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 $\overline W = \{W^1, W^2, ..., W^{L-1}, -1 * W^L_{j}\}$. 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: $R_{\text{CLRP}} = \max(0, R - R_{\text{dual}})$

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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.

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[1] @article{gu2018understanding, title={Understanding Individual Decisions of CNNs via Contrastive Backpropagation}, author={Gu, Jindong and Yang, Yinchong and Tresp, Volker}, journal={arXiv preprint arXiv:1812.02100}, year={2018} }

[2] @article{bach-plos15, author = {Bach, Sebastian AND Binder, Alexander AND Montavon, Gr{'e}goire AND Klauschen, Frederick AND M{"u}ller, Klaus-Robert AND Samek, Wojciech}, journal = {PLoS ONE}, publisher = {Public Library of Science}, title = {On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation}, year = {2015}, month = {07}, volume = {10}, url = {http://dx.doi.org/10.1371%2Fjournal.pone.0130140}, pages = {e0130140}, number = {7}, doi = {10.1371/journal.pone.0130140} }

[3] https://github.com/albermax/innvestigate/