Computationally Efficient Measures of Internal Neuron Importance

TL;DR

This paper introduces Neuron Integrated Gradients, a scalable method for measuring internal neuron importance in neural networks, improving upon previous approaches by combining theoretical soundness with computational efficiency.

Contribution

It demonstrates that Total Conductance can be computed efficiently using standard gradients, leading to the development of Neuron Integrated Gradients, which is both scalable and theoretically grounded.

Findings

Neuron Integrated Gradients is mathematically equivalent to Total Conductance.

DeepLIFT is faster and empirically effective but lacks certain theoretical guarantees.

Neuron Integrated Gradients offers a theoretically sound and scalable solution for internal neuron attribution.

Abstract

The challenge of assigning importance to individual neurons in a network is of interest when interpreting deep learning models. In recent work, Dhamdhere et al. proposed Total Conductance, a "natural refinement of Integrated Gradients" for attributing importance to internal neurons. Unfortunately, the authors found that calculating conductance in tensorflow required the addition of several custom gradient operators and did not scale well. In this work, we show that the formula for Total Conductance is mathematically equivalent to Path Integrated Gradients computed on a hidden layer in the network. We provide a scalable implementation of Total Conductance using standard tensorflow gradient operators that we call Neuron Integrated Gradients. We compare Neuron Integrated Gradients to DeepLIFT, a pre-existing computationally efficient approach that is applicable to calculating internal neuron importance. We find that DeepLIFT produces strong empirical results and is faster to compute, but because it lacks the theoretical properties of Neuron Integrated Gradients, it may not always be preferred in practice. Colab notebook reproducing results: http://bit.ly/neuronintegratedgradients