Audio note: this article contains 182 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

I (Subhash) am a Masters student in the Tegmark AI Safety Lab at MIT. I am interested in recruiting for full time roles this Spring - please reach out if you're interested in working together!

TLDR 

This blog post accompanies the paper "Language Models Use Trigonometry to Do Addition." Key findings:

• We show that LLMs represent numbers on a helix
  • This helix has circular features (sines and cosines) with periods _T = [2,5,10,100]_ and a linear component
• To solve _a+b_, we claim that LLMs manipulate the helix for _a_ and _b_ to create the helix for _a+b_ using a form of the Clock algorithm introduced by Nanda, et al.
  • This is conceptually akin to going from _cos(a), cos(b)_ to _cos(a+b)_
  • Intuitively, it's like adding angles on a [...]

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Outline:

(00:30) TLDR

(01:28) Motivation and Problem Setting

(02:18) LLMs Represent Numbers on a Helix

(02:23) Investigating the Structure of Numbers

(02:48) Periodicity

(03:49) Linearity

(04:39) Parameterizing Numbers as a Helix

(05:39) Fitting a Helix

(07:12) Evaluating the Helical Fit

(08:57) Relation to the Linear Representation Hypothesis

(10:28) Is the helix the full story?

(12:15) LLMs Use the Clock Algorithm to Compute Addition

(14:23) Understanding MLPs

(16:24) Zooming in on Neurons

(17:07) Modeling Neuron Preactivations

(18:53) Understanding MLP Inputs

(20:34) Interpreting Model Errors

(24:11) Limitations

(25:49) Conclusion

The original text contained 9 footnotes which were omitted from this narration.

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First published:

Source:

Narrated by TYPE III AUDIO.

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