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Equation 9 · Part 6 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

Symbol θ

x^=Wdf(x)+bd,f(x)=JumpReLUθ(Wex+be),L(x)=∥x−x^∥22+λ∥f(x)∥0.\hat x = W_d f(x) + b_d, \qquad f(x) = \mathrm{JumpReLU}_\theta\big(W_e x + b_e\big), \qquad \mathcal L(x) = \lVert x - \hat x \rVert_2^2 + \lambda \lVert f(x) \rVert_0.
θ\theta

What this part means

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

Its job in the formula

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

The passage around this formula

…feature, distorting reconstruction in a way that has nothing to do with how many features are active. Rajamanoharan and colleagues introduced JumpReLU, a thresholded activation function with a learned per-feature cutoff θ\theta trained through a straight-through gradient estimator, which lets the objective penalise the true count of active features, ∥\lVert f(x) ∥0\rVert_0 , directly rather than through the ℓ1\ell_1 proxy, and reported state-of-the-art reconstruction fidelity at matched sparsity against both the earlier…

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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 surrounding passage

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