Audio note: this article contains 73 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Epistemic status: This post is a synthesis of ideas that are, in my experience, widespread among researchers at frontier labs and in mechanistic interpretability, but rarely written down comprehensively in one place - different communities tend to know different pieces of evidence. The core hypothesis - that deep learning is performing something like tractable program synthesis - is not original to me (even to me, the ideas are ~3 years old), and I suspect it has been arrived at independently many times. (See the appendix on related work).

This is also far from finished research - more a snapshot of a hypothesis that seems increasingly hard to avoid, and a case for why formalization is worth pursuing. I discuss the key barriers and how tools like singular learning theory might address them towards the end of the post.

Thanks to Dan Murfet, Jesse Hoogland, Max Hennick, and Rumi Salazar for feedback on this post.

Sam Altman: Why does unsupervised learning work?

Dan Selsam: Compression. So, the ideal intelligence [...]

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Outline:

(02:31) Background

(09:06) Looking inside

(09:09) Grokking

(16:04) Vision circuits

(22:37) The hypothesis

(26:04) Why this isnt enough

(27:22) Indirect evidence

(32:44) The paradox of approximation

(38:34) The paradox of generalization

(45:44) The paradox of convergence

(51:46) The path forward

(53:20) The representation problem

(58:38) The search problem

(01:07:20) Appendix

(01:07:23) Related work

The original text contained 14 footnotes which were omitted from this narration.

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First published:
January 20th, 2026

Source:
https://www.lesswrong.com/posts/Dw8mskAvBX37MxvXo/deep-learning-as-program-synthesis-1

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Narrated by TYPE III AUDIO.

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Images from the article:

The modular addition transformer from Power et al. (2022) learns to generalize rapidly (top), at the same time as Fourier modes in the weights appear (bottom right). Illustration by Pearce et al. (2023).

"The inaugural Redwood Research podcast" by Buck, ryan_greenblatt

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