Equation 25 · Part 5 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

Symbol x_i^+

v_\ell = \frac{1}{|P|}\sum_{i \in P} h_\ell(x_i^{+}) \;-\; \frac{1}{|N|}\sum_{i \in N} h_\ell(x_i^{-}), \qquad h_\ell \leftarrow h_\ell + \alpha\, v_\ell,

x_i^{+}

What this part means

$x_i^+$ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

$x_i^+$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol x_i^+Article meaning

The passage around this formula

The construction is a mean-difference direction, added back into the residual stream with a tunable strength at inference time: $v_\ell = \frac{1}{|P|}\sum_{i \in P} h_\ell(x_i^{+}) \;-\; \frac{1}{|N|}\sum_{i \in N} h_\ell(x_i^{-}), \qquad h_\ell \leftarrow h_\ell + \alpha\, v_\ell$ . where P and N index matched positive and negative examples of the target behaviour, $h_\ell$ is the residual-stream activation at layer $\ell$ , and $\alpha$ is a coefficient the operator sets by hand. Nothing in this construction requires understanding why the network represents the concept along this direction, only that adding it produces the intended behavioural shift.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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