Equation 8 · How Mechanistic Interpretability Research Is Actually Done
What does this equation mean?
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.
Read it piece by piece
Symbol hat a
hat a is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Sparse dictionary learning is the field’s answer, and it is a second and different act of extraction rather than a departure from the first: a sparse autoencoder is trained on the very same activation vectors the probe was reading, learning an overcomplete basis in which each vector is reconstructed as a sparse combination of dictionary elements. Writing a for the activation, z for its sparse code and for the reconstruction,
Sources cited in the article section
- [6] Sparse Autoencoders Find Highly Interpretable Features in Language Models ↗
- [7] Towards Monosemanticity: Decomposing Language Models With Dictionary Learning ↗
- [8] Scaling and evaluating sparse autoencoders ↗
- [9] Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders ↗
- [10] Interpreting Attention Layer Outputs with Sparse Autoencoders ↗
These citations give research context. Read each source to check which claims it supports.
Return to How Mechanistic Interpretability Research Is Actually Done