C$^{2}$R: Cross-sample Consistency Regularization Mitigates Feature Splitting and Absorption in Sparse Autoencoders

Haoran Jin, Xiting Wang, Shijie Ren, Hong Xie, Defu Lian

Sparse Autoencoders (SAEs) are widely used to interpret large language models by decomposing activations into sparse, human-understandable features, but scaling to large dictionaries exposes fundamental challenges. Systematic studies reveal pervasive feature splitting that fragments coherent concepts into non-atomic latents and widespread feature absorption that creates arbitrary exceptions in general features, severely compromising latent reliability. These issues stem from inconsistent latent assignment across samples: without cross-sample constraints, per-sample optimization often allows a single underlying concept to be inconsistently distributed across multiple redundant or interfering latents. To address this, we introduce C$^2$R (\underline{\textbf{C}}ross-sample \underline{\textbf{C}}onsistency \underline{\textbf{R}}egularization). C$^2$R explicitly encourages that each semantic feature is consistently represented by a unified latent across the batch by penalizing the co-activation of directionally similar latents. Comprehensive evaluation demonstrates that C$^2$R effectively mitigates both splitting and absorption while, crucially, preserving reconstruction fidelity, providing a principled solution that enhances latent interpretability without degrading model performance. Source code is available at https://github.com/hr-jin/Cross-sample-Consistency-Regularization.