Carrying over algorithm in transformers

• URL: http://arxiv.org/abs/2401.07993v2
• Date: Wed, 17 Jan 2024 16:02:27 GMT
• Title: Carrying over algorithm in transformers
• Authors: Jorrit Kruthoff
• Abstract summary: carrying over 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 three 7B large language models.

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