Title: Feature Hedging: Correlated Features Break Narrow Sparse Autoencoders
Venue: NeurIPS 2025
Accepted: no
Keywords: sparse autoencoders

SAEs

interpretability

NLP
Abstract: 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. Our work shows there remain fundamental issues with SAEs, but we are hopeful that that highlighting feature hedging will catalyze future advances that allow SAEs to achieve their full potential of interpreting LLMs at scale.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents the new concept of feature hedging in Sparse Autoencoders (SAEs), where correlated and hierarchical features are mixed into one latent when the number of latent is lower than the number of true features. In opposition to feature absorption, where a child feature prevents a parent feature from firing, hedging happens in narrow SAEs. After illustrating this phenomenon on a toy example, the authors propose a score (the hedging degree) to measure how much hedging occurs in a given SAE. Based on these insights, they propose to add a new term to Matryoshka SAEs to balance hedging and absorption.\n\nSTRENGTHS AND WEAKNESSES:\nQuality \n=====\n[+] The methods used are appropriate, and the claims are generally well-supported\n\n[+] I like the fact that the authors carefully present the studied phenomenon (feature hedging) through a toy example before. \n\n[+] The limitations of this work are discussed.\n\n[-] I am not entirely sure of the soundness of the proposed hedging degree score. This is my primary concern, as a good part of the paper is based on the results of the hedging degree (see questions 1-2)\n\n[-] The experimental section is limited to one LLM (see question 4)\n\n[-] The claim of providing a theoretical study of hedging is misleading (see question 5)\n\n\nClarity\n=====\n[+] The paper is well-written, well-structured, and easy to follow\n\n[-] Some minor details are lacking to fully understand some parts of the experiment (see question 3 and minor comments)\n\n[-] The readability of some figures could be improved (see minor comments)\n\n[-] I think there is a small typo in Eq.7 (see minor comments)\n\nSignificance\n=========\n[+]  The results could help the community design better SAEs\n\n[-] The proposed solution (the weighted Matryoshka SAE) is not fully convincing, but the authors acknowledge that.\n\nOriginality\n========\n[+] As far as I know, the observed phenomenon was not discussed in the SAE literature before.\n\n[+] This provides new insights into the poor performance of SAEs compared to other methods.\n\n[-] The fact that multiple features will be encoded into one latent variable if the number of latent variables is low enough is not very surprising. A related issue was discussed in the VAE disentanglement literature a few years ago in [1,2].\n\nReferences:\n=========\n[1] Dai, B., & Wipf, D. (2019). Diagnosing and Enhancing VAE Models. International Conference on Learning Representations. Retrieved from https://openreview.net/forum?id=B1e0X3C9tQ\n[2] Rolinek, M., Zietlow, D., & Martius, G. (2019). Variational autoencoders pursue pca directions (by accident). In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (pp. 12406-12415).\n\nRebuttal\n=======\nI did not raise my score higher as the computational cost of the proposed method and its limited evaluation (also discussed by reviewer qeRK) lower its applicability and broader impact.\n\nQUESTIONS:\nMajor comments\n=============\n___My main concern is about the stability of the proposed hedging degree (see questions 1-2). I will be happy to raise my score should these questions be satisfactorily answered.___\n\n  \n1. l. 151-157: How can we be sure that the \"parent\" decoder (this is $W_{dec}^1[0:L]$, correct?) remains unchanged? Is it possible that in some cases $W_{dec}^1[0:L]$ learns a mix of $f_1$ and $f_2$ (as in the first row of fig. 1b) and $f_1$ is correctly tracked by $W_{dec}^1[L:L+N]$. If so, how does this impact Eq.5-7? If not, why?\n2. If I understand correctly, in Eq.5 when there is no hedging and no absorption, we have $\\\\delta_L \\\\approx 0$, so we should have $h \\\\approx 0$, which makes sense. When there is some hedging, fewer features would be learned in one latent when we increase the dimensionality, so we would expect to have $| \\\\delta_L |  > 0$ where $| \\\\cdot | $ is the absolute value. Because these features are learned somewhere in the N new latents, we would expect to have $h > 0$. Assuming that absorption will only happen in the N new latents (see comment 1. about this), we should obtain the same $h$ regardless of whether absorption occurs in the new latents or not. All this is fine (if the assumption holds), but what happens when we add more latents to an SAE already showing some absorption? Could we have some cases there where $h > 0$ because of this? I would be happy to raise my score if the authors provide some justification for this and the assumption discussed in question 1, which can alleviate my concern that $h > 0$ may not only be due to hedging.\n3. If I get this correctly, the encoder cosine similarity is $cos\\\\_sim(f(a), a)$, but I don't know how the decoder cosine similarity is computed. Is this $cos\\\\_sim(\\\\hat{a}, a)$? something else? A clarification about this would ease the reading.\n4. It would be nice to have an analysis of more than one LLM in the experimental section. However, I am aware that this is time-consuming and may not be feasible within the allocated time.\n5. l. 10 The phrasing \"We study it both theoretically in toy models [...]\" could be misleading as what is presented is an empirical observation on toy models, not a mathematical proof of feature hedging. Please rephrase this to clarify it.\n\nMinor comments\n=============\n___These comments are easy fixes which would, in my opinion, ease the reading of the paper.___\n\n- Fig 1 is not black-and-white printer-friendly. Adding the corresponding cosine similarity scores, as in Fig.2, would significantly improve this.\n- Fig. 7b slightly stretches over the margin. Truncating a bit of the text in 7.b may help reduce the size of this figure and fix this issue.\n- The norm is already used in Eq. 7, so I think it is not necessary in Eq. 6, especially since this is a projection.\n- In Eq. 7, it would ease the reading to explain that $\\\\delta_L[i]$ is the difference between the weights of the $i^{th}$ feature.\n- In A4, it would be nice to have larger figures.\n- References with a large number of authors would be more readable with ellipses after the 20th, as per APA standards.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper investigates feature hedging, a failure mode of sparse auto-encoders (SAEs) in which correlated features collapse into a single latent when the dictionary is narrower than the number of underlying features, breaking monosemanticity. The authors demonstrate this issue theoretically in toy models and contrast it with the feature absorption failure mode. They then introduce hedging degree, a simple retrain-and-compare metric that isolates hedging. They empirically evaluate the impact of feature hedging in SAEs trained on LLMs. They show that feature hedging arises from the reconstruction loss term dominating the sparsity term when the latent width is too narrow. Finally, they propose balance matryoshka SAEs, which weigh the nested-loss terms so that positive (hedging) and negative (absorption) cross-feature interactions cancel, offering relative improvements on SAEBench interpretability metrics such as TPP and SCR.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n* The paper provides a very good theoretical analysis of feature hedging and demonstrates its existence.\n\n* The authors introduce hedging degree, as a new metric that isolates feature hedging.\n\n* The paper empirically evaluates the impact of feature hedging in SAEs trained on LLMs.\n\n* The paper proposes balance matryoshka SAEs, which offer good relative improvements on SAEBench interpretability metrics.\n\n* Good supplementary material with detailed experiments and analysis.\n\n**Weaknesses**\n\n* It appears that the hedging degree metric involves costly re-training, limiting practical applicability.\n\n* There is no clear evaluation against other supervised baselines mentioned in the paper, such as supervised SAEs. With only the relative results, and with the literature the paper cites, it is unclear whether the absolute performance is still lower than supervised SAEs. Given the paper is about unsupervised SAEs, this may not be strictly necessary for the core contribution. However, the comparison would be very useful.\n\n* Although the paper presents a thoughtful analysis of feature hedging and a neat loss-balancing fix, the absence of evaluations against direct baselines weakens the paper's position on broader impact. Perhaps, authors can discuss this aspect or consider adding some direct comparisons.\n\n* While the empirical results are compelling, they are limited to specific models (Gemma-2-2B and Llama-3.2-1b). Broader validation across more models or architectures could strengthen the findings. While it is understood that this may not be possible within a short time-frame, authors should at least discuss relevant aspects. \n\n* The proposed solution is promising but may not universally balance hedging and absorption across the entire feature space, which authors acknowledge. Further exploration of per-latent balancing could strengthen the paper.\n\nQUESTIONS:\nPlease see the Strengths and Weaknesses Section for more details.\n\n1. As stated before, computing the hedging-degree metric is not cheap. Can authors discuss or devise a cheaper proxy that avoids retraining with N new latents, especially exploiting other proxies, such as second-order gradients?\n\n2. The paper states (line#238) that 'balancing both hedging and absorption with a single $\\beta_m$ is not always possible'. Yet the proposed solution still couples every nested-loss weight to one global multiplier. Could the authors clarify whether, after selecting the best multiplier, any individual latents  still hedge (or absorb)? Perhaps this can be visualised using a plot illustrating per-latent hedging degree vs. $\\beta_m$ (or similar). Although such a plot would not make the situation fully transparent,  it would  still useful. Secondly, if such a subset of latents exists, can it be detected early to avoid unnecessary multiplier sweeps?  Addressing these points would clarify how far a single global multiplier goes toward balancing hedging and absorption.\n\n3.\tThe paper acknowledges the divergence between the SCR and TPP curves in the multiplier sweep, but does not provide a clear explanation for this phenomenon. This discrepancy leaves it unclear which metric should carry more weight. Does the pattern persist if the ablation budget k is varied, for example, comparing the results for $k=10$, $k=2$ and $k=20$? Could the authors analyse the root cause of this behaviour (for example, dataset imbalance, probe capacity, or differences in the metric definitions), and add a discussion? Resolving (or at least clarifying) this issue would strengthen the empirical section.\n\n4.\tIs the hedging phenomenon also common (or at least measurable) in other modalities, for example, in  vision models? If so, how straightforward is it to port the full framework (including metric, and balanced matryoshka loss) to a new setting? In particular, are there any obstacles to finding a suitable weight-balancing schedule for vision SAEs?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors discovered a phenomenon called \"feature hedging,\" where correlated features are merged into a single SAE latent unit. This effect is particularly pronounced in small-sized SAEs. The paper also explores ways to minimize feature hedging and proposes a coefficient for the Matryoshka SAE.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nS1. The motivation is clear, study of the phenomenon is extensive and experiments are thorough.\n\nS2. Analysis builds up on up-to-date research and contributions are novel, including not only analysis of discovered hedging phenomenon but also a method to balance it with absorption.\n\nS3. The experiments are performed with two LLM families, namely Gemma and Llama, which strenghtens the generalizability of results. Analyzed SAEs are of practical dictionary sizes, up to 65k features.\n\nS4. Experimental details are detailed enough to follow and reproduce. Paper is well-written and is relatively easy to understand.\n\nWeaknesses\n\nW1. The paper does not include experiments demonstrating how hedging mitigation influences performance or interpretability on realistic downstream tasks, beyond what's presented in a SAE Bench. It remains unclear whether there exist a real use-cases where we could sacrifice absorption score in favor of better hedging properties, or something like that.\n\nW2. The conclusion about balancing between absorption and hedging relies on toy example setting, where low or high balance ratio $\\beta$ results in more pronounced hedging or absorption score, respectively. Then this result generalizes to the LLM with 2B parameters trained on a highly complicated dataset. The following experiments presented in a Figure 9 suggest that increasing $\\beta$ result in lower absorption rate, but it is unclear how does hedging presence change; only proxy metrics from benchmarks are available. The claim could be strenghtened by adding a discussion about this dynamics.\n\nQUESTIONS:\nQ1: In Section 3 you say that no bias term is added, but in 3.1 you mention the learned decoder bias; could you elaborate on this?\n\nQ2: Have you tried to rule out other causes of feature hedging? Have you identified any plausible alternative explanations?\n\nQ3: Have you analysed the connections of this phenomenon to the feature composition phenomenon that you mention in a Related Work section, where the e.g. feature \"red triangle\" is expected to be a sum of two or more features, but represents a standalone feature? Is this a reverse of hedging?\n\nLIMITATIONS:\nThe authors adequately addressed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces an issue of SAE, referred to as feature hedging, in which SAE merges correlated features into a single latent, leading to degraded interpretability. The authors explain the mechanism of feature hedging: it emerges when the width of SAE is relatively narrow compared to the number of underlying true features. They also demonstrate that the MSE objective contributes to feature hedging, as shown through an analysis of the loss curves. Furthermore, the authors demonstrate that feature hedging indeed occurs in practical settings with Gemma and Llama. To prevent the emergence of feature hedging, the authors introduce a scaling coefficient into the matryoshka SAE objective and show that the proposed method performs well on synthetic data and SAEBench.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. This paper identifies the emergence of the feature hedging problem and explains its underlying mechanism.\n2. A metric for feature hedging is presented.\n3. The authors propose a method to prevent the emergence of feature hedging.\n4. The experimental results show that the proposed method outperforms the baselines on synthetic data and SAEBench.\n\nWeaknesses:\n\nSome parts of the content were difficult to follow:\n\n1. The figures (e.g., Figure 1) are difficult to understand. Please clarify how the cosine similarity is computed. Are these values the cosine similarities between the weight matrices and the input vector (not latents)?\n2. The definition of $f$ appears to be inconsistent. In the introduction, $f$ represents the true feature, while in section 2, it is defined as the encoder’s output (latents). Please clarify or unify the notation.\n3. I understand that hedging and absorbing have opposite effects, and aligning them might diminish both. But, it is unclear why introducing the scaling coefficient would lead to such alignment. Could you please clarify this point?\n4. The authors state, “Under feature absorption … arriving at Figure 1b.” (Lines 153-156). While the example in Figure 1 supports this claim, it is unclear whether this observation holds more generally. Could the authors clarify whether this is a general trend or a case-specific finding?\n5. Based on the analysis, the hedging symmetrically affects the encoder and decoder. But, Figure 8 (a) does not appear to reflect this symmetry. My understanding could be incorrect. Could the authors clarify how to interpret this figure in terms of the symmetry?\n6. I recommend using bold font for vectors and matrices (e.g., Eq. (1)).\n7. I recommend using math font for norms such as L1 and L0 (e.g., line 68).\n8. Please clearly define the meaning of the square bracket notation, especially $\\delta_L[i]$, as used in Eq. (7).\n9. It is unclear why projecting the difference of the updated original latents onto the added N latents in Eq. (7) mitigates noise.\n10. As noted in the limitations, the proposed hedging metric is costly and may be less practical.\n\nQUESTIONS:\nMy concerns and questions are listed in the Weaknesses section.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-04"}