$$\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}}$$

Equation 17 · AI Research

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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: $\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}}$. 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.

Meanings in this article

• $C$: copied from one run into the other.
• $m_{\text{patch}}$: that same metric after the activations of component set $\mathcal C$ are copied from one run into the other.
• $m_{\text{corrupt}}$: a chosen behavioural metric measured on the clean and corrupted runs.
• $m_{\text{clean}}$: a chosen behavioural metric measured on the clean and corrupted runs.

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