Reproduce “A Mathematical Theory of the Jacobian Lens” on OpenResearch

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About this paper

Mitchell Ostrow, Daoyuan Qian, Toni Liu, Ila Fiete

The J-lens favors hidden-state directions whose effects are strong and consistent across model depth, future token positions, and prompts. Its strength reflects magnitude, lag coherence, and context coherence, not activation variance alone. In a hidden Markov model, theory predicts a ranking crossover at persistence 0.649; a toy transformer transfers it approximately, with error O(0.01). This validation is limited to toy systems.

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