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Linear layers in neural networks (NNs) trained by gradient descent can beexpressed as a key-value memory system which stores all training datapoints andthe initial weights, and produces outputs using unnormalised dot attention overthe entire training experience. While this has been technically known since the1960s, no prior work has effectively studied the operations of NNs in such aform, presumably due to prohibitive time and space complexities and impracticalmodel sizes, all of them growing linearly with the number of training patternswhich may get very large. However, this dual formulation offers a possibilityof directly visualising how an NN makes use of training patterns at test time,by examining the corresponding attention weights. We conduct experiments onsmall scale supervised image classification tasks in single-task, multi-task,and continual learning settings, as well as language modelling, and discusspotentials and limits of this view for better understanding and interpretinghow NNs exploit training patterns. Our code is public.

The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention