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Equation 17 · Part 9 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

Numerator: m_patch(mathcal C) - m_corrupt

score(C)=mpatch(C)−mcorruptmclean−mcorrupt,\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}},
mpatch(C)−mcorruptm_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}

What this part means

The complete quantity above the fraction bar.

Its job in the formula

mpm_patch(mathcal C) - mcm_corrupt occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The general operation, activation patching, is usually reported as a normalised score rather than a raw difference, isolating exactly how much of the gap between clean and corrupted behaviour a given component set closes: score(C)=mpatch(C)−mcorruptmclean−mcorrupt\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}}. where mcleanm_{\text{clean}} and mcorruptm_{\text{corrupt}} are a chosen behavioural metric measured on the clean and corrupted runs, and mpatch(C)m_{\text{patch}}(\mathcal C) is that same metric after the activations of component set C\mathcal C are copied from one run into the other. A score near one means patching C\mathcal C alone restores nearly all of the clean behaviour; a score near zero means it restores almost none.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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