Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multi-dimensional function. From this point of view, this form of learning is closely related to regularization theory, and we have previously shown (Poggio and Girosi, 1990a, 1990b) the equivalence between reglilari at.ioll and a. class of three-layer networks that we call regularization networks.

The problem of learning is arguably at the very core of the problem of intelligence, both biological and artificial. In this article, we review our work over the last 10 years in the area of supervised learning, focusing on three interlinked directions of research--(1) theory, (2) engineering applications (making intelligent software), and (3) neuroscience (understanding the brain's mechanisms of learnings)--that contribute to and complement each other. Because seeing is intelligence, learning is also becoming a key to the study of artificial and biological vision. In the last few years, both computer vision--which attempts to build machines that see--and visual neuroscience--which aims to understand how our visual system works--are undergoing a fundamental change in their approaches. Visual neuroscience is beginning to focus on the mechanisms that allow the cortex to adapt its circuitry and learn a new task.

The figure shows an ideal continuous loop from theory to feasibility understanding the problem of intelligence. In reality, the learning is also becoming a key to the study of interactions--as one might expect--are less artificial and biological vision. For example in years, both computer vision--which attempts 1990, ideas from the mathematics of learning to build machines that see--and visual neuroscience--which theory--radial basis function networks--suggested aims to understand how our a model for biological object recognition visual system works--are undergoing a fundamental that led to the physiological experiments change in their approaches. Visual neuroscience in cortex described later in the article. It was is beginning to focus on the mechanisms only later that the same idea found its way into that allow the cortex to adapt its the computer graphics applications described circuitry and learn a new task. In this article, we concentrate on one aspect of Vision systems that learn and adapt represent learning: supervised learning.

Learning a map from an input set to an output set is similar to the problem of reconstructing hypersurfaces from sparse data (Poggio and Girosi, 1990). In this framework, we discuss the problem of automatically selecting "minimal" surface data. The objective is to be able to approximately reconstruct the surface from the selected sparse data. We show that this problem is equivalent to the one of compressing information by data removal and the one oflearning how to teach. Our key step is to introduce a process that statistically selects the data according to the model. During the process of data selection (learning how to teach) our system (teacher) is capable of predicting the new surface, the approximated one provided by the selected data.

Learning a map from an input set to an output set is similar to the problem of reconstructing hypersurfaces from sparse data (Poggio and Girosi, 1990). In this framework, we discuss the problem of automatically selecting "minimal" surface data. The objective is to be able to approximately reconstruct the surface from the selected sparse data. We show that this problem is equivalent to the one of compressing information by data removal and the one oflearning how to teach. Our key step is to introduce a process that statistically selects the data according to the model. During the process of data selection (learning how to teach) our system (teacher) is capable of predicting the new surface, the approximated one provided by the selected data.

Marques Pereira Dipartimento di Informatica Universita di Trento Via Inama 7, Trento, TN 38100 ITALY Abstract Learning a map from an input set to an output set is similar to the problem ofreconstructing hypersurfaces from sparse data (Poggio and Girosi, 1990). In this framework, we discuss the problem of automatically selecting "minimal"surface data. The objective is to be able to approximately reconstruct the surface from the selected sparse data. We show that this problem is equivalent to the one of compressing information by data removal andthe one oflearning how to teach. Our key step is to introduce a process that statistically selects the data according to the model. During the process of data selection (learning how to teach) our system (teacher) is capable of predicting the new surface, the approximated one provided by the selected data.

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

Bruno Caprile I.R.S.T. Povo, Italy, 38050 Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.