A mathematical theory of Anthropic's J-lens: why it finds working-memory-like features
burny_tech · x · 2026-10-27
A new paper builds a mathematical theory of Anthropic's Jacobian lens (J-lens), explaining which mechanistic properties make features detectable to it.
- J-lens had identified working-memory-like linear directions in frontier LLM hidden states, but why was unclear
- The paper shows J-lens preferentially identifies coherent features — directions acting like leading, spatially coherent Lyapunov modes: small perturbations amplify across layers, stay roughly constant across token positions, and are consistent across contexts
- Validated on a Bayes filter and toy transformer predicting HMM emissions; modulating task parameters predictively modulates J-lens response
- Introduces a family of ω-J-lenses emphasizing different temporal scales of information processing
Related event: MIT Researchers Build Mathematical Theory for Anthropic's Jacobian Lens(3 posts)→
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