---
author:
- |
    Xuchan Bao, James Lucas, Sushant Sachdeva, Roger Grosse\
    University of Toronto; Vector Institute\
    `{jennybao,jlucas,sachdeva,bellkathy@example.com`\
bibliography:
- 'references.bib'
title: 'Regularized linear autoencoders recover the principal components, eventually'
---

Broader Impact {#broader-impact .unnumbered}
==============

The contribution of this work is the theoretical understanding of learning the optimal representations in LAEs with gradient-based optimizers. We believe that the discussion of broader impact is not applicable to this work.

We thank Jonathan Bloom, Richard Zemel, Juhan Bae and Cem Anil for helpful discussions.

XB is supported by a Natural Sciences and Engineering Research council (NSERC) Discovery Grant. JL is supported by grants from NSERC and Samsung. SS's research is supported in part by an NSERC Discovery grant. RG acknowledges support from the CIFAR Canadian AI Chairs program. Part of this research was conducted when SS and RG were visitors at the Special year on Optimization, Statistics, and Theoretical Machine Learning at the School of Mathematics, Institute for Advanced Study, Princeton.

{'source': 'arXiv_out/2007'}