Short Horizons and Sparse Concepts: a Mathematical View of the Readout in the J-lens
The Jacobian lens (J-lens) has been proposed as a way to read verbalizable representations from language models. However, its principle and meaning lack a detailed and theoretical discussion. We provide a mathematical view of this interpretation and of its assumed causal structure. Besides treating the J-lens as a heuristic probe, we further regard it as a first-order causal transfer operator from intermediate activations to expected future readouts. We study the Jacobian matrix as the optimal local linear approximation of the downstream mapping, analyze its global approximation behavior and bias, and identify its mathematical meaning as an expectation over anticipated future readouts. Fu...
| Authors | Shi-Qi Yan, Kai-Xuan Ding, Chao-Hong Tan et al. |
|---|---|
| Primary category | cs.CL |
| Published | 26 August 2026 |
| Last updated at source | 26 August 2026 |
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