New theory paper explains what Anthropic's Jacobian lens actually detects in LLMs
wgilpin0 · x · 2026-10-27
Anthropic's Jacobian lens (J-lens) found evidence of a "global workspace"-like divide in Claude. A new arXiv paper, "A Mathematical Theory of the Jacobian Lens" by Mitchell Ostrow et al. (MIT, related to J-lens authors Wes Gurnee and Jack Lindsey), explains why:
- J-lens preferentially identifies coherent features — directions acting like spatially coherent Lyapunov modes: small perturbations amplify across layers, stay roughly constant across token positions, and persist across contexts
- The authors stay agnostic on whether these properties imply a "Global Workspace," but the derived preferences explain prior empirical results across model classes
- Validated on a Bayes filter and a toy transformer predicting HMM emissions: modulating task parameters that change feature coherence predictably modulates J-lens response
- Introduces ω-J-lenses, a family emphasizing different temporal scales of information processing
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