What is Layer-wise relevance propagation

Exploring Layer-wise relevance propagation

Layer-wise relevance propagation (LRP) is an increasingly popular technique for interpreting deep neural networks. It is a method for explaining the predictions of neural networks by highlighting the most relevant input features that contributed to the output. In this article, we will explore LRP in detail, including its history, working, and applications.

History of Layer-wise relevance propagation

LRP was first introduced in 2015 by Sebastian Bach, a PhD student at the University of Montreal. Bach's paper introduced the idea of using the backward flow of gradients in neural networks to identify the input features that were most relevant for producing the final output. Bach and his co-author Joost van Amersfoort proposed a technique known as "affine LRP" that involved decomposing a layer into its linear and nonlinear components and then propagating relevance scores back through each of these components.

Since its introduction, LRP has undergone many modifications and extensions, including Deep Taylor Decomposition (DTD), which extends affine LRP to non-linearities other than ReLU.

How LRP works

LRP is a technique for explaining the predictions of neural networks by assigning relevance scores to each input feature, based on its contribution to the output of the neural network. The goal of LRP is to determine which input features were most relevant for producing a particular output value. Essentially, LRP works by reversing the forward propagation of the neural network, and then redistributing the output relevance score backwards to the input features.

To understand how LRP works, consider a simple neural network with a single hidden layer. Let X be the input to the network, and let Y be the output. For a given input X, the output Y is produced by a series of linear and nonlinear transformations, which we collectively refer to as f. That is, Y = f(X).

To apply LRP to this network, we first calculate the output relevance score R_Y. This score represents the contribution of the output Y to the overall prediction. We can then distribute this score back through the network using the following equation:

R_X = ∑((f(X) - b) . R_f(f(X))) / ∑((f(X) - b) + ϵ)

Here, R_f is the relevance score for the function f, and ϵ is a small positive constant to prevent division by zero. b is a bias term that is subtracted from the output of f to ensure that the relevance score is centered.

The above equation essentially distributes the relevance score from the output Y to the input X by weighting each input feature according to its contribution to the output. For example, if an input feature has a large positive weight in the network transformation, then it will be assigned a correspondingly large relevance score.

Applications of LRP

LRP has been used in a number of applications, including image recognition, natural language processing, and bioinformatics. In image recognition, LRP has been used to identify the regions of an image that were most important for a given classification decision. In natural language processing, LRP has been used to determine which words in a sentence were most relevant for a particular sentiment analysis task. In bioinformatics, LRP has been used to identify the most important gene expressions for a particular disease outcome.


Layer-wise relevance propagation is a promising technique for interpreting the predictions of deep neural networks. It works by redistributing the output relevance score backwards through the neural network, assigning scores to each input feature based on its contribution to the output. While LRP has many promising applications, it is still an active area of research, and there is much work to be done in terms of improving its performance and scalability.