Reproduce “How Optimality Structures Sparse Dictionaries: Theory for Interpreting SAE Representations” on OpenResearch
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About this paper
William Dorrell
The authors derive a necessary condition for local optima in dictionary learning, relating each feature direction to the convex hull of activity patterns when that feature is off. The condition makes distinct-direction hierarchies unstable, explaining splitting and absorption as effects of the objective. In GPT-2-small’s layer-8 SAE, no violations appeared among 3,700 features on OpenWebText; this diagnostic does not prove optimality.
Summary by alphaXiv.
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