What the Books Get Wrong about AI [Double Descent]

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Sections
0:00 - Intro
3:43 - AlexNet & Overfitting
5:19 - Overfitting
6:45 - Rethinking Generalization
11:05 - KiwiCo is Awesome
12:28 - The Double Descent Hypothesis
13:57 - Double Descent is Real!
16:01 - Double Descent with Polynomial Curvefitting?!
20:36 - But why?
22:35 - Should I throw out my books?
24:28 - The Bias-Variance Tradeoff
28:30 - My take
30:47 - I’ve written a new book on AI!

Books with U-shaped test set error curves:
Murphy, Kevin P. Probabilistic machine learning: an introduction. MIT press, 2022.
Goodfellow, Ian, et al. *Deep learning*. Vol. 1. No. 2. Cambridge: MIT press, 2016.
Russell, Stuart Jonathan, and Peter Norvig, eds. *Prentice Hall series in artificial intelligence*. Englewood Cliffs, NJ:: Prentice Hall, 1995.
Bishop, Christopher M., and Nasser M. Nasrabadi. *Pattern recognition and machine learning*. Vol. 4. No. 4. New York: springer, 2006.
Learning, Machine. "Tom mitchell." *Publisher: McGraw Hill* (1997): 31.
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. "The elements of statistical learning." (2009).
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. "An introduction to statistical learning." (2009).
Abu-Mostafa, Yaser S., Malik Magdon-Ismail, and Hsuan-Tien Lin. *Learning from data*. Vol. 4. New York: AMLBook, 2012.
MacKay, David JC. *Information theory, inference and learning algorithms*. Cambridge university press, 2003.

Harvard Team’s code & results:
https://gitlab.com/harvard-machine-learning/double-descent

Great repo showing polynomial double descent:
https://github.com/RylanSchaeffer/Stanford-AI-Alignment-Double-Descent-Tutorial

Technical Notes
- 26:25 For these linear fits, we’re using N=15 instead of N=5 points. This increases the bias and reduces the variance of these fits, making the bias variance trade-off more clear, but also pushes out the interpolation threshold. Full results are here: https://github.com/stephencwelch/manim_videos/blob/master/_2025/generalization/Final Video Polynomial Examples.ipynb
- 27:38 It’s tricky to show the full bias-variance results here, as the variance explodes ad Degree=4. Instead we’ve chosen to show qualitative breakdowns, showing which terms dominate the overall error at each degree. Full results can be seen here: https://github.com/stephencwelch/manim_videos/blob/master/_2025/generalization/Final%20Video%20Polynomial%20Examples.ipynb

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Written by: Stephen Welch
Produced by: Stephen Welch, Sam Baskin, and Pranav Gundu

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