While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems. Several Bayesian uncertainty quantification (UQ) methods exist that are either cheap or reliable, but not both. We propose a post-hoc, sampling-based UQ method for over-parameterized networks at the end of training. Our approach constructs efficient and meaningful deep ensembles by employing a (stochastic) gradient-descent sampling process on appropriately linearized networks. We demonstrate that our method effectively approximates the posterior of a Gaussian process using the empirical Neural Tangent Kernel. Through a series of numerical experiments, we show that our method not only outperforms competing approaches in computational efficiency-often reducing costs by multiple factors-but also maintains state-of-the-art performance across a variety of UQ metrics for both regression and classification tasks.

翻译：尽管神经网络在各种任务中展现出卓越的性能，但准确量化其预测中的不确定性对于确保其可信度并推动其在关键系统中的广泛应用至关重要。现有多种贝叶斯不确定性量化方法，它们要么计算成本低廉要么结果可靠，但难以同时兼顾两者。本文针对训练完成的过参数化网络，提出一种后验采样式不确定性量化方法。该方法通过在适当线性化的网络上执行（随机）梯度下降采样过程，构建高效且具有实际意义的深度集成模型。我们证明，该方法能利用经验神经正切核有效逼近高斯过程的后验分布。通过一系列数值实验，我们表明该方法不仅在计算效率上超越现有方法（通常可降低数倍计算成本），而且在回归与分类任务的各种不确定性量化指标上均保持最先进的性能水平。