# Uncovering Intermediate Variables in Transformers using Circuit Probing

arXiv: https://arxiv.org/abs/2311.04354 · HTML: https://mlsanity.com/paper/2311.04354/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 69 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Ethical and social risks of harm from Language Models](https://mlsanity.com/paper/2112.04359/) (2021)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Gender Bias in Coreference Resolution](https://mlsanity.com/paper/1804.09301/) (2018)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [On Measuring Social Biases in Sentence Encoders](https://mlsanity.com/paper/1903.10561/) (2019)
- [Assessing the Ability of LSTMs to Learn Syntax-Sensitive Dependencies](https://mlsanity.com/paper/1611.01368/) (2016)
- [What BERT is not: Lessons from a new suite of psycholinguistic diagnostics for language models](https://mlsanity.com/paper/1907.13528/) (2019)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [Analyzing the Structure of Attention in a Transformer Language Model](https://mlsanity.com/paper/1906.04284/) (2019)
- [Targeted Syntactic Evaluation of Language Models](https://mlsanity.com/paper/1808.09031/) (2018)

## Built on by (most cited first, 12 of 12)

- [A Primer on the Inner Workings of Transformer-based Language Models](https://mlsanity.com/paper/2405.00208/) (2024)
- [pyvene: A Library for Understanding and Improving PyTorch Models via Interventions](https://mlsanity.com/paper/2403.07809/) (2024)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [Position: An Inner Interpretability Framework for AI Inspired by Lessons from Cognitive Neuroscience](https://mlsanity.com/paper/2406.01352/) (2024)
- [Different types of syntactic agreement recruit the same units within large language models](https://mlsanity.com/paper/2512.03676/) (2025)
- [Validating Mechanistic Interpretations: An Axiomatic Approach](https://mlsanity.com/paper/2407.13594/) (2024)
- [Modularity is the Bedrock of Natural and Artificial Intelligence](https://mlsanity.com/paper/2602.18960/) (2026)
- [Over-Refusal and Representation Subspaces: A Mechanistic Analysis of Task-Conditioned Refusal in Aligned LLMs](https://mlsanity.com/paper/2603.27518/) (2026)
- [Observable Propagation: Uncovering Feature Vectors in Transformers](https://mlsanity.com/paper/2312.16291/) (2023)
- [A Review of Developmental Interpretability in Large Language Models](https://mlsanity.com/paper/2508.15841/) (2025)
- [Judge Circuits Explain Format-Induced Inconsistency in LLM-as-a-Judge](https://mlsanity.com/paper/2605.16023/) (2026)
- [Building Interpretable Models for Moral Decision-Making](https://mlsanity.com/paper/2602.03351/) (2026)

## Abstract (arXiv)

Neural network models have achieved high performance on a wide variety of complex tasks, but the algorithms that they implement are notoriously difficult to interpret. It is often necessary to hypothesize intermediate variables involved in a network's computation in order to understand these algorithms. For example, does a language model depend on particular syntactic properties when generating a sentence? Yet, existing analysis tools make it difficult to test hypotheses of this type. We propose a new analysis technique - circuit probing - that automatically uncovers low-level circuits that compute hypothesized intermediate variables. This enables causal analysis through targeted ablation at the level of model parameters. We apply this method to models trained on simple arithmetic tasks, demonstrating its effectiveness at (1) deciphering the algorithms that models have learned, (2) revealing modular structure within a model, and (3) tracking the development of circuits over training. Across these three experiments we demonstrate that circuit probing combines and extends the capabilities of existing methods, providing one unified approach for a variety of analyses. Finally, we demonstrate circuit probing on a real-world use case: uncovering circuits that are responsible for subject-verb agreement and reflexive anaphora in GPT2-Small and Medium.