SOURCE-LINKED INTELLIGENCE

Short Horizons and Sparse Concepts: a Mathematical View of the Readout in the J-lens

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

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 b

Read original source ↗ Open in workspace

recordType

paper

region

Global