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

TL;DR

This paper explores the complexity of learning sparse features in models using feedback from agents like LLMs, providing theoretical bounds and validating results through experiments on feature recovery and dictionary extraction.

Contribution

It introduces tight bounds on feedback complexity for learning feature matrices in sparse settings and demonstrates strong upper bounds with limited feedback.

Findings

Established tight bounds for feature learning with feedback.

Demonstrated effective feature recovery in experiments.

Validated theoretical bounds through practical applications.

Abstract

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 \tt{triplet 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.