Machine Learning and the Curse of Highly-Variable Functions Yoshua Bengio Université de Montréal Computer Science This is an introductory talk about fundamental concepts in machine learning and in recent machine learning research. After reviewing the basic idea of generalization and exploiting similarity to do so, we focus on a long-standing challenge, formerly called the curse of dimensionality. We regard it instead as the difficulty of learning highly-variable functions, the kind of complex high-dimensional functions that are probably necessary to capture the complicated structures in music and other AI tasks. We discuss the notion of distributed representation to efficiently represent complex inputs, and give the example of learning an embedding for symbols, which has been extremely successful in modeling natural language symbolic sequences. We close with a few words on a new brain-inspired approach that promises a breakthrough in learning highly-variable functions: deep architectures.