Invited talks

Tomaso Poggio
Massachusetts Institute of Technology


Towards A Theory Of The Visual Cortex And Of Deep Convolutional Architectures


Primate visual cortex has a long record of good performance in several visual tasks relevant for robotics. Learning networks with a qualitatively similar hierarchical architectures, called Deep Convolutional Networks, have recently achieved very good performance in object recognition and other vision tasks. Ironically, our understanding of why they work so well is not better than of why visual cortex sees so well. This is the motivation for working on a theory based on the hypothesis that invariant and selective representations of images are the main computational goal of the ventral stream in visual cortex. Invariant representations can be proved to lead to lower sample complexity in image recognition. i-theory suggest a biologically plausible simple-complex cells module (HW module) for computing components of an invariant signature. For transformations that have the structure of a locally compact group invariance and selectivity can be proved.

I will describe an extension of i-theory to incorporate not only pooling but also rectifying nonlinearities in an extended HW module (eHW) designed for supervised learning. The two operations roughly correspond to invariance and selectivity, respectively. Under the assumption of normalized inputs, appropriate linear combinations of rectifying nonlinearities are equivalent to radial kernels. If pooling is present an equivalent kernel also exist. Thus present-day DCNs (Deep Convolutional Networks) can be exactly equivalent to a hierarchy of kernel machines with pooling and non-pooling layers. Finally, I will describe a conjecture for theoretically understanding hierarchies of such modules. A main consequence of the conjecture is that hierarchies of eHW modules minimize memory requirements while computing a selective and invariant representation.


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., 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.