Goodfire AI researchers identify shape-rotating calculator in language models
Goodfire AI researchers identified an internal mechanism in large language models that performs addition and related operations by rotating shapes in high-dimensional neural space. The reusable structure interfaces with Fourier features and reads from geometric representations learned during training. It extends to other computational tasks and builds on a 2023 arXiv paper on modular addition circuits. Released visualizations display shifting activation clusters in scatter plots.
Very interesting finding! Reminds me of the structures Xiaoyan and Itamar found in multiplication reasoning:

Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)
LLMs are wordcels AND shape rotators
Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)
BREAKING: LLMs are just stochastic parrots
They have no idea of the real world. How could they? They are just storing text in their database and regurgitating it !!1
Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)
(if you fell for this you are regarded)
BREAKING: LLMs are just stochastic parrots They have no idea of the real world. How could they? They are just storing text in their database and regurgitating it !!1
the stochastic parrot LLMs have obviously stolen this concept from mechanical calculators https://en.wikipedia.org/wiki/Mechanical_calculator
the stochastic parrot LLMs have obviously stolen this concept from mechanical calculators

@scaling01 that's not true. as you can see. they rotate it
so cool. win for the shape rotators! @ericho_goodfire
Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)
I figured we’d get here eventually.
It’s beautiful.
Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)
the world inside neural networks is so beautiful. gradient descent learned to make a general-purpose addition module!
Neural networks do math by rotating shapes. We found a shape-rotating calculator hidden inside an LLM – and it’s used for more than just math! (1/6)