Taming Polysemanticity in LLMs: Provable Feature Recovery via Sparse
  Autoencoders
Authors: name: Siyu Chen, name: Heejune Sheen, name: Xuyuan Xiong, name: Tianhao Wang, name: Zhuoran Yang

We study the challenge of achieving theoretically grounded feature recovery
using Sparse Autoencoders (SAEs) for the interpretation of Large Language
Models. Existing SAE training algorithms often lack rigorous mathematical
guarantees and suffer from practical limitations such as hyperparameter
sensitivity and instability. To address these issues, we first propose a novel
statistical framework for the feature recovery problem, which includes a new
notion of feature identifiability by modeling polysemantic features as sparse
mixtures of underlying monosemantic concepts. Building on this framework, we
introduce a new SAE training algorithm based on ``bias adaptation'', a
technique that adaptively adjusts neural network bias parameters to ensure
appropriate activation sparsity. We theoretically prove that this
algorithm correctly recovers all monosemantic features when input data is
sampled from our proposed statistical model. Furthermore, we develop an
improved empirical variant, Group Bias Adaptation (GBA), and
demonstrate its superior performance against benchmark methods when
applied to LLMs with up to 1.5 billion parameters. This work represents a
foundational step in demystifying SAE training by providing the first SAE
algorithm with theoretical recovery guarantees, thereby advancing the
development of more transparent and trustworthy AI systems through enhanced
mechanistic interpretability.