# Successor Heads: Recurring, Interpretable Attention Heads In The Wild

arXiv: https://arxiv.org/abs/2312.09230 · HTML: https://mlsanity.com/paper/2312.09230/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Builds on (most cited first, 20 of 20)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [The Hydra Effect: Emergent Self-repair in Language Model Computations](https://mlsanity.com/paper/2307.15771/) (2023)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [Language Models Implement Simple Word2Vec-style Vector Arithmetic](https://mlsanity.com/paper/2305.16130/) (2023)
- [Copy Suppression: Comprehensively Understanding an Attention Head](https://mlsanity.com/paper/2310.04625/) (2023)
- [Generalizing Backpropagation for Gradient-Based Interpretability](https://mlsanity.com/paper/2307.03056/) (2023)

## Built on by (most cited first, 30 of 77)

- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Transcoders Find Interpretable LLM Feature Circuits](https://mlsanity.com/paper/2406.11944/) (2024)
- [The Remarkable Robustness of LLMs: Stages of Inference?](https://mlsanity.com/paper/2406.19384/) (2024)
- [A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models](https://mlsanity.com/paper/2407.02646/) (2024)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [Universal Neurons in GPT2 Language Models](https://mlsanity.com/paper/2401.12181/) (2024)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [Attention Tracker: Detecting Prompt Injection Attacks in LLMs](https://mlsanity.com/paper/2411.00348/) (2024)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [On the Role of Attention Heads in Large Language Model Safety](https://mlsanity.com/paper/2410.13708/) (2024)
- [Attention Heads of Large Language Models: A Survey](https://mlsanity.com/paper/2409.03752/) (2024)
- [LLM Circuit Analyses Are Consistent Across Training and Scale](https://mlsanity.com/paper/2407.10827/) (2024)
- [Knowledge Mechanisms in Large Language Models: A Survey and Perspective](https://mlsanity.com/paper/2407.15017/) (2024)
- [Do Language Models Use Their Depth Efficiently?](https://mlsanity.com/paper/2505.13898/) (2025)
- [Softmax is not Enough (for Sharp Size Generalisation)](https://mlsanity.com/paper/2410.01104/) (2024)
- [Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient](https://mlsanity.com/paper/2410.02984/) (2024)
- [Neuron-Level Knowledge Attribution in Large Language Models](https://mlsanity.com/paper/2312.12141/) (2023)
- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Interpreting Arithmetic Mechanism in Large Language Models through Comparative Neuron Analysis](https://mlsanity.com/paper/2409.14144/) (2024)
- [What Do VLMs NOTICE? A Mechanistic Interpretability Pipeline for Gaussian-Noise-free Text-Image Corruption and Evaluation](https://mlsanity.com/paper/2406.16320/) (2024)
- [No Two Devils Alike: Unveiling Distinct Mechanisms of Fine-tuning Attacks](https://mlsanity.com/paper/2405.16229/) (2024)
- [Out-of-distribution generalization via composition: a lens through induction heads in Transformers](https://mlsanity.com/paper/2408.09503/) (2024)
- [Missed Causes and Ambiguous Effects: Counterfactuals Pose Challenges for Interpreting Neural Networks](https://mlsanity.com/paper/2407.04690/) (2024)
- [Back Attention: Understanding and Enhancing Multi-Hop Reasoning in Large Language Models](https://mlsanity.com/paper/2502.10835/) (2025)
- [Towards Understanding Fine-Tuning Mechanisms of LLMs via Circuit Analysis](https://mlsanity.com/paper/2502.11812/) (2025)
- [Hallucination Detection in LLMs with Topological Divergence on Attention Graphs](https://mlsanity.com/paper/2504.10063/) (2025)

## Abstract (arXiv)

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.