# Beyond Components: Singular Vector-Based Interpretability of Transformer Circuits

arXiv: https://arxiv.org/abs/2511.20273 · HTML: https://mlsanity.com/paper/2511.20273/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 19 of 19)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [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)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [How to use and interpret activation patching](https://mlsanity.com/paper/2404.15255/) (2024)
- [Attribution Patching Outperforms Automated Circuit Discovery](https://mlsanity.com/paper/2310.10348/) (2023)
- [How does GPT-2 compute greater-than?: Interpreting mathematical abilities in a pre-trained language model](https://mlsanity.com/paper/2305.00586/) (2023)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Circuit Component Reuse Across Tasks in Transformer Language Models](https://mlsanity.com/paper/2310.08744/) (2023)
- [Finding Transformer Circuits with Edge Pruning](https://mlsanity.com/paper/2406.16778/) (2024)
- [Talking Heads: Understanding Inter-layer Communication in Transformer Language Models](https://mlsanity.com/paper/2406.09519/) (2024)
- [Efficient Automated Circuit Discovery in Transformers using Contextual Decomposition](https://mlsanity.com/paper/2407.00886/) (2024)
- [Calibration Across Layers: Understanding Calibration Evolution in LLMs](https://mlsanity.com/paper/2511.00280/) (2025)
- [COLD: Causal reasOning in cLosed Daily activities](https://mlsanity.com/paper/2411.19500/) (2024)
- [Towards Quantifying Commonsense Reasoning with Mechanistic Insights](https://mlsanity.com/paper/2504.10077/) (2025)

## Built on by (most cited first, 7 of 7)

- [Decomposing Query-Key Feature Interactions Using Contrastive Covariances](https://mlsanity.com/paper/2602.04752/) (2026)
- [Compressed Sensing for Capability Localization in Large Language Models](https://mlsanity.com/paper/2603.03335/) (2026)
- [Singular Vectors of Attention Heads Align with Features](https://mlsanity.com/paper/2602.13524/) (2026)
- [Necessary, Decodable and Reversible, Yet Not Transferable: A Stress Test for Attention-Head Role Claims](https://mlsanity.com/paper/2606.08292/) (2026)
- [Finding Usable Weight Mechanisms with Tiled SVD](https://mlsanity.com/paper/2608.06969/) (2026)
- [Can Graph Learning Learn Circuits?](https://mlsanity.com/paper/2608.08536/) (2026)
- [Every Ablation Is a Dose: Counterweights and the Semblance of Self-Repair](https://mlsanity.com/paper/2610.02173/) (2026)

## Abstract (arXiv)

Transformer-based language models exhibit complex and distributed behavior, yet their internal computations remain poorly understood. Existing mechanistic interpretability methods typically treat attention heads and multilayer perceptron layers (MLPs) (the building blocks of a transformer architecture) as indivisible units, overlooking possibilities of functional substructure learned within them. In this work, we introduce a more fine-grained perspective that decomposes these components into orthogonal singular directions, revealing superposed and independent computations within a single head or MLP. We validate our perspective on widely used standard tasks like Indirect Object Identification (IOI), Gender Pronoun (GP), and Greater Than (GT), showing that previously identified canonical functional heads, such as the name mover, encode multiple overlapping subfunctions aligned with distinct singular directions. Nodes in a computational graph, that are previously identified as circuit elements show strong activation along specific low-rank directions, suggesting that meaningful computations reside in compact subspaces. While some directions remain challenging to interpret fully, our results highlight that transformer computations are more distributed, structured, and compositional than previously assumed. This perspective opens new avenues for fine-grained mechanistic interpretability and a deeper understanding of model internals.