Complete the MAIS-O43 sparse-autoencoder phase diagram

Complete the MAIS-O43 experiment by measuring the probabilities of dictionary recovery, feature merging, and feature splitting across the full $11\times5\times3$ grid of nesting fraction $\gamma$, sparsity penalty $\lambda$, and dictionary size $M$, using the specified synthetic generator, training protocol, and independent initializations.

Background

The MAIS-O43 agenda defines a controlled experiment for determining when a sparse autoencoder recovers a known synthetic feature dictionary and when systematic feature co-occurrence instead produces merging or splitting. The protocol varies nesting fraction, sparsity penalty, and dictionary size over 165 grid cells and prescribes 20 independently initialized fits per cell.

The paper measures only ten canonical full-batch cells, while the remaining canonical cells are not measured under the complete prescribed protocol. Although an off-protocol minibatch companion grid covers all cells, it does not complete the canonical MAIS-O43 experiment.

References

The MAIS research agenda \citep{mais2026} formalizes this phenomenon geometrically and poses, as open problem MAIS-O43, a fully specified experiment: measure the probabilities of recovery, merging, and splitting of a known synthetic dictionary over an $11\times5\times3$ grid of nesting fraction $\gamma$, sparsity penalty $\lambda$, and dictionary size $M$, with 20 independent initializations per cell (3{,}300 fits).

— A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram  (2609.10299 - Plascencia, 9 Sep 2026) in Section 1, Introduction

Whether those architectures raise the low matched fractions under the MAIS-O43 generator is an open and, given Probe~B's cost figures, inexpensive question.

— A Dominant Diffuse Phase in the Sparse Autoencoder Phase Diagram  (2609.10299 - Plascencia, 9 Sep 2026) in Section 7, Discussion, paragraph “Practical reading”