@inproceedings{du-etal-2023-generalizing,
    title = "Generalizing Backpropagation for Gradient-Based Interpretability",
    author = "Du, Kevin  and
      Torroba Hennigen, Lucas  and
      Stoehr, Niklas  and
      Warstadt, Alex  and
      Cotterell, Ryan",
    editor = "Rogers, Anna  and
      Boyd-Graber, Jordan  and
      Okazaki, Naoaki",
    booktitle = "Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2023",
    address = "Toronto, Canada",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2023.acl-long.669",
    doi = "10.18653/v1/2023.acl-long.669",
    pages = "11979--11995",
    abstract = "Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model{'}s output with respect to its inputs. While these methods can indicate which input features may be important for the model{'}s prediction, they reveal little about the inner workings of the model itself. In this paper, we observe that the gradient computation of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics about the gradient graph of a neural network, such as the highest-weighted path and entropy. We implement this generalized algorithm, evaluate it on synthetic datasets to better understand the statistics it computes, and apply it to study BERT{'}s behavior on the subject{--}verb number agreement task (SVA). With this method, we (a) validate that the amount of gradient flow through a component of a model reflects its importance to a prediction and (b) for SVA, identify which pathways of the self-attention mechanism are most important.",
}

Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model{'}s output with respect to its inputs. While these methods can indicate which input features may be important for the model{'}s prediction, they reveal little about the inner workings of the model itself. In this paper, we observe that the gradient computation of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics about the gradient graph of a neural network, such as the highest-weighted path and entropy. We implement this generalized algorithm, evaluate it on synthetic datasets to better understand the statistics it computes, and apply it to study BERT{'}s behavior on the subject{--}verb number agreement task (SVA). With this method, we (a) validate that the amount of gradient flow through a component of a model reflects its importance to a prediction and (b) for SVA, identify which pathways of the self-attention mechanism are most important.
Du, Kevin Torroba Hennigen, Lucas Stoehr, Niklas Warstadt, Alex Cotterell, Ryan
Generalizing Backpropagation for Gradient-Based Interpretability