PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decoding
This addresses the limitation of SAEs in interpretability for neural networks, particularly in language models, by enabling decomposition of compound concepts into interpretable constituents, though it is an incremental improvement over existing SAE methods.
The paper tackles the problem that sparse autoencoders (SAEs) cannot capture compositional structure in neural network representations due to linear reconstruction assumptions, and introduces PolySAE, which extends SAEs with polynomial decoding to model feature interactions, achieving an average 8% improvement in probing F1 across models while maintaining reconstruction error.
Sparse autoencoders (SAEs) have emerged as a promising method for interpreting neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume that features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether "Starbucks" arises from the composition of "star" and "coffee" features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3% on GPT2). Across four language models and three SAE variants, PolySAE achieves an average improvement of approximately 8% in probing F1 while maintaining comparable reconstruction error, and produces 2-10$\times$ larger Wasserstein distances between class-conditional feature distributions. Critically, learned interaction weights exhibit negligible correlation with co-occurrence frequency ($r = 0.06$ vs. $r = 0.82$ for SAE feature covariance), suggesting that polynomial terms capture compositional structure, such as morphological binding and phrasal composition, largely independent of surface statistics.