Equation 15 · How Mechanistic Interpretability Research Is Actually Done
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol theta_i
thet is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
keeping only the k largest pre-activations and zeroing the rest, and used it to train a sixteen-million-latent dictionary on GPT-4 activations over forty billion tokens, reporting metrics that improve consistently as dictionary size grows [ 8 ] . Rajamanoharan and colleagues took a different route to the same problem, keeping a continuous encoder but replacing the fixed zero threshold with a learned per-feature threshold — a feature only activates once its pre-activation clears — and report state-of-the-art reconstruction fidelity at matched sparsity on Gemma 2 activations against both the and top- k alternatives [ 9 ] .
Sources cited in the surrounding passage
- [8] Scaling and evaluating sparse autoencoders ↗
- [9] Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders ↗
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