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

Kazuki Irie, Róbert Csordás, Jürgen Schmidhuber
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9639-9659, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-irie22a, title = {The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention}, author = {Irie, Kazuki and Csord{\'a}s, R{\'o}bert and Schmidhuber, J{\"u}rgen}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {9639--9659}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/irie22a/irie22a.pdf}, url = {https://proceedings.mlr.press/v162/irie22a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention %A Kazuki Irie %A Róbert Csordás %A Jürgen Schmidhuber %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-irie22a %I PMLR %P 9639--9659 %U https://proceedings.mlr.press/v162/irie22a.html %V 162 %X 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.
APA
Irie, K., Csordás, R. & Schmidhuber, J.. (2022). The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:9639-9659 Available from https://proceedings.mlr.press/v162/irie22a.html.

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