Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems
Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for inverse problems with multimodal posteriors. By the law of total variance, point estimators trained to minimize MSE or MAE produce a marginal spectrum strictly narrower than the truth whenever the posterior has nonzero width. The resulting bias is independent of architecture, training, and dataset size, and it compresses precisely the spectral features - tails, modes, shapes - that downstream scientific measurements rely on. We propose a three-part evalua...
| Authors | Mads H. Baattrup, Jörn Bach, Laurids Jeppe et al. |
|---|---|
| Primary category | cs.LG |
| Published | 21 May 2026 |
| Last updated at source | 21 May 2026 |
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