Does Higher Interpretability Imply Better Utility? A Pairwise Analysis on Sparse Autoencoders
Authors: Xu Wang
Yan Hu
Benyou Wang
Difan Zou
Venue: ICLR 2026 Poster (2026)
Keywords: Sparse Autoencoders; Interpretability; Utility
Primary area: interpretability and explainable AI

Abstract: Sparse Autoencoders (SAEs) are widely used to steer large language models (LLMs), based on the assumption that their interpretable features naturally enable effective model behavior steering. Yet a fundamental question remains: does higher interpretability imply better steering utility? To answer this, we train 90 SAEs across three LLMs (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B), spanning five architectures and six sparsity levels. We evaluate interpretability with SAEBench (Karvonen et al., 2025) and steering utility with AxBench (Wu et al., 2025), and analyze rank agreement via Kendall’s rank coefficient $\tau_b$. Our analysis reveals only a relatively weak positive association ($\tau_b \approx 0.298$), indicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability–utility gap stems from feature selection: not all SAE features are equally effective for steering. To identify features that truly steer LLM behavior, we propose a novel selection criterion, $\Delta$ Token Confidence, which measures how much amplifying a feature changes the next-token distribution. Our method improves steering performance on three LLMs by **52.52\%** compared to the best prior output score–based criterion (Arad et al., 2025). Strikingly, after selecting features with high $\Delta$ Token Confidence, the correlation between interpretability and utility vanishes ($\tau_b \approx 0$) and can even become negative, further highlighting their divergence for the most effective steering features.

Published as a conference paper at ICLR 2026
DOES HIGHER INTERPRETABILITY IMPLY BETTER UTILITY? A PAIRWISE ANALYSIS ON SPARSE AU- TOENCODERS
Xu Wang 1,233, Yan Hu².,, Benyou Wang?* Difan Zo The University of Hong Kong
The Chinese University of Hong Kong, Shenzhen
3 Shenzhen Loop Area Institute
National Health Data Institute, Shenzhen
ABSTRACT
Sparse Autoencoders (SAEs) are widely used to steer large language models (LLMs), based on the assumption that their interpretable features naturally enable effective model behavior steering. Yet, fundamental question remains unan- swered: does higher interpretability indeed imply better steering utility? To an- swer this question, we train 90 SABs across three LLMs (Gemma-2-22B, Qwen- 2.5-3B, Gemma-2-9B) spanning five architectures and six sparsity levels, and evaluate their interpretability and steering utility based on SAEBENCH (Karvonen et al. 2025) and AXBENCH (Wu et al., 2025) respectively, and perform a rank- agreement analysis via Kendall's rank coefficients тъ- Based the framework, our analysis reveals only a relatively weak positive association (T) RJ 0.298), in- dicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability-ttill tures not all of them are equally effective for steering. To further find features that truly steer the behavior of LLMs, we propose a novel selection criterion: A Token Confidence, which measures how much amplifying a feature changes the next token distribution. We show that our method improves the steering perfor- mance three LLMs by 52.52% % compared to the current best output score-based criterion AArad et al. 2025). Strikingly, after selecting features with high A Token Confidence, the correlation between interpretability and utility vanishes (Te Ro 0), and can become negative. This further highlights the divergence between in- terpretability and utility for the most effective steering features. Code is available at hhttts::/gitthhi com Xu061 SAE44Sterr
gap may stem from the selection of SAE fea-
INTRODUCTION
As Large Language Models (LLMs) become more widely used in real-world applications, ensur- ing the safety of their outputs is increasingly important (Kumar et al. 2024 Ji et al., 2023 Inan jet al., (023). Reliable and controllable behavior essential for deploying these LLMs in more situations (Chen al. 2024). Fine-tuning is the standard way improve controllability. but it quires labeled data, significant training time, and compute resources (Hu et al. 2022 Wang et al.) 2025ch. This has spawned a series of representation- based interventions, i.e., steering, that guide LLM inference by manipulating internal representations, aiming for faster and more lightweight output control (Turner et al. 2023 Turner al., 2024 Wang et al. 20256 Stolfo et al., 2025).
However, activation-level edits are often coarse: they mix multiple semantics, a phenomenon called polysemanticity (Bricken et al., 2023). Recently, Sparse Autoencoders (SAEs) have become valu- able tool in the interpretability field. They are trained to actively decompose the hidden states of the LLM into sparse and human readable features (Templeton et al., 2024 Mudide et al. 2025)
First author. Email: sunny 61 wew.onnnncctteeeeeeeeeeee
1 CCoresponding author. Email: d dzcu@hku.ht

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Published as a conference paper at ICLR 2026
Interpretability
Utiliyy
SAE
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SAEs work to decompese the hidden stale into meaningful fealures
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Stuering: Insert "Cake' concrpt
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7
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Figure 1: Overview of our goal: building bridge for SAE interpretabilityy and utility. In- terpretahility (left): an SAE attached to the L.M decomposes hidden states into sparse, human- describable features. An L.LM judge yields an interpretability score for the SAE (Paulo et 2025) Utility (right): at inference, we activate target SAE feature (e.g., 'cake') to steer generation. An LLM judge yields steering utility score (Wu et al. 2025).
Their interpretable nature has subsequently spurred research into leveraging SAE features for more precise, concept-level control over model behavior (Ferrando et al. 2025 Chalnev al,, 2024).
Despite this progress, a critical question remains unanswered: does higher interpretability truly imply better utility? Since SAEs are trained balance reconstruction and sparsity to yield human- readable features (Cnnningham et al., 2023 Makelov 2024 O O'Brien et al. 2025). their utility for downstream tasks not primary objective. Understanding and characterizing this gap critical to enabling more interpretable and effective steering with SAEs, because (i) it clarifies when in- terpretability scores can (and cannot) be used as a practical proxy for utility, and (ii) it motivates training objectives that explicitly balance reconstruction, interpretability, and downstream steering performance. To this end, we conduct a systematic study to build a bridge between SAE inter- pretability and steering utility (see Figure
To perform comprehensive association analysis. we train 90 SAEs across three LLMs (Gemma-22 2- 2B (Team et al. 2024), Qwen-2.5-3B (Yang al. 2024), and Gemma-2-9B) spanning diverse archi- tectures and sparsity levels. We compute interpretability using SAEBENCH (Karvonen et al.) 2025) and steering utility using AXBENCII (Wu et al. 2025). Then, we leverage pairwise-controlless framework to evaluate whether interpretability predicts steering performance across the pool of trained SAEs. To quantify this relationship. follow the idea of prior works (Tiang et al. 2020 Hu et al. 2024) and measure rank agreement between interpretability and utility using Kendall's 's rank coeffeiien 7g. We control confounders with an axis-conditioned analysis, isolating each design axis (architecture, sparsity, model) by varying one at time and aggregating per-axis metrics.
Furthermore, as identified Arad al. (2025); ; Wu et al. 2025). not all interpretable features in SAE are equally effective for steering. This motivates our next objective to identify the specific features critical for behavior control and steering utility analysis. Motivated by the recent progress on the entropy mechanism in LLM reasoning (Fu et al.) 2025] Wang et al., (225a)). we propose an innovative selection criterion for SAE features: Token Confidence, which measures the degree to which amplifying single feature shifts the model's next-token distribution. Features that induce the most substantial change in model confidence are identified as high-utility candidates features for steering, they exert measurable and targeted influence model behavior. Finally, we leverage these critical features to conduct a refined analysis of the interrrttaiilityutiife gap.
The primary contributions and insights of this paper summarized as follows:
1. (3.4) Interpretability shows a relatively weak positive association with utility. Across 90 SAES that are trained across three model sizes, five architectures, and six sparsity levels,
2

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Published as a conference paper at ICLR 2026
find that higher interpretabilitt score tends shows a relatively weak positive association with steering performance (the Kendall's rank coefficient T6 0.298)). This identifies a notable interpretability-utiin gap of the existing SAEs.
($4.2) A Token Confidence effectively selects features with strong steering performance. To identify the SAE features that critical for steering, introduce A Token Confidence, innovative metric that identifies sicering-criticat SAE features by measuring their impact on the model's next-token distribution. When benchmarked against the best existing output score-based method (Arad et al., 2025), our approach yields a substantial 52.52% average improvement in steering score. This result validates the superiority of our method and underscores the critical role of feature selection in characterizing and enhancing the steering utility of SAES.
($4.3) The interpretability-uiiiie our association analysis exclusively to SAE features with strong steering utility, we uncover countcrintuitive finding: the interpretability-ttiin
gap widens among high-utility features. By reapplying
correlation vanishes or even becomes negative (Kendall's 's rank coefficient т6 s 0). This indicates that for the most effective steering features, interpretability is at best irrelevant and potentially detrimental, further emphasizing the critical gap.
nature of the interpretabillty-utiin
Our results demonstrate a significant divergence between SAE's interpretability and steering utility, suggesting that prioritizing interpretability does not enable improved steering performance. This gap highlights& a crucial research direction: mitigating will likely necessitate advanced post-training feature selection protocols or fundamentally new, utility-oriented SAE training paradigms.
PRELIMINARY
2.1
SPARSE AUTOENCODERS
Sparse Autoencoders (SAEs) decompose internal model activations x into sparse. higher- dimensional features h that can be linearly decoded back the original space (Cunningham al. Leask et al. 2025). A standard SAE with column-normalize decoder weights (Bricken et al., Karvonen et al. (024) is defined by the following forward map and optimization objective:
2023
2023
| 212 + A|hI11, where h = ReLU + bg), Wph + bp.
where Wg, by encoder parameters, WD. by decoder parameters, is the reconstruction, and controls sparsity. This training balances reconstruction accuracy with sparse representations.
2.2 INTERPRETABILITY. AUTOMATED INTERPRETABILITY SCORE
SAEBENCH Karvonen al. 2025 uses LLM-as-judge (Paulo al. 2025 assess each latent: the judge drafts the description from examples and then predicts. on held-out set, which sequences activate The Automated Interpretability Score the average precision of the judge's prediction.
M 1 yml]
Autolnterp Score
where ym {0, 1} indicates whether the latent activates in the sequence m and I.. is the judge's prediction. We use this score as our interpretability metric. For the complete details, see Appendix Throughout this paper, interpretability refers specifically the interpretability of SAE features as measured by automated metrics (e.g., SAEBENCH), rather than interpretability methods in general.
2.3 UTILITY: STEERING SCORE
SAE steering injects the SAE decoder atom By (the f-t column of the column-normalize decoder Wace (f') into the residual stream at target layer to push the hidden state along a chosen feature direction (Durmus et al. 2024). Given a feature index f. a steering factor a, and a per-sample seale my (e.g., the feature's 's maximum activation), the intervention is
stoor
(a m))) Ug-
3

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Published as a conference paper at ICLR 2026
$1 Calculate À Autolnterp Steering
$2.Aman nalyza Pairwise Consistency
Interprelability is weakly moderately correlated with utility.
Gap
Further showing the critical nature the inter interpetaabilttyuiii gap.
Interpretability
Utility
$4 nalyze Pairwise C Consästency
Choose
Is the conclusion flawed because features steer poorly?
Feature
Selection
Figure 2: Overview of pairwise-controlled workflow linking SAE interpretability with steering utility. (S1) Compute interpretability score and steering score for each SAE. (S2) Pair- wise analysis across SAEs and get an insight (the top-right green box), revealing an interpretabil- ity-utility gap. The red box (lower right) is our further inference based on the above green box and previous studies (Wu et al. 2025). (S3) Use A Token Confidence to select higher-utility features. (S4) Compute steering score after selection per SAE, then do the pairwise analysis between steering score and interpretability. The green box in the middle left is our final conclusion.
Through the above formula T we can use SAE features for steering to achieve the output of control- ling LLM. AXBENCH (Wu et al.) 2025) measures causal control by steering internal representations during generation and asking LLM judge rate three aspects, each on discrete scale {0, 1, 2): Concept (C), Instruction (I), and Fluency (F). The overall Steering Score is the harmonic mean:
Steering Score HM(C,T,F)
C + [0,2].
Following AXBENCH, for each concept we sample instructions (e.g.. 10 from Alpaca-Eval (Dubois al., 2023 ) generate continuations under different steering factors, pick the best factor
split, and evaluate the held-out split with the judge to obtain the final utility score averaged across prompts (Gu al., 2025). The complete scoring procedure is detailed in Appendix C Likewise, our notion of utility is limited to steering ulility-the effectiveness of using SAE features to causally model generations under the AxBENCH protocol.
CAN SAE INTERPRETABILITY INDICATE STEERING PERFORMANCE?
3.1 EXPERIMENTAL SETUP
Dataset. For each trained SAE, score 1,000 latents with LLM-as-judge (Paulo al. 2025) and randomly sample 100 to form that SAE's CONCEPT 100: 100 human-readable concept descriptions per evaluation set, each pairing a latent (layer, feature id) with a description (see details in Ap- pendix FF. For steering, we sample 10 Alpaca-Eval instructions, allow up to 128 generated tokens, and test steering factors; the instructions are split 5/5 for factor selection vs. held-out evaluation.
Model. We evaluate three open LLMs: Gemma-2-2B TTeam et al. 2024). Qwen-2.5-3B (Yang) et al. 2024). and Gemma-2-91 (Team al.) 2024). SAFS are trained on residual-stream activations at fixed mid-layer for each model: Layer 12 for Gemma-2-2B. Layer 17 for Qwen-2.5-3B, and Layer 20 for Gemma-2-9p and steering is applied to the corresponding layer.
SAE with different architectures We train 90 SAEs covering a range of architectures and spar- sity. All SAES use a latent dictionary width of 16k. We instantiate five variants: BatchTopK (Buss- mann al. 2024), Gated (Rajamanoharan al. 2024a), JumpReLU (Rajamanoharan et al. 2024b), ReLU Team (2024), TopK (Gao et al. (2024) and sweep six target sparsity levels with approximate per-token activations T.g Rs 50, 80. 160, 320, 520, 820. Further details are provided in Appendix

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Published as a conference paper at ICLR 2026
3.2 PAIRWISE RANK CONSISTENCY BETWEEN INTERPRETABILIN AND UTILITY
We test whether higher interpretability of SAE is predictive of higher steering performance across set of trained SAEs attached fixed LM. For each SAE in pool 6, we record pair (u((0,, (()) E IR? where μ is the SAE-level Interpretabilityy Score and is an aggregated Steering Score over standardized evaluation suite.
Given two SAEs 0g 03 E O define the concordance indicator
Vty (())( m(0,)) sign(g(0)) -0(,)) E [-1,0,+1},
(2)
Kendall's tie-corrected rank coefficient (Kendall 1938) summarizes agreement over unordered pairs and reduces to average concordance when there are no ties:
Σ
E E|-1,1) 1],
(3)
[u(0.) + m(0)]
[g(O.) + [(0)]]
In this study, instantiate μ with the Interpretabilityy Score and g with the Steering Score, then compute 7 for three model-layer settings (Gemma-2-2B: Qwen-2.5-3B, Gemma-2-9B) Each setting includes 30 SAEs spanning architectures and sparsity ensure sufficient pair coverage.
3.3 GRANULATED KENDALL'S COEFFICIENT TO CONTROL CONFOUNDERS
Global rank agreement can be confounded by hyperparameters that jointly influence interpretability and utility. To obtain an axis-controlled assessment, we factor the SAE design space into orthogonal axes and evaluate rank consistency while varying one axis at time and holding the others fixed.
We define three conditioning axes: (A) Architecture - fix architecture (and layer), vary sparsity; (B) Sparsity compare architectures at matched sparsity ranks; (C) Model - fix the base model, compare all SAEs within it. For axis i, partition θ into groups G3 that are matched on all axes except i. Within each group G G, compute Kendall's coefficient in {(((0), (()) O G}, and average between groups to obtain the statistic at the axis level:
V
Σ GEG.
(((((),((0))000
9
Aggregate the axis-level outcomes by
V
(5)
where is the number of axes. Each s/s captures rank consistency conditioned axis i (varying only that axis while matching the others), and V/ aggregates these into single axis-controlled measure. This construction mitigates cross-axis trends-e.g. e.g. architecture, sparsity, or model-driven shifts that can obscure local relationships between interpretability and utility.
We report the per-axis statistics dù together with the aggregate for the same model settings in section 3.2 providing both axis-specific and aggregated assessments.
3.4 PAIRWISE ANALYSIS RESULTS
In this section, we assess whether higher SAE interpretability predicts stronger steering by comput- ing Kendall's т& between the Interpretability Score μ²() and the Steering Score (b)se()) (before any feature selection) over a pooled set SAEs attached to a fixed LLM.
To control confounders and localize effects, apply the axis- cdis-conditioned procedure defined in section 3.3 For each axis, we form matched groups, compute within group Tr, average to obtain a per-axis summary, and aggregate these summaries into overall axis-controlled coefficient.
5

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Table 1: Pairwise Analysis Between Interpretabillity Score s((0) and Steering Score (hme Here Jeuse (9) stcering score before any feature selection. We report Kendall's т overall and by axis-controlled measures VA (Architecture), V (Matched Sparsity), and Ve (Model). n number of SAEs; Pairs number of pairwise comparisons; p permutation p-value for testing He = 0 within each group (by shuffling steering scores); 95% CI = 95% bootstrap percentile confidence interval for
Axis
SAEs
n
Pairs
95% CI
Overall
SAEs
90
4005
0.2979
0.0002
0.1591, 0.4191
0.2575 (SE 0.1163, 95%
boot CT [0.0222,
0.3961])
BatchTopK
18
153
0.3203
0,0712
[0.0000, 0.6429)
Gated
153
-0.2026
0.2577
[-0.5493, 0.1918]
VA: Architecture
JumpReLU
18
153
0.4248
0.0160
0.05563, 0.7183]
ReLU
18
153
0.3595
0,0392
[0.0274, 0.6528
TopK
18
153
0.3856
0.0272
(0.0282, 0.6966]
UB
0.1651 (SE
RJ 0.1112,
95% boot CI [-0.2886,
0.3587J)
Lu == 50
15
105
0,5429
0.0034
[0.1578, 0.8737]
Lo R 80
15
105
0.3524
0.0740
0.0000, 0.6304]
Lo = 160
15
105
0.1810
0,3821
-0.2501, 0.5464
Wp Sparsity
Lo = 320
15
105
0.1810
0.3673
-..1599, 0.5208
Lo R 520
15
105
-0.2190
0.2837
0.5914, 0.1648)
Lo Re 820
15
105
-0.0476
0,8484
0.4409, 0.3750
Ve
0.3272 (SE 0.0698, 95% boot
[0.2184,
0.4575))
Gemma-2-22
30
435
0.2184
0,0980
1-006444 0.4764]
Ve: Model
Qwen- 2.5-3B
30
435
0.4575
0.0008
0.20066, 0.6580]
Gemma-22
30
435
0.3057
0.0166
0.0521, 0.5277
VV
V.
Vc)
0.2499
We complement each cor-coorelation estimate with both hypothesis testing and uncertainty quan- tification (Table [T] Specifically, for each matched group, we report Kendall's ть along with per- mutation test y-value for Ho = O, obtained by shuffling steering scores within the group while keeping interpretability scores fixed. We also report 95% bootstrap percentile confidence in- tervals (CI) for 7 to capture sampling variability. In addition, for each axis-conditioned summary L A. B. V.. we provide its standard eιror and 95% bootstrap CI, and finally aggregate them into an overall axis-controlled coefficient V.
Table shows that across SAEs, higher interpretability tends to be modestly associated with better steering average, pointing to consistent but limited impact. The pooled Kendall's Tr R 0.30 is positive, and the axis-controlled aggregate remains positive (v = 0.25), indicating that more interpretable features generally translate into better steering utility across designs and models.
The strength of the link between interpretability and utility depends on SAE architecture, sparsity, and the base model. By architecture, the association is positive average (V A 0.26), with ReLU-like variants reinforcing the trend and Gated weakening it. By sparsity, alignment is strongest when the SAE more sparse and weakens- Someeimes reversing the number of active features increases. By model, the underlying LM shapes the effect, with the signal clearest in Qwen- 2.5-3B and weaker in Gemma-2-2B. while the model-wise summary remains positive (V 0.33).
Interpretability shows a relatively weak positive correlation with steering performance, highlighting notable gap between interpretability and utility across SAES.
Key Observation 1:
FROM INTERPRETABILITY TO UTILITY: WHICH SAE FEATURES ACTUALLY STEER?
In Sec. 3.4 We find that SAE interpretability relatively weak prior for steering utility. Prior work (Arad et al.) 2025) shows many features lack steerability and we speculate that this factor may render the previous conclusion inaceurate. Therefore, we introduce a metric to identify steering- effective features. Metrics derived from model's internal token distributions can assess reasoning

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Published as a conference paper at ICLR 2026
Distribution of A Token Confidence across All SAEs
The with the Desired Steering Features Owen-2.5-38
400
250
400
200
200
3.0
200
1.0
100
50
Confidence
Tokon Confidence
Token Confidence
Figure 3: Distribution of per-feature A Token Confidence across all SAEs. Panels show his- tograms for Gemma-2-2B. Qwen-2.5-3B, and Gemma-2-99: the r-axis is AC₁ (negative values indicate increased confidence, positive values decreased confidence) and the y-axis the number of SAE features. The shaded area marks the high-magnitude tails from which candidate steering fea- tures are selected, while the central mass near 0 indicates features with little distributional impact.
quality (Kang et al. 2025). In particular, token entropy offers unified view: high entropy highlights critical decision points (Fu et al. 2025 Wang et al. 2025a). We apply this idea to SAE steering.
4.1 FEATURE SELECTION VIA TOKEN CONFIDENCE
start from the model's s next-token distribution. Given logits = E IR and p = softmax(z) over vocabulary of size V. the token entropy is
V Σ
H(p) =
Pj log
(6)
Entropy summarizes dispersion over the vocabulary: smaller values reflect a sharper, more concen- trated prediction, while larger values indicate greater uncertainty given position.
To focus on the head the distribution that matters most for sampling, we use token confidence.
Let [p) S (1,....,u V) denote the indices of the k largest probabilities in p. The top-k token confidence is the negative average log-probabilit over these entries:
C2(p)
Σ (EI.(
log
Lower Cj implies higher confidence, while higher C& implies a flatter top-k distribution. Unlike entropy, Cs directly captures the sharpness of the outcomes that drive next-token behavior.
We turn confidence into feature-level selector via hinglefeeture SAE intervention. Consider an SAE feature f at layer f. We amplify only the coefficient of ʃ by factor a > 0 in the SAE reconstruction, leaving the base model and all other features unchanged. Denote the baseline next- token distribution by p base and the intervened distribution by ff
int A Token Confidence is
ACI(f:L,a) Ca(pint.o)
Ca(pbase).
(8)
Negative values AC < mean that amplifying sharpens the top-k distribution, while positive values indicate greater dispersion. We compute this using one baseline and intervened forward pass via an SAE hook. Implementation details and hyperparameters are provided in Appendix D
We select features with extreme signed changes in token confidence under single- feature SAE inter- ventions, and pick the better direction (see Figure 33). For each feature, we compute ACk, rank by |AC&], form tiers, evaluate subsets for steering, and keep the best per SAF.

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Steering Score Different Architectures
Output
Gemma 2B
Owen 2.5 30
Gamma 2 9B
Outpst Score Dane: 74.07%
Output Score SAE Base: 70.4%%
Ostput Score SAE Bawe: 80.
[Durs] SAT
44"
0.209
9460
0.31
0.493
Scare
8.300
6.192
0.543
B.19
0.140
6377
8.54
6142
6.1
6.3
61
Figure 4: Comparison of different SAE steering methods with five SAE architecture across three LLMs. Panels correspond to Gemma-2-2B, Qwen-2.5-3B, and Gemma-2-9B. The horizontal axis groups SAE architectures (Ba,chTopK, Gated, JumpReLU, ReLU, TopK), and the vertical axis reports the steering score. Bars show three conditions: SAE Base (no feature selection), Output Score Selection, and Token Confidence Selection (ours). Panel annotations summarize the average lift of each selection method relative the SAB-based steering.
4.2 STEERING PERFORMANCE RESULTS AFTER FEATURE SELECTION
Arad et al. (2025) has shown that SAE steering works well if features are chosen by their causal impact model outputs, introducing the oulput score as metric to identify output-aligned features. For a given SAE feature, a logit-lens procedure is used to select a representative token set M. Let P and Pin (MM) denote the aggregate support for M in the base and intervened (feature- amplified) runs, respectively, where
P(M) = (1- min rank(i)
max p(i),
[V]
xEM
with [V| the vocabulary size, rank(i) the rank token i, and p(i) its probability. The single-feature steering score is then
Sont = Pmn(M Prose (M),
which is large when amplifying the feature increases the rank and probability of representative token set. Following this insight, we evaluate our A token confidence selection on three base LLMs (Gemma-2-2BB Qwen-2.5-3B, Gemma-2-9B using the CONCEPTI00 (see details in 3. We set in our A token confidence selection. In ablations over E {1,3, 5, 10) on Gemma and Qwen, all choices of k yield large gains over the SAE baseline, and k = 1 is in fact the test-performing setting on both models, so we adopt it as our default (see Appendix [ The experiments on steering performance improvement of each SAE can be referred to Appendix
Table 2 shows that our selection yields consistent gains across all models, out- performing the vanilla SAE baseline by large margins, and also improving over an seaet-scorr--bsseee selector. These gains indicate that ranking and filtering by the magnitude of distributional change cap- tured by ACt. reliably isolates features with the strongest steering utility.
Table 2: Steering score after feature selection com- pared with SAE-based steering. Columns report scores (higher better) for 2emma-2-2B, Qwen-2.5- 3B, and Gemma-2-9BB Rows: 'SAE-based' uses all SAE features without selection (Wu et al.] (025); 'OOuputt' selects features using Sour (Arad al.] 2025); "+AC,, (Ours)" selects by the A Token Con-
Jidence. Boldface indicates the best method per model.
Furthermore, we conducted a comparative analysis of SAEs of different architectures on three models. For fair comparison, the two feature selection methods use the same subset size. comprere steer- ing scores across SAE architectures and
Method
Gemma-2-2B Qwen-2.5-3B
Gemma-2-9R
SAE-based
0.133
0.171
0.142
+Output
0.233
0.292
0.255
(OCr(Ours)
0.328
0.399
0.289
8

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selection methods. In all three models, selecting features by A Token Confidence consistently out- performs both the no-selection SAE baseline and the output-score selector across architectures.
On average, method improves steering performance by 52.52% over the strongest competing baseline. The Batch architecture is the one that has the most stable and significant improvement in steering capabilities models of different sizes among the five SAE architectures.
Key Observation 2: A Token Confidence reliably selects high-utility SAE features across mod- els. Among SAE architectures, BatchTopK achieves the most stable and sizable steering score.
4.3 PAIRWISE ANALYSIS AFTER HIGH-CONFIDENCE FEATURE SELECTION
Building on the high A Token Confidence feature selection introduced above, we now ask whether SAE interpretability can serve as a prior for post-selection steering performance. For each SAE 0, we write (ose (0) for its Steering Score before feature selection and 9high (0) for the best score achieved after selecting features with high Token Confidence. Both quantities are measured the same steering metrie; Shigh (0) is simply the steering score recomputed restricted set of high A Token Confidence features for the same SAE.
We quantify the relationship between interpretability and post-selection steering by computing Kendall's 's Tr between the Interpretability Score p(0) of SAEs and the Steering Score 9high( As in Section 3.4 we report both pooled coefficients and axis-conditioned summaries that control for design and model factors (architecture, sparsity and model). In addition, Section [3.4 and Table [ report the corresponding coefficients for u(0) vs. (0)s allowing direct comparison between "before" and "after" feature selection using the same steering metric.
Overall, Table 3 shows that interpretability is not reliable prior for steering performance after selection. The pooled association between ((0) and (O) is small and statistically indistinguish- able from zero (n, 0.08), and the controlled aggregate is likewise close to zero (v' 0.07). Estimates across architectures, sparsity levels, and models cluster around zero and are mostly non- significant. These results indicate that once we focus on features that are most useful for steering (as selected by high A Token Confidence), higher interpretability can't 't predict better steering scores.
Key Observation 3: Surprisingly, the interpretability-utiil gap widens after feature selection: higher interpretability scores can't provide prior for which SAEs achieve better steering.
RELATED WORK
5.1
REPRESENTATION BASED STEERING
Activation- based steering arose as a lightweight alternative to fine-tuning, enabling on-the-fly con- trol of LLM behavior without retraining (Giulianelli et al. 2018 Vig et al.) 2020 Geiger et al. 2021 2025). The core idea is to inject carefully chosen directions into hidden states, typically in the residual stream, scaling interventions by gain and selecting layers for maximal effect (Zou et al.) 2025 Rimsky et al. 2024: van der Weij et al. 2024). It has been applied to safety and moderation, persona and sentiment control, and instruction adherence, promising low-latency deployment-tine adjustment but facing polysemantic entanglement and brittleness that motivate standardized evalua- tion (Chen et al.) 2025 Liu et al. 2024). However, this approach injects polysemants activations at intervention time, yielding coarse- -raained effects for output control (Bricken et al.) 2023). Our work related to activation level interventions, but differs by grounding directions in sparse, interpretable SAE features and applying utility-oriente feature selection to mitigate these failure modes.
5.2 SAE-BASED STEERING
Sparse Autoencoders (SAEs) decompose activations into sparse, headan-e features to mit- igate polysemanticity and expose concept-level structure (Bricken et al.) 2023 Templeton et al. 2024 Gao et al. 2024). For steering, practitioners use decoder atoms as directions and add scaled injections at chosen layers, with architecture and sparsity choices trading reconstruction for feature

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Published as a conference paper at ICLR 2026
Table 3: Pairwise Analysis Between Interpretability Score j((0) and Steering Score Thigh (f). Here Dhigh (9) steering score after selecting features with high Token Confidence. We report Kendall's ть overall and under axis-controlled summaries A (Architecture), Vg (Matched Sparsity), and c (Model). n number of SAEs; Pairs = number of pairwise comparisons;
permutation p-value for testing Ho Th 0 within each
group (by shuffling steering scores); 95% C1 Axis
95% bootstrap percentile confidence interval for Th.
SAEs
7
Pairs
95% CT
Overall
All SAEs
4005
0.0823
0.2665
-0.0560, 0.22433
0.0618 (SE 0.1136, 95% boot CT [-0.1 0.1199,,
0.2810)
BatchTopK
18
153
-0,1895
0.2933
[-0.5694, 0.1918]
Gated
0.0338
0.8764
0.3655,, 0.3853]
VA: Architecture
JumpReLU
18
153
0.0950
0.6209
-0.3373, 0.4697]
ReLU
18
153
-0,1007
0,5803
-0.4833, 0.2857]
TopK
18
153
0.4702
0.0078
00.0794, 0.8043)
BB
0.1002 (SE R: 0.0700,
95% boot CI [-0.0288,
0.2188)
Lu == 50
15
105
0,2488
0.2212
[00.1828, 0.6300]
Lo 80
15
105
0.2899
0.1602
-0.0673, 0.5876]
Lo R 160
15
105
0.1183
0.5747
-0.2357, 0.4151]
Wp Sparsity
La
0.1171
0,5803
-0.3531, 0.5209
Lo R 520
15
105
-0.1827
0.3747
0.6490, 0.3524]
La = 820
15
105
0,0097
1,0000
0.3724, 0.3572
Ve
0.0538 (SE
0.0700, 95% boot
--000540,
0.1850)
Gemma-2-2B
30
435
-0,0540
0.6963
0..127, 0.2125]
Ve: Model
Qwen-2.5-22 2.5-BB
435
0.1850
0.1668
0.0872, 0.4413)
Gemma-2-95
30
435
0.0303
0.8284
0.2552, 0.3233]
V
(DA
VB + Wc)
0.0719
granularity (Zhao al., 2025 Wang al. 2025d Ferrando et al. 2025). SAE-based steering ables targeted safety control, style modulation, and instruction emphasis, yet the utility of individual features varies widely (Chalnev al.) 2024 Mayne et al. 2024). While the connection between SAE interpretability and steering utility remains unclear, and our goal is to build a principled bridge between them. To this end, we conduct large-scale experiments across multiple model sizes and SAE architectures, demonstrating the critical nature of the interpretabilit- gap.
CONCLUSION AND DISCUSSION
We study a focused but practically important question: within the SAE paradigm, does higher SAE feature interpretability predict better sleering utility? Across 90 SAEs spanning three base LLMs, five architectures, and six sparsity levels, interpretability shows only a weak positive association with steering utility (n, 0.298), revealing clear interpretabillty-uiile with A Token Confidence substantially improves steering, yet among the highest-utility features the correlation collapses toward zero and can even turn negative, suggesting that interpretability and steerability diverge most in the regime that matters for control.
gap. Feature selection
key practical implication is that SAE interpretability scores are hard use as reliable indica- for for downstream performance in SAF-based applications. Optimizing or selecting SAEs purely by interpretability can mis-rank models when the goal is controllable generation, and utility-aware selection training objectives are often necessary. Looking forward, narrowing this gap likely quires either (i) post-training protocols that identify causally effective features, or (ii) utility-oriented SAE training paradigms that directly optimize controllability under sparsity.
Finally, SAE feature explanations remain highly valuable: we expect human-readabe readable SAE descrip- tions to support broader workflows such data filtering, targeted data synthesis, and concept-level steering. Our results therefore do not diminish the promise of SAE explanations; they clarify that current interpretability scores alone are insufficient for selecting SAEs for downstream
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Published as a conference paper at ICLR 2026
ACKNOWLEDGMENTS
We would like to thank the anonymous reviewers and area chairs for their helpful comments. We ac- knowledge the support from NSFC 62306252, Hong Kong ECS award 27309624, Guangdong NSF 1124A1515012444 and the International Science and Technology Cooperation Center, Ministry of Science and Technology of China (under grant 2024YFE0203000).
REPRODUCIBILITY STATEMENT
We aim to facilitate full reproduction of our results. All model code, training and evaluation scripts, and experiment logs are released at the repository part of the supplementary materials: http://github..oo//ubbb...
Training architectures, hyperparameters. sparsity sched- ules, and optimization details specified in the main text and Appendix |A2 (see also the per- family settings in Appendix A). The datasets used are openly licensed: all SÁEs are trained on The Common Pile v0.1 (Kandpal al. (025) as described in Appendix F our evaluation concepts (CONCEPT 100) and their automatic generation pipeline are documented in Appendix
B and Ap- pendix F.. The complete procedures for automated interpretability scoring (SAEBENCH) and steer- ing utility (AxBENCH), including sampling, judging protocols, and scoring functions, are detailed in Appendix B and Appendix C with the A Token Confidence selector defined in Appendix D and the post-selection results summarized in Appendix [L] Hardware, runtime, and memory footprints for aBd
both SAEBENCH and AXBENCH are reported in Appendices [B.3 and C.2 Together, these materi- als, along with seed-controlled configuration files and exact command- line invocations provided in the repository, are intended to enable independent researchers to replicate and extend our findings.
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Qwen An Yang, Baosong Yang. Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxin Yang. Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingfeng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yi-Chao
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Zhang, Yunyang Wan, Yuqi Liu, Zeyu Cui, Zhenru Zhang, Zihan Qiu, Shanghaoran Quan, and Zekun Wang. Qwen2.5 technical report. ArXiv, abs/2412.15115, 2024. URL https://api.
Yu Zhao, Alessio Devoto, Giwon Hong. Xiaotang Du, Aryo Pradipta Gema, Hongru Wang, Xuanli Hc, Kam-Fai Wong, and Pasquale Minervini. Stecring knowledge selection behaviours in LLMs via SAE-based representation engineering. In Luis Chiruzzo, Alan Ritter, and Lu Wang (eds.), Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Pupers), pp- 5117-5136, Albuquerque, New Mexico, April 2025. Association for Computational Linguistics.
URL https: https///aaaaaatthtagcae org/ 2025 naacl maacl-long.200 264/
Andy Zou, Long Phan, Sarah Chen, James Campbell, Phillip Guo, Richard Ren, Alexander Pan. Xuwang Yin, Mantas Mazeika, Ann-Kathrin Dombrowski. Shashwat Goel, Nathaniel Li, Michael Byun, Zifan Wang, Alex Mallen, Steven Basart, Sanmi Koyejo, Dawn Song, Matt Fredrikson, J. Zico Kolter, and Dan Hendrycks. Representation engineering: A top-down ap- proach ai transparency, 2025. URL hwtpss//aarr....o//aa////20.
LLM USAGE
In preparing this paper, large language models (LLMs) were used as an assistive tool for minor language polishing and stylistic improvements. All technical contributions, results, and conclusions solely the work of the authors.
A SAE ARCHITECTURES AND TRAINING DETAILS
We train 90 SAEs (30 per base model) across five architectures and six target sparsity levels. Unless stated otherwise, the dictionary width is 16K codes (6,354,) SAEs are attached the residual stream at the layer described in the main text, and decoder columns are nornoaalliedd All models are trained on The Common Pile v0.1 (Kandpal et al. 2025).
A.1 ARCHITECTURES AND PARAMETERIZATION
We list the five SAE families with their named parameters (as implemented) and the correspond- ing shapes. The last column records architecture-specffi thresholdingggating fields when present. Shapes assume residual dimension d=2304 and dictionary width F F-16,34
Architectures
W
Denc
Waee
Threshold / Extras
ReLU
encoder.weight. encoder.bias: shape (16,384, 2,304)
wecoder.weight: bias: shape shape (2,304, 16,384)
shape (16,384)
(2,304)
Gated
encoder.weight: gate_bias: shape (16,384, 2,304)
decoder. weight: decoder shape (2,304, 16,384)
r_mag: shape (16,384); mag bias: shape (16,384) k
shape (16,384)
shape (2,304)
TopK
weight:. shape (16,384, 2,304)
encoder. shape (16,384)
weight: b.dec: shape shape (2,304, 16,384)
(2,304)
BatchTopK
weeoddr.wweiht. shape (16,384, 2,304)
uncoder.bias shape (16,384)
bacoder.weight. b dec: shape shape (2,304,
k
(2,304)
16,384)
JumpReLU
Wenn: shape (2,004, 16,384)
b.ene: shape (16,384)
W dec: shape (16,384,
b.dec: shape (2,304)
threshold:
shape (16,384)
2,304)
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A.2 TRAINING, SPARSITY, AND COMPUTE SETUP
Optimization and schedule. Adam with learning rate 3x 3x10-"; LR warmup 1000 steps; sparsity warmup 5000 steps; LR decay starting at 80% of total steps. Precision: bfloatl 6. LM batch size = 4, context length 2048, SAE batch size = 2048. Each run trains on ~ 5x 10 tokens.
Sparsity controls. We sweep six target activity levels
Lo {50, 80, 160, 320, 520, 820).
For TopK/BatchTopk we set & equal to the chosen Lo (aux-k coefficient 1 1/32; moving-threshool momentum 0.999; threshold tracking begins step 1000). JumpReLU uses the same via target 1 0. For -e-palllieed families, we search the following penalty grids:
Family
Lj penalty values (used to span sparsity levels)
Standard Standard-Noc Gated SAE
0.012, 0,015, 0.020, 0.030, 0.040, 0.060 0.012, 0.018, 0.024, 0.040, 0.060, 0.080
Training details. All training uses two NVIDIA RTX A800 GPUs. The table below reports the aggregated artifacts and training time (hours) for 30 SAEs per model (total 90), together with the runtime configuration. Times and sizes approximate.
Model
#SAEs
Disk (GB)
Traing Time (H)
LM Batch
Context
SAE Batch
Peak Mem (GB)
Gemma-
30
17
2048
2048
20
2-2B
Gemma-
30
13.2
60
4
2048
2048
70
2-9B
Qwen-
30
7.7
37
2048
2048
30
2.5-3B
B SAEBENCH DETAILS, RESULTS AND OUR COSTS
B. AUTOMATED INTERPRETABILIT SCORE PROCESS
SAEBENCH (Karvonen et al. 2025) follow an LLM-as-judge pipeline to assign automated in- terpretability score to each SAE latent. First, we collect layer activations by running the base LM with caching and encoding the residual stream through the SAE obtain h E g xXXX" We define a token window of length 21 (buffer = 10) around any center (i. t) and, unless stated otherwise, mask BOS/PAD/EOS positions. For latent f, sample three window types: (i) Top (n 12 non-overlapping peaks of A[: ;, {), (ii) Importance- importance-Weighted (n 7, sampled proportional to ac- tivation after removing values least large as the smallest Top peak), and (iii) Random
10, uniform over valid centers). Let Umax be the maximum activation seen in any Top window position and set a global threshold Tast 0.01 Umax-
We split the sampled windows into a generation set (10 Top + IW) and a scoring set (2 Top + IW + 10 Random, shuffled). In generation, tokens with activation > Tast are bracketed highlight evidence; the judge LLM receives these 15 windows and returns a short English description of when the latent fires. In scoring, the judge sees the description and the 14 held-out windows withour highlights and outputs comma-separated list of indices it predicts as activations (or None).
Ground truth for a window If [max hsuu, {) > Taa)- The per-latent score is the accuracy over the M = 14 scoring windows, i.e.,
1 M
Score(!) = M m=l
Σ Im Mm).
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where Fm {0, 1 is the judge prediction and Um is the label defined above. For each SAE 8, evaluate 1,000 latents and report the mean over a random CONCEPT 100 100 subset:
1
(())
Score(C).
100
RECONCEPTIO0
B.2 PERFORMANCE OF SAES ON THREE MODELS ON SAEBENCH
Across the three backbones, the six SAEBENCH metrics (for information about these indicators, see SAEBENCH (Karvonen al. 2025p reveal how sparsity mechanisms balance interpretabil- ity, faithfulness, and causal structure. Automated Interpretability is strongest when encoders enforce compact latent usage (e.g., TopK/BatchTopk and ReLU at lower Lo), and it gradually softens pacity expands. The Absorption metric (considered via its complement in the plots) indicates that de- signs concentrating signal into small effective capacity encourages redundancy and competition across latents. Meanwhile, Core/Loss- Recovered remains uniformly high, showing that even sparse codes closely preserve original model behavior; increasing Lo pushes faithfulness toward ceiling without overturning the core trade-offs visible in the other metrics.
latents are less prone feature stcaling, whereas higher
Gemma-2-2B. As shown in Fig. Gemma-2-22 exhibits balanced profile: interpretability stays robust for TopK/BatchTopk and ReLU at modest sparsity; absorption is contained when the code remains compact; and Core is eetrrsaturated across the range. Improvements SCR @ 20 are steady but measured, suggesting targeted debiasing with small k. Sparse Probing indicates that relatively few latents already carry much the predictive signal, while RAVEL strengthens with moderate capacity, reflecting cleaner separation of attributes without undermining compactness.
SAEBench Gemma-2-22
Interpretability
Absorption
(Loss Racovered)
0.9
1.0
0.98
Autoliturr Score
0.8
0.96
Abcoration
0.94
0.7
0.90
0.6
107
10a
10'
16'
(Spersity)
(Sparsity)
SCR@20
Sparse Probing Top-1
0.1.6
0.78
0.75
0.14
0.78
0.65
SCR3
6.74
0.60
0.08
0.50
0.45
202
10'
10a
10
10'
10'
(Spariity)
(Spareity)
La (Spariity)
RaLU
-
Gated
BatchTopk
Topk
JumpRaLU
Figure 5: SAEbench results for Gemma-2-22 interpretability remains strong at lower Lu, absorp- tion stays low for compact codes, Core is near ceiling, and structure (SCR/RAVEL) improves with moderate capacity.
Qwen-2.5-3B. For Qwen-2.5-3B (Fig, 6b. interpretability at tive tive- especialy for TopK and JumpReLU yet the model is more sensitive to absorption as ca- pacity grows, implying greater latent competition and signal spread. Core remains excellent,
Lo is competi-
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reconstructions are faithful; however, SCR gains flatten high Lo where residual spurious reappear. Sparse Probing solid but a touch behind the strongest Gemma configurations, consis- tent with its flatter RAVEL patterns: causal structure is present but less crisply disentangled when attributes begin to diffuse across latents.
SAEBench Qwen-2.5-3B
Interpretability
Absorption
0.9
1.0
1.00
Absorption Score
Autointerp Scove
0.7
0.8
0.94
0.6
0.92
0.0
0.90
10
10'
10'
10a
10'
10*
Lx (Sparsity)
La (Sparsity)
L. (Sparsity)
SCR@20
Sparse Probing Top-1
RAVEL
0.20
0.70
Scho20
Diventanglemaet
0.458
West
0.497
0.88
0.00
0.496
0.495
-0.05
102
(Sparsity)
(Sparaity)
(Sparsity)
Gated
BatchTopk
RELu
JumpReLU
Figure 6: SAEbench results for Qwen-2.5-3B: strong interpretability lower Lo, rising absorption with capacity, consistently high Core, and more fragile SCR/RAVEL at the highest capacities.
Gemma-2-9B. Gemma-2-98 (Fig. pushes the upper envelope on structure: interpretability re- mains solid for compact encoders; absorption is low at moderate Lo that avoids unnecessary latent proliferation; and Core is near its ceiling. SCR @ 20 the most decisive among the three, pointing to cleaner isolation of spurious factors with small, targeted ablations. Sparse Probing is strong and, together with higher RAVEL, indicates that only a handful of latents capture both predictive signal and causally specific attributes with minimal collateral interference.
B.3 SAEBENCH RUNTIME COST
The computational requirements for running SAEBench evaluations were measured on two NVIDIA RTX A800 GPUs using 16K-width SAFS trained on the Gemma-2-28 (Team al., 2024). Qwen- 2.5-3B (Yang et al. 2024) and Gemma-2-9B. Table 4 summarizes the per-SAE runtime for each evaluation type. Several evaluations include one-time setup phase (e.g., precomputing activations or training probes) that can be reused across multiple SAEs; after this setup, each evaluation has its own runtime per SAE. We therefore report amortized per-SAE minutes.
Table 4: Approximate SAEBench runtime per SAE (minutes). Values are per-SAE and represent amortized minutes after any one-time setup; each minute figure is an approximation and may vary with hardware and I/O.
Model
Core
Interpretabillty
Absorption
Sparse Probing
Ravel
SCR
Gemma-2-28
Q.53BB
Gomma-2-0B
30
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SAEBench
Gemma-2-9B
Interpretabllity
Absorption
(Loss Recovered)
0.975
0.950
Autointerp Score
0.925
0.00
0.90
0.855
0.50
0.85
0.6
0.225
0.000
0.80
0.775
104
10
10:
(Sparsity)
SCR@20
Sparse Probing Top-1
0.80
SCR830
0.14
20p-1
0.74
107
10'
167
10a
10'
16a
(Sporsity)
(Sparsity)
(Sparsity)
TopK
BatchTopk
JumpReLU
Gated
ReWU
Figure 7: SAEbench results for Gemma-2-9B. robust interpretability with compact codes, low ab- sorption at moderate Lo, near-ceiling Core, and the clearest gains in SCR/RAVEL among the three backbones.
C AXBENCH DETAILS AND OUR COSTS
C.1 STEERING SCORE PROCESS
For each SAE feature (concept) evaluate steering utility with an AXBENCH-style judge (Wu (ct al. 2025). Given the concept description from SAEBench and the intervention rule in Eq, equa- tion we sample 10 instructions (Alpaca-Eval style) and split them 5/5 into development set for factor selection and a held-out set for evaluation. We generate continuations (up to 128 tokens) for grid of steering factors generated continuation, an LLM judge assigns three subscores on the discrete scale {0, 1, 2} (floats 2)): Concept (C: does the output express the concept?), Instruction (I;
AA by injecting the feature direction at the target layer. For each
allowed but clamped is it on-topic for the instruction?), and Fluency (F'; is it well-formed?). We aggregate with the harmonic mean
if C'500n or I50 or F50,
H,,,,,,F)
E [0, 2].
otherwise,
On the development split we pick a* = arg max. & Σ HM, then evaluate the held-out split with at to obtain the per-concept Steering Score (mean HM over the 5 held-out prompts). SAE-level utility g(0) the average of per-concept scores over the evaluation set for that SAE.
JONCEPT.TEMPLAN
[System]
Please as impartial judge and evaluate whether the specified concept is presented in the
fragment provided below. Focus solely on whether the concept is clearly incorporated, without regard for grammar or logical coherence.
Begin your evaluation by providing short explanation of whether the concept is clearly incorporated. Point out references the concept the fragment, noting any minimal awkward incorporations. After providing your explanation, rate concept's relevance on scale from 2, where 0 indicates the
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concept is not present all. 1 indicates the concept is somewhat present but minimally awkwardly incorporated, and indicates the concept is fully and effectively incorporated, with stronger and more natural integration. Provide your rating using this exact format: "Rating: [[score]]".
[Concept Start) {concept) [Concept End] [Sentence Fragment Start] {sentence) [Sentence Fragment End]
INSTRUCT TEMPLATE
[Syxtem]
Please impartial judge and evaluate whether the sentence fragment provided below is related the instruction. Focus solely on the degree relatedness terms topic, regardless of grammar, coherence, or informativeness.
Begin your ovaluation by providing brief explanation of whether the sentence is related to the instruction, and point out references related to the instruction. After providing your explanation, rate the instruction relevance scale from to 2, where indicates the sentence is unrelated to the instruction, 1 indicates it is somewhat related but only minimally or indirectly relevant in terms of topic, and 2 indicates more clearly and directly related to the instruction. Provide your rating using this exact format: "Rating: [[score]]".
[Instruction Start] finstruction) [Instruction End]
[Sentence Fragment Start] (sentence) [Sentence Fragment End]
FLUENCY.TEMPLATE TEMPLATE
[System]
Please act as an impartial judge and evaluate the fluency of the sentence fragment provided below. Focus soicly on fluency, disregarding its completeness, relevance, coherence with any broader context, or infor- mativeness.
Begin your evaluation by briefly describing the fluency of the sentence, noting any unnatural phrasing, awkward transitions, grammatical errors, or repetitive structures that may hinder readability. After provid- ing your explanation, rate the sentence's fluency on a scale from 0 to 2, where 0 indicates the sentence not fluent and highly unnatural (e.g.. incomprehensible or repetitive). indicates it is somewhat fluent but contains noticeable
awkward phrasing. and indicates the sentence is fluent and almost perfect. Provide your rating using this exact format: "Rating: [[score]]". [Sentence Fragment Start] {sentence) |Sentence Fragment End]
C.2 AXBENCH STEERING EVALUATION COST
All steering-score evaluations were run on two NVIDIA RTX A800 GPUs. The LLM-as-judge backend was pppt-4omml judge API fees; with 90 SAES total (x 30 per model), the per-model API cost is about $150. Table lists approximate per-SAE runtime and peak VRAM for each model.
Evaluating
SAE CONCEPTI00 costs approximately $5 in
Table 5: AxBench steering evaluation cost per SAE. Runtimes are per-SAE (hours) and approxi- mate; VRAM is peak memory (GB). Judge fees assume gpt-4o-
40 44o-mii:::: ~ $5 per SAE on CON- CEPT100; -Model Cost assumes 30 SAEs/model (== $150).
Model
Runtime / SAE (h) Peak VRAM (GB)
Per-Model Cost (USD)
Gemma-2-2B
15
10
150
Qwcn-2.5-3B
16
12
150
Gemma-2-9B
150
D IMPLEMENTATION OF A TOKEN CONFIDENCE
For fixed, neutral prefix s (we use "From my experience," ", following the previous work al., 2025)) we compare the next-token distribution of the base model with that of an intervened model in which a single SAE feature amplified layer T. by factor a. The intervention applied via the same SAE hook point used during training (on the residual stream of block L). We then compute the change in a confidence surrogate built from the top-k probabilities.
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Token confidence. (Fu et al., 2025) For distribution p over the vocabulary, let p(1) P(() be the top-k probabilities.
k
Cx(p) - - Σ
log P())
Delta token confidence. With Plase from a standard forward pass and Pimt from a pass with the SAE feature intervention,
AC,(;;a = Ci((mn)) Ci(Pbase).
Each feature evaluated with two single-step forwards on the same prefix s: (i) a baseline pass; (ii) an intervened pass where scale the code for f by before decoding it into the residual at layer L while keeping all other codes at zero. Hooks are removed immediately after the intervened pass to prevent accumulation across evaluations. In this work, choose 10 and k = 1.
Feature selection from ACk- For each SAE we rank its features by AC₁ in two directions: UP (largest positive AC2) and DOWN (most negative AC&). We form selection sets using either (i) top- K by magnitude with E {1, 2,3, 3, 4, 5) per direction, or (ii) upper/lower-tail quantiles (e.g., g E {0.99, 0.95. 0.90, 0.80] mirrored for the lower tail). These sets are then carried into AXBENCII Wu 2025 to measure utility lift.
et al.
E STEERING RESULTS OF SAE ARCHITECTURES AFTER FEATURE SELECTION
We quantify steering with the AXBENCH judge after selecting features using A Token Confidence (Appendix D). Unless otherwise noted, lifts are reported as the percentage change of a given SAE's steering score relative its own baseline (no selection). Results are organized at three levels: aggregate across SAEs per base model, per-SAE rankings, and distribution by architecture.
All SAEs base vs. after selection
Qwen-2.5-3B
0.40
0.30
0.35
0.25
Steering Score
0.25
Stoering Score
0.30
Steering Score
0.20
0.25
0.15
0.142
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
0.00
Figure 8: Overall steering score before and after feature selection. For each base model, the panel shows two bars: the average baseline steering score across its SAEs and the average after applying A Token Confidence-banl selection. Bars are annotated with the corresponding values; axes share the same scale across panels.
X summarizes how selection affects the mean steering score across all SAEs of base model. Using A Token Confidence for feature selection markedly improves the steering score across all three models in the figure. For Gemma-2-2B, the score rises from 0.133 to 0.328, which is 146.6% relative improvement. Qwen-2.5-3B increases from 0.171 to 0.399, 133.3% improvement, and achieves the highest post-selection score overall. Gemma-2-99 moves from 0.142 to 0.289, 103.5% improvement.
The aggregate view Figure
Conclusions: (i) feature selection via A Token Confidence consistently boosts steering for all mod- els; (ii) relative gains largest for the smallest model (Gemma-2-25 and smallest for the largest model (Gemma-2-99) suggesting diminishing relative returns with scale; and (iii) in absolute terms, Qwen-2.5-3B reaches the strongest final steering score after selection.
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Per-SAE lifts after Token Confidence feature selection (ranked)
Gemma-2-28
Qwen-2.5-38
Gemma-2-98
Architecurre
BatchTopk
Gated
JumpReLU
ReLU
Topk
660
100
360
560
-100
1.00
200
Lift (36) vs. SAE-based steering score
Lift (16) SAE based oring score
Lift (76) vs. SAE-based steering score
Figure 9: Per-SAE percentage lift after A Token Confidence selection. Each panel corresponds to base model. Horizontal bars report the percent lift of the SAE-level steering score relative to its own baseline, sorted from largest to smallest within the panel. Bar colors indicate the SAE training architecture (legend shared across panels).
Figure ranks SAES within each model by their relative lift. Architecturally, no single SAE train- ing approach dominates; however, the top-ranked lifts are frequently occupied by BatchTopK and Gated variants, with ReLU'JumpReLL also contributing strongly and TopK showing more mixed outcomes. Overall, Token Confidence yields consistent per-SAE gains, with variance decreas- ing and stability increasing as model size grows, while architectural diversity remains valuable for capturing the largest lifts.
Lift distribution by architecture
Gemma-2-2B
Qwen-2.5-3B
Gemma-2-98
500
400
600
400
300
Lift 153
400
200
100
200
100
-100
BatchToop Gated jumpkeLU ReLu
TopK
BatchTopkGated JumpRteU Reiu
TooK
Batch'To pK Gotted Jumpike ReLU
TopK
Figure 10: Lift distributions by SAE architecture. For each base model, box-and- whisker plots (with individual points overlaid) summarize the distribution of percentage lifts grouped by training architecture. Dashed horizontal lines denote the mean within each group, and whiskers follow the conventional interquartile rule.
Figure 10 groups lifts by architecture to visualize differences in central tendency and dispersion under the same selection and evaluation protocol. Read together with the per-SAE ranking, this distributional view helps disentangle architecture effects from model-specific variation and indi- cates which families tend to produce more stable or more variable outcomes after feature selection. BatchTopK and Gated generally occupy the highest central tendency with wide but mostly posi-
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tive -sreed, especially on Gemma-2-22 2-2B and Qwen-2.5-3B. BatchTopk achieves the most stable and sizable steering score. Variance is largest for the smallest model (Gemma-2-2B) indicating architecture-sensitvve wins at small scale.
F DATASET
Training corpus for SAEs. We train all SAEs on The Common Pile v0.1 (Kandpal et al. 2025) an openly licensed ~ TB text collection built for LLM pretraining from ~30 sources spanning research papers, code, books, encyclopedias, educational materials, and speech transcripts. The corpus was curated as principled alternative to unlicensed web text and has been validated by training competitive 7B models on 1-2T tokens. We use it as the sole pretraining dataset for all SAE runs. More training details provided in Appendix A.2
CONCEPT100 for steering utility. compact benchmark of 100 human-readable concept descriptions per evaluation set, pro- duced automatically by our interpretability pipeline (Appendix B Each entry (layer.feature.id description) that summarizes latent's activation pattern in plain lan- guage (e.g., mathematical symbols, scientific terms, pronouns, or domain phrases). These descrip- tions supplied to the AXBENCH judge when computing steering score. The examples below illustrate the style and domain coverage.
evaluate steering, we construct CONCEPT 100:
pair
Gemma-2-9BR BatchTopK, Lo = 80. Ten examples:
1. 20 10-14429, concepts related to optical communication systems and their performance characteristics
2. 20 5795: specific technical terms and chemical compounds often related to scientific contexts
3, 20_7908: terms related to gravitational lensing and its effects in cosmology
4. 20 3042: pronouns and verbs indicating relationships or contributions in various con- texts
5. 20_11897: scientific measurements and units related to energy, concentration, or bi- ological data
6. 20-12944: terms related to cell types and apoptosis mechanisms in scientific contexts
7. 20 8796: references to specific authors and statistical concepts in mathematical con- texts
8. 20.6430: the phrase "action" in mathematical and theoretical contexts
9. 20.2220: chemical elements and compounds, particularly including metals and metal-related terms
20.585: various forms of the word "energy" and related concepts scientific contexts
Qwen-2.5-3B, Gated, Lo R 72, Ten examples:
1. 17_15113: terms related mathematical concepts and various scientific names or terms
2. 17.11476: the phrase "as a function of"" in contexts of measurement and analysis
3. 17 1.62; mathematical symbols and concepts related to coordinates, magnitudes, and parameters in equations
4. 17_2552: dataset identifiers and technical terms common in research and academic documents
5. 17. 16377: mathematical notation and technical terms commonly found formal documents
6. 17_3195: demographic, clinical, and biological characteristics in study populations and related comparisons
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7. 17.9186: specific technical terms and concepts related to networking and program- ming
8. 17.11487:
mathematical notation and variables related to functions and equations
9. 17_1 17_14657: mathematical notations and structures involving angle brackets and prop- erties of functions
10. 17 17-1256 terms related to errors and error correction in coding theory and quantum operations
Gemma-2-22, JumpReL,U, Lo 81. Ten examples:
1. 20_11531: terms related sports, programming, specific keywords from various contexts
2. 20. 10460: terms related to fractional differential equations and numerical methods for solving them
3. 20-4882: terms related to asymptotic theory, robustness, and statistical estimation methods
4. 20.4425: first-person plural pronouns and expressions of intention or conjecture
5. 20.372: technical terms related to measurement and structure in scientific contexts
6. 20-9999: the word "from" and contexts implying deviation distance from some- thing
7. 20.9703: the word "based" in various contexts of theoretical foundations and methodologies
8. 20-15509: technical or numerical concepts in a variety of contexts
9. 20-8218: phrases indicating conditions or assumptions that must be met in theoretical contexts
10. 20_4614: time intervals and durations mentioned in the context of studies or obser- vations
We currently maintain 90 SAEs (30 per base model). Beyond the CONCEPT 100 sets evaluated in this paper, we have constructed CONCEPT 1000 and CONCEPTI 6K suites that scale the number of hemabbre concepts up to 16K. We will extend training and evaluation to these larger suites in forthcoming releases to further substantiate the reliability and generality of this work.
G ANALYSIS OF STEERING STRENGTH ACROSS INTERPRETABILITE LEVELS
To directly address the concern that highly interpretable SAE features might have negligible steering effects, we conduct an additional analysis combining interpretability scores with steering scores at the feature level.
We do not find that interpretable SAE features have negligible steering effects. As the first set of panels in Figure [] shows, high-interpretability features span the full range of steering strengths, including many strongly steering latents; high-interpretability features are not dominated by weak steering. Conversely, the second set of panels in Figure IT shows that strongly steering features (top steering quartile) also cover almost the full range of interpretability scores, and many of them are only moderately or weakly interpretable according to interpretability score. In the SAEs under Qwen-2.5-3B, we found that features with extremely high steering scores also tend to have higher interpretability scores. This explains why, in Appendix [ only the SAE model under Qwen-2.5-3B shows improved steering performance when using high interpretability scores. However, below 1.0, the performance becomes highly dispersed again.
Taken together, these two views indicate that (i) high interpretability does not guarantee strong steering, and (ii) strong steering does not require high interpretability. In other words, feature-level interpretability scores provide limited information about how strongly latent direction pushes the logits, reinforcing our claim that interpretability and steering strength are nearly orthogonal at the feature level.
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Cemms--277
Cemmss-2-58
5-38
Steee TO Ovene LOCO
Stum no snocoal VerT
62-
04
05
8.7
03
03
04
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00
23
0.7
0.0
Astoll Sappsaae
AdMruap AATE
Germin-2225
Germea-2-0
Qwan-255:36
1.0
122
122
02
Stewring
Stowiing overal
Steni 12 overral
Figure 11: Feature-level relationship between interpretability and steering strength across models. Panels are shown separately for Gemma-2-2B, Gemma-2-9B, and Qwen-2.5-3B. The first set of panels plots interpretability score (AutoInterp) against steering overall score for every latent. The second set of panels flips the axes and highlights the top steering quartile in orange, with all latents shown in blue.
H INSTRUCTION UNDER SAATURE-SELECTINN STRATEGIES
To address whether our Ceature-selection metric surfaces features that make model outputs inco- herent, we compare the AxBench Instruction subscore when steering with three strategies: using all SAE features ("SAE Base"), using features selected by the Output Score baseline, and using features selected by our A Token Confidence metric. For each model and SAE architecture, we aggregate the instruction subscores of the steered generations and plot them in Figure
12
Instruct Subscore SAE Architectures
SAE Output Score Token Conf selections
Output Score Selection
Token Selection
Gemma 2B
Qwen 2.5 3B
Gemma
2.0-
2.0
1.6
1.6
1.6
osted
ReLU
Beli
Tope
Osted
Geli
Topk
Osted
ReL
Dell
Tope
Figure 12: Instruction subscore across SAE architectures when steering with different feature- selection strategies. For each model, we compare the AxBench Instruction score under three setups: using all SAE features (SAE Base), using Output Score selection, and using A Token Confidence selection.
Across all models, both selection methods keep the instruction subscore close to the base level (typ- ically in the 1.5-2.0 range on a (-2 scale), indicating that neither Output Score nor A Token Con- fidence systematically degrades instruction following. This behavior is expected because coherence
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is primarily controlled by the steering factor in the intervention
d x + (amy) -
which scales how strongly feature is injected into the hidden state. AxBench already tunes per feature to balance concept shift against instruction following and fluency. The role of A Token Confidence is not push the model into incoherent regimes, but select features for which even small interventions induce a strong, directional change in the token-level logits.
I EXPLORING THE STEERING UTILITY OF SAES WITH HIGH INTERPRETABILITY
To directly test whether selecting features by interpretability also selects for high steering utility, we run a controlled comparison at the feature level. For each SAE in our three model-layer settings, we compute three steering configurations on AxBench: (i) SAE Base, which steers with all evaluated features; (ii) Interpretability selection, which steers using only the top-p% latents by AutoInterp score (we use p 10% in Figure 13); (iii) A Token Confidence selection
Stearing Score of Different SAE Architectures
Interpretability Selection
Tokan Conf Selection
Gemmaa 2.
Qwen 2.5 3B
Gamma 2 9B
Intergreta Basei Tokan [Durs) SAE 145.20%
Interpretability
-18.86%
Token (Durs)
132.80%
Token Cont (Durs) SAE Base: 110.78%
0.44
0.4
0.392
0.4
0.315
9,325
0.6
0,203
0.201
0.240
0.254
0.33
9.385
0.2
0,132
0,343
0.11
0.132
0,127
0,059
0.2701
0,333
61-
0,046
0.00
8,905
BetchTapK Gated Jumptel
TopK
BatchTopK Gated JampRaLU ReUU
Topk
BatchTopp Gatel JamphatU RGLU
TopK
Figure 13: Steering scores under different feature-selection strategies across SAE architectures and three models. Bars show the AxBench overall steering score for (left) steering with all features (SAE Base), (middle) steering with the top-10% most interpretable features (AutoInterp), and (right) steering with features selected by A Token Confidence. The hanners report the macro-average percentage lift over the SAE Base.
Across all three models, selecting features by interpretability alone yields at best modest and often negative changes in steering strength relative to using all SAE features (about 35% for Gemma-2-2B. +10% for Qwen-2.5-3B. and 19% for Gemma-2-99 2-9B), whereas Token Confidence consistently deliv- ers large gains of roughly 1. 1-15xx over the same SAE base. This pattern indicates that feature-level interpretability is weak signal for steering utility, while Token Confidence reliably concentrates probability mass on features that produce substantially stronger steering effects.
J SIGNIFICANCE ANALYSIS FOR DIFFERENT SAE STEERING METHODS
To address the question of whether the improvements in Figure are statistically significant, we reran the analysis at the SAE level and, for each model and architecture, computed the mean steering score and its 95% confidence interval across SAES (shown as error bars in Figure 14). In addition, we performed paired bootstrap tests over SAEs for three contrasts: (i) A Token Confidence selection SAE Base, and (ii) A Token Confidence selection vs. Output Score selection. Finally, we repeated the paired bootstrap test pooled over all 90 SAES.
The error bars in Figure 14 show that Token Confidence selection consistently lifts steering scores above the SAE Base across architectures and models.
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Steering Score Different Architectures Token Conf Selection
SAE Base
Output Score Selection
Gemmaa
Owan 70.43%
Output Score vS SAE Basel 74.07%
Output Score SAE Base!
Output Score SAE Basel
$0.03%
Token Conf [Durs) SAE Bean: 140.21%%
Token Cont [Durs] Bens: 132..9%
Token Cont (Durs) va SAC Base: 103.73%
0.7
6-454
6.335
I-44R
6.c-
6.353
6,393
6.300
0.389
8,313
0.00
ScorTe
0.354
0.335
0.313
6.271
9.250
6.187
6:177
6.201
9.257
0121
6:42
0:103
6117
6,11
61-
0.
ButchTspK Gated Jumpteti ReLU
Topk
ButchTupk Gateel JumpRoLU ReUU
Topk
BatchTopk Gatei Jumphatu
ReLU
Topa
Figure 14: Error-bar version of Figure 4. Mean steering score and 95% confidence intervals across SAEs for the SAE Base, Output Score selection, and A Token Confidence selection, grouped by architecture and model. When aggregated across SAFs, there a statistically significant difference between A Token Confidence and the baselines.
In this experiment, steering scores are first computed for each of the 90 SAFs under three conditions: SAE Base (no feature selection), Output Score-based selection, and ATTkenConf-baal We then form per-SAE paired differences and apply paired bootstrap over SAEs to estimate the mean difference, its 95% confidence interval, and a two-sided p-value, yielding the global signifi- cance results summarized in Table
selection.
Table 6: Pooled paired-bootstre comparison of steering scores across all 90 SAEs. For each con- trast, report the mean Per-SAE difference in steering score, a 95% bootstrap confidence interval, the two-sided p-value, and whether the effect is significant at the 5% level.
Comparison
Mean difference
95% bootstrap CI Two-sided Significant at 5%?
ATokenConf
Base
0.1899
[0.1454, 0.2339]
2y 0.0000
Yes
ATokenConf - Output Score
0.0786
[0.0261, 0. 03105 Rs 0.0032
Yes
Concretely, we find that our selection method yields a statistically significant improvement in steer- ing score both relative to the SAE Base and relative to the Output Score selection.
K ANALYSIS OF GAP BETWEEN SAE INTERPRETABILITY AND UTILITY
Regarding why there is a gap, our view is that the root cause lies in the training paradigm of SAEs. Current SAE training is almost entirely reconstruction-centric the objective is to accurately recon- struet internal activations while enforcing sparsity, so as obtain more monosemantic basis in disher-dimensional space. This is precisely what makes SAE features interpretable, but it does not directly optimize how useful those features are for steering. In other words, the training objective aligned with reconstruction fidelity and monosemanticity not with control over model oulputs.
To make this concrete, we perform a pairwise Kendall-m, analysis over all 90 SAEs, relating inter- pretability, steering, and two standard reconstruction-side metrics (both higher-is-betterr (i) the CE loss score and (ii) explained variance. TableeJreport T,, bootstrap standard error, a 95% bootstrap confidence interval, and permutation p-value for the null H₂ TU 0 for each pair of metrics.
As Table shows, the reconstruction metrics exhibit only a weak association with steering ((76l ss 0.2), but a substantially stronger association with interpretability (17al = 0.4). In other words, the reconstruction focuuuesetoo-oeeeedeeeeoeee training objective is much more predictive of which SAEs score well under interpretability metrics than of which SAEs actually good for steering, and is close orthogonal
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Table 7: Pairwise Kendall-7, between interpretability, reconstruction metries, and steering score over all 90 SAEs. "CE loss score" and "explained variance" are standard post-hoc reconstruction metries (higher is better).
Pair
7b
SE
95% bootstrap CI
perm p Ho: Tb 0)
Interpretability CE loss score
-0.433
0.056
-0.539,
-0.322)
0.0002
Interpretability Explained variance
-0.405
0.059
-0.521,
-0.289
0.0002
CE loss score Steering Explained variance - Steering
-0.243
0.067
-0.377,
-0.112
0.0006
-0.195
0.066
-0.323,
-0.062)
0.0062
steering utility. This supports our claim that the observed interpretability uutilit gap is not an artifact of our evaluation, but structural consequence of the current SAE training paradigm, in which reconstruction fidelity-rather than steering behavior-is the primary optimization target.
L ABLATION ON THE TOP-k IN A TOKEN CONFIDENCE
In our token confidence selection, we measure how much feature shifts the model's confidence over the top-k tokens in the output distribution. Unless otherwise noted, all main experiments 1, so that the score directly tracks the change in probability the top-1 predicted token, which typically dominates next-token behavior in standard generation settings.
To verify that this choice is not artificially restrictive, we run an ablation over (1, 3, 5, 10) on Gemma-2-2B and Qwen-2.5-3B. Table & reports the resulting steering scores (higher is better) after applying A token confidence selection.
Table 8: Ablation over the top-k parameter in A token confidence selection.
(top-k)
Gemma-2-2B
Qwen-2.5-3B
0.328
0.399
3
0.264
0.370
5
0.314
0.302
10
0.245
0.343
All tested values of & yield substantial gains over the SAE baseline (not shown), and k = 1 is in fact the best-po rest-performing setting on both models. We therefore adopt as an empirically validated default in all main experiments.
M EXAMPLES OF TTTTAPPETABLE-BBT--NHELLLL VS. HILLFFUL-BUT-HARD-- EEPOOXIX FEATURES
To complement our quantitative analysis, we provide qualitative examples of features where inter- pretability and steering utility diverge. Type A features are highly interpretable but not steerable (high interpretability score, near-zero steering score), while Type features are moderately inter- pretable but strongly steerable. All generations in Table 9 are produced with temperature 0 using the fixed prefix heard that' and intervening on a single feature.
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Table 9: Qualitative examples of features where interpretability and steering diverge. Type A: inter- pretable but not steerable (interpretability z 1.0, steering = 0). Type B: moderately interpretable but clearly steerable. All generations use temperature O with the prefix "I heard that".
Fidi
Grnase 22:AA
Qwar25 CAl
Gennnu 28
Qwar25 58
Type
keaperabiig
1.0
0.50
Simning
3.00
B00
Explnaatin
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manetical volkau rolaad compations
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Reviews:
[{"review_id": "6fKXfGXSy8", "reviewer": "Reviewer_AA1u", "summary": "This paper studies the extent to which SAE interpretability metrics correlate with how effective an SAE's latents are for steering, finding a small positive association. They then introduce a metric—a feature's steering effect on the log probability of the most probable tokens—that selects for features that are very effective for steering.", "questions": "Why are so many of the confidence intervals in table 1 identical? E.g. the upper confidence bound for every row in the \"Sparsity\" section is 0.3714 despite different tau_b values.", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The finding that an SAE's interpretability score doesn't correlate well with steering efficacy is interesting.\n2. The authors sweep over a comprehensive set of SAEs from different models.", "weaknesses": "1. The result that SAE interpretability score isn't well-correlated with steering score is interesting, but I think it would be much more valuable to present an analysis of why this is the case. Do interpretable SAE features tend to have negligible steering effects? Do they tend to cause degeneration in instruction following? I feel like this result is mainly interesting insofar as it raises follow-up questions, none of which are addressed here.\n2. Similarly for the result on delta token confidence selecting for features with a high steering score: Why specifically does this work? Is it because it's selecting for features that have a non-negligible steering effect? Why doesn't this metric surface many features that make model outputs incoherent? In this case, I don't feel like the stand-alone result is very important, but it could be used as a springboard for additional analysis.\n3. The result on delta token confidence selecting for high steering score is presented as an improvement on selecting on interpretability, but in fact this is a very apples-to-oranges comparison. In one case, the result is that selecting for *SAEs* with a high interpretability score doesn't result in *SAEs* with a high steering score; in the other case, the selection is being done at the level of features. An apples-to-apples comparison could be to show that *SAEs* whose average feature has a high delta token confidence have high steering scores (computed in terms of Kendall's rank coefficient). Alternatively, you could test whether selecting for interpretability at the feature level also selects for high steering score. At minimum, you should remove claims like \"This result validates the superiority of our method\" given that you haven't actually demonstrated that delta token confidence is superior to anything. (Unless you mean that delta token confidence is superior to the other methods in table 2, in which case that should be made clear. Also, if the comparison in table 2 is being treated as a core contribution, then the authors should (1) explain what the Arad et al. (2025) S_out metric is, given that it's very similar to the delta token confidence metric used here, (2) present some analysis of why delta token confidence is more effective than S_out, and (3) motivate why introducing metrics that select for high steering score features is important.)\n4. The equation given for tau_b is actually the equation for the non-tie-corrected tau_a; it's unclear which one the authors actually used.\n5. It's possible that I'm misunderstanding something here, but the descriptions in the abstract and introduction of the result in section 4.3 seems incorrect. In the abstract it says \"Strikingly, after selecting features with high ∆ Token Confidence, the correlation between interpretability and utility vanishes (τb ≈ 0)\". However, the actual result seems to be  that selecting for high interpretability score *SAEs* does not select for *SAEs* such that \"steering gain\" is large. I can't actually tell what \"steering gain\" is in section 4.3 (it's defined as \" the percentage lift of the selected-steering score over the same SAE’s base\" which is too vague for me to parse), but the same term is used elsewhere in the paper to mean \"the increasing in steering score after selecting for high delta token confidence features.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ocxgJ0JhTU", "reviewer": "Reviewer_MCfE", "summary": "This paper considers sparse autoencoders (SAEs), a popular technique in mechanistic interpretability, and seeks to uncover the relationship between the interpretability of a latent (i.e. to what extent the latent corresponds to a robust concept) and the utility of the latent (its ability to steer downstream generation towards or away from that concept). The paper uses two popular benchmarks to encode these ideas: SAEBench for interpretability and AxBench for utility. Despite the conventional wisdom being that interpretability and utility would be strongly correlated, the paper finds only a weak positive association (0.298). Furthermore, after filtering to only the top latents in terms of their impact on the logit distribution, the association drop to near 0 (whereas one might expect it to be positive). This is a counterintuitive result. The study is comprehensive across 90 SAEs from different architectures, sparcities etc.", "questions": "- I was confused by *steering gain* (sec. 4.3). From my understanding, this is a different metric to *steering score* in the earlier parts of the paper. If this is correct, are we calculating the same metric $tau_b$ in the section case (filtering for only the top token confidence latents)? If not, are these two $tau_b$ metrics directly comparable? The way I interpreted the method from the description is that we would filter for the top tokens by confidence latents, and then calculate the exact same metric, but I don't think this is the case, right? Thanks.", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The study is comprehensive. It considers 90 SAEs with varying architectures and sparsity levels. This is a strong point of the paper since the results are generalisable to all SAEs. The one axis that isn't varied is the dictionary size, always being 16k; however, there is sufficient variation elsewhere.\n- The paper is generally well-written and easy to read. Figures 1 and 2 are informative.\n- The methodology used allows a hierarchical analysis of differences between models of different architectures, etc. I have questions about the statistical significance of these results (see next section), but this analysis is really nice since it allows claims of which architecture provides the smallest interpretability-utility gap. \n- Fundamentally, this is an unexpected result and should be of interest to the community. It is odd that latents which are more interpretable are not necessarily more useful for steering!", "weaknesses": "I've ordered these by importance.\n- **The definition of interpretability:** My main concern is around the definition of interpretability of a latent. The paper assumes a *correlational scoring* approach following one of the methods set out in [1]. Quoting from the paper under review, \"the judge drafts the description from examples and then predicts, on a held-out set\" (L135). This is correlational because it only considers when the latent activates and when it doesn't. The paper writes like this is the default definition of interpretability, and then compares the derived scores to the utility scores. However, in reality, people often evaluate interpretability using an *intervention scoring* method as well as just the correlational method [1]. To quote from Paulo et al. 2025 (the same paper used to define the AutoInterp metric: \n> \"intervention scoring, evaluates the interpretability of the effects of intervening on a feature, which we find explains features that are not recalled by existing methods.\"\n\n    In short, the authors' operationalisation of *utility* is often used by other papers as a way of measuring *interpretability*. As a result, the distinction of interpretability/utiliy is not as obvious as it may seem. It remains a very interesting result that interpretability from correlational scoring seems to be unrelated to interpretability from interventional scoring, or utility, but the phrasing of the result needs a bit of work in my opinion.\n\n- **Statistical testing:** Many of the results rely on the point value of the $\\tau_b$; however, this would benefit from showing standard errors and doing hypothesis tests to examine whether it is statistically significantly different from 0. In particular, (i) when we change it to only consider those with high Token Confidence, is the change in $\\tau_b$ statistically significant? (ii) When you compare different architectures, are any of those changes statistically significant? (iii) In Figure 4, if we add error bars to the plot, are any of the comparisons statistically significant? This seems really important to support the main results. Table 3 does show standard errors for the axis-controlled summaries, but the CIs are quite large, which makes me suspect that some of the results reported (e.g. the comparisons between architectures) are not significant.\n- **Clarification on why the gap matters:** Most readers probably work it out quickly, but explicitly describing why the gap between interpretability and utility matters for downstream tasks would be nice. (In fact, explicitly defining \"the gap\" would also be helpful).\n- **Examples:** As mentioned, I think this main result is weird and unexpected, which makes it interesting! It would be great to see some examples of features that are interpretable but not steerability, and vice versa. \n- **How do you select $k$?** A smaller point, but how do you establish $k$ in the token confidence calculation? In the appendix, it says $k=1$ for all experiments. Is this the correct interpretation? If so, I feel this should be in the main text, and it feels somewhat limiting given that the metric is explained in the context of changing the logit distribution. \n- **Writing:** In general, the writing is strong, but there are a few places where metrics are not clearly defined, e.g. *CONCEPT100*. The paper sends the reader to the appendix for a definition, but it would be best to define these terms in the main body.\n\nThis paper studies an interesting question and has a lot of potential, but I feel there are some critical questions that need to be addressed before it is ready for publication.\n\n**Typos:**\n- L053 missing year in citation.  \n- L212 citation capitalisation\n\n---\n[1] Paulo et al., 2025", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7oJr5uDJop", "reviewer": "Reviewer_2ZdN", "summary": "This paper studies two aspects of SAEs evaluation: the interpretability aspect and the utility aspect (especially steering). The authors have conducted correlation analysis on 90 SAEs from 3 base models and find that there is little to no correlation between interpretability and utility scores. The authors also propose a new method that improves steering performance, and find the new method further weakens the correlation between interpretability and utility.", "questions": "Please see the weakness. In particular, it would be great if authors could provide more insights/analyses into why there is a gap between interpretability and utility.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* This work offers an interesting perspective on SAE evaluation. In particular, the authors frame it as a tension between how interpretable the features are, i.e., interpretability score, and how useful the features are for steering, i.e., utility score. This framing could inspire new evaluation metrics and design on SAEs.\n* The authors have conducted extensive experiment on 90 SAEs over 3 base models that cover common SAE architecture variations. This provides solid emperical evidence.", "weaknesses": "*  While the paper frames the findings as a tension between \"interpretability\" and \"utility\", the experiment operationalized \"interpretability\" and \"utility\" in a much narrower sense, i.e., as performance on SAEBench (the auto-interp task) and AxBench (the steering task).\n    * For \"Interpretability\", it is unclear what exactly \"interpretability\" entails in the paper. The auto-interp score is not an intrinsic metric to the feature space learned by SAE, but rather confounded with the quality of the auto-interp pipeline and how closely it is aligned to human understandable concept space.\n    * The \"utility\" is exclusively measured as \"steering utility\", while there are clearly other downstream applications of SAEs. For example, [Peng et al. 2025](https://arxiv.org/pdf/2506.23845) argues that SAE could be used on discovering unknown concepts. I would encourage the authors to be precise here and quantify the scope of study to match what actually done in the paper, for example, in the paper title, directly stating \"steering utility\" instead of \"utility\".\n\n* The authors experimented with how different SAE architecture/features affect the gap, however, there is still a bit lack of insights on why there is a gap between \"interpretability\" and \"utility\". In particular, both interpretability score and utility score are extrinsic evaluation metrics that measure the success of a system as a whole, with SAE being one component. For example, interpretability score relies on the auto-interp pipeline, which is known to produce inaccurate description sometimes and these descriptions are often biased towards the role of the feature space in detecting concepts in inputs. Thus, is the gap between interpretability and utility a failure of the auto-interp pipeline, or more of a fundamental problem of SAEs?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "yhwCvJ5Mdv", "reviewer": "Reviewer_vNrz", "summary": "This work investigates the correlation of interpretability and steering utility of SAE latents by comparing rankings via  kendall's tau coefficient, and finds low correlation. After introducing a new method for selecting SAE features for steering, the correlation surprisingly vanishes.", "questions": "- Should we use SAE latents for steering at all? How does the delta token confidence based steering compare to non-SAE based steering methods from AxBench?\n- Are you open-sourcing the trained suite of SAEs?\n- Can you provide max-activating inputs for features selected by delta-token-confidence? I'd be interested to see whether they are interpretable at all.\n- Based on your results, do you deem interpretability scores as actively misleading, should we only rely on steering ability when judging SAE quality? Or are interpretability and steering utility rather complementary characteristics?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "- This paper provides quantitative evidence that interpretability scores are not indicative of steering utility. This contribution is relevant to the field -- interpretability is often treated as a universal score for the quality of learned features. I personally updated on putting less weight on automated interpretability as a measure for overall SAE quality.\n- The writing is very clear, highlighting key takeaways, and motivating experiments.\n- They train a wide range of SAEs\n- Controlling for confounders when computing the correlation.\n- The paper uses established metrics for interpretability (SAEBench) and steering success (AxBench)", "weaknesses": "- Looking at any code file in the anonymous repo link throws the error \"The requested file is not found.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)