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Many popular feature-attribution methods for interpreting deep neuralnetworks rely on computing the gradients of a model's output with respect toits inputs. While these methods can indicate which input features may beimportant for the model's prediction, they reveal little about the innerworkings of the model itself. In this paper, we observe that the gradientcomputation of a model is a special case of a more general formulation usingsemirings. This observation allows us to generalize the backpropagationalgorithm to efficiently compute other interpretable statistics about thegradient graph of a neural network, such as the highest-weighted path andentropy. We implement this generalized algorithm, evaluate it on syntheticdatasets to better understand the statistics it computes, and apply it to studyBERT's behavior on the subject-verb number agreement task (SVA). With thismethod, we (a) validate that the amount of gradient flow through a component ofa model reflects its importance to a prediction and (b) for SVA, identify whichpathways of the self-attention mechanism are most important.

Generalizing Backpropagation for Gradient-Based Interpretability