issue leads to the design of massively redundant networks. Our
approach results in substantially concise nets, having $100 \times$ fewer
parameters, while achieving a much lower $(10\times)$ MSE loss at scale than
reported in prior works. Further, we show that the width of a dense net is
acutely dependent on the feature complexity. This is in contrast to the
dimension dependent width choice reported in prior theoretical works. To the
best of our knowledge, this is the first time these issues and contradictions
have been reported and experimentally verified. With our design guidelines we
render transparency in terms of a low-weight network design. We share our codes
for full reproducibility available at
https://github.com/smjtgupta/Dense_Net_Regress.
