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arXiv 1902.00407cs.LGstat.ML
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理解高阶损失近似和特征在深度学习解释中的影响

Understanding Impacts of High-Order Loss Approximations and Features in Deep Learning Interpretation

University of Maryland(马里兰大学)

Sahil Singla, Eric Wallace, Shi Feng, Soheil Feizi

摘要:

当前通过生成显着图来解释深度学习模型的方法通常依赖于两个关键假设。首先,他们使用损失函数的一阶近似,忽略了高阶项,如损失曲率。其次,他们孤立地评估每个功能的重要性,忽略了它们的相互依赖性。在这项工作中,我们研究放松这两个假设的影响。首先,通过表征深度ReLU网络的Hessian矩阵的封闭式公式,我们证明了,对于具有大量类的分类问题,如果输入具有高置信度分类得分,则包含Hessian项对最终解决方案的影响很小。我们证明了这一结果表明,在这种情况下的海森矩阵是近似的秩1和其领导的特征向量几乎平行的梯度的损失函数。我们对ImageNet样本的实证实验与我们的理论一致。这一结果也可能对其他相关问题产生影响,例如对抗性例子。其次,我们通过引入稀疏正则化项来计算深度学习解释中的组特征的重要性。我们使用$L_0-L_1$松弛技术以及近端梯度下降来有效地计算组特征重要性分数。我们的实证结果表明,考虑群体特征可以显着提高深度学习解释。

英文摘要:

Current methods to interpret deep learning models by generating saliency maps generally rely on two key assumptions. First, they use first-order approximations of the loss function neglecting higher-order terms such as the loss curvatures. Second, they evaluate each feature's importance in isolation, ignoring their inter-dependencies. In this work, we study the effect of relaxing these two assumptions. First, by characterizing a closed-form formula for the Hessian matrix of a deep ReLU network, we prove that, for a classification problem with a large number of classes, if an input has a high confidence classification score, the inclusion of the Hessian term has small impacts in the final solution. We prove this result by showing that in this case the Hessian matrix is approximately of rank one and its leading eigenvector is almost parallel to the gradient of the loss function. Our empirical experiments on ImageNet samples are consistent with our theory. This result can have implications in other related problems such as adversarial examples as well. Second, we compute the importance of group-features in deep learning interpretation by introducing a sparsity regularization term. We use the $L_0-L_1$ relaxation technique along with the proximal gradient descent to have an efficient computation of group feature importance scores. Our empirical results indicate that considering group features can improve deep learning interpretation significantly.

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