Behavioral Compositionality of Sparse Autoencoder Representations
Sparse autoencoders (SAEs) represent model activations with sparse, linearly decoded features, but the downstream effects of those features need not compose additively. We introduce SAE Additivity Residuals (SAR), which measure the behavioral variation left unexplained above a chosen interaction order. Under independent feature subset sampling, population SAR is exactly the normalized energy of interactions above that order and bounds coalition ordering error for the optimal low order approximation. To distinguish compositionality associated with the SAE representation from that induced by downstream computation, we compare learned SAE coordinates with sum preserving random rotations of t...
| Authors | Haotian Ma, Ziye Mei, Frederic Sala |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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