In recent years, multiparameter persistent homology (MPH) has been developed to address the limitations of traditional single-parameter persistence. While much progress has been made on the theoretical aspects of MPH, practical applications have mostly been limited to the special case of two parameters. Building on recent developments in the computation of MPH in more than two parameters, we propose and implement a new algorithm for the computation of multiparameter persistence landscapes in this setting. We apply this work to compute landscapes of three-parameter persistence modules built on spatiotemporal data arising in biology.
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The talk is jointly organized by the EPFL AI Center and the EPFL Machine Learning for Biomedicine Lab (MLBIO) as part of the AI Fundamentals seminar series.
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\r\nAgents That Know What They Know: Interpretability and Introspection for Lifelong Learning
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\r\nAbstract
\r\nOne of the hallmarks of intelligence is the ability to learn from experience. In artificial intelligence, we frame this as lifelong learning: autonomous agents that continue to adapt after deployment as they encounter new tasks and environments. In this talk, I will argue that successful lifelong learning agents require a form of introspection: they must be able to reason about the scope and limits of their own knowledge. This self-knowledge allows an agent to answer three fundamental questions. What do I know? When can I reuse what I know? And what do I still need to learn? I will present recent work from my group showing how ideas from interpretability and explainability can surface the knowledge needed to answer these questions. I will first show how learned representations can be used to identify when inputs are novel, enabling out-of-distribution detection. Then, I will discuss how this can be built upon to give agents a way to distinguish between situations where prior knowledge can be safely reused and situations where new learning is needed. Together, this work shows that interpretability is not only a tool for transparency, but a mechanism for building agents that recognize, reuse, and acquire knowledge over time.
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\r\nBio
\r\nJoseph Campbell is an Assistant Professor in the Department of Computer Science at Purdue University, where he leads the Collaborative AI for Machines and People Lab. His research bridges machine learning and robotics, with a focus on explainable machine learning and lifelong learning. Before joining Purdue, he was a Postdoctoral Fellow in the Robotics Institute at Carnegie Mellon University, and he received his Ph.D., M.S., and B.S. degrees from Arizona State University. His research is supported by Amazon, the Toyota Research Institute, and the National Science Foundation.
Stein's Restriction conjecture concerns functions whose Fourier transform is supported on the unit sphere in R^n. Over the decades, progress on this problem has drawn on tools from combinatorics, real algebraic geometry, and other areas. We will survey the development of the conjecture and discuss its recent connections to projection theory.
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