As we increase the number of features in the SAE, hierarchical features tend to split into finer features ("math" may split into "algebra", "geometry", etc.), a phenomenon referred to as feature splitting. However, we show that sparse decomposition and splitting of hierarchical features is not robust. Specifically, we show that seemingly monosemantic features fail to fire where they should, and instead get "absorbed" into their children features. We coin this phenomenon feature absorption, and show that it is caused by optimizing for sparsity in SAEs whenever the underlying features form a hierarchy. We introduce a metric to detect absorption in SAEs, and validate our findings empirically on hundreds of LLM SAEs. Our investigation suggests that varying SAE sizes or sparsity is insufficient to solve this issue. We discuss the implications of feature absorption in SAEs and some potential approaches to solve the fundamental theoretical issues before SAEs can be used for interpreting LLMs robustly and at scale.

As we increase the number of features in the SAE, hierarchical features tend to split into finer features ("math" may split into "algebra", "geometry", etc.), a phenomenon referred to as feature splitting. However, we show that sparse decomposition and splitting of hierarchical features is not robust. Specifically, we show that seemingly monosemantic features fail to fire where they should, and instead get "absorbed" into their children features. We coin this phenomenon feature absorption, and show that it is caused by optimizing for sparsity in SAEs whenever the underlying features form a hierarchy. We introduce a metric to detect absorption in SAEs, and validate our findings empirically on hundreds of LLM SAEs. Our investigation suggests that varying SAE sizes or sparsity is insufficient to solve this issue. We discuss the implications of feature absorption in SAEs and some potential approaches to solve the fundamental theoretical issues before SAEs can be used for interpreting LLMs robustly and at scale.

Understanding the internal representations of large language models is crucial for ensuring their reliability and safety, with sparse autoencoders (SAEs) emerging as a promising interpretability approach. However, current SAE training methods face feature absorption, where features (or neurons) are absorbed into each other to minimize $L_1$ penalty, making it difficult to consistently identify and analyze model behaviors. We introduce Adaptive Temporal Masking (ATM), a novel training approach that dynamically adjusts feature selection by tracking activation magnitudes, frequencies, and reconstruction contributions to compute importance scores that evolve over time. ATM applies a probabilistic masking mechanism based on statistical thresholding of these importance scores, creating a more natural feature selection process. Through extensive experiments on the Gemma-2-2b model, we demonstrate that ATM achieves substantially lower absorption scores compared to existing methods like TopK and JumpReLU SAEs, while maintaining excellent reconstruction quality. These results establish ATM as a principled solution for learning stable, interpretable features in neural networks, providing a foundation for more reliable model analysis.

It is assumed that sparse autoencoders (SAEs) decompose polysemantic activations into interpretable linear directions, as long as the activations are composed of sparse linear combinations of underlying features. However, we find that if an SAE is more narrow than the number of underlying "true features" on which it is trained, and there is correlation between features, the SAE will merge components of correlated features together, thus destroying monosemanticity. In LLM SAEs, these two conditions are almost certainly true. This phenomenon, which we call feature hedging, is caused by SAE reconstruction loss, and is more severe the narrower the SAE. In this work, we introduce the problem of feature hedging and study it both theoretically in toy models and empirically in SAEs trained on LLMs. We suspect that feature hedging may be one of the core reasons that SAEs consistently underperform supervised baselines. Finally, we use our understanding of feature hedging to propose an improved variant of matryoshka SAEs. Importantly, our work shows that SAE width is not a neutral hyperparameter: narrower SAEs suffer more from hedging than wider SAEs. As large language models (LLMs) are deployed in real-world applications, it is increasingly important to understand their internal workings. SAEs have the advantage of operating completely unsupervised, and can easily be scaled to millions of neurons in its hidden layer (hereafter called "latents" While SAEs showed promising results, recent work has cast doubt on the performance of SAEs relative to baseline techniques. Wu et al. (2025) show that SAEs underperform on both concept steering and detection relative to baselines, and Kantamneni et al. (2025) show that SAEs underperform simple linear probes on both in-domain and out-of-domain detection, even when the probes have very few training samples. The question, then, is why do SAEs underperform relative to other techniques? And if we can identify the problems holding back SAEs, can we then fix those problems?

Sparse autoencoders (SAEs) are a technique for sparse decomposition of neural network activations into human-interpretable features. However, current SAEs suffer from feature absorption, where specialized features capture instances of general features creating representation holes, and feature composition, where independent features merge into composite representations. In this work, we introduce Orthogonal SAE (OrtSAE), a novel approach aimed to mitigate these issues by enforcing orthogonality between the learned features. By implementing a new training procedure that penalizes high pairwise cosine similarity between SAE features, OrtSAE promotes the development of disentangled features while scaling linearly with the SAE size, avoiding significant computational overhead. We train OrtSAE across different models and layers and compare it with other methods. We find that OrtSAE discovers 9% more distinct features, reduces feature absorption (by 65%) and composition (by 15%), improves performance on spurious correlation removal (+6%), and achieves on-par performance for other downstream tasks compared to traditional SAEs.

Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting neural networks by extracting the concepts represented in their activations. However, choosing the size of the SAE dictionary (i.e. number of learned concepts) creates a tension: as dictionary size increases to capture more relevant concepts, sparsity incentivizes features to be split or absorbed into more specific features, leaving high-level features missing or warped. We introduce Matryoshka SAEs, a novel variant that addresses these issues by simultaneously training multiple nested dictionaries of increasing size, forcing the smaller dictionaries to independently reconstruct the inputs without using the larger dictionaries. This organizes features hierarchically - the smaller dictionaries learn general concepts, while the larger dictionaries learn more specific concepts, without incentive to absorb the high-level features. We train Matryoshka SAEs on Gemma-2-2B and TinyStories and find superior performance on sparse probing and targeted concept erasure tasks, more disentangled concept representations, and reduced feature absorption. While there is a minor tradeoff with reconstruction performance, we believe Matryoshka SAEs are a superior alternative for practical tasks, as they enable training arbitrarily large SAEs while retaining interpretable features at different levels of abstraction.

Sparse Autoencoders (SAEs) have emerged as a promising approach to decompose the activations of Large Language Models (LLMs) into human-interpretable latents. In this paper, we pose two questions. First, to what extent do SAEs extract monosemantic and interpretable latents? Second, to what extent does varying the sparsity or the size of the SAE affect monosemanticity / interpretability? By investigating these questions in the context of a simple first-letter identification task where we have complete access to ground truth labels for all tokens in the vocabulary, we are able to provide more detail than prior investigations. Critically, we identify a problematic form of feature-splitting we call feature absorption where seemingly monosemantic latents fail to fire in cases where they clearly should. Our investigation suggests that varying SAE size or sparsity is insufficient to solve this issue, and that there are deeper conceptual issues in need of resolution.