On Invariance in Hierarchical Models
Jake Bouvrie · Lorenzo Rosasco · Tomaso Poggio

Mon Dec 7th 07:00 -- 11:59 PM @ None #None

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.

Author Information

Jake Bouvrie (Massachusetts Institute of Technology)
Lorenzo Rosasco (University of Genova- MIT - IIT)
Tomaso Poggio (MIT)

Tomaso A. Poggio, is the Eugene McDermott Professor in the Dept. of Brain & Cognitive Sciences at MIT and the director of the new NSF Center for Brains, Minds and Machines at MIT of which MIT and Harvard are the main member Institutions. He is a member of both the Computer Science and Artificial Intelligence Laboratory and of the McGovern Brain Institute. He is an honorary member of the Neuroscience Research Program, a member of the American Academy of Arts and Sciences, a Founding Fellow of AAAI and a founding member of the McGovern Institute for Brain Research. Among other honors he received the Laurea Honoris Causa from the University of Pavia for the Volta Bicentennial, the 2003 Gabor Award, the Okawa Prize 2009, the AAAS Fellowship and the 2014 Swartz Prize for Theoretical and Computational Neuroscience. He is one of the most cited computational scientists with contributions ranging from the biophysical and behavioral studies of the visual system to the computational analyses of vision and learning in humans and machines. With W. Reichardt he characterized quantitatively the visuo-motor control system in the fly. With D. Marr, he introduced the seminal idea of levels of analysis in computational neuroscience. He introduced regularization as a mathematical framework to approach the ill-posed problems of vision and the key problem of learning from data. In the last decade he has developed an influential hierarchical model of visual recognition in the visual cortex. The citation for the recent 2009 Okawa prize mentions his “…outstanding contributions to the establishment of computational neuroscience, and pioneering researches ranging from the biophysical and behavioral studies of the visual system to the computational analysis of vision and learning in humans and machines.” His research has always been interdisciplinary, between brains and computers. It is now focused on the mathematics of learning theory, the applications of learning techniques to computer vision and especially on computational neuroscience of the visual cortex. A former Corporate Fellow of Thinking Machines Corporation and a former director of PHZ Capital Partners, Inc., he is a director of Mobileye and was involved in starting, or investing in, several other high tech companies including Arris Pharmaceutical, nFX, Imagen, Digital Persona and Deep Mind. Tomaso Poggio Eugene McDermott Professor Director NSF Science & Technology Center for Brains, Minds and Machines(CBMM) Core founding scientific advisor, MIT Quest for Intelligence McGovern Institute CSAIL (Computer Science and Artificial Intelligence Lab) Brain Sciences Department M.I.T., 46-5177B see 43 Vassar Street Cambridge, MA 02142 E-mail: Phone: 617-253-5230 Fax: 617-253-2964 Web: PoggioLab Web page:

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