MAIS-O43 sparse-autoencoder phase-diagram open problem
For the synthetic sparse-coding experiment specified by MAIS-O43, with nesting fraction , sparsity penalty , and dictionary size , determine the phase diagram of trained sparse autoencoders: for each parameter cell, do training runs recover the true dictionary, merge nested features, or converge to another solution such as a diffuse representation? In particular, determine whether trained sparse autoencoders can systematically converge to solutions distinct from global minimizers of the exact sparse-coding objective, despite achieving near-perfect reconstruction, and characterize the conditions under which each behavior occurs.
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Progress summary
A September 2026 computational study found that trained sparse autoencoders can reconstruct data well while learning atoms unlike the intended dictionary, but this does not settle the general problem.
The problem concerns whether trained sparse autoencoders can differ from global minimizers of the exact sparse-coding objective. No proposer or original date is identified in the retrieved material.
September 2026 computational study
A study tested the protocol on ten cells and then the full 165-cell grid, finding atoms typically far from the synthetic dictionary despite near-perfect reconstruction. This is evidence for the tested protocol, not a proof covering all training procedures.
Current status (as of September 2026): The tested training protocol has claimed empirical evidence of a diffuse phase, while the general question about trained models and exact global minimizers remains open.
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