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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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