  Monotonic linear interpolation (MLI) - on the line connecting a random
initialization with the minimizer it converges to, the loss and accuracy are
monotonic - is a phenomenon that is commonly observed in the training of neural
networks. Such a phenomenon may seem to suggest that optimization of neural
networks is easy. In this paper, we show that the MLI property is not
necessarily related to the hardness of optimization problems, and empirical
observations on MLI for deep neural networks depend heavily on biases. In
particular, we show that interpolating both weights and biases linearly leads
to very different influences on the final output, and when different classes
have different last-layer biases on a deep network, there will be a long
plateau in both the loss and accuracy interpolation (which existing theory of
MLI cannot explain). We also show how the last-layer biases for different
classes can be different even on a perfectly balanced dataset using a simple
model. Empirically we demonstrate that similar intuitions hold on practical
networks and realistic datasets.
