Influence Is the Target-Response Jacobian Times Residuals
We introduce the target-response Jacobian $J = [\partial \hat y_i/\partial y_j]$, which measures how model predictions respond to changes in individual training targets. $J$ complements training-data attribution (TDA) methods, which characterize sensitivity to the weights placed on training observations in the loss rather than to their targets, and can be computed matrix-free at the same cost as influence-based TDA methods. We show that sample-weight influence $\mathcal{I}$ and $J$ follow from the same implicit differentiation argument and differ only by a per-example multiplier: for pointwise losses, $\mathcal{I} = J\operatorname{diag}(m)$ exactly at any stationary point with an invertib...
| Authors | Paul Geertsema, Simon Geertsema |
|---|---|
| Primary category | cs.LG |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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