Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural networks (BNNs) address the latter by representing weights as probability distributions, allowing for predictive uncertainty evaluation. Latent binary Bayesian neural networks (LBBNNs) further handle structural uncertainty and sparsify models by removing redundant weights. This article advances LBBNNs by enabling covariates to skip to any succeeding layer or be excluded, simplifying networks and clarifying input impacts on predictions. Ultimately, a linear model or even a constant can be found to be optimal for a specific problem at hand. Furthermore, the input-skip LBBNN approach reduces network density significantly compared to standard LBBNNs, achieving over 99% reduction for small networks and over 99.9% for larger ones, while still maintaining high predictive accuracy and uncertainty measurement. For example, on MNIST, we reached 97% accuracy and great calibration with just 935 weights, reaching state-of-the-art for compression of neural networks. Furthermore, the proposed method accurately identifies the true covariates and adjusts for system non-linearity. The main contribution is the introduction of active paths, enhancing directly designed global and local explanations within the LBBNN framework, that have theoretical guarantees and do not require post hoc external tools for explanations.

本研究解决了人工神经网络（ANNs）在模型解释性和不确定性评估方面的挑战，提出一种新颖的输入跳过的潜在二元贝叶斯神经网络（LBBNNs）方法。该方法简化网络结构并清晰表达输入对预测的影响，显著降低了网络密度，同时确保高预测准确性。研究表明，该方法能够在保持高准确率的情况下，实现神经网络的压缩，并有效识别真实协变量。 

可解释的贝叶斯深度学习通过输入跳过的潜在二元贝叶斯神经网络