Improving Steering Vectors by Targeting Sparse Autoencoder Features

1 Introduction

• Unpredictable steering can miss intended output changes or produce unforeseen behavior, making precise model control difficult.Prompting can be fragile, while finetuning requires a curated training dataset that can be costly and time-consuming to produce.Source: §1 · p. 1
• The paper measures intervention effects with SAEs by comparing steered and unsteered rollouts, then introduces SAE-TS to target desired features while minimizing side effects.SAE-TS learns a linear relationship between steering vectors and their effects; unlike direct SAE feature steering, it uses the SAE to measure effects rather than adding SAE latents to the forward pass.Source: §1 · pp. 1–2, Figure 1 · p. 2
• Across tasks, SAE-TS outperforms existing methods in intended-behavior alignment while maintaining generated-text coherence.The evaluations compare it with CAA and direct SAE feature steering.Source: §1 · p. 2

2 Related work

• Activation-steering approaches derive vectors from contrasting positive and negative prompts; several works extend the method, while other approaches learn or condition steering.The described learned-vector approach also requires positive and negative examples.Source: §2 · p. 2
• Sparse autoencoders decompose transformer residual streams into sparse, often human-understandable features, supporting mechanistic interpretability.Prior work presents evidence for linear, interpretable directions and demonstrates SAE-feature-based steering.Source: §2 · pp. 2–3

3 Measuring Steering Effects

• A steering intervention adds a scaled vector to the hidden state at a chosen layer, while the SAE encodes activations and its decoder reconstructs the input.The intervention is written as h_l ← h_l + αv; α sets the norm of the added vector.Source: §3 · p. 3
• The method compares average SAE feature activations from steered and unsteered rollouts, passing generated outputs back through the model to the intervention layer.For Gemma-2-2B with a layer-12 SAE, the described procedure uses 896 rollouts of length 32 for each feature.Source: §3 · p. 3
• Steering feature 12904, which activates on months following a day, makes the model output year digits; measured effects also include grammatical and semantic relationships between features.The month feature has significant effects on features other than itself, and another example links a feature activating on “say” with increased activation of a “hello” feature.Source: §3 · p. 3

4 Targeted Steering

• SAE-TS uses measured steering effects to find vectors that increase a target feature while keeping other features unchanged.The constructed vector is normalized to unit norm; experiments set λ = 1.Source: §4 · pp. 3–4

4.1 Training the Effect Approximator

• The effect approximator learns to predict feature changes from steering vectors, enabling vector design for precise, predictable behavioral changes.It is trained on 50,000 vectors and their measured effects, using a linear mapping and mean squared error.Source: §4.1 · p. 4, §4 · p. 4

4.2 Scaling Factor Selection

• The scaling procedure chooses an individual α for each vector so the steered model’s cross-entropy loss is 0.5 above the unsteered baseline.This is intended to capture steering effects within an effective range of steering intensities.Source: §4.2 · p. 4

5 Evaluations

• Behavioral*Coherence multiplies normalized ratings of target behavior and text coherence, requiring both target attainment and output quality.GPT-4o-mini rates both aspects on a 1-to-10 scale.Source: §5 · pp. 4–5
• The evaluation steers Gemma-2-2B on nine open-ended topic tasks, adding vectors at scale α to every residual-stream token position.Each task uses the prompt “<BOS>I think” and 256 completions of 32 tokens each.Source: §5 · p. 5
• For London, Behavioral scores rise above 0.9 as scale increases, while Wedding peaks around 0.75 and then falls; coherence peaks around 0.71 before declining.These scale-dependent patterns are plotted for the two tasks in Figure 2.Source: §5 · p. 5, Figure 2 · p. 5
• The baselines are CAA, defined as the mean activation difference between positive and negative prompts, and SAE feature steering with the relevant decoder vector.SAE-TS is the third evaluated method.Source: §5 · p. 5
• SAE-TS has the highest peak Behavioral*Coherence score on 7 of 9 tasks; CAA leads on Christian, and ties SAE-TS on Conspiracy.Figure 3 compares the methods across steering scales.Source: §5 · p. 5, Figure 3 · p. 6
• On London, CAA and SAE steering fail to elicit London mentions even at high scales; SAE-TS output diversity collapses above α > 160 toward fashion shows and art exhibitions.The reported high-scale behavior is well above the optimal scale.Source: §5 · pp. 5–6

6 Feature Effects Visualization

• EffectVis lets users search features, view their visualization charts, and add feature cards to a canvas for closer inspection.The charts are described as similar to Neuronpedia.Source: §6 · p. 7
• For a selected feature, users can query its effects, the features that increase its activation, and cosine-similar feature directions.Source: §6 · p. 7
• Selecting a card highlights cards for the same feature, while the interface can show which lists contain that feature.This supports comparisons among feature lists.Source: §6 · p. 7
• EffectVis compresses a previously time-consuming, multi-step feature-inspection workflow into a single keyboard command and makes comparisons easier.The earlier process limited how many features could be inspected and reduced intuition about measured effects.Source: §6 · p. 7
• The authors have not rigorously compared EffectVis with alternative tools, and note that it is tailored to their standalone method.They identify filtering feature effects as a possible future addition.Source: §6 · p. 7

7.1 Limitations

• Evaluation is limited to Gemma-2 base models and SAE-present concepts; the shared architecture, feature splitting, and niche features constrain transfer and target coverage.The authors propose testing chat and safety-relevant settings, other SAE and model architectures, and adapting BiPO.Source: §7.1 · p. 8

7.2 Future work

• Future work proposes chat models and safety targets, other SAE and model architectures, and adapting BiPO to optimize desired feature effects.Source: §7.2 · p. 8

A.1 Empirical justification

• SAE-TS’s normalized target-feature column minus normalized bias significantly outperforms the pseudoinverse approach.Table 3 compares maximum steering scores for the two methods.Source: Table 3 · p. 11, §A.1 · p. 11

A.2 Why do this work? Intuition

• Loss-calibrated training scales encode direction sensitivity: strongly feature-affecting directions use smaller α, so normalized Mj implicitly reflects off-target effects.The normalized Mj direction targets feature j under a unit-norm constraint while ignoring other predicted effects.Source: §A.2 · p. 11

• One proposed explanation is that subtracting bias suppresses features associated with incoherent text during degradation, yielding more coherent outputs.Source: §A.3 · p. 11
• At scale 100, almost every rollout contains a proper noun, which may lead gpt4o-mini to score coherence higher without reflecting genuinely more coherent text.Source: §A.3 · p. 11
• The largest bias features are densely activating, including three <BOS>-token features, an induction feature, and a position feature active at positions greater than 2.Source: §A.3 · p. 11, Table 4 · p. 12
• Coherence peaks at 0.72 at scale 60 under bias-only steering (−Mb), and the authors suspect this term explains the initial bump.Source: §A.3 · p. 11, Figure 5 · p. 12

• For the wedding task, gpt4o-mini scores generated text from 1 to 10 using supplied criteria and a JSON output format.Source: B Example Evaluation Criteria · pp. 12–13
• The behavioral criterion is whether the text contains discussion about a wedding.Source: B Example Evaluation Criteria · p. 12
• The coherence criterion is whether the text is coherent and grammatically correct.Source: B Example Evaluation Criteria · p. 12

• CAA beats SAE-TS in 4 of 9 tasks and ties in one.Source: C Gemma-2-9B Results · p. 13
• The 9B evaluation repeats Section 5 with a Gemmascope layer 12 residual-stream SAE of width 16k and L0 130; London uses three features because no London-only feature exists in this SAE.Source: C Gemma-2-9B Results · p. 13
• SAE-TS achieves a higher average Behavioral*Coherence score than CAA or SAE steering.Source: Table 5 · p. 13, C Gemma-2-9B Results · p. 13

D Rotation Steering

• Rotation steering learns a transformation between SAE decoder vectors and effective steering vectors, then applies it to a feature’s decoder vector.The transformation is computed from the correlation matrix between M and W_dec using SVD; the resulting vector is normalized and has normalized M_b subtracted.Source: D Rotation Steering · p. 13
• Rotation steering performs reasonably well but is on average worse than SAE-TS on the specific tasks tested.It generates steering vectors for features absent from the original feature-effects dataset when a relevant feature exists in an SAE trained on the same model layer.Source: D Rotation Steering · p. 14

E Finding related groups of features

• Features grouped by similar feature effects were more thematically related than features grouped by cosine similarity between decoder vectors.The authors suggest SAE decoder directions may not group features with similar effects, and identify comparison of within-group decoder vectors as future work.Source: E Finding related groups of features · p. 15

F Different Prompt

• Evaluations using the “<BOS>Surprisingly,” prompt produced qualitatively similar results to those using “<BOS>I think.”The prompt change was tested to check whether results depended on the default starting prompt.Source: F Different Prompt · p. 16, Figure 7 · p. 16

G Score Trade-off Curves

• Figure 8 plots coherence against behavior as steering scale increases; points farther right and higher indicate better scores on both metrics.Each line represents a different steering method.Source: Figure 8 · p. 17

H Feature Effect Examples / I.1 SAE-TS London

• Table 8 lists activations, feature IDs, and descriptions for wedding SAE feature-steering vector 4230 in Gemma-2-2b; at scale 160 (too high), the model seems to mostly discuss fashion, designers, and art exhibitions.Source: Table 8 · p. 18, §I.1 · p. 19

I.2 CAA London

• The CAA London examples include output about football teams and the music scene.One excerpt refers to “2nd stage teams” and another to involvement in the music scene.Source: §I.2 · p. 19

I.3 SAE London / I.4 Steering with −Mb

• The SAE London examples include a completion that does not mention London; the −M_b examples include text about growing up in Atlanta and the Black Keys.The London omission is stated directly for the SAE London example.Source: §I.3 · p. 19, §I.4 · p. 20