Sparse autoencoders learn blurry features instead of true patterns
A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram
Machine Learning
Summary
Sparse autoencoders are tools that try to find meaningful parts inside complex data. This paper tests a special case where the expected parts are known, but instead of finding them clearly, the autoencoders return fuzzy and mixed features. The authors show that even though the autoencoders reconstruct the data well, their learned parts don’t match the true underlying features and use more active pieces than expected. This suggests these models don’t always reach the ideal solution that theory predicts.
What this means in practice
- •For machine learning engineers: Detect when sparse autoencoders may return mixed features instead of true interpretable parts during feature extraction tasks.
- •For data scientists: Assess the limitations of sparse autoencoder training for recovering known feature dictionaries in synthetic or controlled datasets.
Authors
Alexis D. Plascencia
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.