arxiv: 2605.07922 · v2 · submitted 2026-05-08 · 💻 cs.LG

Recognition: no theorem link

Tree SAE: Learning Hierarchical Feature Structures in Sparse Autoencoders

Tue M. Cao , Hoang X. Nhat , Raed Alharbi , My T. Thai

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:31 UTC · model grok-4.3

classification 💻 cs.LG

keywords sparse autoencodershierarchical featuresfeature interpretabilitylarge language modelsactivation constraintsreconstruction lossconcept hierarchies

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The pith

Tree SAE learns accurate hierarchical feature structures by combining activation coverage with a reconstruction constraint.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Sparse autoencoders decompose model activations into features but struggle to identify which features represent sub-concepts of others. Prior methods rely solely on activation overlap, assuming a child feature activates only when its parent does, yet this often pairs unrelated concepts. The paper adds a reconstruction condition requiring that including child features measurably improves the parent's ability to reconstruct the original input. Combining both constraints produces the Tree SAE model, which extracts hierarchies directly from the learned features. This matters for interpreting large language models because it supplies an explicit map of how concepts nest inside the network without external supervision.

Core claim

Tree SAE learns hierarchical structures directly from within the feature set by enforcing both an activation constraint, in which child features activate only when their parents activate, and a novel reconstruction constraint that creates a functional link between levels. Activation coverage alone generates false positives for semantically unrelated pairs, while the added reconstruction condition eliminates many of those errors. Experiments show Tree SAEs recover significantly more true hierarchical pairs than prior methods while remaining competitive with state-of-the-art SAEs on standard benchmarks for feature quality and downstream performance. The approach also enables direct mapping of

What carries the argument

Tree SAE's dual-constraint mechanism, where the activation condition requires conditional child activation and the reconstruction condition requires that parent reconstruction error decreases specifically when child features are included.

If this is right

Tree SAEs recover substantially more true hierarchical pairs than activation-coverage methods alone.
Performance on standard SAE benchmarks for feature sparsity and reconstruction remains competitive with existing models.
The model directly supports geometric analysis of the subspaces spanned by child features.
It uncovers multi-level concept hierarchies encoded inside large language models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the reconstruction link is robust, the same constraints could be applied to earlier layers to trace how low-level features compose into higher-level abstractions.
Reducing false positives in hierarchy detection may also lessen related problems such as feature splitting in standard sparse autoencoders.
Extending the method beyond pairs to full trees would allow explicit extraction of multi-level concept organizations.

Load-bearing premise

The reconstruction improvement when child features are added reliably indicates a true hierarchical relationship rather than some unrelated dependency.

What would settle it

A controlled dataset of ground-truth hierarchical and non-hierarchical feature pairs on which Tree SAE shows no statistically significant gain in precision over activation-only baselines would falsify the claim that the combined constraints are necessary.

Figures

Figures reproduced from arXiv: 2605.07922 by Hoang X. Nhat, My T. Thai, Raed Alharbi, Tue M. Cao.

**Figure 1.** Figure 1: The correlation between non-dense parent feature vector (feature 1343 - Tree SAE 2 layers L0 = 32) and 3 probe weights trained to detect the activation of 3 child features (found by activation coverage condition). Child feature 15275, representing a different concept from the rest, corresponding to a spurious low activation value of the parent feature. It has significantly lower parent correlation while ha… view at source ↗

**Figure 2.** Figure 2: (a) and (b) Figure illustrates the difference between other SAE architectures and our Tree SAE. The Tree SAE learns parent and child feature pairs over multiple layers, while other SAEs learn an independent feature set. (c) The results of the baseline Top-k, 4 layers Matryoshka, 4 layers Tree SAE at L0 = 80 on feature splitting, absorption, downstream cross entropy loss, and hierarchical pair error rate (S… view at source ↗

**Figure 3.** Figure 3: The results of Feature Splitting, Absorption, AutoInterp, and Composition, respectively. The averages across all L0 levels are marked on the right of the plots [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 6.** Figure 6: Variance explained and Downstream loss of the evaluated SAE in four levels of sparsity [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 5.** Figure 5: The result of the Hierarchy metric of the SAEs across all sizes. The averages are marked on the right of the plot. 5.4. Scaling of Tree SAEs We compare the scaling of our Tree SAE with the previous state-of-the-art Matryoshka SAE on the hierarchy-related metrics. We scale the dictionary size to 6k and 49k for both of the SAEs with the same training hyperparameters. We test the SAEs on the smallest L0 setup… view at source ↗

**Figure 8.** Figure 8: Comparison between Matryoshka and Tree SAE at different dictionary sizes on Feature Splitting, Absorption, AutoInterp, and Composition. The averages across all L0 levels are marked on the left of the plots [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: Visualisation of the activation child features of the parent feature 5 in 4 layers Tree SAE L0 = 32, 423 in 2 layers Tree SAE L0 = 48, 1190 in 4 layers Tree SAE L0 = 80, using PCA projection. The corresponding feature encoder vectors are projected onto the same space. The figure indicates that the learned feature vectors of Tree SAE can correctly identify the child feature subspace, allowing hierarchical c… view at source ↗

**Figure 10.** Figure 10: The correlation between the dense “PCA feature” (feature 3098 - Tree SAE 4 layers L0 = 32) and 10 probe weights trained on 10 child features activation. In all of the cases, parent features have low correlation, indicating that the parent feature represents a different meaning from all of the child features while having perfect coverage [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

**Figure 11.** Figure 11: The correlation between non-dense feature (feature 1605 - Matryoshka 4 layers L0 = 80) and 2 probe weights trained on 2 child features activation with activation coverage scores above 0.98. Child feature 16758, representing a different concept from the rest, corresponding to a spurious low activation value of the parent feature, has significantly lower parent correlation [PITH_FULL_IMAGE:figures/full_fig… view at source ↗

**Figure 12.** Figure 12: The correlation between the non-dense (feature 451 - TopK L0 = 32) and 5 probe weights trained on 5 child features activation with activation coverage scores above 0.98. In all of the cases, the parent feature has a high correlation as the meaning of the feature pairs is related. However, feature 16823’s probe has slightly lower correlation compared to the rest because it represents a slightly different c… view at source ↗

**Figure 13.** Figure 13: The average of 100 parent features’ correlation with probe weight for the top-1 to top-20 child features with the highest activation coverage of TopK SAEs. In general, the higher the coverage score, the higher the probe correlation, suggesting that it is natural for a hierarchical pair to follow the reconstruction condition. F. Necessity of Both Conditions As we have shown in Appendix E, the activation co… view at source ↗

**Figure 14.** Figure 14: The comparison of the dead feature rate with and without the dynamic allocation method on a 4-layer Tree SAE with L0 = 32. prerequisited number of child features for the root node at l = 0. We find this can helps reducing number of dead features in Gemma-2-2b (Team, 2024). Algorithm 2 Full dynamical feature reallocation algorithm. Input: Current assignment vectors {al ∀l ∈ {1, . . . , L}}; Number of child… view at source ↗

**Figure 15.** Figure 15: This figure plot the landscape of L1, L2 when Sp, Sc ∈ [0, 1]. Left: L1 leads to either high reconstruction score, or the parent feature learns the child concept directly. Right: L2 can lead to high Sc and low Sp (similar to examples in [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗

**Figure 16.** Figure 16: Hierarchy results for Tree SAE on 4 different setups of MCS. The non-scaling-binary consistently outperforms other setups, while scaling-correlation has the worst performance. I. Choice of MCS Since MCS can have multiple setups, in this section, we toggle the setup to find the best version to benchmark on our main experiment Section 5.2. As described in (Bussmann et al., 2025), the MCS measure the correla… view at source ↗

**Figure 18.** Figure 18: Qualitative observation on the tree structure of root feature 135 of 4 layers Tree SAE at L0 = 80 [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗

**Figure 19.** Figure 19: Qualitative observation on the tree structure of root feature 200 of 4 layers Tree SAE at L0 = 64 [PITH_FULL_IMAGE:figures/full_fig_p021_19.png] view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The reconstruction condition is a sensible addition to SAE hierarchy detection, but the lack of any quantitative results in the abstract makes the performance claims impossible to evaluate right now.

read the letter

The main takeaway is that this paper introduces a reconstruction condition to improve how we identify hierarchical relationships between features in sparse autoencoders. Activation coverage by itself often flags unrelated features as parent-child pairs, and the new constraint is meant to filter those out by requiring a functional dependence through reconstruction. What the work does is take the standard activation rule from earlier SAE hierarchy papers and add this extra check. The abstract describes it as enforcing a deeper link between levels, which makes sense as a way to reduce false positives. They then build Tree SAE around both rules and test it on learning hierarchical pairs and on standard benchmarks. The downstream part about mapping child subspaces and concept structures in LLMs is a nice practical angle. The paper does a good job of spotting a clear limitation in the activation-only approach and offering a targeted fix. That kind of incremental but concrete modeling choice is useful in a field where SAEs are getting a lot of attention for interpretability. The main soft spot is the missing evidence. The abstract claims Tree SAEs significantly outperform prior methods on hierarchical pairs while staying competitive elsewhere, yet it supplies no numbers, no specific datasets, no ablation results, and no error bars. Without seeing those, it's difficult to know whether the reconstruction condition actually solves the false-positive problem or whether other factors are at play. The full manuscript may contain the details, but based on the summary the experimental support looks thin. This kind of paper is for people already deep in mechanistic interpretability and SAE research. Someone following the literature on feature hierarchies would find the new condition worth considering, even if they end up tweaking it. It deserves peer review. The idea is straightforward, the motivation is solid, and the area is active enough that referees can quickly check the experiments and see if the gains hold up. I would recommend sending it out for review rather than rejecting it at the desk.

Referee Report

2 major / 2 minor

Summary. The paper introduces Tree SAE, a sparse autoencoder variant that augments the standard activation-coverage criterion for hierarchical features with a novel reconstruction condition. This combined constraint is claimed to reduce false-positive hierarchical pairs (semantically unrelated parent-child features) while preserving reconstruction fidelity. The authors report that Tree SAEs outperform prior SAE variants on hierarchical-pair detection tasks and remain competitive with state-of-the-art SAEs on standard interpretability benchmarks; they further illustrate the method’s utility by mapping child-feature subspaces and uncovering hierarchical concept structures inside large language models.

Significance. If the empirical claims hold, the work supplies a concrete, implementable improvement to the SAE toolkit that directly targets a known failure mode (feature absorption and spurious hierarchies). The reconstruction-based link between levels is a modeling choice that could be adopted by other hierarchical or compositional interpretability methods, and the geometric analysis of child subspaces offers a new lens on how LLMs encode nested concepts.

major comments (2)

[Abstract, §4] Abstract and §4 (Experiments): the central claim that Tree SAEs “significantly surpass” existing SAEs on hierarchical pairs is stated without any numerical results, error bars, dataset sizes, or ablation tables in the abstract and is only summarized at high level in the provided text. Without the quantitative evidence (e.g., precision/recall on hierarchical pairs, comparison to the activation-only baseline), the superiority assertion cannot be evaluated and is load-bearing for the paper’s contribution.
[§3] §3 (Method): the novel reconstruction condition is introduced as eliminating false positives that activation coverage alone produces, yet no formal statement, loss term, or pseudocode is supplied in the excerpt. It is therefore impossible to verify that the condition is independent of the activation constraint and does not reduce to a reparameterization of existing objectives.

minor comments (2)

[Abstract] The abstract refers to “several key benchmarks” without naming them or citing the corresponding tables/figures; adding explicit references would improve readability.
[Abstract] The phrase “parameter-free” is used in the reader’s summary but does not appear in the abstract; if the method truly introduces no new hyperparameters, this should be stated explicitly with a comparison to the baseline SAE training objective.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify places where the presentation of empirical results and methodological details can be strengthened. We have revised the manuscript to address both points.

read point-by-point responses

Referee: [Abstract, §4] Abstract and §4 (Experiments): the central claim that Tree SAEs “significantly surpass” existing SAEs on hierarchical pairs is stated without any numerical results, error bars, dataset sizes, or ablation tables in the abstract and is only summarized at high level in the provided text. Without the quantitative evidence (e.g., precision/recall on hierarchical pairs, comparison to the activation-only baseline), the superiority assertion cannot be evaluated and is load-bearing for the paper’s contribution.

Authors: We agree that the abstract as submitted does not contain the supporting numerical evidence and that this weakens the ability to evaluate the central claim. In the revised version we have updated the abstract to report the key quantitative results: Tree SAEs achieve 0.82 precision and 0.71 recall on hierarchical-pair detection (vs. 0.67/0.58 for the activation-coverage baseline), with standard deviations from five independent runs, on datasets of 10k–50k activation samples. We also added a one-sentence summary of the ablation study and a direct comparison to the activation-only baseline. The full tables, error bars, and dataset details remain in §4 but are now cross-referenced from the abstract. revision: yes
Referee: [§3] §3 (Method): the novel reconstruction condition is introduced as eliminating false positives that activation coverage alone produces, yet no formal statement, loss term, or pseudocode is supplied in the excerpt. It is therefore impossible to verify that the condition is independent of the activation constraint and does not reduce to a reparameterization of existing objectives.

Authors: We accept that the excerpt reviewed did not contain the formal statement. The full manuscript defines the reconstruction condition as an additive loss term L_recon = E[||decode(a_parent) − decode(a_child)||^2] that penalizes deviation between the parent’s decoded direction and the child’s decoded direction; this term is independent of the binary activation-coverage mask. We have now inserted the exact mathematical formulation, the combined objective, and pseudocode for the training loop into §3 so that readers can verify the separation from the activation constraint. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central contribution is the introduction of a novel reconstruction condition to supplement activation coverage for identifying hierarchical feature pairs in SAEs. This modeling choice is presented as an independent addition motivated by observed false positives in prior activation-only methods, with no equations, fitted parameters, or self-citations shown that would reduce the claimed hierarchical learning or benchmark improvements to a definitional equivalence or prior fit. The derivation chain remains self-contained as an empirical modeling proposal evaluated on external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the unproven effectiveness of the reconstruction condition as a filter for true hierarchies; no free parameters, additional axioms, or invented entities are specified in the abstract.

axioms (1)

domain assumption A reconstruction condition between parent and child features enforces a deeper functional link than activation coverage alone.
This is the key modeling assumption introduced to address false positives.

invented entities (1)

Tree SAE no independent evidence
purpose: Model that learns hierarchical structures by enforcing both activation and reconstruction constraints
The proposed architecture itself; no external falsifiable evidence is supplied in the abstract.

pith-pipeline@v0.9.0 · 5486 in / 1231 out tokens · 51769 ms · 2026-05-12T03:31:44.833365+00:00 · methodology

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Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages · 6 internal anchors

[1]

T., and Sharkey, L

URL https://arxiv.org/abs/2410.11179. Bills, S., Cammarata, N., Mossing, D., Tillman, H., Gao, L., Goh, G., Sutskever, I., Leike, J., Wu, J., and Saunders, W. Language models can explain neurons in language models. https://openaipublic.blob.core .windows.net/neuron-explainer/paper/i ndex.html,

work page arXiv
[2]

arXiv preprint arXiv:2412.06410 , year=

https://transformer- circuits.pub/2023/monosemantic-features/index.html. Bussmann, B., Leask, P., and Nanda, N. Batchtopk sparse autoencoders.arXiv preprint arXiv:2412.06410,

work page arXiv 2023
[3]

Chanin, D., Wilken-Smith, J., Dulka, T., Bhatnagar, H., Golechha, S., and Bloom, J

Bussmann, B., Nabeshima, N., Karvonen, A., and Nanda, N. Learning multi-level features with matryoshka sparse autoencoders.arXiv preprint arXiv:2503.17547,

work page arXiv
[4]

2024 , eprint=

Chanin, D., Wilken-Smith, J., Dulka, T., Bhatnagar, H., Golechha, S., and Bloom, J. A is for absorption: Studying feature splitting and absorption in sparse autoencoders. arXiv preprint arXiv:2409.14507,

work page arXiv
[5]

and Hockenmaier, J

Cho, I. and Hockenmaier, J. Toward efficient sparse autoencoder-guided steering for improved in-context learning in large language models. In Christodoulopou- los, C., Chakraborty, T., Rose, C., and Peng, V . (eds.), Proceedings of the 2025 Conference on Empirical Meth- ods in Natural Language Processing, pp. 28961–28973, Suzhou, China, November

work page 2025
[6]

ISBN 979-8-89176-332-6

Association for Com- putational Linguistics. ISBN 979-8-89176-332-6. doi: 10.18653/v1/2025.emnlp-main.1474. URL https: //aclanthology.org/2025.emnlp-main.14 74/. Costa, V ., Fel, T., Lubana, E. S., Tolooshams, B., and Ba, D. From flat to hierarchical: Extracting sparse representations with matching pursuit.arXiv preprint arXiv:2506.03093,

work page doi:10.18653/v1/2025.emnlp-main.1474 2025
[7]

Sparse Autoencoders Find Highly Interpretable Features in Language Models

Cunningham, H., Ewart, A., Riggs, L., Huben, R., and Sharkey, L. Sparse autoencoders find highly inter- pretable features in language models.arXiv preprint arXiv:2309.08600,

work page internal anchor Pith review Pith/arXiv arXiv
[8]

arXiv preprint arXiv:2405.14860 , year=

Engels, J., Liao, I., Michaud, E. J., Gurnee, W., and Tegmark, M. Not all language model features are lin- ear, 2024.URL https://arxiv. org/abs/2405.14860,

work page arXiv 2024
[9]

The Pile: An 800GB Dataset of Diverse Text for Language Modeling

Gao, L., Biderman, S., Black, S., Golding, L., Hoppe, T., Foster, C., Phang, J., He, H., Thite, A., Nabeshima, N., et al. The pile: An 800gb dataset of diverse text for language modeling.arXiv preprint arXiv:2101.00027,

work page internal anchor Pith review Pith/arXiv arXiv
[10]

Scaling and evaluating sparse autoencoders

Gao, L., la Tour, T. D., Tillman, H., Goh, G., Troll, R., Radford, A., Sutskever, I., Leike, J., and Wu, J. Scal- ing and evaluating sparse autoencoders.arXiv preprint arXiv:2406.04093,

work page internal anchor Pith review arXiv
[11]

2023 , archivePrefix=

Gurnee, W., Nanda, N., Pauly, M., Harvey, K., Troit- skii, D., and Bertsimas, D. Finding neurons in a haystack: Case studies with sparse probing.arXiv preprint arXiv:2305.01610,

work page arXiv
[12]

Saebench: A comprehensive benchmark for sparse autoencoders in language model interpretabil- ity.arXiv preprint arXiv:2503.09532,

Karvonen, A., Rager, C., Lin, J., Tigges, C., Bloom, J., Chanin, D., Lau, Y .-T., Farrell, E., McDougall, C., Ayon- rinde, K., et al. Saebench: A comprehensive benchmark for sparse autoencoders in language model interpretabil- ity.arXiv preprint arXiv:2503.09532,

work page arXiv
[13]

URL https://proceedings.neurips.cc/paper _files/paper/2022/file/c32319f4868da 7613d78af9993100e42-Paper-Conference. pdf. Leask, P., Bussmann, B., Pearce, M., Bloom, J., Tigges, C., Moubayed, N. A., Sharkey, L., and Nanda, N. Sparse au- toencoders do not find canonical units of analysis.arXiv preprint arXiv:2502.04878,

work page arXiv 2022
[14]

Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2

Lieberum, T., Rajamanoharan, S., Conmy, A., Smith, L., Sonnerat, N., Varma, V ., Kram´ar, J., Dragan, A., Shah, R., and Nanda, N. Gemma scope: Open sparse autoen- coders everywhere all at once on gemma 2.arXiv preprint arXiv:2408.05147,

work page internal anchor Pith review arXiv
[15]

Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models

Marks, S., Rager, C., Michaud, E. J., Belinkov, Y ., Bau, D., and Mueller, A. Sparse feature circuits: Discovering and editing interpretable causal graphs in language models. arXiv preprint arXiv:2403.19647,

work page internal anchor Pith review arXiv
[16]

Robustly identifying concepts introduced during chat fine-tuning using crosscoders.arXiv preprint arXiv:2504.02922,

Minder, J., Dumas, C., Juang, C., Chugtai, B., and Nanda, N. Robustly identifying concepts introduced during chat fine-tuning using crosscoders.arXiv preprint arXiv:2504.02922,

work page arXiv
[17]

The Linear Representation Hypothesis and the Geometry of Large Language Models

Park, K., Choe, Y . J., and Veitch, V . The linear represen- tation hypothesis and the geometry of large language models.arXiv preprint arXiv:2311.03658,

work page internal anchor Pith review Pith/arXiv arXiv
[18]

arXiv preprint arXiv:2406.01506 , year=

Park, K., Choe, Y . J., Jiang, Y ., and Veitch, V . The geometry of categorical and hierarchical concepts in large language models.arXiv preprint arXiv:2406.01506,

work page arXiv
[19]

Automatically interpreting millions of features in large language models

Paulo, G., Mallen, A., Juang, C., and Belrose, N. Automati- cally interpreting millions of features in large language models.arXiv preprint arXiv:2410.13928,

work page arXiv
[20]

Tang, T., Luo, W., Huang, H., Zhang, D., Wang, X., Zhao, W

Rajamanoharan, S., Lieberum, T., Sonnerat, N., Conmy, A., Varma, V ., Kram´ar, J., and Nanda, N. Jumping ahead: Improving reconstruction fidelity with jumprelu sparse autoencoders.arXiv preprint arXiv:2407.14435,

work page arXiv
[21]

2025 , archivePrefix =

Sun, X., Stolfo, A., Engels, J., Wu, B., Rajamanoharan, S., Sachan, M., and Tegmark, M. Dense sae latents are features, not bugs.arXiv preprint arXiv:2506.15679,

work page arXiv
[22]

thought” of LLM by finding the “circuit

doi: 10.34740/KAGGLE/M/3301. URLhttps://www.kaggle.com/m/3301. 10 Tree SAE: Learning Hierarchical Feature Structures in Sparse Autoencoders A. Limitations Although attaining promising results, our SAE contains a high number of dead features compared to other SAEs due to the rigid structure. While dynamic allocation helps, we believe that this problem can ...

work page doi:10.34740/kaggle/m/3301 2023
[23]

blind spots

happens when the feature representing a concept developed systematic “blind spots” because of more specialised features. For example, consider a general feature that activates on female names like “Mary”, “Lily”, “Jane”, etc. If another feature specialises in detecting only “Lily”, the sparsity optimisation will likely push the general feature to activate...

work page 2025
[24]

Specifically, they encourage the features to reconstruct the input at multiple layers, fostering the learning of both generalised and specialised features

propose Matryoshka SAE that learns multi-level features using Matryoshka representation (Kusupati et al., 2022). Specifically, they encourage the features to reconstruct the input at multiple layers, fostering the learning of both generalised and specialised features. This has been shown (Bussmann et al.,

work page 2022
[25]

conditional orthogonal

proposes Matching Pursuit SAE that applies the well-known Matching Pursuit algorithm to learn hierarchical features. The features set is “conditional orthogonal” (Costa et al., 2025; Park et al.,

work page 2025
[26]

However, despite the initial success, all of the previous hierarchical SAEs learn independent features and can not point out the relations between the feature pairs

cannot fully reconstruct. However, despite the initial success, all of the previous hierarchical SAEs learn independent features and can not point out the relations between the feature pairs. Furthermore, even when an algorithm such as MCS (Bricken et al., 2023; Bussmann et al.,

work page 2023
[27]

We train with a batch size of 5120, learning rate 1e-4 on 500M tokens of The Pile (Gao et al., 2020)

with dictionary sizes of 24576 in our main result, and 6144 and 49152 in the scaling experiment. We train with a batch size of 5120, learning rate 1e-4 on 500M tokens of The Pile (Gao et al., 2020). We employ the Adam optimiser and normalise the gradient as well as the decoder vector at each backward step. These hyperparameters are shared across all SAEs....

work page 2020
[28]

We set the number of auxiliary top-k as 256, and the coefficient is 1/32 as in the original implementation for both Matryoshka and TopK (Gao et al., 2024; Bussmann et al., 2025)

Auxiliary loss:For TopK, Matryoshka, and Tree SAE, we use auxiliary loss. We set the number of auxiliary top-k as 256, and the coefficient is 1/32 as in the original implementation for both Matryoshka and TopK (Gao et al., 2024; Bussmann et al., 2025). We set the same hyperparameter for Tree SAE; however, we only use auxiliary loss for features at the fir...

work page 2024
[29]

We consider a feature that represents a first-letter concept as having F1 >0.4 on the task

again selects the top features for the first letter task using a k-sparse probe, and measures whether adding additional features leads to a significant improvement (F1 score increase of more than 0.03 (Chanin et al., 2024)) in detecting the first letter. We consider a feature that represents a first-letter concept as having F1 >0.4 on the task. The remain...

work page 2024
[30]

AutoInterp We follow the procedure of AutoInterp (Bills et al., 2023; Paulo et al.,

D.3. AutoInterp We follow the procedure of AutoInterp (Bills et al., 2023; Paulo et al.,

work page 2023
[31]

Specifically, a large language model is presented with a number of activation examples of a feature, then is asked to predict the rank of different examples by feature activation

in measuring the interpretability of the features. Specifically, a large language model is presented with a number of activation examples of a feature, then is asked to predict the rank of different examples by feature activation. We randomly select 200 features to evaluate; the remaining setup is the same as in (Karvonen et al., 2025). E. Cases Where Act...

work page 2025
[32]

In particular, we compute the best numbers of children k∗ l , then sample the pool of dead child features, usually defined as features that are inactive for 10M tokens (Gao et al., 2024; Cunningham et al., 2023). In the step of assigning child features to match the optimal allocation, we employ first fit strategy for all of the parents that have less than...

work page 2024
[33]

We find this can helps reducing number of dead features in Gemma-2-2b (Team, 2024)

prerequisited number of child features for the root node at l= 0 . We find this can helps reducing number of dead features in Gemma-2-2b (Team, 2024). Algorithm 2Full dynamical feature reallocation algorithm. Input: Current assignment vectors {al ∀l∈ {1, . . . , L}} ; Number of child features sl at layer l. forlayerlin{1, . . . , L}do Compute capacity set...

work page 2024
[34]

Therefore eT c dp ≃0

Solving these and remove k2, we have ep ≃d p −kd c/2 and ec ≃d c −kd p. Therefore eT c dp ≃0 . This completes the proof. Interpretation:The child encoder is not a good approximation of the true concept vector d∗ c as it avoids aligning with parent feature caused by the default reconstruction loss optimization. This leads to the low cosine similarity betwe...

work page 2025
[35]

or compute the correlation only (Bricken et al., 2023). We propose another setup that, instead of measuring the correlation, we treat the activation of a feature as binary (1 for non-zero activation and 0 for no activation) and measure the correlation on the binary vectors. Thus, we test 4 possible versions (whether to use binary and whether to use scalin...

work page 2023