Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning?

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples (n→∞). The next phase is likely to focus on algorithms capable of learning from very few labeled examples (n → 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 “good” representation for supervised learning, characterized by small sample complexity (n). We consider the case of visual object recognition though the theory applies to other domains. The starting point is the conjecture, proved in specific cases, that image representations which are invariant to translations, scaling and other transformations can considerably reduce the sample complexity of learning. We prove that an invariant and unique (discriminative) signature can be computed for each image patch, I, in terms of empirical distributions of the dot-products between I and a set of templates stored during unsupervised learning. A module performing filtering and pooling, like the simple and complex cells described by Hubel and Wiesel, can compute such estimates. Hierarchical architectures consisting of this basic Hubel-Wiesel moduli inherit its properties of invariance, stability, and discriminability while capturing the compositional organization of the visual world in terms of wholes and parts. The theory extends 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/images which is invariant to transformations, stable, and discriminative for recognition—and that this representation may be continuously learned in an unsupervised way during development and visual experience. This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF 1231216. http://cbmm.mit.edu CBMM Paper March, 2014 1–24 ar X iv :1 31 1. 41 58 v5 [ cs .C V ] 1 1 M ar 2 01 4 Unsupervised learning of invariant representations with low sample complexity: the magic of sensory cortex or a new framework for machine learning? Fabio Anselmi ∗ †, Joel Z. Leibo ∗ , Lorenzo Rosasco ∗ † , Jim Mutch ∗ , Andrea Tacchetti ∗ † , and Tomaso Poggio ∗ † ∗Center for Brains, Minds and Machines, Massachusetts Institute of Technology, Cambridge, MA 02139, and †Istituto Italiano di Tecnologia, Genova, 16163 The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples (n→∞). The next phase is likely to focus on algorithms capable of learning from very few labeled examples (n → 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 “good” representation for supervised learning, characterized by small sample complexity (n). We consider the case of visual object recognition though the theory applies to other domains. The starting point is the conjecture, proved in specific cases, that image representations which are invariant to translations, scaling and other transformations can considerably reduce the sample complexity of learning. We prove that an invariant and unique (discriminative) signature can be computed for each image patch, I, in terms of empirical distributions of the dot-products between I and a set of templates stored during unsupervised learning. A module performing filtering and pooling, like the simple and complex cells described by Hubel and Wiesel, can compute such estimates. Hierarchical architectures consisting of this basic Hubel-Wiesel moduli inherit its properties of invariance, stability, and discriminability while capturing the compositional organization of the visual world in terms of wholes and parts. The theory extends 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/images which is invariant to transformations, stable, and discriminative for recognition—and that this representation may be continuously learned in an unsupervised way during development and visual experience.1 Invariance | Hierarchy | Convolutional networks | Visual cortex It is known that Hubel and Wiesel’s original proposal [1] for visual area V1—of a module consisting of complex cells (C-units) combining the outputs of sets of simple cells (S-units) with identical orientation preferences but differing retinal positions—can be used to construct translationinvariant detectors. This is the insight underlying many networks for visual recognition, including HMAX [2] and convolutional neural nets [3, 4]. We show here how the original idea can be expanded into a comprehensive theory of visual recognition relevant for computer vision and possibly for visual cortex. The first step in the theory is the conjecture that a representation of images and image patches, with a feature vector that is invariant to a broad range of transformations—such as translation, scale, expression of a face, pose of a body, and viewpoint—makes it possible to recognize objects from only a few labeled examples, as humans do. The second step is proving that hierarchical architectures of Hubel-Wiesel (‘HW’) modules (indicated by ∧ in Fig. 1) can provide such invariant representations while maintaining discriminative information about the original image. Each ∧ -module provides a feature vector, which we call a signature, for the part of the visual field that is inside its “receptive field”; the signature is invariant to (R) affine transformations within the receptive field. The hierarchical architecture, since it computes a set of signatures for l=4