  Knowledge Matters: Importance of Prior Information for Optimization [7], by
Gulcehre et. al., sought to establish the limits of current black-box, deep
learning techniques by posing problems which are difficult to learn without
engineering knowledge into the model or training procedure. In our work, we
completely solve the previous Knowledge Matters problem using a generic model,
pose a more difficult and scalable problem, All-Pairs, and advance this new
problem by introducing a new learned, spatially-varying histogram model called
TypeNet which outperforms conventional models on the problem. We present
results on All-Pairs where our model achieves 100% test accuracy while the best
ResNet models achieve 79% accuracy. In addition, our model is more than an
order of magnitude smaller than Resnet-34. The challenge of solving
larger-scale All-Pairs problems with high accuracy is presented to the
community for investigation.
