On invariance in hierarchical models
Name
Bouvrie-2014-On invariance.pdf
Size
316.02 KB
Format
Adobe PDF
Checksum (MD5)
7292e3ea1499340de63c9547cf894fd0
Author(s)
Bouvrie, Jacob Vincent
Rosasco, Lorenzo Andrea
Poggio, Tomaso A.
Date Issued
2009
Journal
Advances in Neural Information Processing Systems (NIPS)
Publisher
Neural Information Processing Systems Foundation
Citation
Bouvrie, Jake, Lorenzo Rosasco, and Tomaso Poggio. "On invariance in Hierarchical models." Advances in Neural Information Processing 22 (NIPS 2009).
Version
Final published version
Abstract
A goal of central importance in the study of hierarchical models for object recognition -- and indeed the visual cortex -- is that of understanding quantitatively the trade-off between invariance and selectivity, and how invariance and discrimination properties contribute towards providing an improved representation useful for learning from data. In this work we provide a general group-theoretic framework for characterizing and understanding invariance in a family of hierarchical models. We show that by taking an algebraic perspective, one can provide a concise set of conditions which must be met to establish invariance, as well as a constructive prescription for meeting those conditions. Analyses in specific cases of particular relevance to computer vision and text processing are given, yielding insight into how and when invariance can be achieved. We find that the minimal sets of transformations intrinsic to the hierarchical model needed to support a particular invariance can be clearly described, thereby encouraging efficient computational implementations.
MIT Department
Massachusetts Institute of Technology. Center for Biological & Computational Learning
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
McGovern Institute for Brain Research at MIT
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://papers.nips.cc/paper/3732-on-invariance-in-hierarchical-models
