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Equation 1 · Part 3 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

Symbol σ

y^(x)=σ(w⊤hℓ(x)+b),\hat y(x) = \sigma\big(w^\top h_\ell(x) + b\big),
σ\sigma

What this part means

σ is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

σ is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Formally, a probe is a function fitted independently of the network under study: y^(x)=σ(w⊤hℓ(x)+b)\hat y(x) = \sigma\big(w^\top h_\ell(x) + b\big). where hℓ(x)h_\ell(x) is the frozen activation the network produces at layer ℓ\ell for input x , and w, b are the probe’s own parameters, trained on labelled examples the network never saw during its own training. Nothing in that objective touches the network’s weights or its downstream computation. A probe reports only whether some linear function of this one activation predicts the label well.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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