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Equation 13 · Part 1 · Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared

Symbol f

∥f(x)∥0\lVert f(x) \rVert_0
ff

What this part means

f is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

f is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…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 ℓ1\ell_1 formulation and a competing gated variant [ 7 ] . That the field kept revising the sparsity penalty is itself evidence of how much…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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