Equation 6 · Part 3 · How Do We Know an Interpretability Claim Is Actually Right?

Symbol x

\phi(f_\theta, x) \neq \phi(f_{\theta_{\mathrm{rand}}}, x) \quad \text{for typical } x .

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x 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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…independent of what training had actually done [ 6 ] . Stated as a minimal necessary condition, if $\theta$ are a trained model’s weights, $\theta_{\mathrm{rand}}$ the same architecture reinitialized at random, and $\phi(f, x)$ the explanation a method produces for input x under model f , then a method worth trusting should satisfy $\phi(f_\theta, x) \neq \phi(f_{\theta_{\mathrm{rand}}}, x) \quad \text{for typical } x$ . An explanation that is identical whether or not training happened cannot be reporting anything about what training did; it is a function of the architecture and the…

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Sources cited in the surrounding passage

[6] Sanity Checks for Saliency Maps ↗

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