arXiv:2605.22891cs.LGhep-ex2026-05被引 2

传统误差评估会误导多模态逆问题,新协议更科学地判断重建质量。

Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems

论文配图:Pointwise Metrics Mislead: An Evaluation Protocol for Multimodal Inverse Problems
图 1 · 摘自论文原文
  • 用分布评估替代点估计,避免因后验宽度导致的系统性偏差
  • 在粒子物理真实案例中,模型排名因评估方式反转,证明点误差不可靠
  • 适合做科学重建、需可信不确定性的研究者,如高能物理或医学成像

科学重建中的评估长期依赖点对点指标(如RMSE、MAE、每事件分辨率),隐含假设是误差越低重建越好。我们证明:当后验分布具有多模态特征时,该假设在结构上失效。根据全方差定律,以最小化MSE或MAE为目标训练的点估计器,其边缘谱总比真实情况更窄,无论模型架构、训练方式或数据集大小如何。这种偏差压缩了尾部、多峰、形状等下游科学测量依赖的关键频谱特征。我们提出三步评估协议:通过CRPS评估事件级分布准确性,用谱保真度诊断评估群体边缘精度,以覆盖率校准评估不确定性可信度。在具有解析后验的合成基准和粒子物理中的真实多对一逆问题上,模型排名在点对点与分布指标间发生反转,校准进一步区分了原本在CRPS下无法分辨的模型。评估协议本身决定了科学结论。

原文摘要 · Abstract (English)

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 evaluation protocol where each step targets a failure mode the others miss: per-event distributional accuracy via CRPS, population-level marginal accuracy via a spectrum-fidelity diagnostic, and uncertainty trustworthiness via coverage-based calibration. On a synthetic benchmark with an analytic posterior and on a realistic many-to-one inverse problem from particle physics, model rankings reverse between pointwise and distributional metrics, and calibration further separates architectures indistinguishable under CRPS. The evaluation protocol, not the model, determines the scientific conclusion.

逆问题分布评估科学重建不确定性

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