From data to functa: Your data point is a function and you can treat it like one

Emilien Dupont, Hyunjik Kim, S. M. Ali Eslami, Danilo Jimenez Rezende, Dan Rosenbaum
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:5694-5725, 2022.

Abstract

It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-dupont22a, title = {From data to functa: Your data point is a function and you can treat it like one}, author = {Dupont, Emilien and Kim, Hyunjik and Eslami, S. M. Ali and Rezende, Danilo Jimenez and Rosenbaum, Dan}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {5694--5725}, 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/dupont22a/dupont22a.pdf}, url = {https://proceedings.mlr.press/v162/dupont22a.html}, abstract = {It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification.} }
Endnote
%0 Conference Paper %T From data to functa: Your data point is a function and you can treat it like one %A Emilien Dupont %A Hyunjik Kim %A S. M. Ali Eslami %A Danilo Jimenez Rezende %A Dan Rosenbaum %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-dupont22a %I PMLR %P 5694--5725 %U https://proceedings.mlr.press/v162/dupont22a.html %V 162 %X It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an image. A powerful continuous alternative is then to represent these measurements using an implicit neural representation, a neural function trained to output the appropriate measurement value for any input spatial location. In this paper, we take this idea to its next level: what would it take to perform deep learning on these functions instead, treating them as data? In this context we refer to the data as functa, and propose a framework for deep learning on functa. This view presents a number of challenges around efficient conversion from data to functa, compact representation of functa, and effectively solving downstream tasks on functa. We outline a recipe to overcome these challenges and apply it to a wide range of data modalities including images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We demonstrate that this approach has various compelling properties across data modalities, in particular on the canonical tasks of generative modeling, data imputation, novel view synthesis and classification.
APA
Dupont, E., Kim, H., Eslami, S.M.A., Rezende, D.J. & Rosenbaum, D.. (2022). From data to functa: Your data point is a function and you can treat it like one. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:5694-5725 Available from https://proceedings.mlr.press/v162/dupont22a.html.

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