  Loss landscape analysis is extremely useful for a deeper understanding of the
generalization ability of deep neural network models. In this work, we propose
a layerwise loss landscape analysis where the loss surface at every layer is
studied independently and also on how each correlates to the overall loss
surface. We study the layerwise loss landscape by studying the eigenspectra of
the Hessian at each layer. In particular, our results show that the layerwise
Hessian geometry is largely similar to the entire Hessian. We also report an
interesting phenomenon where the Hessian eigenspectrum of middle layers of the
deep neural network are observed to most similar to the overall Hessian
eigenspectrum. We also show that the maximum eigenvalue and the trace of the
Hessian (both full network and layerwise) reduce as training of the network
progresses. We leverage on these observations to propose a new regularizer
based on the trace of the layerwise Hessian. Penalizing the trace of the
Hessian at every layer indirectly forces Stochastic Gradient Descent to
converge to flatter minima, which are shown to have better generalization
performance. In particular, we show that such a layerwise regularizer can be
leveraged to penalize the middlemost layers alone, which yields promising
results. Our empirical studies on well-known deep nets across datasets support
the claims of this work
