  State-of-the-art neural network architectures continue to scale in size and
deliver impressive generalization results, although this comes at the expense
of limited interpretability. In particular, a key challenge is to determine
when to stop training the model, as this has a significant impact on
generalization. Convolutional neural networks (ConvNets) comprise
high-dimensional feature spaces formed by the aggregation of multiple channels,
where analyzing intermediate data representations and the model's evolution can
be challenging owing to the curse of dimensionality. We present channel-wise
DeepNNK (CW-DeepNNK), a novel channel-wise generalization estimate based on
non-negative kernel regression (NNK) graphs with which we perform local
polytope interpolation on low-dimensional channels. This method leads to
instance-based interpretability of both the learned data representations and
the relationship between channels. Motivated by our observations, we use
CW-DeepNNK to propose a novel early stopping criterion that (i) does not
require a validation set, (ii) is based on a task performance metric, and (iii)
allows stopping to be reached at different points for each channel. Our
experiments demonstrate that our proposed method has advantages as compared to
the standard criterion based on validation set performance.
