Jacobian lens（J-lens）的数学理论

View PDF HTML (experimental)

Abstract:Recent work from Anthropic introduced a new interpretability tool, called the Jacobian lens (J-lens, Gurnee et al., 2026). This method identified linear directions in the hidden states of frontier language models that had properties reminiscent of working memory-like representations. However, it is unclear what mechanistic properties of such features make them detectable to the J-lens. To this end, we introduce a mathematical theory of the J-lens, and show that it preferentially identifies coherent features -- directions that act like leading, spatially coherent Lyapunov modes. Small perturbations along these directions amplify across layers, remain roughly constant across token positions, and are consistent across different contexts. While we are agnostic to whether these properties are necessarily associated with a ``Global Workspace'', the analytically derived preferences of the J-lens nevertheless explain prior empirical applied to both model classes. We validate our analysis on a Bayes filter and a toy transformer, each optimally predicting next tokens emitted from a Hidden Markov Model (HMM). We show how modulating task parameters that change the coherence of features in the Bayes filter correspondingly and predictively modulates the response of the J-lens . We also introduce of a family of J-lenses built to emphasize different temporal scales of information processing in LLMs, which we call $\omega$-J-lenses.

Comments:	27 pages, 19 figures
Subjects:	Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Neurons and Cognition (q-bio.NC)
Cite as:	arXiv:2610.31955 [cs.LG]
	(or arXiv:2610.31955v1 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2610.31955 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Mitchell Ostrow [view email]
[v1] Thu, 22 Oct 2026 22:03:03 UTC (927 KB)