Carrying over Algorithm in Transformers
Primary Area: visualization or interpretation of learned representations
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Interpretability, Transformers, Mechanistic Interpretability, Circuits, Integer Addition in LLMs
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We reverse engineer small transformer models trained on integer addition and find they implement the carrying over algorithm.
Abstract: Addition is perhaps one of the simplest arithmetic tasks one can think of and is usually performed using the carrying over algorithm. This algorithm consists of two tasks: adding digits in the same position and carrying over a one whenever necessary. We study how transformer models implement this algorithm and how the two aforementioned tasks are allocated to different parts of the network. We first focus on two-layer encoder-only models and show that the carrying over algorithm is implemented in a modular fashion. The first layer is mostly responsible for adding digits in the same position. The second layer first decides, in the attention, which positions need a carried one or not, and then performs the carrying of the one in the final MLP. We provide a simple way of precisely identifying which neurons are responsible for that task. This implementation of the carrying over algorithm occurs across a range of hyperparameters for two as well as three-layer models. For small decoder-only models, we observe the same implementation and provide suggestive evidence for its existence in Alpaca 7B.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 4064
Loading