The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention
This work provides a tool for interpreting neural network decisions by connecting test-time predictions to specific training patterns, though it is incremental as it builds on a known but understudied formulation.
The paper revisits the dual form of neural networks, which expresses linear layers as a key-value memory system using attention over training patterns, and demonstrates its application for visualizing how networks utilize training data during test time across small-scale image classification and language modeling tasks.
Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the entire training experience. While this has been technically known since the 1960s, no prior work has effectively studied the operations of NNs in such a form, presumably due to prohibitive time and space complexities and impractical model sizes, all of them growing linearly with the number of training patterns which may get very large. However, this dual formulation offers a possibility of directly visualising how an NN makes use of training patterns at test time, by examining the corresponding attention weights. We conduct experiments on small scale supervised image classification tasks in single-task, multi-task, and continual learning settings, as well as language modelling, and discuss potentials and limits of this view for better understanding and interpreting how NNs exploit training patterns. Our code is public.