Linear representations of concepts in modern AI models
summary
Claim: many human concepts inside LLMs sit on one-dimensional directions recoverable by linear probes, i.e. single index models, and can be found and used to steer behavior. Method: apply a supervised feature-extraction loop based on Recursive Feature Machines and the average gradient outer product (a supervised PCA analog), bootstrap predictors on ~4,000 examples, iterate, and extract one steering vector per transformer block. Results: vectors reliably flip outputs (SSN leakage, Golden Gate prompts, English↔Chinese and Python↔C++ translation) on open LLaMA models and often preserve or improve correctness.
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chapters (9)
- 0:00Introduction
- 0:22AI model mathematics
- 8:53Dimensionality puzzle
- 12:18Linear representation hypothesis
- 17:22Single-index models
- 20:47Supervised dimensionality reduction
- 26:50Steering LLM outputs
- 31:58Why steering vectors work
- 34:07Conclusion
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