Steering with SAE features requires per-feature coefficient tuning, which currently demands intervention sweeps. We ask whether properties of the SAE itself, computable before any forward pass, predict which features will be cheap or expensive to steer. We show that variation in SAE feature steerability is partially predicted by decoder-space geometry: neighbor density and maximum cosine similarity to nearby decoder directions, both computable from the SAE weight matrix before any intervention, rank features by how much steering they require for a fixed behavioral effect (ρ up to −0.546, p<10−6, AUROC 0.610-0.822 across conditions; the signal is rank-based, consistent with grid discreteness). This geometry-steerability relationship replicates across two Gemma-2 model scales (2B and 9B), two SAE widths (16K and 65K), and is detectable cross-architecturally on Llama-3.1-8B-Instruct (ρ=−0.266, n=300). On Qwen3-8B with BatchTopK SAEs, geometry predicts whether a feature is steerable at all but not the continuous ordering among responsive features, revealing a boundary condition tied to SAE training regime. The signal weakens at deep proportional layer depth in both models, where the cost of steering exceeds our intervention budget, a consistent depth boundary. These results provide preliminary evidence that pre-steering geometry can partially inform coefficient selection, offering a path toward screening features for controllability before deployment.
Figures & tables
Figure 1: Illustration of the geometry–steerability relationship. (a) Two SAE features in decoder space. The isolated feature ( vf , blue) has few nearby decoder directions; the crowded feature ( vg , red) sits in a dense cluster. Grey arrows are other features in the same dictionary. (b) Steering each feature: the crowded one crosses the refusal threshold T at a much smaller α∗ than the isolated one. weight matrix before any steering — predicts this gap. Curves are schematic; empirical results are shown in Figure 2 .
Model
SAE
Layer(s)
Dict.
Rel. depth
Gemma-2-2B
GemmaScope 16K
20, 22, 24
16K
77%, 85%, 92%
Gemma-2-2B
GemmaScope 65K
20
65K
77%
Gemma-2-9B
GemmaScope 16K
20, 36
16K
48%, 86%
Llama-3.1-8B
BatchTopK
15
131K
47%
Llama-3.1-8B
BatchTopK
23
131K
72%
Qwen3-8B
BatchTopK
18
32K
50%
Table 1: Experimental conditions.
Model
Condition
Rel. depth
Runs
N
Ncens (%)
Mean α∗
Median α∗
2B
L20 16K
77%
3
100
12 (12%)
3.39
3.0
L22 16K
85%
3
100
27 (27%)
3.84
3.0
L24 16K †
92%
3
100
—
—
—
L20 65K
77%
4
100
11 (11%)
3.39
3.0
9B
L20 16K
48%
3
75
2 (3%)
4.25
3.0
L36 16K
86%
2
100
46 (46%)
4.83
5.0
Table 2: Steerability distribution across experimental conditions. Ncens is the number of right-censored features ( α∗>αmax ). Mean and median α∗ are computed over uncensored features only. Relative depth is layer index divided by total layers. Runs is the number of independent pipeline runs completed for each condition. † Distribution collapsed due to coherence collapse at high αmax ; excluded from primary inference per Section 3.2 .
Condition
Metric
rfull
pfull
rnocens
pnocens
n
2B L20 16K (3 runs)
max_cosine
−0.192
0.055
−0.299
0.005
88
neighbor_density
−0.206
0.039
−0.288
0.006
88
coactivation
+0.030
0.765
+0.184
0.087
88
2B L22 16K (3 runs)
max_cosine
−0.293
0.003
−0.425
0.0002
73
neighbor_density
−0.222
0.026
−0.512
3.6×10−6
73
coactivation
+0.147
0.145
+0.147
0.214
73
Table 3: Spearman correlations between pre-steering metrics and logα∗(f) . rfull includes censored features (rank-based handling of ties at boundary); rnocens excludes them. n is the number of uncensored features used for rnocens . For Llama-3.1-8B, rfull=rnocens since censoring is zero. Qwen3-8B results are reported in Appendix F .
Condition
n
CV R2
AUROC
Perm. null ρ95
LOO: drop density
LOO: drop max cos
2B L20 16K
88
0.068
0.610
0.168
0.054
0.075
2B L22 16K
73
0.047
0.736
0.194
− 0.045
0.109
2B L20 65K
89
− 0.005
0.686
0.172
− 0.048
0.022
9B L20 16K
73
0.025
0.822
0.197
− 0.028
0.053
9B L36 16K †
54
− 0.698
0.723
0.225
− 0.607
− 0.742
Llama L15 131K
300
—
0.653
—
—
—
Table 4: Predictability analysis: cross-validated R2 (ridge regression on all three metrics), AUROC (steerable α∗≤3 vs. hard-to-steer), and permutation-null 95th percentile ρ across well-identified conditions. Censored features excluded from R2 and AUROC; included (rank-tied) in Spearman. Llama-3.1-8B L23 is omitted; cross-architecture Spearman correlations for that condition are reported in Table 3 .
Figure 2: Pre-steering metrics versus log steerability for the 9B model at layer 20 (strongest signal condition). Each point is one SAE feature; red triangles indicate right-censored features ( α∗=20 ). Trend line shows LOWESS fit; shaded band is bootstrap 95% CI. Neighbor density: ρ=−0.546 , p=5.75×10−7 . Max cosine similarity: ρ=−0.490 , p=1.10×10−5 . Co-activation correlation: zero-inflated; see text.
Figure 3: Spearman ρ (neighbor density vs. logα∗ ) as a function of relative layer depth across all conditions. The geometry–steerability signal is strongest at shallow-to-mid depth and weakens consistently as the intervention layer approaches the output. Open marker indicates a not-well-identified condition (Section 3.2 ). Error bars show approximate 95% CIs via Fisher z -transform. Shaded region marks the deep-depth boundary.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Condition
ND mean
ND std
MC mean
MC std
2B L20 16K
0.194
0.053
0.392
0.143
2B L22 16K
0.178
0.049
0.368
0.141
2B L20 65K
0.323
0.078
0.547
0.139
9B L20 16K
0.212
0.045
0.400
0.110
9B L36 16K
0.180
0.045
0.373
0.127
Appendix
Table 5: Pre-steering geometry statistics per condition.
Sparse autoencoders (SAEs) disentangle model activations into interpretable features and are widely used for steering large language models. Most existing SAE-based steering methods select features by applying a top- filter based on statistical scores, assuming that higher-scoring features yield stronger steering effects. In this paper, we show that this assumption is often invalid, leading to suboptimal feature selection. Our analysis reveals that effective steering features may be distributed among representationally adjacent, semantically similar groups induced by feature splitting in SAEs. Within such groups, features may exhibit disparate statistical scores despite having comparable steering influence, causing score-based selection to overlook important features. Based on these observations, we propose Neighbor Integrated Feature Selection (NIFS), a plug-and-play strategy that leverages representation similarity to improve feature selection for steering. We evaluate NIFS across multiple SAE-based steering methods and tasks, and demonstrate consistent performance gains over conventional top-k selection.
Yutian Liu, Xu Wang, Difan Zou
The University of Hong Kong · University of Science and Technology of China
Sparse autoencoder (SAE) features are increasingly used to steer language models, but feature steering is rarely clean: the same intervention can behave inconsistently across contexts and perturb unrelated features. We introduce a pre-intervention screening framework for forecasting SAE steering side effects from feature statistics computed before steering. We operationalize side effects along two axes of steering modularity, effect stability and collateral spread, and evaluate GPT-2-small, Pythia-70M-deduped, Gemma-2-2B, and Llama-3.1-8B across ReLU, JumpReLU, and TopK SAE dictionaries. Across these settings, decoder geometry, activation statistics, co-activation structure, and direct-logit footprint predict steering modularity better than frequency-only and activation-magnitude baselines. The signal is strongest in GPT-2-small, Pythia-70M, and Llama-3.1-8B, where it survives residualization against magnitude-related confounds, and weaker in Gemma-2-2B. Held-out screening shows that ranking unseen features by predicted cleanliness can select features that steer more cleanly on fresh contexts, but the successful axis varies by setting: GPT-2 improves most cleanly, Pythia improves mainly on stability, Llama mainly on collateral, and Gemma only partially. A controlled Llama Scope width comparison shows that the predictive signal persists under a 32K-to-128K dictionary-width change, although the screening payoff becomes less stable. Overall, SAE steering side effects are predictable in advance, but the useful predictor signature and transferred modularity axis are model- and dictionary-setting dependent.
The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.
Phu Gia Hoang, Anwoy Chatterjee, Tanmoy Chakraborty +2
UKP Lab, Technical University of Darmstadt · Department of Electrical Engineering Indian Institute of Technology Delhi, India