Jacobian Rank Collapse in Decision-Focused Learning

Excerpt

arXiv:2609.39261v1 Announce Type: new Abstract: Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by the optimizer from the parameter directions available to learning. Rank-one Jacobians make nonzero per-example gradients collinear; a conditional spect