Abstract

This paper presents a reproducibility study of "Bilinear MLPs enable weight-based mechanistic interpretability" by Pearce et al. (2025), which proposes that bilinear architectures possess intrinsic interpretability properties accessible via eigenvalue decomposition. We verify the core empirical image classification claims. Our results confirm the findings for image classification: bilinear layers consistently exhibit an interpretable low-rank structure where the leading eigenvectors capture the majority of task-relevant information, allowing for significant truncation without performance loss. Furthermore, we validate that these eigenstructures are stable across random initializations and varying model sizes. Additionally, we explore extensions to the original work, demonstrating that adversarial training (specifically PGD) enhances the interpretability of eigenvector features on MNIST. Finally, we explored generalization on more complex RGB datasets, such as CIFAR-10, CIFAR-100, and Tiny ImageNet, which have generated eigenvectors with uninterpretable structures. All our code is publicly available: https://github.com/Honza0105/Bilinear-MLPs-reproducibility-study