Attenuation bias -- the systematic underestimation of regression coefficients due to measurement errors in input variables -- affects astronomical data-driven models. For linear regression, this problem was solved by treating the true input values as latent variables to be estimated alongside model parameters. In this paper, we show that neural networks suffer from the same attenuation bias and that the latent variable solution generalizes directly to neural networks. We introduce LatentNN, a method that jointly optimizes network parameters and latent input values by maximizing the joint likelihood of observing both inputs and outputs. We demonstrate the correction on one-dimensional regression, multivariate inputs with correlated features, and stellar spectroscopy applications. LatentNN reduces attenuation bias across a range of signal-to-noise ratios where standard neural networks show large bias. This provides a framework for improved neural network inference in the low signal-to-noise regime characteristic of astronomical data. This bias correction is most effective when measurement errors are less than roughly half the intrinsic data range; in the regime of very low signal-to-noise and few informative features. Code is available at https://github.com/tingyuansen/LatentNN.

翻译：衰减偏差——由于输入变量中的测量误差导致回归系数的系统性低估——影响着天文数据驱动模型。对于线性回归，这一问题已通过将真实输入值视为待与模型参数一同估计的潜变量得到了解决。本文表明，神经网络同样遭受衰减偏差的影响，且潜变量解决方案可直接推广至神经网络。我们提出LatentNN方法，该方法通过最大化同时观测到输入与输出的联合似然，联合优化网络参数与潜变量输入值。我们在单变量回归、含相关特征的多变量输入以及恒星光谱应用中验证了该校正效果。LatentNN在标准神经网络显示显著偏差的一系列信噪比范围内减少了衰减偏差。这为在天文数据典型的低信噪比条件下改进神经网络推断提供了框架。当测量误差小于固有数据范围约一半时，且在极低信噪比与信息特征较少的条件下，该偏差校正最为有效。代码见https://github.com/tingyuansen/LatentNN。