Jacobian Rank Collapse in Decision-Focused Learning
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 spectral bound describes near-collinearity. A batch-subspace characterization and counterexamples show why these local statements imply neither common minimizers nor collinear batch updates. Experiments examine when geometry translates into decision ...
| Authors | Aojie Yuan, Haiyue Zhang, Zijian Su |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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