Grokking Group Multiplication with Cosets

We use the group Fourier transform over the symmetric group $S_n$ to reverse engineer a 1-layer feedforward network that has "grokked" the multiplication of $S_5$ and $S_6$. Each model discovers the true subgroup structure of the full group and converges on circuits that decompose the group multiplication into the multiplication of the group's conjugate subgroups. We demonstrate the value of using the symmetries of the data and models to understand their mechanisms and hold up the ``coset circuit'' that the model uses as a fascinating example of the way neural networks implement computations. We also draw attention to current challenges in conducting mechanistic interpretability research by comparing our work to Chughtai et al. [6] which alleges to find a different algorithm for this same problem.

VQGAN-CLIP: Open Domain Image Generation and Editing with Natural Language Guidance

Generating and editing images from open domain text prompts is a challenging task that heretofore has required expensive and specially trained models. We demonstrate a novel methodology for both tasks which is capable of producing images of high visual quality from text prompts of significant semantic complexity without any training by using a multimodal encoder to guide image generations. We demonstrate on a variety of tasks how using CLIP [37] to guide VQGAN [11] produces higher visual quality outputs than prior, less flexible approaches like DALL-E [38], GLIDE [33] and Open-Edit [24], despite not being trained for the tasks presented. Our code is available in a public repository.