Does higher interpretability imply better utility? A Pairwise Analysis on Sparse Autoencoders

Does higher interpretability imply better utility? A Pairwise Analysis on Sparse Autoencoders Xu Wang1 Yan Hu2 Benyou Wang2 Difan Zou1 1School of Computing and Data Science, The University of Hong Kong 2School of Data Science, The Chinese University of Hong Kong, Shenzhen sunny615@connect.hku.hk, dzou@cs.hku.hk Lead author.Corresponding author. 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 unanswered: does higher interpretability indeed imply better steering utility? To answer this question, we train 90 SAEs across three LLMs (Gemma-2-2B, 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 τb _b. Based on the framework, Our analysis reveals only a relatively weak positive association (τb≈0.298 _b≈ 0.298), indicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability-utility gap may stem from the selection of SAE features as 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: Δ Token Confidence, which measures how much amplifying a feature changes the next token distribution. We show that our method improves the steering performance of three LLMs by 52.52% compared to the current best output score-based criterion (Arad et al., 2025). Strikingly, after selecting features with high Δ Token Confidence, the correlation between interpretability and utility vanishes (τb≈0 _b≈ 0), and can even become negative. This further highlights the divergence between interpretability and utility for the most effective steering features. 1 Introduction As Large Language Models (LLMs) become more widely used in real-world applications, ensuring the safety of their outputs is increasingly important (Kumar et al., 2024; Ji et al., 2023; Inan et al., 2023). Reliable and controllable behavior is essential for deploying these LLMs in more situations (Chen et al., 2024). Fine-tuning is the standard way to improve controllability, but it requires labeled data, significant training time, and compute resources (Hu et al., 2022; Wang et al., 2025a). 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, 2024; Wang et al., 2025b; 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 a valuable 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). 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 et al., 2024). Despite this progress, a critical question remains unanswered: does higher interpretability truly imply better utility? Since SAEs are trained to balance reconstruction and sparsity to yield human-readable features (Cunningham et al., 2023; Makelov, 2024; O’Brien et al., ), their utility for downstream tasks is not a primary objective. Understanding and characterizing this gap is critical to enabling more interpretable and effective steering over the LLM. To this end, we conduct a systematic study to build a bridge between SAE interpretability and steering utility (see Figure 1). Figure 1: Overview of our goal: building a bridge for SAE interpretability and utility. Interpretability (left): an SAE attached to the LLM decomposes hidden states into sparse, human-describable features. An LLM judge yields an interpretability score for the SAE (Paulo et al., 2025). Utility (right): at inference, we activate a target SAE feature (e.g., ‘cake’) to steer generation. An LLM judge yields steering utility score (Wu et al., 2025). To perform a comprehensive association analysis, we train 90 SAEs across three LLMs (Gemma-2-2B (Team et al., 2024), Qwen-2.5-3B (Yang et al., 2024), and Gemma-2-9B) spanning diverse architectures and sparsity levels. We compute interpretability using SAEBench (Karvonen et al., 2025) and steering utility using AxBench (Wu et al., 2025). Then, we leverage a pairwise-controlled framework to evaluate whether interpretability predicts steering performance across the pool of trained SAEs. To quantify this relationship, we follow the idea of prior works (Jiang et al., 2020; Hu et al., 2024) and measure rank agreement between interpretability and utility using Kendall’s rank coefficient τb _b. We control confounders with an axis-conditioned analysis, isolating each design axis (architecture, sparsity, model) by varying one at a time and aggregating per-axis metrics. Furthermore, as identified in Arad et 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., 2025c), we propose an innovative selection criterion for SAE features: Δ Token Confidence, which measures the degree to which amplifying a 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, as they exert a measurable and targeted influence on model behavior. Finally, we leverage these critical features to conduct a refined analysis of the interpretability-utility gap. The primary contributions and insights of this paper are 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, we find that a higher interpretability score tends to shows a relatively weak positive association with steering performance (the Kendall’s rank coefficient τb≈0.298) _b≈ 0.298)). This identifies a notable interpretability-utility gap of the existing SAEs. 2. (§4.2) Δ Token Confidence effectively selects features with strong steering performance. To identify the SAE features that are critical for steering, we introduce Δ Token Confidence, an innovative metric that identifies steering-critical 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. 3. (§4.3) The interpretability-utility gap widens among high-utility features. By reapplying our association analysis exclusively to SAE features with strong steering utility, we uncover a counterintuitive finding: the interpretability-utility correlation vanishes or even becomes negative (Kendall’s rank coefficient τb≈0 _b≈ 0). This indicates that for the most effective steering features, interpretability is at best irrelevant and potentially detrimental, further emphasizing the critical nature of the interpretability-utility gap. 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 it will likely necessitate advanced post-training feature selection protocols or fundamentally new, utility-oriented SAE training paradigms. 2 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 to the original space (Cunningham et al., 2023; Leask et al., 2025). A standard SAE with column-normalized decoder weights (Bricken et al., 2023; Karvonen et al., 2024) is defined by the following forward map and optimization objective: ℒ=‖x−x^‖22+λ​‖h‖1,where​h=ReLU​(WE​x+bE),x^=WD​h+bD, \;=\;\|x- x\|_2^2\;+\;λ\|h\|_1,\ where\ h=ReLU(W_Ex+b_E),\ x=W_Dh+b_D,\ where WE,bEW_E,b_E are encoder parameters, WD,bDW_D,b_D are decoder parameters, x x is the reconstruction, and λ controls sparsity. This training balances reconstruction accuracy with sparse representations. 2.2 Interpretability: Automated Interpretability Score SAEBench (Karvonen et al., 2025) uses an LLM-as-judge (Paulo et al., 2025) to assess each latent: the judge drafts the description from examples and then predicts, on a held-out set, which sequences activate it. The Automated Interpretability Score is the average precision of the judge’s prediction. AutoInterp​Score=1M​∑m=1M​[y^m=ym], \ Score\;=\; 1M _m=1^M1\! [ y_m=y_m ], where ym∈0,1y_m∈\0,1\ indicates whether the latent activates in the sequence m and y^m y_m is the judge’s prediction. We use this score as our interpretability metric. For the complete details, see Appendix B. 2.3 Utility: Steering Score SAE steering injects the SAE decoder atom vfv_f (the f-th column of the column-normalized decoder Wdec​[f]W_dec[f]) into the residual stream at a target layer to push the hidden state x along a chosen feature direction (Durmus et al., 2024). Given a feature index f, a steering factor α, and a per-sample scale mfm_f (e.g., the feature’s maximum activation), the intervention is xsteer=x+(α​mf)⋅vf. x^steer\;=\;x\;+\;(α\,m_f)· v_f. (1) Through the above formula (1), we can use SAE features for steering to achieve the output of controlling LLM. AxBench (Wu et al., 2025) measures causal control by steering internal representations during generation and asking an LLM judge to rate three aspects, each on a discrete scale 0,1,2\0,1,2\: Concept (C), Instruction (I), and Fluency (F). The overall Steering Score is the harmonic mean: Steering​Score=HM​(C,I,F)=31C+1I+1F∈[0,2]. \ Score\;=\;HM(C,I,F)\;=\; 3 1C+ 1I+ 1F\;∈\;[0,2]. Following AxBench, for each concept we sample instructions (e.g., 1010 from Alpaca-Eval (Dubois et al., 2023)), generate continuations under different steering factors, pick the best factor on one split, and evaluate the held-out split with the judge to obtain the final utility score averaged across prompts (Gu et al., 2025). The complete scoring procedure is detailed in Appendix C. Figure 2: Overview of our pairwise-controlled workflow linking SAE interpretability with steering utility. (S1) Compute interpretability score and steering score for each SAE. (S2) Pairwise analysis across SAEs and get an insight (the top-right green box), revealing an interpretability–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 Δ Token Confidence to select higher-utility features. (S4) Compute steering gains after selection per SAE, then do the pairwise analysis between steering gains and interpretability. The green box in the middle left is our final conclusion. 3 Can SAE Interpretability Indicate Steering Performance? 3.1 Experimental Setup Dataset. For each trained SAE, we score 1,000 latents with LLM-as-judge (Paulo et al., 2025) and randomly sample 100 to form that SAE’s Concept100 (see Appendix F). For steering, we sample 10 Alpaca-Eval instructions, allow up to 128 generated tokens, and test 6 steering factors; the 10 instructions are split 5/5 for factor selection vs. held-out evaluation. Model. We evaluate three open LLMs: Gemma-2-2B (Team et al., 2024), Qwen-2.5-3B (Yang et al., 2024), and Gemma-2-9B (Team et al., 2024). SAEs are trained on residual-stream activations at a fixed mid-layer for each model: Layer 12 for Gemma-2-2B, Layer 17 for Qwen-2.5-3B, and Layer 20 for Gemma-2-9B—and steering is applied to the corresponding layer. SAE with different architectures We train 90 SAEs covering a range of architectures and sparsity. All SAEs use a latent dictionary width of 16k. We instantiate five variants: BatchTopK (Bussmann et al., 2024), Gated (Rajamanoharan et 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 L0≈50,80,160,320,520,820L_0≈50,80,160,320,520,820. Further details are provided in Appendix A. 3.2 Pairwise Rank Consistency between Interpretability and Utility We test whether higher interpretability of SAE is predictive of higher steering performance across a set of trained SAEs attached to a fixed LM. For each SAE θ in a pool Θ , we record a pair (μ​(θ),g​(θ))∈ℝ2(μ(θ),\,g(θ)) ^2, where μ is the SAE-level Interpretability Score and g is an aggregated Steering Score over a standardized evaluation suite. Given two SAEs θi,θj∈Θ _i, _j∈ , define the concordance indicator vi​j=sign⁡(μ​(θi)−μ​(θj))⋅sign⁡(g​(θi)−g​(θj))∈−1,0,+1. v_ij\;=\;sign\! (μ( _i)-μ( _j) )·sign\! (g( _i)-g( _j) )∈\-1,0,+1\. (2) Kendall’s tie-corrected rank coefficient τb _b (KENDALL, 1938) summarizes agreement over unordered pairs and reduces to average concordance when there are no ties: τb=1(|Θ|2)​∑i<jvi​j∈[−1,1]. _b\;=\; 1 | |2 _i<jv_ij∈[-1,1]. (3) In this study, we instantiate μ with the Interpretability Score and g with the Steering Score, then compute τ for three model–layer settings (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B). Each setting includes 3030 SAEs spanning architectures and sparsity to 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 a 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 iG_i that are matched on all axes except i. Within each group G∈iG _i, compute Kendall’s coefficient in (μ​(θ),g​(θ)):θ∈G\(μ(θ),g(θ)):θ∈ G\, and average between groups to obtain the statistic at the axis level: ψi=1|i|​∑G∈iτ​((μ​(θ),g​(θ)):θ∈G). _i\;=\; 1|G_i| _G _iτ\! (\(μ(θ),g(θ)):θ∈ G\ ). (4) Aggregate the axis-level outcomes by Ψ=1n​∑i=1nψi, \;=\; 1n _i=1^n _i, (5) where n is the number of axes. Each ψi _i captures rank consistency conditioned on axis i (varying only that axis while matching the others), and Ψ aggregates these into a single axis-controlled measure. This construction mitigates cross-axis trends—e.g., architecture, sparsity, or model-driven shifts that can obscure local relationships between interpretability and utility. We report the per-axis statistics ψi _i together with the aggregate Ψ for the same model settings as in section 3.2, providing both axis-specific and aggregated assessments. Table 1: Pairwise Analysis Between Interpretability Score μ​(θ)μ(θ) and Steering Score g​(θ)g(θ). We report Kendall’s τb _b overall and by axis-controlled measures ΨA _A (Architecture), ΨB _B (Matched Sparsity), and ΨC _C (Model). n = number of SAEs; Pairs = number of pairwise comparisons; p = permutation p-value; 95% CI = confidence interval (overall uses BCa bootstrap; subgroups use permutation-based CIs). Axis SAEs n Pairs τb _b p 95% CI Overall All SAEs 90 4005 0.2979 — [0.1590, 0.4191][0.1590,\,0.4191] ΨA=0.2575 _A=0.2575 (SE ≈0.1163≈ 0.1163, 95% boot CI [0.0222, 0.3961][0.0222,\,0.3961]) ΨA _A: Architecture BatchTopK 18 153 0.3203 0.0712 [−0.3464, 0.3464][-0.3464,\,0.3464] Gated 18 153 -0.2026 0.2577 [−0.3464, 0.3333][-0.3464,\,0.3333] JumpReLU 18 153 0.4248 0.0160 [−0.3333, 0.3333][-0.3333,\,0.3333] ReLU 18 153 0.3595 0.0392 [−0.3333, 0.3333][-0.3333,\,0.3333] TopK 18 153 0.3856 0.0272 [−0.3333, 0.3333][-0.3333,\,0.3333] ΨB=0.1651 _B=0.1651 (SE ≈0.1112≈ 0.1112, 95% boot CI [−0.0286, 0.3587][-0.0286,\,0.3587]) ΨB _B: Sparsity L0≈50L_0≈ 50 15 105 0.5429 0.0034 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈80L_0≈ 80 15 105 0.3524 0.0740 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈160L_0≈ 160 15 105 0.1810 0.3821 [−0.3905, 0.3714][-0.3905,\,0.3714] L0≈320L_0≈ 320 15 105 0.1810 0.3673 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈520L_0≈ 520 15 105 -0.2190 0.2837 [−0.3905, 0.3714][-0.3905,\,0.3714] L0≈820L_0≈ 820 15 105 -0.0476 0.8484 [−0.3905, 0.3714][-0.3905,\,0.3714] ΨC=0.3272 _C=0.3272 (SE ≈0.0698≈ 0.0698, 95% boot CI [0.2184, 0.4575][0.2184,\,0.4575]) ΨC _C: Model Gemma-2-2B 30 435 0.2184 0.0980 [−0.2598, 0.2552][-0.2598,\,0.2552] Qwen-2.5-3B 30 435 0.4575 0.0008 [−0.2506, 0.2506][-0.2506,\,0.2506] Gemma-2-9B 30 435 0.3057 0.0166 [−0.2506, 0.2461][-0.2506,\,0.2461] Ψ=(ΨA+ΨB+ΨC)/3=0.2499 = ( _A+ _B+ _C )/3\;=\;0.2499 3.4 Pairwise Analysis Results In this section, we assess whether higher SAE interpretability predicts stronger steering by computing Kendall’s τb _b between the Interpretability Score μ​(θ)μ(θ) and the aggregated Steering Score g​(θ)g(θ) over a pooled set of SAEs attached to a fixed LLM. To control confounders and localize effects, we apply the axis-conditioned procedure defined in section 3.3. For each axis, we form matched groups, compute within-group τb _b, average to obtain a per-axis summary, and aggregate these summaries into an overall axis-controlled coefficient. Table 1 shows that across SAEs, higher interpretability tends to be modestly associated with better steering on average, pointing to a consistent but limited impact. The pooled Kendall’s τb≈0.30 _b≈ 0.30 is positive, and the axis-controlled aggregate remains positive (Ψ≈0.25 ≈ 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 on average (ΨA≈0.26 _A≈ 0.26), with ReLU-like variants reinforcing the trend and Gated weakening it. By sparsity, alignment is strongest when the SAE is more sparse and weakens—sometimes reversing—as 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 (ΨC≈0.33 _C≈ 0.33). Key Observation 1: Interpretability shows a relatively weak positive correlation with steering performance, highlighting a notable gap between interpretability and utility across SAEs. 4 From Interpretability to Utility: Which SAE Features Actually Steer? In Sec. 3.4, We find that SAE interpretability is a 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 inaccurate. Therefore, we introduce a metric to identify steering-effective features. Metrics derived from a model’s internal token distributions can assess reasoning quality (Kang et al., 2025). In particular, token entropy offers a unified view: high entropy highlights critical decision points (Fu et al., 2025; Wang et al., 2025c). We apply this idea to SAE steering. 4.1 Feature Selection via Δ Token Confidence We start from the model’s next-token distribution. Given logits z∈ℝVz ^V and p=softmax⁡(z)p=softmax(z) over a vocabulary of size V, the token entropy is H​(p)=−∑j=1Vpj​log⁡pj,H(p)\;=\;- _j=1^Vp_j\, p_j, (6) Entropy summarizes dispersion over the vocabulary: smaller values reflect a sharper, more concentrated prediction, while larger values indicate greater uncertainty at a given position. To focus on the head of the distribution that matters most for sampling, we use token confidence. Let ℐk​(p)⊆1,…,VI_k(p) \1,…,V\ denote the indices of the k largest probabilities in p. The top-k token confidence is the negative average log-probability over these entries: Ck​(p)=−1k​∑j∈ℐk​(p)log⁡pj.C_k(p)\;=\;- 1k _j _k(p) p_j. (7) Lower CkC_k implies higher confidence, while higher CkC_k implies a flatter top-k distribution. Unlike entropy, CkC_k directly captures the sharpness of the outcomes that drive next-token behavior. We turn confidence into a feature-level selector via a single-feature SAE intervention. Consider an SAE feature f at layer ℓ . We amplify only the coefficient of f by a factor α>0α>0 in the SAE reconstruction, leaving the base model and all other features unchanged. Denote the baseline next-token distribution by pbasep^base and the intervened distribution by pf,ℓ,αintp^int_f, ,α. Δ Token Confidence is Δ​Ck​(f;ℓ,α)=Ck​(pf,ℓ,αint)−Ck​(pbase). C_k(f; ,α)\;=\;C_k\! (p^int_f, ,α )\;-\;C_k\! (p^base ). (8) Negative values Δ​Ck<0 C_k<0 mean that amplifying f sharpens the top-k distribution, while positive values indicate greater dispersion. We compute this using one baseline and one intervened forward pass via an SAE hook. Implementation details and hyperparameters are provided in Appendix D. We select features with the largest absolute change in token confidence under single-feature SAE interventions, i.e., maximal |Δ​Ck|| C_k| (see Figure 3). For each feature, we compute Δ​Ck C_k, rank by |Δ​Ck|| C_k|, form tiers, evaluate subsets for steering, and keep the best per SAE. Figure 3: Distribution of per-feature Δ Token Confidence across all SAEs. Panels show histograms for Gemma-2-2B, Qwen-2.5-3B, and Gemma-2-9B; the x-axis is Δ​Ck C_k (negative values indicate increased confidence, positive values decreased confidence) and the y-axis is the number of SAE features. The shaded area marks the high-magnitude tails from which candidate steering features are selected, while the central mass near 0 indicates features with little distributional impact. 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 on model outputs, introducing the output score as a metric to identify output-aligned features. Following this insight, we evaluate our Δ token confidence selection on three base LLMs (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B) using the CONCEPT100 (see details in 3.1). The experiments on steering performance improvement of each SAE can be referred to Appendix E. Table 2: Steering score after feature selection compared with SAE-based steering. Columns report scores (higher is better) for Gemma-2-2B, Qwen-2.5-3B, and Gemma-2-9B. Rows: ‘SAE-based’ uses all SAE features without selection (Wu et al., 2025); ‘+Output’ selects features using SoutS_out (Arad et al., 2025); “+Δ​Ck C_k (Ours)” selects by the Δ Token Confidence. Boldface indicates the best method per model. Method Gemma-2-2B Qwen-2.5-3B Gemma-2-9B SAE-based 0.133 0.171 0.142 +Output 0.233 0.292 0.255 !50+Δ​Ck C_k(Ours) 0.328 0.399 0.289 Table 2 shows that our selection yields consistent gains across all models, outperforming the vanilla SAE baseline by large margins, and also improving over an output-score–based selector. These gains indicate that ranking and filtering by the magnitude of distributional change captured by Δ​Ck C_k reliably isolates features with the strongest steering utility. 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 (BatchTopK, 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 Δ Token Confidence Selection (ours). Panel annotations summarize the average lift of each selection method relative to the SAE-based steering. 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. Figure 4 compares steering scores across SAE architectures and selection methods. In all three models, selecting features by Δ Token Confidence consistently outperforms both the no-selection SAE baseline and the output-score selector across architectures. On average, our method improves steering performance by 52.52% over the strongest competing baseline. The BatchTopK architecture is the one that has the most stable and significant improvement in steering capabilities on models of different sizes among the five SAE architectures. Key Observation 2: Δ Token Confidence reliably selects high-utility SAE features across models. Among SAE architectures, BatchTopK achieves the most stable and sizable steering gains. 4.3 Pairwise Analysis Between Interpretability and Steering Gain Building on the above steering gains, we further examine whether SAE interpretability can serve as a prior for steering gain, the extent to which a trained SAE benefits from feature selection. We quantify this relationship by computing Kendall’s τb _b between the Interpretability Score μ​(θ)μ(θ) of SAEs and the Steering Gain L​(θ)L(θ), defined as the percentage lift of the selected-steering score over the same SAE’s base. 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). Overall, table 3 indicates that interpretability is not a reliable prior for steering gain after selection: the pooled association is small and slightly negative (τb≈−0.069)( _b≈-0.069) , and the axis-controlled aggregate is likewise near zero and negative (Ψ≈−0.057)( ≈-0.057). Estimates cluster near zero across design axes, being slightly negative within architecture, sparsity, and model, and effectively null at matched-sparsity slots, indicating no consistent link between higher interpretability and larger gains. Key Observation 3: Surprisingly, the interpretability–utility gap widens when we focus on SAE features that deliver substantial steering gains. Table 3: Pairwise Analysis Between Interpretability μ​(θ)μ(θ) and Steering Gain L​(θ)L(θ). We report Kendall’s τb _b overall and under axis-controlled summaries ΨA _A (Architecture), ΨB _B (Matched Sparsity), and ΨC _C (Model). Columns: n=n= number of SAEs; Pairs == number of pairwise comparisons; p=p= permutation p-value; 95% CI == confidence interval (overall uses BCa bootstrap; subgroups use permutation-based CIs). Axis SAEs n Pairs τb _b p 95% CI Overall All SAEs 90 4005 -0.0692 — [−0.2019, 0.0666][-0.2019,\,0.0666] ΨA=-0.0719 _A=-0.0719 (SE ≈0.0781≈ 0.0781, 95% boot CI [−0.2078, 0.0614][-0.2078,\,0.0614]) ΨA _A: Architecture BatchTopK 18 153 -0.2288 0.2004 [−0.3333, 0.3464][-0.3333,\,0.3464] Gated 18 153 0.0327 0.8792 [−0.3464, 0.3333][-0.3464,\,0.3333] JumpReLU 18 153 -0.0065 1.0000 [−0.3464, 0.3203][-0.3464,\,0.3203] ReLU 18 153 -0.2810 0.1096 [−0.3333, 0.3464][-0.3333,\,0.3464] TopK 18 153 0.1242 0.4985 [−0.3464, 0.3337][-0.3464,\,0.3337] ΨB=0.0127 _B=0.0127 (SE ≈0.0457≈ 0.0457, 95% boot CI [−0.0762, 0.0889][-0.0762,\,0.0889]) ΨB _B: Sparsity L0≈50L_0≈ 50 15 105 0.0476 0.8466 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈80L_0≈ 80 15 105 0.1619 0.4437 [−0.3905, 0.3714][-0.3905,\,0.3714] L0≈160L_0≈ 160 15 105 0.0095 1.0000 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈320L_0≈ 320 15 105 0.0476 0.8452 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈520L_0≈ 520 15 105 -0.1810 0.3797 [−0.3714, 0.3714][-0.3714,\,0.3714] L0≈820L_0≈ 820 15 105 -0.0095 1.0000 [−0.3714, 0.3905][-0.3714,\,0.3905] ΨC=-0.1111 _C=-0.1111 (SE ≈0.0314≈ 0.0314, 95% boot CI [−0.1448,−0.0483][-0.1448,\,-0.0483]) ΨC _C: Model Gemma-2-2B 30 435 -0.1402 0.2911 [−0.2552, 0.2598][-0.2552,\,0.2598] Qwen-2.5-3B 30 435 -0.1448 0.2781 [−0.2507, 0.2460][-0.2507,\,0.2460] Gemma-2-9B 30 435 -0.0483 0.7157 [−0.2506, 0.2552][-0.2506,\,0.2552] Ψ=(ΨA+ΨB+ΨC)/3=-0.0568 = ( _A+ _B+ _C )/3\;=\;-0.0568 5 Related Work 5.1 Representation-Based Steering Activation-based steering arose as a lightweight alternative to fine-tuning, enabling on-the-fly control 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 a 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-time adjustment but facing polysemantic entanglement and brittleness that motivate standardized evaluation (Chen et al., 2025; Liu et al., 2024). However, this approach injects polysemantic activations at intervention time, yielding coarse-grained effects for output control (Bricken et al., 2023). Our work is related to activation-level interventions, but differs by grounding directions in sparse, interpretable SAE features and applying utility-oriented feature selection to mitigate these failure modes. 5.2 SAE-Based Steering Sparse Autoencoders (SAEs) decompose activations into sparse, human-readable features to mitigate 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 granularity (Zhao et al., 2025; Wang et al., 2025d; Ferrando et al., 2025). SAE-based steering enables targeted safety control, style modulation, and instruction emphasis, yet the utility of individual features varies widely (Chalnev et 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 a large-scale experiments across multiple model sizes and SAE architectures, demonstrating the critical nature of the interpretability-utility gap. 6 Conclusion and Discussion In summary, SAE interpretability shows relatively weak positive association with steering utility across 90 SAEs (τb≈0.298 _b≈ 0.298), revealing a clear interpretability–utility gap. Selecting features with Δ Token Confidence yields substantial gains (average +52.52%+52.52\% over the strongest existing baseline). Surprisingly, when analyzing steering gains after selection, the correlation with interpretability collapses toward zero and can even turn negative for the highest-utility features, further underscoring this gap. This gap points to a key direction: develop task-general utility indicators that reliably predict steerability across models, or design training objectives that directly optimize controllability under sparsity so features are utility-calibrated without heavy post-hoc selection. Our work provides valuable insight for the further development of SAEs as interpretable tools. Reproducibility Statement We aim to facilitate full reproduction of our results. All model code, training and evaluation scripts, configuration files, and experiment logs are released at an anonymous repository as part of the supplementary materials: https://anonymous.4open.science/r/SAE4Steer. Training architectures, hyperparameters, sparsity schedules, and optimization details are specified in the main text and Appendix A.2 (see also the per-family settings in Appendix A). The datasets used are openly licensed: all SAEs are trained on The Common Pile v0.1 (Kandpal et al., 2025) as described in Appendix F; our evaluation concepts (Concept100) and their automatic generation pipeline are documented in Appendix B and Appendix F. The complete procedures for automated interpretability scoring (SAEBench) and steering utility (AxBench), including sampling, judging protocols, and scoring functions, are detailed in Appendix B and Appendix C, with the Δ Token Confidence selector defined in Appendix D and the post-selection results summarized in Appendix E. Hardware, runtime, and memory footprints for both SAEBench and AxBench are reported in Appendices B.3 and C.2. Together, these materials, along with seed-controlled configuration files and exact command-line invocations provided in the anonymous repository, are intended to enable independent researchers to replicate and extend our findings. References Karvonen et al. 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Feder Cooper, Aviya Skowron, Shayne Longpre, Lintang Sutawika, Alon Albalak, Zhenlin Xu, Guilherme Penedo, Loubna Ben Allal, Elie Bakouch, John David Pressman, Honglu Fan, Dashiell Stander, Guangyu Song, Aaron Gokaslan, John Kirchenbauer, Tom Goldstein, Brian R. Bartoldson, Bhavya Kailkhura, and Tyler Murray. The Common Pile v0.1: An 8TB Dataset of Public Domain and Openly Licensed Text. arXiv preprint arXiv:2506.05209, 2025. 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 are solely the work of the authors. Appendix 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 (F=16,384F=16,384), SAEs are attached to the residual stream at the layer described in the main text, and decoder columns are ℓ2 _2–normalized. 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 corresponding shapes. The last column records architecture-specific thresholding/gating fields when present. Shapes assume residual dimension d=2304d=2304 and dictionary width F=16,384F=16,384. Architectures WencW_enc bencb_enc WdecW_dec bdecb_dec Threshold / Extras ReLU encoder.weight: shape (16,384, 2,304) encoder.bias: shape (16,384) decoder.weight: shape (2,304, 16,384) bias: shape (2,304) — Gated encoder.weight: shape (16,384, 2,304) gate_bias: shape (16,384) decoder.weight: shape (2,304, 16,384) decoder_bias: shape (2,304) r_mag: shape (16,384); mag_bias: shape (16,384) TopK encoder.weight: shape (16,384, 2,304) encoder.bias: shape (16,384) decoder.weight: shape (2,304, 16,384) b_dec: shape (2,304) k BatchTopK encoder.weight: shape (16,384, 2,304) encoder.bias: shape (16,384) decoder.weight: shape (2,304, 16,384) b_dec: shape (2,304) k JumpReLU W_enc: shape (2,304, 16,384) b_enc: shape (16,384) W_dec: shape (16,384, 2,304) b_dec: shape (2,304) threshold: shape (16,384) A.2 Training, Sparsity, and Compute Setup Optimization and schedule. Adam with learning rate 3×10−43×10^-4; LR warmup 10001000 steps; sparsity warmup 50005000 steps; LR decay starting at 80%80\% of total steps. Precision: bfloat16. LM batch size =4=4, context length =2048=2048, SAE batch size =2048=2048. Each run trains on ∼5×108 5×10^8 tokens. Sparsity controls. We sweep six target activity levels L0≈50, 80, 160, 320, 520, 820.L_0≈\50,\,80,\,160,\,320,\,520,\,820\. For TopK/BatchTopK we set k equal to the chosen L0L_0 (aux-k coefficient 1/321/32; moving-threshold momentum 0.9990.999; threshold tracking begins at step 10001000). JumpReLU uses the same set via target_l0. For L1L_1–penalized families, we search the following penalty grids: Family L1L_1 penalty values (used to span sparsity levels) Standard / Standard-New 0.012, 0.015, 0.020, 0.030, 0.040, 0.060 Gated SAE 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 are approximate. Model #SAEs Disk (GB) Traing Time (H) LM Batch Context SAE Batch Peak Mem (GB) Gemma-2-2B 30 8.7 17 4 2048 2048 20 Gemma-2-9B 30 13.2 60 4 2048 2048 70 Qwen-2.5-3B 30 7.7 37 4 2048 2048 30 Appendix B SAEBench Details, Results and Our Costs B.1 Automated Interpretability Score Process SAEBench [Karvonen et al., 2025] follow an LLM-as-judge pipeline to assign an automated interpretability 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 to obtain h∈ℝN×L×Fh ^N× L× F. We define a token window of length 2121 (buffer =10=10) around any center (i,t)(i,t) and, unless stated otherwise, mask BOS/PAD/EOS positions. For a latent ℓ , we sample three window types: (i) Top (n=12n=12 non-overlapping peaks of h​[:,:,ℓ]h[:,:, ]), (i) Importance-Weighted (n=7n=7, sampled proportional to activation after removing values at least as large as the smallest Top peak), and (i) Random (n=10n=10, uniform over valid centers). Let vmaxv_ be the maximum activation seen in any Top window position and set a global threshold τact=0.01​vmax _act=0.01\,v_ . We split the sampled windows into a generation set (1010 Top ++ 55 IW) and a scoring set (22 Top ++ 22 IW ++ 1010 Random, shuffled). In generation, tokens with activation >τact> _act are bracketed to highlight evidence; the judge LLM receives these 1515 windows and returns a short English description of when the latent fires. In scoring, the judge sees the description and the 1414 held-out windows without highlights and outputs a comma-separated list of indices it predicts as activations (or None). Ground truth for a window W is ​[maxu∈⁡h​[u,ℓ]>τact]1[ _u h[u, ]> _act]. The per-latent score is the accuracy over the M=14M=14 scoring windows, i.e., Score​(ℓ)=1M​∑m=1M​[y^m=ym],Score( )= 1M _m=1^M1 [ y_m=y_m ], where y^m∈0,1 y_m∈\0,1\ is the judge prediction and ymy_m is the label defined above. For each SAE θ, we evaluate 1,0001,000 latents and report the mean over a random Concept100 subset: μ​(θ)=1100​∑ℓ∈Concept100Score​(ℓ).μ(θ)= 1100 _ ∈ Concept100Score( ). 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 et al., 2025])jointly reveal how sparsity mechanisms balance interpretability, faithfulness, and causal structure. Automated Interpretability is strongest when encoders enforce compact latent usage (e.g., TopK/BatchTopK and ReLU at lower L0L_0), and it gradually softens as capacity expands. The Absorption metric (considered via its complement in the plots) indicates that designs concentrating signal into a small set of latents are less prone to feature stealing, whereas higher 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 L0L_0 pushes faithfulness toward a ceiling without overturning the core trade-offs visible in the other metrics. Gemma-2-2B. As shown in Fig. 5, Gemma-2-2B exhibits a balanced profile: interpretability stays robust for TopK/BatchTopK and ReLU at modest sparsity; absorption is contained when the code remains compact; and Core is near-saturated across the range. Improvements in SCR@20 are steady but measured, suggesting targeted debiasing with small k. Sparse Probing indicates that relatively few latents already carry much of the predictive signal, while RAVEL strengthens with moderate capacity, reflecting cleaner separation of attributes without undermining compactness. Figure 5: SAEbench results for Gemma-2-2B: interpretability remains strong at lower L0L_0, absorption 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. 6), interpretability at low–to–moderate L0L_0 is competitive—especially for TopK and JumpReLU—yet the model is more sensitive to absorption as capacity grows, implying greater latent competition and signal spread. Core remains excellent, so reconstructions are faithful; however, SCR gains can flatten at high L0L_0 where residual spurious cues reappear. Sparse Probing is solid but a touch behind the strongest Gemma configurations, consistent with its flatter RAVEL patterns: causal structure is present but less crisply disentangled when attributes begin to diffuse across latents. Figure 6: SAEbench results for Qwen-2.5-3B: strong interpretability at lower L0L_0, rising absorption with capacity, consistently high Core, and more fragile SCR/RAVEL at the highest capacities. Gemma-2-9B. Gemma-2-9B (Fig. 7) pushes the upper envelope on structure: interpretability remains solid for compact encoders; absorption is low at moderate L0L_0 that avoids unnecessary latent proliferation; and Core is near its ceiling. SCR@20 is 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. Figure 7: SAEbench results for Gemma-2-9B: robust interpretability with compact codes, low absorption at moderate L0L_0, near-ceiling Core, and the clearest gains in SCR/RAVEL among the three backbones. B.3 SAEBench Runtime Cost The computational requirements for running SAEBench evaluations were measured on two NVIDIA RTX A800 GPUs using 16K-width SAEs trained on the Gemma-2-2B [Team et 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 a 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 Interpretability Absorption Sparse Probing Ravel SCR Gemma-2-2B 4 8 12 2 18 10 Qwen-2.5-3B 7 9 15 8 17 16 Gemma-2-9B 11 12 17 30 40 28 Appendix C AxBench Details and Our Costs C.1 Steering Score Process For each SAE feature (concept) we evaluate steering utility with an AxBench-style judge [Wu et al., 2025]. Given the concept description from SAEBench and the intervention rule in Eq. equation 1, we sample 1010 instructions (Alpaca-Eval style) and split them 5/55/5 into a development set for factor selection and a held-out set for evaluation. We generate continuations (up to 128128 tokens) for a grid of steering factors α∈α by injecting the feature direction at the target layer. For each generated continuation, an LLM judge assigns three subscores on the discrete scale 0,1,2\0,1,2\ (floats allowed but clamped to [0,2][0,2]): Concept (C; does the output express the concept?), Instruction (I; is it on-topic for the instruction?), and Fluency (F; is it well-formed?). We aggregate with the harmonic mean HM(C,I,F)=0,if ​C≤0​ or ​I≤0​ or ​F≤0,31C+1I+1F,otherwise,∈[0,2].HM(C,I,F)= cases0,&if C≤0 or I≤0 or F≤0,\\[2.0pt] 3 1C+ 1I+ 1F,&otherwise, cases ∈[0,2]. On the development split we pick α⋆=arg⁡maxα∈⁡15​∑HMα = _α 15 , then evaluate the held-out split with α⋆α to obtain the per-concept Steering Score (mean HM over the 55 held-out prompts). SAE-level utility g​(θ)g(θ) is the average of per-concept scores over the evaluation set for that SAE. CONCEPT_TEMPLATE [System] Please act as an impartial judge and evaluate whether the specified concept is presented in the sentence fragment provided below. Focus solely on whether the concept is clearly incorporated, without regard for grammar or logical coherence. Begin your evaluation by providing a short explanation of whether the concept is clearly incorporated. Point out references to the concept in the fragment, noting any minimal or awkward incorporations. After providing your explanation, rate the concept’s relevance on a scale from 0 to 2, where 0 indicates the concept is not present at all, 1 indicates the concept is somewhat present but minimally or awkwardly incorporated, and 2 indicates the concept is more 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 [System] Please act as an impartial judge and evaluate whether the sentence fragment provided below is related to the instruction. Focus solely on the degree of relatedness in terms of topic, regardless of grammar, coherence, or informativeness. Begin your evaluation by providing a 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 on a scale from 0 to 2, where 0 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 it is more clearly and directly related to the instruction. Provide your rating using this exact format: “Rating: [[score]]”. [Instruction Start] instruction [Instruction End] [Sentence Fragment Start] sentence [Sentence Fragment End] FLUENCY_TEMPLATE [System] Please act as an impartial judge and evaluate the fluency of the sentence fragment provided below. Focus solely on fluency, disregarding its completeness, relevance, coherence with any broader context, or informativeness. 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 providing your explanation, rate the sentence’s fluency on a scale from 0 to 2, where 0 indicates the sentence is not fluent and highly unnatural (e.g., incomprehensible or repetitive), 1 indicates it is somewhat fluent but contains noticeable errors or awkward phrasing, and 2 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 gpt-4o-mini. Evaluating one SAE on Concept100 costs approximately $5 in judge API fees; with 90 SAEs total (≈30≈ 30 per model), the per-model API cost is about $150. Table 5 lists approximate per-SAE runtime and peak VRAM for each model. Table 5: AxBench steering evaluation cost per SAE. Runtimes are per-SAE (hours) and approximate; VRAM is peak memory (GB). Judge fees assume gpt-4o-mini: ∼$​5 5 per SAE on Concept100; Per-Model Cost assumes ∼30 30 SAEs/model (≈$​150≈ 150). Model Runtime / SAE (h) Peak VRAM (GB) Per-Model Cost (USD) Gemma-2-2B 15 10 150 Qwen-2.5-3B 16 12 150 Gemma-2-9B 23 36 150 Appendix D Implementation of Δ Token Confidence For a fixed, neutral prefix s (we use “From my experience,”, following the previous work[Arad et al., 2025]) we compare the next-token distribution of the base model with that of an intervened model in which a single SAE feature is amplified at layer L by a factor α. The intervention is 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. Token confidence. [Fu et al., 2025] For a distribution p over the vocabulary, let p(1)≥⋯≥p(k)p_(1)\!≥\!·s\!≥\!p_(k) be the top-k probabilities. Ck​(p)=−1k​∑i=1klog⁡p(i).C_k(p)\;=\;- 1k _i=1^k p_(i). Delta token confidence. With pbasep_base from a standard forward pass and pintp_int from a pass with the SAE feature intervention, Δ​Ck​(f;α,L)=Ck​(pint)−Ck​(pbase). C_k(f;α,L)\;=\;C_k\! (p_int )\;-\;C_k\! (p_base ). Each feature f is evaluated with two single-step forwards on the same prefix s: (i) a baseline pass; (i) an intervened pass where we scale the code for f by α 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, we choose α=10α=10 and k=1k=1. Feature selection from Δ​Ck C_k. For each SAE we rank its features by Δ​Ck C_k in two directions: UP (largest positive Δ​Ck C_k) and DOWN (most negative Δ​Ck C_k). We form selection sets using either (i) top-K by magnitude with K∈1,2,3,4,5K∈\1,2,3,4,5\ per direction, or (i) upper/lower-tail quantiles (e.g., q∈0.99,0.95,0.90,0.80q\!∈\!\0.99,0.95,0.90,0.80\ mirrored for the lower tail). These sets are then carried into AXBench [Wu et al., 2025] to measure utility lift. Appendix E Steering Results of SAE Architectures After Feature Selection We quantify steering with the AXBench judge after selecting features using Δ Token Confidence (Appendix D). Unless otherwise noted, lifts are reported as the percentage change of a given SAE’s steering score relative to its own baseline (no selection). Results are organized at three levels: aggregate across SAEs per base model, per-SAE rankings, and distribution by architecture. 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 Δ Token Confidence–based selection. Bars are annotated with the corresponding values; axes share the same scale across panels. The aggregate view in Figure 8 summarizes how selection affects the mean steering score across all SAEs of a base model. Using Δ 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 0.1330.133 to 0.3280.328, which is a 146.6%146.6\% relative improvement. Qwen-2.5-3B increases from 0.1710.171 to 0.3990.399, a 133.3%133.3\% improvement, and achieves the highest post-selection score overall. Gemma-2-9B moves from 0.1420.142 to 0.2890.289, a 103.5%103.5\% improvement. Conclusions: (i) feature selection via Δ Token Confidence consistently boosts steering for all models; (i) relative gains are largest for the smallest model (Gemma-2-2B) and smallest for the largest model (Gemma-2-9B), suggesting diminishing relative returns with scale; and (i) in absolute terms, Qwen-2.5-3B reaches the strongest final steering score after selection. Figure 9: Per-SAE percentage lift after Δ Token Confidence selection. Each panel corresponds to a 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 9 ranks SAEs within each model by their relative lift. Architecturally, no single SAE training approach dominates; however, the top-ranked lifts are frequently occupied by BatchTopK and Gated variants, with ReLU/JumpReLU also contributing strongly and TopK showing more mixed outcomes. Overall, Δ Token Confidence yields consistent per-SAE gains, with variance decreasing and stability increasing as model size grows, while architectural diversity remains valuable for capturing the largest lifts. 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 indicates 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 positive—spread, especially on Gemma-2-2B and Qwen-2.5-3B. BatchTopK achieves the most stable and sizable steering gains. Variance is largest for the smallest model (Gemma-2-2B), indicating architecture-sensitive wins at small scale. Appendix F Dataset Training corpus for SAEs. We train all SAEs on The Common Pile v0.1 [Kandpal et al., 2025], an openly licensed ∼ 8 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 a 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. To evaluate steering, we construct Concept100: a compact benchmark of 100 human-readable concept descriptions per evaluation set, produced automatically by our interpretability pipeline (Appendix B). Each entry is a pair (layer_feature_id,description)( layer\_feature\_id, description) that summarizes a latent’s activation pattern in plain language (e.g., mathematical symbols, scientific terms, pronouns, or domain phrases). These descriptions are supplied to the AXBench judge when computing steering score. The examples below illustrate the style and domain coverage. Gemma-2-9B, BatchTopK, L0≈80L_0≈ 80. Ten examples: 1. 20_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 contexts 5. 20_11897: scientific measurements and units related to energy, concentration, or biological 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 contexts 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 10. 20_585: various forms of the word “energy” and related concepts in scientific contexts Qwen-2.5-3B, Gated, L0≈72L_0≈ 72. Ten examples: 1. 17_15113: terms related to 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_162: 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 in formal documents 6. 17_3195: demographic, clinical, and biological characteristics in study populations and related comparisons 7. 17_9186: specific technical terms and concepts related to networking and programming 8. 17_11487: mathematical notation and variables related to functions and equations 9. 17_14657: mathematical notations and structures involving angle brackets and properties of functions 10. 17_1256: terms related to errors and error correction in coding theory and quantum operations Gemma-2-2B, JumpReLU, L0≈81L_0≈ 81. Ten examples: 1. 20_11531: terms related to sports, programming, or 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 or distance from something 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 observations We currently maintain 90 SAEs (30 per base model). Beyond the Concept100 sets evaluated in this paper, we have constructed the Concept1000 and Concept16K suites that scale the number of human‐readable 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.