Equation 17 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared
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Symbol m_patch
that same metric after the activations of component set are copied from one run into the other.
Symbol m_corrupt
a chosen behavioural metric measured on the clean and corrupted runs.
Symbol m_clean
a chosen behavioural metric measured on the clean and corrupted runs.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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subscript
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Numerator: m_patch(mathcal C) - m_corrupt
The complete quantity above the fraction bar.
Denominator: m_clean - m_corrupt
The complete quantity below the fraction bar; it must be nonzero for this division.
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What the article says around this equation
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: . where and are a chosen behavioural metric measured on the clean and corrupted runs, and is that same metric after the activations of component set are copied from one run into the other. A score near one means patching alone restores nearly all of the clean behaviour; a score near zero means it restores almost none.
Sources cited in the article section
- [9] Causal Mediation Analysis for Interpreting Neural NLP: The Case of Gender Bias ↗
- [10] Locating and Editing Factual Associations in GPT ↗
- [11] How to Use and Interpret Activation Patching ↗
These citations give research context. Read each source to check which claims it supports.