HH-SAE: Discovering and Steering Hierarchical Knowledge of Complex Manifolds

Learning hierarchical features in Sparse Autoencoders (SAEs) is essential for capturing the structured nature of real-world data and mitigating issues like feature absorption or splitting. Existing works attempt to identify hierarchical relationships within independent feature sets by relying on activation coverage, the assumption that child feature should only activate when its parent feature activates. However, we demonstrate that this condition alone is insufficient; that is, it often produces false positives where parent and child concepts are semantically unrelated. To address this, we introduce a novel reconstruction condition that enforces a deeper functional link between hierarchical levels. By combining both activation and reconstruction constraints, we propose the Tree SAE, a model designed to learn hierarchical structures directly from within the feature set. Our results demonstrate that Tree SAEs significantly surpass the existing SAEs at learning hierarchical pairs while maintaining competitive performance to the state-of-the-art on several key benchmarks. Finally, we demonstrate the practical utility of our Tree SAE in mapping the geometry of child feature subspaces and uncovering the complex hierarchical concept structures encoded within large language models.

While sparse autoencoders (SAEs) have generated significant excitement, a series of negative results have added to skepticism about their usefulness. Here, we establish a conceptual distinction that reconciles competing narratives surrounding SAEs. We argue that even if SAEs may be less effective for \textit{acting on known concepts}, SAEs are especially powerful tools for \textit{discovering unknown concepts}. This distinction separates existing negative results from positive results, and suggests several classes of SAE applications. Specifically, we outline use cases for SAEs in (i) ML interpretability, explainability, fairness, auditing, and safety, and (ii) social and health sciences.

Sparse autoencoders (SAEs) have become an important tool for unsupervised concept discovery in large models. To make the resulting feature spaces more interpretable and manageable, recent approaches have begun imposing hierarchical structure, either explicitly or as an implicit effect of training constraints, yet rigorous comparison remains difficult. There are no agreed-upon requirements for what a meaningful feature hierarchy should satisfy, and evaluation has largely relied on qualitative illustrations with fragmented quantitative protocols. To address this, we derive a set of key requirements for generalization/specialization hierarchies in unsupervised concept discovery, drawing on semantic net and taxonomy research alongside recent SAE work, and use them to derive a concrete evaluation protocol. Applying this protocol to current SAE approaches trained on visual data, we find that while feature spaces generally provide a basis for sensible hierarchies, establishing good hierarchical structure remains challenging. In particular, feature absorption, both in its well-known hard form and in a continuous, soft form, systematically compromises hierarchy quality, pointing to a fundamental tension that future approaches will need to navigate.