Equation 18 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

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m_{\text{clean}}

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a chosen behavioural metric measured on the clean and corrupted runs. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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m_{\text{clean}}

Symbol m_clean

a chosen behavioural metric measured on the clean and corrupted runs.

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subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

where $m_{\text{clean}}$ and $m_{\text{corrupt}}$ are a chosen behavioural metric measured on the clean and corrupted runs, and $m_{\text{patch}}(\mathcal C)$ is that same metric after the activations of component set $\mathcal C$ are copied from one run into the other. A score near one means patching $\mathcal C$ alone restores nearly all of the clean behaviour; a score near zero means it restores almost none.

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