# Hearing the Shape of a State Space: New Frontiers in Representation Discovery

In this talk, we will explore new frontiers in representation discovery, where agents construct a basis for approximation of functions on a space well-adapted to its nonlinear geometry. For example, most spatial environments contain significant bottlenecks (e.g. doors, elevators, exits) that factor into our daily decision-making. Similarly, discovery of latent structure in collections of images or text documents is also facilitated by a deeper understanding of the geometry of particular document or image spaces.

We will describe an approach to representation discovery where agents construct novel bases by "hearing the shape" of the underlying state space. Formally, the proposed framework builds on recent advances in harmonic analysis, specifically Fourier and wavelet analysis on graphs, which transform spatial and temporal structure to frequency-oriented representations. Efficient algorithms for basis construction involves computational challenges, which will be addressed by sampling, matrix compression, and domain knowledge.

A range of case studies will be presented, including a novel paradigm for solving Markov decision processes where representation and control are learned simultaneously; a novel multiscale wavelet method for clustering of text documents where the topic hierarchy is automatically constructed; and a new compression method for computer graphics based on multiscale analysis of object geometry.

# Speaker Bio

Professor Sridhar Mahadevan is Co-Director of the Autonomous Learning Laboratory at the Department of Computer Science, University of Massachusetts, Amherst. His research interests are in artificial intelligence and machine learning. He is an associate editor of the Journal of Machine Learning Research, and was a tutorial speaker at AAAI 2007, IJCAI 2007, and ICML 2006.