The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples (n{\textrightarrow}$\infty$n{\textrightarrow}$\infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled examples (n{\textrightarrow}1n{\textrightarrow}1), like humans seem able to do. We propose an approach to this problem and describe the underlying theory, based on the unsupervised, automatic learning of a {\textquotedblleft}good{\textquotedblright} representation for supervised learning, characterized by small sample complexity. We consider the case of visual object recognition, though the theory also applies to other domains like speech. The starting point is the conjecture, proved in specific cases, that image representations which are invariant to translation, scaling and other transformations can considerably reduce the sample complexity of learning. We prove that an invariant and selective signature can be computed for each image or image patch: the invariance can be exact in the case of group transformations and approximate under non-group transformations. A module performing filtering and pooling, like the simple and complex cells described by Hubel and Wiesel, can compute such signature. The theory offers novel unsupervised learning algorithms for {\textquotedblleft}deep{\textquotedblright} architectures for image and speech recognition. We conjecture that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of new objects/images which is invariant to transformations, stable, and selective for recognition{\textemdash}and show how this representation may be continuously learned in an unsupervised way during development and visual experience.

}, keywords = {convolutional networks, Cortex, Hierarchy, Invariance}, doi = {10.1016/j.tcs.2015.06.048}, url = {http://www.sciencedirect.com/science/article/pii/S0304397515005587}, author = {F. Anselmi and JZ. Leibo and Lorenzo Rosasco and Jim Mutch and Andrea Tacchetti and Tomaso Poggio} } @article {443, title = {Computational role of eccentricity dependent cortical magnification.}, number = {017}, year = {2014}, month = {06/2014}, abstract = {We develop a sampling extension of M-theory focused on invariance to scale and translation. Quite surprisingly, the theory predicts an architecture of early vision with increasing receptive field sizes and a high resolution fovea {\textemdash} in agreement with data about the cortical magnification factor, V1 and the retina. From the slope of the inverse of the magnification factor, M-theory predicts a cortical {\textquotedblleft}fovea{\textquotedblright} in V1 in the order of 40 by 40 basic units at each receptive field size {\textemdash} corresponding to a foveola of size around 26 minutes of arc at the highest resolution, ≈6 degrees at the lowest resolution. It also predicts uniform scale invariance over a fixed range of scales independently of eccentricity, while translation invariance should depend linearly on spatial frequency. Bouma{\textquoteright}s law of crowding follows in the theory as an effect of cortical area-by-cortical area pooling; the Bouma constant is the value expected if the signature responsible for recognition in the crowding experiments originates in V2. From a broader perspective, the emerging picture suggests that visual recognition under natural conditions takes place by composing information from a set of fixations, with each fixation providing recognition from a space-scale image fragment {\textemdash} that is an image patch represented at a set of increasing sizes and decreasing resolutions.

}, keywords = {Invariance, Theories for Intelligence}, author = {Tomaso Poggio and Jim Mutch and Leyla Isik} } @proceedings {387, title = {Unsupervised Learning of Invariant Representations in Hierarchical Architectures.}, year = {2013}, month = {11/2013}, abstract = {Representations that are invariant to translation, scale and other transformations, can considerably reduce the sample complexity of learning, allowing recognition of new object classes from very few examples {\textendash} a hallmark of human recognition. Empirical estimates of one-dimensional projections of the distribution induced by a group of affine transformations are proven to represent a unique and invariant signature associated with an image. We show how projections yielding invariant signatures for future images can be learned automatically, and updated continuously, during unsupervised visual experience. A module performing filtering and pooling, like simple and complex cells as proposed by Hubel and Wiesel, can compute such estimates. Under this view, a pooling stage estimates a one-dimensional probability distribution. Invariance from observations through a restricted window is equivalent to a sparsity property w.r.t. to a transformation, which yields templates that are a) Gabor for optimal simultaneous invariance to translation and scale or b) very specific for complex, class-dependent transformations such as rotation in depth of faces. Hierarchical architectures consisting of this basic Hubel-Wiesel module inherit its properties of invariance, stability, and discriminability while capturing the compositional organization of the visual world in terms of wholes and parts, and are invariant to complex transformations that may only be locally affine. The theory applies to several existing deep learning convolutional architectures for image and speech recognition. It also suggests that the main computational goal of the ventral stream of visual cortex is to provide a hierarchical representation of new objects which is invariant to transformations, stable, and discriminative for recognition {\textendash} this representation may be learned in an unsupervised way from natural visual experience.

}, keywords = {convolutional networks, Hierarchy, Invariance, visual cortex}, author = {F. Anselmi and JZ. Leibo and Lorenzo Rosasco and Jim Mutch and Andrea Tacchetti and Tomaso Poggio} }