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Equation 4 · Part 1 · How Mechanistic Interpretability Research Is Actually Done

Symbol hat p_θ

p^θ(y∣aℓ)=σ ⁣(w⊤aℓ+b),θ={w,b},\hat p_\theta(y \mid a_\ell) = \sigma\!\left(w^{\top} a_\ell + b\right), \qquad \theta = \{w, b\},
p^θ\hat p_\theta

What this part means

hat p_θ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

hat p_θ is part of the quantity the equation computes from the expression on the right.

The passage around this formula

The first concrete operation in almost any interpretability project is the least glamorous: run the model forward on a batch of inputs, and at some chosen point in the computation — a residual-stream position, an attention head’s output, a particular MLP layer — copy the activation tensor out before it is overwritten by the next step of the forward pass. This is extraction, and it produces nothing on its own beyond a large table of vectors. What turns it into evidence is probing: fitting a small, separately trained classifier to predict some property of interest directly from those vectors, while the model’s own weights stay frozen. Formally, for an activation aℓa_\ell read out at layer ℓ\ell…

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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 surrounding passage

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