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.

Have suggestions for future podcast guests (or other feedback)? Let us know here or reach us at editor@thegradient.pub

Subscribe to The Gradient Podcast:  Apple Podcasts  | Spotify | Pocket Casts | RSSFollow The Gradient on Twitter

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



Get full access to The Gradient at thegradientpub.substack.com/subscribe

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.
Author: Language: English Episodes: 100

The Gradient: Perspectives on AI
Podcast Episodes
Andrew Lee: How AI will Shape the Future of Email [not-audio_url] [/not-audio_url]

Duration: 1:03:40
In episode 118 of The Gradient Podcast, Daniel Bashir speaks to Andrew Lee.Andrew is co-founder and CEO of Shortwave, a company dedicated to building a better product experience for email, particularly by leveraging AI.…
Joss Fong: Videomaking, AI, and Science Communication [not-audio_url] [/not-audio_url]

Duration: 1:23:59
Episode 117“You get more of what you engage with. Everyone who complains about coverage should understand that every click, every quote tweet, every argument is registered by these publications as engagement. If what you…
Kate Park: Data Engines for Vision and Language [not-audio_url] [/not-audio_url]

Duration: 41:34
In episode 116 of The Gradient Podcast, Daniel Bashir speaks to Kate Park. Kate is the Director of Product at Scale AI. Prior to joining Scale, Kate worked on Tesla Autopilot as the AI team’s first and lead product manag…
Ben Wellington: ML for Finance and Storytelling through Data [not-audio_url] [/not-audio_url]

Duration: 1:07:40
In episode 115 of The Gradient Podcast, Daniel Bashir speaks to Ben Wellington.Ben is the Deputy Head of Feature Forecasting at Two Sigma, a financial sciences company. Ben has been at Two Sigma for more than 15 years, a…
Venkatesh Rao: Protocols, Intelligence, and Scaling [not-audio_url] [/not-audio_url]

Duration: 2:18:35
“There is this move from generality in a relative sense of ‘we are not as specialized as insects’ to generality in the sense of omnipotent, omniscient, godlike capabilities. And I think there's something very dangerous t…
Sasha Rush: Building Better NLP Systems [not-audio_url] [/not-audio_url]

Duration: 54:03
In episode 113 of The Gradient Podcast, Daniel Bashir speaks to Professor Sasha Rush.Professor Rush is an Associate Professor at Cornell University and a Researcher at HuggingFace. His research aims to develop natural la…
Nicholas Thompson: AI and Journalism [not-audio_url] [/not-audio_url]

Duration: 59:43
In episode 111 of The Gradient Podcast, Daniel Bashir speaks to Nicholas Thompson.Nicholas is the CEO of The Atlantic. Previously, he served as editor-in-chief of Wired and editor of Newyorker.com. Nick also cofounded At…
Russ Maschmeyer: Spatial Commerce and AI in Retail [not-audio_url] [/not-audio_url]

Duration: 55:41
In episode 109 of The Gradient Podcast, Daniel Bashir speaks to Russ Maschmeyer.Russ is the Product Lead for AI and Spatial Commerce at Shopify. At Shopify, he leads a team that looks at how AI can better empower entrepr…