Gil Strang: Linear Algebra and Deep Learning

Gil Strang: Linear Algebra and Deep Learning

Author: Daniel Bashir August 17, 2023 Duration: 1:00:36

In episode 86 of The Gradient Podcast, Daniel Bashir speaks to Professor Gil Strang.

Professor Strang is one of the world’s foremost mathematics educators and a mathematician with contributions to finite element theory, the calculus of variations, wavelet analysis, and linear algebra. He has spent six decades teaching mathematics at MIT, where he was the MathWorks Professor of Mathematics. He was among the first MIT faculty members to publish a course on MIT’s OpenCourseware and has since championed both linear algebra education and open courseware.

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Outline:

* (00:00) Intro

* (02:00) Professor Strang’s background and journey into teaching linear algebra

* (04:55) Undergrad interests

* (07:10) Writing textbooks

* (10:20) Prof. Strang’s interests in deep learning

* (11:00) How Professor Strang thought about teaching early on

* (16:20) MIT OpenCourseWare and education accessibility

* (19:50) Prof Strang’s applied/example-based approach to teaching linear algebra and closing the theory-practice gap

* (22:00) Examples!

* (27:20) Orthogonality

* (29:15) Singular values

* (34:40) Professor Strang’s favorite topics in linear algebra

* (37:55) Pedagogical approaches to deep learning, mathematical ingredients of deep learning’s complexity

* (42:04) Generalization and double descent in deep learning, powers and limitations

* (46:20) Did deep learning have to evolve as it did?

* (48:30) Teaching deep learning to younger students

* (50:50) How Prof. Strang’s approach to teaching linear algebra has evolved over time

* (53:00) The Four Fundamental Subspaces

* (56:15) Reflections on a career in teaching

* (59:49) Outro

Links:

* Professor Strang’s homepage



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Hosted by Daniel Bashir, The Gradient: Perspectives on AI moves beyond surface-level headlines to explore the intricate machinery and human ideas shaping artificial intelligence. Each episode is built on a foundation of deep research, leading to conversations that are both technically substantive and broadly accessible. You'll hear from researchers, engineers, and philosophers who are actively building and critiquing our technological future, discussing not just how AI systems work, but the larger implications of their integration into society. This isn't about speculative hype; it's a grounded examination of real progress, persistent challenges, and ethical considerations from those on the front lines. The discussions peel back layers on topics like model architecture, policy, and the fundamental science behind the algorithms becoming part of our daily lives. For anyone curious about the substance behind the buzz-whether you have a technical background or are simply keen to understand a defining technology of our age-this podcast offers a crucial and thoughtful resource. Tune in for a consistently detailed and nuanced take that treats artificial intelligence with the complexity it deserves.
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