Source: IAS, 2017
Design of algorithms and machines capable of “intelligent” comprehension and decision making is one of the major scientific and technological challenges of this century.
It is also a challenge for mathematics because it calls for new paradigms for mathematical reasoning, such as formalizing the “meaning” or “information content” of a piece of text or an image or scientific data.
It is a challenge for mathematical optimization because the algorithms involved must scale to very large input sizes. It is a challenge for theoretical computer science because the obvious ways of formalizing many computational tasks in machine learning are provably intractable in a worst-case sense, and thus calls for new modes of analysis.
Related Resource: 2019-2020 Special Year @ IAS
This Special Year will focus on developing the mathematical underpinnings of this field, including machine learning theory, optimization (convex and nonconvex), statistics, graph theoretic algorithms, etc.
It will build upon the extensive frameworks that already exist and create new avenues of research. Connections will be explored to neighboring fields such as big data algorithms, computer vision, natural language processing, neuroscience and biology.
The special year will bring 15-20 visiting researchers to the IAS on visits ranging from a semester to a year. They will organize and participate in activities including discussion groups, seminar series, workshops, and distinguished colloquia. The following is a nonexclusive list of sample research foci.
- Design and analysis of efficient optimization algorithms for any settings arising in machine learning and analysis of large data sets and graphs. The problems in question may be convex, nonconvex, or multi-objective.
- Models and methods for unsupervised learning (i.e., learning with data that has not been labeled by humans), which may leverage ideas from deep learning, statistics, information theory, optimization etc.
- New theory to support recent experimental advances in reinforcement learning, game playing, etc.
- Achieving better understanding of deep learning and related models involving deep nets with memory or attention mechanisms.
The special year will be led by Sanjeev Arora, who holds a dual appointment as Professor of Computer Science at Princeton University and long term visiting professor at the IAS.