Related papers: A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram

A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram

URL: http://arxiv.org/abs/2609.10299v1
Date: Wed, 09 Sep 2026 15:13:42 GMT
Title: A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram
Abstract summary: Sparse autoencoders (SAEs) are increasingly used to recover interpretable features from neural-network activations.<n>The MAIS-O43 open problem proposes a controlled experiment to characterize when recovery of a true synthetic dictionary gives way to feature merging.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Sparse autoencoders (SAEs) are increasingly used to recover interpretable features from neural-network activations, yet systematic feature co-occurrence can cause distinct features to be absorbed or merged. The MAIS-O43 open problem proposes a controlled experiment to characterize when recovery of a true synthetic dictionary gives way to feature merging as the nesting fraction $γ$, sparsity penalty $λ$, and dictionary size $M$ vary. We implement the specified protocol and evaluate 200 independently initialized fits across ten of the 165 grid cells. We observe zero full-dictionary recoveries and zero merges. Instead, every run converges to a reproducible diffuse phase: reconstruction is nearly perfect, but learned atoms typically remain far from the true features (median best cosine 0.5-0.7 against a 0.95 recovery criterion) and learned codes are an order of magnitude denser than the ground truth. This behavior persists under robustness checks and across the full 165-cell grid using standard minibatch Adam (3,300 additional fits). Since the global optimum of the exact sparse-coding objective is known to merge nested features in the two-feature case, these results suggest that trained SAEs need not reach the corresponding minima, and that the phase diagram of trained models may differ fundamentally from that of objective minimizers.

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