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Relative Layer-Wise Relevance Propagation: a more Robust Neural Networks eXplaination

Eric Nyiri, Olivier Gibaru

TL;DR

This paper addresses the need for robust, interpretable explanations of neural network decisions by improving Layer-Wise Relevance Propagation through Relative LRP (R-LRP). R-LRP computes relative input contributions without dividing by small denominators or requiring hyperparameters, preserving a conservation property up to a common factor. Empirical results across MNIST-like data, Cat-vs-Dog, and ImageNet-1K with VGG16/19 and ResNet50 show that R-LRP yields more object-centric, stable attributions, and that using absolute-value contributions often enhances localization for small relevance budgets. The findings suggest R-LRP provides practical, architecture-agnostic explanations with better focus on relevant image regions, and the authors plan to extend the approach to MLP-Mixer and attention-based architectures.

Abstract

Machine learning methods are solving very successfully a plethora of tasks, but they have the disadvantage of not providing any information about their decision. Consequently, estimating the reasoning of the system provides additional information. For this, Layer-Wise Relevance Propagation (LRP) is one of the methods in eXplainable Machine Learning (XML). Its purpose is to provide contributions of any neural network output in the domain of its input. The main drawback of current methods is mainly due to division by small values. To overcome this problem, we provide a new definition called Relative LRP where the classical conservation law is satisfied up to a multiplicative factor but without divisions by small values except for Resnet skip connection. In this article, we will focus on image classification. This allows us to visualize the contributions of a pixel to the predictions of a multi-layer neural network. Pixel contributions provide a focus to further analysis on regions of potential interest. R-LRP can be applied for any dense, CNN or residual neural networks. Moreover, R-LRP doesn't need any hyperparameters to tune contrary to other LRP methods. We then compare the R-LRP method on different datasets with simple CNN, VGG16, VGG19 and Resnet50 networks.

Relative Layer-Wise Relevance Propagation: a more Robust Neural Networks eXplaination

TL;DR

This paper addresses the need for robust, interpretable explanations of neural network decisions by improving Layer-Wise Relevance Propagation through Relative LRP (R-LRP). R-LRP computes relative input contributions without dividing by small denominators or requiring hyperparameters, preserving a conservation property up to a common factor. Empirical results across MNIST-like data, Cat-vs-Dog, and ImageNet-1K with VGG16/19 and ResNet50 show that R-LRP yields more object-centric, stable attributions, and that using absolute-value contributions often enhances localization for small relevance budgets. The findings suggest R-LRP provides practical, architecture-agnostic explanations with better focus on relevant image regions, and the authors plan to extend the approach to MLP-Mixer and attention-based architectures.

Abstract

Machine learning methods are solving very successfully a plethora of tasks, but they have the disadvantage of not providing any information about their decision. Consequently, estimating the reasoning of the system provides additional information. For this, Layer-Wise Relevance Propagation (LRP) is one of the methods in eXplainable Machine Learning (XML). Its purpose is to provide contributions of any neural network output in the domain of its input. The main drawback of current methods is mainly due to division by small values. To overcome this problem, we provide a new definition called Relative LRP where the classical conservation law is satisfied up to a multiplicative factor but without divisions by small values except for Resnet skip connection. In this article, we will focus on image classification. This allows us to visualize the contributions of a pixel to the predictions of a multi-layer neural network. Pixel contributions provide a focus to further analysis on regions of potential interest. R-LRP can be applied for any dense, CNN or residual neural networks. Moreover, R-LRP doesn't need any hyperparameters to tune contrary to other LRP methods. We then compare the R-LRP method on different datasets with simple CNN, VGG16, VGG19 and Resnet50 networks.
Paper Structure (26 sections, 10 theorems, 23 equations, 30 figures)

This paper contains 26 sections, 10 theorems, 23 equations, 30 figures.

Table of Contents

  1. LRP Introduction
  2. DAGs for feed-forward networks
  3. LRP background
  4. LRP0 drawback
  5. LRP modified formulas
  6. Relative LRP or R-LRP method
  7. Introduction
  8. Effective R-LRP calculations from CNN layer components
  9. R-LRP calculations with ResNet
  10. Evaluations with MNIST-like dataset
  11. Using positive and negative contributions
  12. R-LRP validation with cat vs dog dataset
  13. Training process
  14. Contributions using R-LRP formula vs other LPR methods
  15. Evaluations
  16. ...and 11 more sections

Key Result

Proposition 2

Let us given a feed-forward neural network $\mathcal{N}$ (see Definition def:1) and $x \in \mathbb{R}^d$ with $d=card(\mathcal{I})$ then is a function mapping $\mathbb{R}^d$ into $\mathbb{R}^p$ where $p=card(\mathcal{O})$, called the output of $\mathcal{N}$.

Figures (30)

  • Figure 1: Softmax implementation example in 1D.
  • Figure 2: Convolution part implementation example in 1D
  • Figure 3: A residual learning building block.
  • Figure 4: Images showing percentage of the most relevant pixels using LRP0 on a modified MNIST dataset using a simple dense network. Mask images are in black and white
  • Figure 5: Images showing percentage of the most relevant inputs using LRP0 on two images from Imagenet dataset with VGG16.
  • ...and 25 more figures

Theorems & Definitions (14)

  • Definition 1: Feed-forward neural network
  • Proposition 2: Feed-forward neural network output
  • Proposition 3: Fully-connected Neural networks
  • Proposition 4: Convolutional Neural networks part
  • Proposition 5: Sequential Convolutional Neural networks
  • Proposition 6: ResNet-Block type Neural networks
  • Definition 7: LRP0
  • Definition 8: Conservation Law
  • Definition 9: R-LRP
  • Proposition 10: R-LRP contribution and activation
  • ...and 4 more