# Discovering Variable Binding Circuitry with Desiderata

arXiv: https://arxiv.org/abs/2307.03637 · HTML: https://mlsanity.com/paper/2307.03637/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 7 Jul 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Toward Transparent AI: A Survey on Interpreting the Inner Structures of Deep Neural Networks](https://mlsanity.com/paper/2207.13243/) (2022)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [Characterizing Manipulation from AI Systems](https://mlsanity.com/paper/2303.09387/) (2023)

## Built on by (most cited first, 30 of 34)

- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Recurrent Neural Networks Learn to Store and Generate Sequences using Non-Linear Representations](https://mlsanity.com/paper/2408.10920/) (2024)
- [Language Models use Lookbacks to Track Beliefs](https://mlsanity.com/paper/2505.14685/) (2025)
- [Mixing Mechanisms: How Language Models Retrieve Bound Entities In-Context](https://mlsanity.com/paper/2510.06182/) (2025)
- [Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior](https://mlsanity.com/paper/2605.05115/) (2026)
- [Interpretability Illusions in the Generalization of Simplified Models](https://mlsanity.com/paper/2312.03656/) (2023)
- [Grokking Group Multiplication with Cosets](https://mlsanity.com/paper/2312.06581/) (2023)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [How Do Transformers Learn Variable Binding in Symbolic Programs?](https://mlsanity.com/paper/2505.20896/) (2025)
- [Look Before You Leap: A Universal Emergent Decomposition of Retrieval Tasks in Language Models](https://mlsanity.com/paper/2312.10091/) (2023)
- [From Directions to Regions: Decomposing Activations in Language Models via Local Geometry](https://mlsanity.com/paper/2602.02464/) (2026)
- [How Causal Abstraction Underpins Computational Explanation](https://mlsanity.com/paper/2508.11214/) (2025)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [Arithmetic in the Wild: Llama uses Base-10 Addition to Reason About Cyclic Concepts](https://mlsanity.com/paper/2605.01148/) (2026)
- [LLMs Process Lists With General Filter Heads](https://mlsanity.com/paper/2510.26784/) (2025)
- [Do Language Models Track Entities Across State Changes?](https://mlsanity.com/paper/2605.30233/) (2026)
- [Philosophy of Cognitive Science in the Age of Deep Learning](https://mlsanity.com/paper/2405.04048/) (2024)
- [The Dual Mechanisms of Spatial Variable Binding in Vision-Language Models](https://mlsanity.com/paper/2603.22278/) (2026)
- [Neuroplasticity and Corruption in Model Mechanisms: A Case Study Of Indirect Object Identification](https://mlsanity.com/paper/2503.01896/) (2025)
- [Mechanistic origins of catastrophic forgetting: why RL preserves circuits better than SFT?](https://mlsanity.com/paper/2605.28860/) (2026)
- [Data-driven Circuit Discovery for Interpretability of Language Models](https://mlsanity.com/paper/2605.09129/) (2026)
- [Constructive Circuit Amplification: Improving Math Reasoning in LLMs via Targeted Sub-Network Updates](https://mlsanity.com/paper/2512.16914/) (2025)
- [Test, then Route: How Language Models Execute In-Context Conditional Rules Across Models and Languages](https://mlsanity.com/paper/2608.04183/) (2026)
- [Matryoshka attribution: Learning to attribute language model outputs to representations and weights](https://mlsanity.com/paper/2609.25518/) (2026)
- [Who Says What: Symbolic Trimodal Binding Mechanisms in Audio-Visual LLMs](https://mlsanity.com/paper/2609.31193/) (2026)
- [Cultural Binding Heads in Language Models](https://mlsanity.com/paper/2605.28543/) (2026)
- [Assign and Add: A Mechanistic Study of Compositional Arithmetic](https://mlsanity.com/paper/2605.31497/) (2026)

## Abstract (arXiv)

Recent work has shown that computation in language models may be human-understandable, with successful efforts to localize and intervene on both single-unit features and input-output circuits. Here, we introduce an approach which extends causal mediation experiments to automatically identify model components responsible for performing a specific subtask by solely specifying a set of textitdesiderata, or causal attributes of the model components executing that subtask. As a proof of concept, we apply our method to automatically discover shared textitvariable binding circuitry in LLaMA-13B, which retrieves variable values for multiple arithmetic tasks. Our method successfully localizes variable binding to only 9 attention heads (of the 1.6k) and one MLP in the final token's residual stream.