Abstract
Neural network classifiers are known to be able to learn very accurate models. In the recent past, researchers have even been able to train neural networks with multiple hidden layers (deep neural networks) more effectively and efficiently. However, the major downside of neural networks is that it is not trivial to understand the way how they derive their classification decisions. To solve this problem, there has been research on extracting better understandable rules from neural networks. However, most authors focus on nets with only one single hidden layer. The present paper introduces a new decompositional algorithm – DeepRED – that is able to extract rules from deep neural networks.
The evaluation of the proposed algorithm shows its ability to outperform a pedagogical baseline on several tasks, including the successful extraction of rules from a neural network realizing the XOR function.
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Notes
- 1.
The merging may produce rules of the form \(i_1<0.1\) AND \(i_1>0.2\), or \(i_1>0.4\) AND \(i_1>0.5\).
- 2.
Input instances are drawn randomly from \({x} \in \{ 0, 0.5, 1 \} \times \{ 0, 0.25, 0.5, 0.75, 1 \} \times [0, 1]^3\). For artif-I \({y}=\lambda _1\) if \(x_1 = x_2\), if \(x_1 > x_2\) AND \(x_3 > 0.4\), or if \(x_3 > x_4\) AND \(x_4 > x_5\) AND \(x_2 > 0\), else \({y} = \lambda _2\), whereas for artif-I \({y}=\lambda _1\) if \(x_1 = x_2\), if \(x_1 > x_2\) AND \( x_3 > 0.4\), or IF \(x_5 > 0.8\).
- 3.
You might notice that, earlier, we mentioned that there are 36 experiments per dataset. However, to avoid sophisticating the outcomes, we discard those experiments where the RxREN pruning results in no pruned inputs at all.
- 4.
An abortion could either be the case if the experiment exceeds the allocated memory space (10000 MB) or if DeepRED needs more than the maximum execution time (24 h).
- 5.
An example of a sufficient training set with the instance notation \({x} = x_{1} x_{2} x_{3} x_{4}\) would be 0011, 1101, 1000, and 0110. It contains all combinations of \(x_1\)/\(x_2\) and \(x_3\)/\(x_4\).
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Zilke, J.R., Loza Mencía, E., Janssen, F. (2016). DeepRED – Rule Extraction from Deep Neural Networks. In: Calders, T., Ceci, M., Malerba, D. (eds) Discovery Science. DS 2016. Lecture Notes in Computer Science(), vol 9956. Springer, Cham. https://doi.org/10.1007/978-3-319-46307-0_29
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