# Dictionary Learning: The Complexity of Learning Sparse Superposed Features with Feedback

arXiv: https://arxiv.org/abs/2502.05407 · HTML: https://mlsanity.com/paper/2502.05407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 8 Feb 2025.

## Builds on (most cited first, 22 of 22)

- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Neural Networks can Learn Representations with Gradient Descent](https://mlsanity.com/paper/2206.15144/) (2022)
- [High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representation](https://mlsanity.com/paper/2205.01445/) (2022)
- [The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks](https://mlsanity.com/paper/2202.08658/) (2022)
- [Transformer visualization via dictionary learning: contextualized embedding as a linear superposition of transformer factors](https://mlsanity.com/paper/2103.15949/) (2021)
- [Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks](https://mlsanity.com/paper/2205.09653/) (2022)
- [An Overview of Machine Teaching](https://mlsanity.com/paper/1801.05927/) (2018)
- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [A Theoretical Analysis on Feature Learning in Neural Networks: Emergence from Inputs and Advantage over Fixed Features](https://mlsanity.com/paper/2206.01717/) (2022)
- [Sparse Overcomplete Word Vector Representations](https://mlsanity.com/paper/1506.02004/) (2015)
- [New Algorithms for Learning Incoherent and Overcomplete Dictionaries](https://mlsanity.com/paper/1308.6273/) (2013)
- [Exact and Stable Covariance Estimation from Quadratic Sampling via Convex Programming](https://mlsanity.com/paper/1310.0807/) (2013)
- [Word Embedding Visualization Via Dictionary Learning](https://mlsanity.com/paper/1910.03833/) (2019)
- [Sparse and spurious: dictionary learning with noise and outliers](https://mlsanity.com/paper/1407.5155/) (2014)
- [Learning Low-Dimensional Metrics](https://mlsanity.com/paper/1709.06171/) (2017)

## Abstract (arXiv)

The success of deep networks is crucially attributed to their ability to capture latent features within a representation space. In this work, we investigate whether the underlying learned features of a model can be efficiently retrieved through feedback from an agent, such as a large language model (LLM), in the form of relative tttriplet comparisons. These features may represent various constructs, including dictionaries in LLMs or a covariance matrix of Mahalanobis distances. We analyze the feedback complexity associated with learning a feature matrix in sparse settings. Our results establish tight bounds when the agent is permitted to construct activations and demonstrate strong upper bounds in sparse scenarios when the agent's feedback is limited to distributional information. We validate our theoretical findings through experiments on two distinct applications: feature recovery from Recursive Feature Machines and dictionary extraction from sparse autoencoders trained on Large Language Models.