Holographic Feature Representations of Deep Networks

Martin A. Zinkevich, Alex Davies, Dale Schuurmans
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:401-410, 2017.

Abstract

It is often asserted that deep networks learn “features”, traditionally expressed by the ac- tivations of intermediate nodes. We explore an alternative concept by defining features as partial derivatives of model output with re- spect to model parameters—extending a sim- ple yet powerful idea from generalized linear models. The resulting features are not equiva- lent to node activations, and we show that they can induce a holographic representation of the complete model: the network’s output on given data can be exactly replicated by a simple lin- ear model over such features extracted from any ordered cut. We demonstrate useful advan- tages for this feature representation over stan- dard representations based on node activations.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-zinkevich17a, title = {Holographic Feature Representations of Deep Networks}, author = {Zinkevich, Martin A. and Davies, Alex and Schuurmans, Dale}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {401--410}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/zinkevich17a/zinkevich17a.pdf}, url = {https://proceedings.mlr.press/r15/zinkevich17a.html}, abstract = {It is often asserted that deep networks learn “features”, traditionally expressed by the ac- tivations of intermediate nodes. We explore an alternative concept by defining features as partial derivatives of model output with re- spect to model parameters—extending a sim- ple yet powerful idea from generalized linear models. The resulting features are not equiva- lent to node activations, and we show that they can induce a holographic representation of the complete model: the network’s output on given data can be exactly replicated by a simple lin- ear model over such features extracted from any ordered cut. We demonstrate useful advan- tages for this feature representation over stan- dard representations based on node activations.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Holographic Feature Representations of Deep Networks %A Martin A. Zinkevich %A Alex Davies %A Dale Schuurmans %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-zinkevich17a %I PMLR %P 401--410 %U https://proceedings.mlr.press/r15/zinkevich17a.html %V R15 %X It is often asserted that deep networks learn “features”, traditionally expressed by the ac- tivations of intermediate nodes. We explore an alternative concept by defining features as partial derivatives of model output with re- spect to model parameters—extending a sim- ple yet powerful idea from generalized linear models. The resulting features are not equiva- lent to node activations, and we show that they can induce a holographic representation of the complete model: the network’s output on given data can be exactly replicated by a simple lin- ear model over such features extracted from any ordered cut. We demonstrate useful advan- tages for this feature representation over stan- dard representations based on node activations. %Z Reissued by PMLR on 04 October 2026.
APA
Zinkevich, M.A., Davies, A. & Schuurmans, D.. (2017). Holographic Feature Representations of Deep Networks. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:401-410 Available from https://proceedings.mlr.press/r15/zinkevich17a.html. Reissued by PMLR on 04 October 2026.

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