<aside> 🧑‍🏫 Layer-wise Relevance Propagation brings explainability that can scale up to complex networks by propagating prediction backward using purposely designed propagation rules

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Spurious correlations between data lead to bad learning

😕How can we prevent this?

1. Feature selection
   • Bad for image models
2. Explainable machine learning
   • Train without caring about models
   • Look at the features learned by models → remove bad features

Layer-Wise Relevance Propagation

→ Propagating prediction $f(x)$ backward in the neural network by designed rules

$z_{jk}$ → models the extent to which neuron $j$ has contributed to make neuron $k$ relevant

✅ 뒤(output에 가까운)에서 앞(input에 가까운)으로 propagate하는 동안 $\sum_jz_{jk}$ 로 normalize하기 때문에 layer-wise conservation/Global conservation property를 갖는다

$$ R_j = \sum_k \frac{z_{jk}}{\sum_jz_{jk}}R_k $$

LRP for RELU

Deep rectifier network neurons

$$ a_k = max\bigg(0,\sum_{0,j}a_jw_{jk}\bigg) $$

Basic-Rule (LRP-0)

$$ R_j = \sum_k \frac{a_jw_{jk}}{\sum_{0,j}a_jw_{jk}}R_k $$

Epsilon Rule(LRP-$\epsilon$)

$$ R_j = \sum_k \frac{a_jw_{jk}}{\epsilon + \sum_{0,j}a_jw_{jk}}R_k $$

• $\epsilon$ for absorbing relevance when contributions to the activation of neuron $k$ are weak → as $\epsilon$ $\uparrow$ only salient explantion survives