Equation 6 · The Hardest Unsolved Problems in Mechanistic Interpretability
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Symbol g
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with g itself sparse. A direction that a large dictionary presents as one unit is recoverable as a sparse combination of a smaller dictionary’s units, which means the large dictionary’s “atoms” are not atomic. Put the incompleteness and the non-atomicity results together and no dictionary size is privileged: a smaller one misses real structure, a larger one is decomposable into something smaller, and the paper’s own recommendation is not to keep searching for the canonical size but to pick a dictionary size pragmatically for the task at hand, because no single size is the network’s true feature set [ 3 ] . The number of features a sparse autoencoder reports is, on this evidence, a property…
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with g itself sparse. A direction that a large dictionary presents as one unit is recoverable as a sparse combination of a smaller dictionary’s units, which means the large dictionary’s “atoms” are not atomic. Put the incompleteness and the non-atomicity results together and no dictionary size is privileged: a smaller one misses real structure, a larger one is decomposable into something smaller, and the paper’s own recommendation is not to keep searching for the canonical size but to pick a dictionary size pragmatically for the task at hand, because no single size is the network’s true feature set [ 3 ] . The number of features a sparse autoencoder reports is, on this evidence, a property of the hyperparameter chosen, not a discovery about the network.
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