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Equation 6 · Part 4 · How Do We Know an Interpretability Claim Is Actually Right?

Symbol f_theta_rand

ϕ(fθ,x)≠ϕ(fθrand,x)for typical x.\phi(f_\theta, x) \neq \phi(f_{\theta_{\mathrm{rand}}}, x) \quad \text{for typical } x .
fθrandf_{\theta_{\mathrm{rand}}}

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ftf_thetara_rand is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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ftf_thetara_rand is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

This kind of benchmark descends from an older and more basic validation move: check whether an explanation changes when it should have to. Adebayo and colleagues showed that several popular saliency methods for image classifiers produce visually similar output whether the underlying model has been trained at all or left at its random initialization, meaning the “explanation” was substantially independent of what training had actually done [ 6 ] . Stated as a minimal necessary condition, if θ\theta are a trained model’s weights, θrand\theta_{\mathrm{rand}} the same architecture reinitialized at random, and ϕ(f,x)\phi(f, x) the explanation a method produces for input x under model f , then a method worth…

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