A prediction rigidity formalism for low-cost uncertainties in trained neural networks

Quantifying the uncertainty of regression models is essential to ensure their reliability, particularly since their application often extends beyond their training domain. Based on the solution of a constrained optimization problem, this work proposes 'prediction rigidities' as a formalism to obtain uncertainties of arbitrary pre-trained regressors. A clear connection between the suggested framework and Bayesian inference is established, and a last-layer approximation is developed and rigorously justified to enable the application of the method to neural networks. This extension affords cheap uncertainties without any modification to the neural network itself or its training procedure. The effectiveness of this approach is shown for a wide range of regression tasks, ranging from simple toy models to applications in chemistry and meteorology.
This record includes computational experiments supporting the MLST paper titled "A prediction rigidity formalism for low-cost uncertainties in trained neural networks".

量化回归模型的不确定性是保障其可靠性的核心要务，尤其当模型的应用场景往往超出其训练分布范围时。本研究基于约束优化问题的求解，提出「预测刚性（prediction rigidities）」形式化方法，以获取任意预训练回归器的不确定性。本研究建立了所提框架与贝叶斯推断（Bayesian inference）间的明确关联，并开发了末层近似方法，经严格理论论证后可将该方法应用于神经网络。该扩展方案无需对神经网络本身或其训练流程进行任何修改，即可实现低成本不确定性量化。本方法的有效性在多类回归任务中得到验证，覆盖从简单玩具模型到化学、气象学应用的广泛场景。
本数据集包含支撑题为《面向训练后神经网络低成本不确定性的预测刚性形式化方法》的MLST论文的计算实验数据。