  In this work we present successor heads: attention heads that increment
tokens with a natural ordering, such as numbers, months, and days. For example,
successor heads increment 'Monday' into 'Tuesday'. We explain the successor
head behavior with an approach rooted in mechanistic interpretability, the
field that aims to explain how models complete tasks in human-understandable
terms. Existing research in this area has found interpretable language model
components in small toy models. However, results in toy models have not yet led
to insights that explain the internals of frontier models and little is
currently understood about the internal operations of large language models. In
this paper, we analyze the behavior of successor heads in large language models
(LLMs) and find that they implement abstract representations that are common to
different architectures. They form in LLMs with as few as 31 million
parameters, and at least as many as 12 billion parameters, such as GPT-2,
Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how
successor heads increment in LLMs across different architectures and sizes. We
perform vector arithmetic with these features to edit head behavior and provide
insights into numeric representations within LLMs. Additionally, we study the
behavior of successor heads on natural language data, identifying interpretable
polysemanticity in a Pythia successor head.
