DeepLIFT is a method for decomposing the output prediction of a neural network on a specific input by backpropagating the contributions of all neurons to every feature of the input. It compares the activation of each neuron to its 'reference activation' and assigns contribution scores based on the difference. DeepLIFT can reveal dependencies missed by other approaches by optionally considering positive and negative contributions separately. Scores are computed efficiently in a single backward pass. DeepLIFT was applied to models trained on MNIST and simulated genomic data, showing significant advantages over gradient-based methods. DeepLIFT explains the difference in output from a 'reference' output in terms of the difference of the input from a 'reference' input. It addresses limitations of gradients by propagating importance even when the gradient is zero, avoiding discontinuities caused by bias terms. The method uses multipliers and the chain rule to compute contribution scores for each neuron to its immediate inputs. DeepLIFT allows separate treatment of positive and negative contributions, improving its ability to identify dependencies. The RevealCancel rule is an improved approximation of Shapley values, which helps in cases where Rescale may provide misleading results. It considers the impact of positive and negative terms in the absence of each other, reducing issues caused by cancellation. DeepLIFT also addresses saturation and thresholding problems illustrated in figures, providing more accurate importance scores. For softmax layers, contributions are computed to the linear layer preceding the final nonlinearity to avoid attenuation. Adjustments are made to normalize contributions to the linear layer, ensuring fair comparison across classes. In experiments on MNIST and genomic data, DeepLIFT with the RevealCancel rule outperformed other methods in identifying important pixels for digit classification and detecting regulatory DNA motifs. It provided more accurate and reliable importance scores compared to gradient-based methods, which often failed to address saturation and thresholding issues. DeepLIFT is particularly useful in scenarios where gradients are zero, such as in recurrent neural networks with saturating activations. The method offers a more robust and interpretable way to understand neural network decisions.DeepLIFT is a method for decomposing the output prediction of a neural network on a specific input by backpropagating the contributions of all neurons to every feature of the input. It compares the activation of each neuron to its 'reference activation' and assigns contribution scores based on the difference. DeepLIFT can reveal dependencies missed by other approaches by optionally considering positive and negative contributions separately. Scores are computed efficiently in a single backward pass. DeepLIFT was applied to models trained on MNIST and simulated genomic data, showing significant advantages over gradient-based methods. DeepLIFT explains the difference in output from a 'reference' output in terms of the difference of the input from a 'reference' input. It addresses limitations of gradients by propagating importance even when the gradient is zero, avoiding discontinuities caused by bias terms. The method uses multipliers and the chain rule to compute contribution scores for each neuron to its immediate inputs. DeepLIFT allows separate treatment of positive and negative contributions, improving its ability to identify dependencies. The RevealCancel rule is an improved approximation of Shapley values, which helps in cases where Rescale may provide misleading results. It considers the impact of positive and negative terms in the absence of each other, reducing issues caused by cancellation. DeepLIFT also addresses saturation and thresholding problems illustrated in figures, providing more accurate importance scores. For softmax layers, contributions are computed to the linear layer preceding the final nonlinearity to avoid attenuation. Adjustments are made to normalize contributions to the linear layer, ensuring fair comparison across classes. In experiments on MNIST and genomic data, DeepLIFT with the RevealCancel rule outperformed other methods in identifying important pixels for digit classification and detecting regulatory DNA motifs. It provided more accurate and reliable importance scores compared to gradient-based methods, which often failed to address saturation and thresholding issues. DeepLIFT is particularly useful in scenarios where gradients are zero, such as in recurrent neural networks with saturating activations. The method offers a more robust and interpretable way to understand neural network decisions.