SCALAR: Benchmarking SAE Interaction Sparsity in Toy LLMs
This work addresses a bottleneck in interpretability research by providing tools to measure and improve interaction sparsity in SAEs, though it is incremental as it builds on existing SAE methods.
The paper tackles the problem of sparse cross-layer connections in sparse autoencoders (SAEs) for mechanistic interpretability, introducing the SCALAR benchmark and Staircase SAEs, which improve relative sparsity by 59.67% in feedforward layers and 63.15% in transformer blocks compared to baseline methods.
Mechanistic interpretability aims to decompose neural networks into interpretable features and map their connecting circuits. The standard approach trains sparse autoencoders (SAEs) on each layer's activations. However, SAEs trained in isolation don't encourage sparse cross-layer connections, inflating extracted circuits where upstream features needlessly affect multiple downstream features. Current evaluations focus on individual SAE performance, leaving interaction sparsity unexamined. We introduce SCALAR (Sparse Connectivity Assessment of Latent Activation Relationships), a benchmark measuring interaction sparsity between SAE features. We also propose "Staircase SAEs", using weight-sharing to limit upstream feature duplication across downstream features. Using SCALAR, we compare TopK SAEs, Jacobian SAEs (JSAEs), and Staircase SAEs. Staircase SAEs improve relative sparsity over TopK SAEs by $59.67\% \pm 1.83\%$ (feedforward) and $63.15\% \pm 1.35\%$ (transformer blocks). JSAEs provide $8.54\% \pm 0.38\%$ improvement over TopK for feedforward layers but cannot train effectively across transformer blocks, unlike Staircase and TopK SAEs which work anywhere in the residual stream. We validate on a $216$K-parameter toy model and GPT-$2$ Small ($124$M), where Staircase SAEs maintain interaction sparsity improvements while preserving feature interpretability. Our work highlights the importance of interaction sparsity in SAEs through benchmarking and comparing promising architectures.