Kronecker Factorization Improves Efficiency and Interpretability of Sparse Autoencoders

Sparse Autoencoders (SAEs) have demonstrated significant promise in interpreting the hidden states of language models by decomposing them into interpretable latent directions. However, training and interpreting SAEs at scale remains challenging, especially when large dictionary sizes are used. While decoders can leverage sparse-aware kernels for efficiency, encoders still require computationally intensive linear operations with large output dimensions. To address this, we propose KronSAE, a novel architecture that factorizes the latent representation via Kronecker product decomposition, drastically reducing memory and computational overhead. Furthermore, we introduce mAND, a differentiable activation function approximating the binary AND operation, which improves interpretability and performance in our factorized framework.