Geodesics of Learned Representations
Abstract
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional subspace. Given two reference images (typically, differing by some transformation), we synthesize a sequence of images lying on a path between them that is of minimal length in the space of the representation (a "representational geodesic"). If the transformation relating the two reference images is linearized by the representation, this sequence should follow the gradual evolution of this transformation. We use this method to assess the invariance properties of a state-of-the-art image classification network and find that geodesics generated for image pairs differing by translation, rotation, and dilation do not evolve according to their associated transformations. Our method also suggests a remedy for these failures, and following this prescription, we show that the modified representation is able to linearize a variety of geometric image transformations.
Cite
Text
Hénaff and Simoncelli. "Geodesics of Learned Representations." International Conference on Learning Representations, 2016.Markdown
[Hénaff and Simoncelli. "Geodesics of Learned Representations." International Conference on Learning Representations, 2016.](https://mlanthology.org/iclr/2016/henaff2016iclr-geodesics/)BibTeX
@inproceedings{henaff2016iclr-geodesics,
title = {{Geodesics of Learned Representations}},
author = {Hénaff, Olivier J. and Simoncelli, Eero P.},
booktitle = {International Conference on Learning Representations},
year = {2016},
url = {https://mlanthology.org/iclr/2016/henaff2016iclr-geodesics/}
}