Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory.
In an earlier post I mentioned that one goal of the new introductory curriculum at Carnegie Mellon is to teach parallelism as the general case of computing, rather than an esoteric, specialized subject for advanced students. Many people are incredulous when I tell them this, because it immediately conjures in their mind the myriad complexities…
The program focused on the following four themes:
- Optimization: How and why can deep models be fit to observed (training) data?
- Generalization: Why do these trained models work well on similar but unobserved (test) data?
- Robustness: How can we analyze and improve the performance of these models when applied outside their intended conditions?
- Generative methods: How can deep learning be used to model probability distributions?
This program aims to reunite researchers across disciplines that have played a role in developing the theory of reinforcement learning. It will review past developments and identify promising directions of research, with an emphasis on addressing existing open problems, ranging from the design of efficient, scalable algorithms for exploration to how to control learning and planning. It also aims to deepen the understanding of model-free vs. model-based learning and control, and the design of efficient methods to exploit structure and adapt to easier environments.
R. Sharipov. (2004)cite arxiv:math/0412421Comment: The textbook, AmSTeX, 132 pages, amsppt style, prepared for double side printing on letter size paper.