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Implementing Contrastive Layer-wise Relevance Propagation with Innvestigate

Contrastive Layer-wise Relevance Propagation[1] or CLRP is a modification of standard Layer-wise Relevance Propagation[2] (LRP) with the goal of making the output (more) class discriminative. This notebook will use the LRP library Innvestigate[3] to attempt to implement CLRP.

A general overview of CLRP is as follows:

  1. Given an output neuron $y_j$ which represent concept $O$ we try to construct a dual virtual concept $\overline O$ which represents the opposite concept of $O$.
  2. This concept $\overline O$ can be represented in two different ways:
    A. CLRP1: The concept is represented by the selected classes with weights $\overline W = \{W^1, W^2, ..., W^{L-1}, W^L_{-j}\}$. Here $W_{-j}$ means the weights connected to the output layer excluding the $j$-th neuron.
    B. CLRP2: The concept is represented by the selected classes with weights$\overline W = \{W^1, W^2, ..., W^{L-1}, W^L_{-j}\}$. Which means all the weights are the same, except for the last layer where the weights to neuron $j$ are negated.
  3. (?) The score $S_{y_j}$ of target class is uniformly redistributted to other classes.
  4. $R_{\text{LRP}} = f_{\text{LRP}}(X, W, S_{y_j})$
  5. Given the same input example $X$ LRP generates an explanation $R_{\text{dual}} = f_{\text{LRP}}(X, \overline W, S_{y_j})$ for the dual concept.
  6. Then CLRP is defined as follows: $R_{\text{CLRP}} = \max(0, R - R_{\text{dual}})$

Here are some results from the CLRP paper which shows a very clear class discrimitative property. These results are from using VGG16 pre-trained on imagenet and applying the $z^\beta$-rule in the first convolution layer and for all the other convulutional layers the $z^+$-rule. For more details read the paper.

results

[1] Gu, Jindong, Yinchong Yang, and Volker Tresp. "Understanding Individual Decisions of CNNs via Contrastive Backpropagation." Asian Conference on Computer Vision. Springer, Cham, 2018

[2] Bach, Sebastian, et al. "On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation." PloS one 10.7 (2015): e0130140.

[3] iNNvestigate neural networks! - github repository