Deep Taylor default setting violates conservation property

[enryH]

Dear team, i finally got some time to look into your latest version of iNNvestigate. Thank you very much for providing the package!

I want to use DTD and I wonder how the current implementation currently works exactly:

• Do you choose according to the layer-type or activation type different root points corresponding to decomposition rules?

  • I see that you pick lrp-rules, but I do not really get the logic of your implementation.

• In your old implementation you wanted to change the basic DTD setup, see here. Might it be the changed got lost?

Based on your introduction notebook I started to check the conversation property. Full code including your utiliy functions is here.

-i Test image is a 9

Having no bias constraint

• some relevances is "leaking" as described by Sebastian Lapuschkin.
• Source

# Create analyzer
analyzer = innvestigate.create_analyzer("deep_taylor", model_wo_sm)

# Applying the analyzer
analysis = analyzer.analyze(image)

# Check Conservation
scores = model_wo_sm.predict(image)
print("Maximum Score: {:.3f} with label {}".format(scores.max(), scores.argmax()))
print("sum of relevances assigned to inputs: {:.3f}".format(analysis.sum()))
try:
    assert abs(scores.max() - analysis.sum()) < 0.001
except AssertionError:
    print("not equal...")
# Biases are included and conversation property in DTD framework fails

Maximum Score: 11.711 with label 9
sum of relevances assigned to inputs: 11.561
not equal...

# LRP-Alpha_1-Beta_0 without biases is z+ rule in DTD paper
from innvestigate.analyzer.relevance_based.relevance_analyzer import LRPAlpha1Beta0IgnoreBias
analyzer = LRPAlpha1Beta0IgnoreBias(model_wo_sm)

# Applying the analyzer
analysis = analyzer.analyze(image)

# Check Conservation
scores = model_wo_sm.predict(image)
print("Maximum Score: {:.3f} with label {}".format(scores.max(), scores.argmax()))
print("sum of relevances assigned to inputs: {:3f}".format(analysis.sum()))
assert abs(scores.max() - analysis.sum()) < 0.001

Maximum Score: 11.711 with label 9
sum of relevances assigned to inputs: 11.711

Constrainig the bias in ReLUs to be negative as in DTD paper

• relevance over inputs is larger as output score using default setup
• Source

  
  # Create analyzer
  analyzer = innvestigate.create_analyzer("deep_taylor", model_wo_sm)

Applying the analyzer

analysis = analyzer.analyze(image)

Check Conservation

scores = model_wo_sm.predict(image) print("Maximum Score: {:.3f} with label {}".format(scores.max(), scores.argmax())) print("sum of relevances assigned to inputs: {:.3f}".format(analysis.sum())) try: assert abs(scores.max() - analysis.sum()) < 0.001 except AssertionError: print("not equal...")

Biases are included and conversation property in DTD framework fails

Maximum Score: 12.835 with label 9 sum of relevances assigned to inputs: 13.338 not equal...

```python
# LRP-Alpha_1-Beta_0 without biases is z+ rule in DTD paper
from innvestigate.analyzer.relevance_based.relevance_analyzer import LRPAlpha1Beta0IgnoreBias
analyzer = LRPAlpha1Beta0IgnoreBias(model_wo_sm)

# Applying the analyzer
analysis = analyzer.analyze(image)

# Check Conservation
scores = model_wo_sm.predict(image)
print("Maximum Score: {:.3f} with label {}".format(scores.max(), scores.argmax()))
print("sum of relevances assigned to inputs: {:3f}".format(analysis.sum()))
assert abs(scores.max() - analysis.sum()) < 0.001

Maximum Score: 12.835 with label 9
sum of relevances assigned to inputs: 12.835