Activation steering controls LLM behavior at inference time by adding learned directions to hidden states, but existing methods handle one concept at a time. Pluralistic alignment, where different stakeholders need different value emphases, requires steering multiple dimensions simultaneously. We show that naive steering produces substantial spillover: the effect intended for one value leaks into others. This parallels the treatment-versus-spillover decomposition in causal inference. We trace spillover to geometric entanglement of steering directions, captured by their Gram matrix, and derive a zero-cost correction from an activation-norm-penalized objective that decouples each direction's contribution exactly. Our end-to-end pipeline requires no fine-tuning, no reward model, and no manual prompt engineering: given only domain questions, it automatically discovers value dimensions, extracts directions, diagnoses entanglement, and applies corrected steering. On climate discourse, the correction improves the net steering effect from +5.9% to +14.0%, validated over 100,000 pairwise judgments.
Figures & tables
Direction
κ(G)
H
Target
Spillover
NSE
Contrast
24.4
G−1
56.8%
42.9%
+14.0%
I
55.2%
49.4%
+5.9%
RepE
7.8
G−1
57.5%
49.5%
+7.8%
I
53.3%
49.6%
+3.7%
ActAdd
14.2
G−1
53.4%
46.9%
+6.4%
I
52.1%
48.2%
+3.2%
Table 1: Net steering effect on Llama-3.2-3B-Instruct (200 questions, 4 target dimensions, 3 judges per comparison). Each generative direction type is shown with and without G−1 correction. The condition number κ(G) measures direction entanglement (§ 4 ).
Method
Target dim
Target
Spillover
NSE
contrast_ginv
Accuracy
65.0%
48.8%
+16.3%
TechEcon
53.0%
39.6%
+13.4%
SocialJustice
60.5%
37.2%
+23.2%
FutureEthics
48.8%
46.0%
+2.7%
repe_ginv
Accuracy
61.8%
49.6%
+12.2%
TechEcon
55.5%
41.4%
+14.1%
Table 2: Per-dimension breakdown for the two best corrected methods (Llama-3.2-3B-Instruct, 200 questions). The two methods have complementary strengths across value dimensions. Full breakdown for all 9 methods is in Appendix J .
Figure 1: G−1 NSE gain by direction type on three models: Llama-3.2-3B, Llama-3.1-8B, and Qwen2.5-7B (RepE was not extracted for Qwen). Gray bars show naive steering ( H=I ); colored bars show corrected steering ( H=G−1 ); numbers above bars give NSE in percentage points. The correction improves every direction type on every model. Full 8B and Qwen tables are in Appendices J and O .
Appendix figures & tables31 assets
Supplementary material from the paper’s appendix.
Appendix
Dimension
Description
Prev.
Accuracy
Factual precision, scientific evidence
91.4%
Ecology
Ecosystem health, biodiversity
41.9%
Equity_Present
Distributive justice, vulnerable communities
18.3%
Equity_Future
Intergenerational obligations
28.9%
Efficiency
Cost-effectiveness, resource optimization
34.9%
TechOpt
Technological innovation, engineering solutions
23.7%
Appendix
Table 3: Twelve candidate value dimensions and their prevalence in the StackExchange climate dataset ( n=1,255 ). Prevalence is the fraction of questions labeled as involving each dimension.
Group
Removed sub-dim
Labels changed
TechEcon
Efficiency
14.4%
TechEcon
TechOpt
3.3%
SocialJustice
Equity_Present
1.9%
SocialJustice
Care
3.2%
SocialJustice
Procedural
3.3%
SocialJustice
Liberty
1.2%
Appendix
Table 4: Within-group label stability. Each row shows the fraction of questions whose compressed label changes when one sub-dimension is removed. Accuracy is a single dimension and is not ablated.
Accuracy
TechEcon
SocialJustice
FutureEthics
F1 (mean ± std)
0.93±0.04
0.79±0.02
0.65±0.03
0.76±0.02
Appendix
Table 5: Probe F1 scores at layer 20 (Llama-3.1-8B-Instruct, 5-fold CV, n=1,255 ).
Model
Probe
ActAdd
Contrast
RepE
Llama-3.2-3B
1.90
14.15
24.37
7.77
Llama-3.1-8B
1.75
11.45
16.37
11.33
Qwen2.5-7B
1.74
10.73
11.78
—
Appendix
Table 6: Gram matrix condition number κ(G) across models and direction types. Generative directions are consistently an order of magnitude more entangled than discriminative ones. RepE was not extracted for Qwen.
Model
Direction
λ1
λ2
λ3
λ4
3B
Probe
36.3%
24.0%
20.6%
19.1%
ActAdd
63.6%
21.0%
10.9%
4.5%
Contrast
76.7%
13.9%
6.3%
3.1%
RepE
55.3%
22.8%
14.8%
7.1%
8B
Probe
34.6%
24.4%
21.2%
19.8%
ActAdd
60.3%
22.4%
12.1%
5.3%
Appendix
Table 7: Eigenvalue distribution (percentage of total variance) of Gram matrices. Generative directions concentrate 55–77% of variance in a single eigenvalue; probe directions distribute variance nearly uniformly.
3B Probe ( κ=1.90 )
Acc
TE
SJ
FE
Acc
1.00
−0.12
−0.10
−0.05
TE
−0.12
1.00
+0.18
+0.21
SJ
−0.10
+0.18
1.00
+0.21
FE
−0.05
+0.21
+0.21
1.00
3B Contrast ( κ=24.37 )
Appendix
Table 8: Full Gram matrices for Llama-3.2-3B-Instruct (layer 14). Entries are cosine similarities between unit-normalized directions.
8B Probe ( κ=1.75 )
Acc
TE
SJ
FE
Acc
1.00
−0.08
−0.11
−0.05
TE
−0.08
1.00
+0.16
+0.20
SJ
−0.11
+0.16
1.00
+0.14
FE
−0.05
+0.20
+0.14
1.00
8B Contrast ( κ=16.37 )
Appendix
Table 9: Full Gram matrices for Llama-3.1-8B-Instruct (layer 20).
Qwen Probe ( κ=1.74 )
Acc
TE
SJ
FE
Acc
1.00
−0.05
−0.10
−0.05
TE
−0.05
1.00
+0.19
+0.18
SJ
−0.10
+0.19
1.00
+0.18
FE
−0.05
+0.18
+0.18
1.00
Qwen Contrast ( κ=11.78 )
Appendix
Table 10: Full Gram matrices for Qwen2.5-7B-Instruct (layer 16). RepE directions were not extracted for Qwen.
Dimension
Contrast
ActAdd
RepE
Random
Accuracy
0.093
0.082
0.082
TechEcon
0.019
0.024
0.061
SocialJustice
0.020
0.057
0.034
FutureEthics
0.011
0.027
0.028
Mean
0.036
0.048
0.051
0.012±0.009
Appendix
Table 11: Cosine similarity between probe and generative directions at layer 20 (Llama-3.1-8B-Instruct). All values are comparable to the random baseline in R4096 , indicating that discriminative and generative directions occupy near-orthogonal subspaces.
Persona ↓ \ Judged →
Acc
TE
SJ
FE
Accuracy
+0.65
−0.25
−0.25
+0.10
TechEcon
−1.00
+2.55
−0.25
−0.50
SocialJustice
−0.75
−0.40
+2.80
+0.90
FutureEthics
−0.80
−0.65
+0.05
+2.80
Appendix
Table 12: Persona generation lift matrix. Entry (i,j) is the mean score under persona i minus the neutral baseline score, judged on dimension j . n=20 questions, 0–10 absolute scoring. Diagonal entries (bold) show that each persona specifically increases its target dimension; off-diagonal entries are predominantly negative.
Acc
TE
SJ
FE
M in probe basis
αAcc
−0.021
−0.003
−0.007
−0.016
αTE
−0.031
+0.013
+0.013
+0.008
αSJ
−0.003
+0.012
+0.002
+0.014
αFE
−0.005
−0.003
+0.012
+0.016
M in contrast basis
Appendix
Table 13: Estimated causal Jacobian M . Entry in row j , column k is the estimated ∂Vk/∂αj : how steering along direction j affects value score k . All entries are O(10−2) , indicating negligible linear causal effect at the first-order level.
Figure 2: Estimated causal Jacobian M in probe (left) and contrast (right) direction bases. Black squares mark diagonal entries. A well-behaved M would show strong positive diagonal and weak off-diagonal; instead, all entries are O(10−2) with no clear diagonal structure.
α
ε
Target
Spillover
NSE
15
0
45.0%
45.4%
−0.4 %
15
0.1
45.0%
45.0%
+0.0 %
20
0
57.5%
45.0%
+12.5 %
20
0.1
51.2%
46.3%
+5.0 %
20
0.3
43.8%
44.2%
−0.4 %
20
0.5
42.5%
47.5%
−5.0 %
Appendix
Table 14: 8B actadd_ginv sweep ( n=20 questions, 2 target dims, 3 judges). Best configuration: α=20 , ε=0 (pure G−1 , no regularization). Only a subset of the 4×4 grid is shown; omitted entries have NSE below +2% .
Method
Target
Spillover
NSE
contrast_ginv, α=15
71.2%
64.6%
+6.7 %
contrast_naive, α=15
62.5%
63.1%
−0.6 %
contrast_ginv, α=20
74.4%
61.0%
+13.3 %
contrast_naive, α=20
65.6%
64.6%
+1.0 %
contrast_ginv, α=26
73.8%
63.3%
+10.4 %
contrast_naive, α=26
68.1%
63.7%
+4.4 %
Appendix
Table 15: 3B contrast sweep ( n=20 questions, 4 target dims, 3 judges). G−1 correction improves NSE at every alpha level, with the gap widening as α increases.
Method
Target dim
Target
Spillover
NSE
contrast_ginv
Accuracy
64.8%
49.7%
+15.1 %
TechEcon
53.1%
40.1%
+13.0 %
SocialJustice
59.4%
37.7%
+21.7 %
FutureEthics
50.9%
46.3%
+4.6 %
contrast_naive
Accuracy
59.9%
50.7%
+9.2 %
TechEcon
51.9%
49.9%
+2.0 %
Appendix
Table 16: Per-dimension results for all methods on Llama-3.2-3B-Instruct (200 questions, 3 judges per comparison, ties counted as 0.5).
Method
H
Target
Spillover
NSE
actadd_ginv
G−1
52.8%
49.6%
+3.3 %
actadd_naive
I
51.3%
49.4%
+1.9 %
contrast_ginv
G−1
52.9%
48.9%
+4.0 %
contrast_naive
I
50.2%
48.9%
+1.2 %
repe_ginv
G−1
50.9%
48.3%
+2.7 %
repe_naive
I
51.2%
48.9%
+2.3 %
Appendix
Table 17: Full 8B results (Llama-3.1-8B-Instruct, 100 questions, layer 20, α=20 ). G−1 correction improves all three generative direction types. Effect magnitudes are smaller than 3B, consistent with the reduced entanglement at larger scale ( κcontrast=16.4 vs 24.4).
Method
Target dim
Target
Spillover
NSE
actadd_ginv
Accuracy
55.0%
50.2%
+4.8 %
TechEcon
52.8%
50.7%
+2.0 %
SocialJustice
52.5%
48.5%
+4.0 %
FutureEthics
51.1%
48.9%
+2.2 %
actadd_naive
Accuracy
51.2%
50.2%
+1.0 %
TechEcon
51.6%
48.2%
+3.4 %
Appendix
Table 18: Per-dimension breakdown for 8B (combined v2+v3, 100 questions per target dimension). Probe and layer_sep per-dimension results are omitted as both have near-chance mean NSE.
Domain
n
Silhouette
Energy policy
518
0.255
Medical ethics
741
0.234
AI governance
673
0.234
Economic inequality
800
0.227
Education policy
482
0.224
Immigration
800
0.223
Appendix
Table 19: Unsupervised clustering results across 10 domains (K-means, K=2 ). All domains select K=2 as optimal. Silhouette scores are uniformly low, and the resulting clusters reflect question format rather than value structure.
Experiment
Model
Methods
Questions
Dims
Judgments
3B main (§ 5.2 )
Llama-3.2-3B
9
200
4
86,400
8B v2 (§ 5.3 )
Llama-3.1-8B
9
50
4
21,600
8B v3 (§ 5.3 )
Llama-3.1-8B
9
150
4
64,800
Qwen (App. O )
Qwen2.5-7B
4
50
4
9,600
3B sweep (App. I )
Llama-3.2-3B
10
20
4
—
8B sweep (App. I )
Llama-3.1-8B
10
20
2
—
Appendix
Table 20: Experimental configuration summary. “Judgments” counts individual judge votes (3 per comparison ×K evaluated dimensions × questions × methods). Sweep experiments are excluded from the total as they use a different checkpoint format.
NSE (pp)
Fidelity
Configuration
Naive
Ginv
Prompt
Naive
Ginv
Prompt
Acc+SJ
−5.00
+5.50
+5.50
−0.34
+0.69
+0.60
TE+FE
+0.50
−1.25
+6.00
+0.07
−0.16
+0.38
Acc+FE
+0.00
+4.50
+6.00
+0.00
+0.61
+0.44
Acc+TE+SJ
−6.00
−3.67
+4.33
−0.91
−0.42
+0.67
Acc+SJ+FE
−2.50
+4.17
+9.00
+0.04
+0.62
+0.82
Appendix
Table 21: Mixed- w results on Llama-3.2-3B-Instruct ( n=100 questions per configuration and condition). Weights are equal on the named support, e.g. wAcc+SJ=(0.5,0,0.5,0) ; Uniform is (0.25,0.25,0.25,0.25) . NSE is the mean win rate on active dimensions minus the mean on inactive dimensions; it is undefined for Uniform, which has no inactive dimensions. Fidelity is defined in the text. NSE means are over the five non-uniform configurations; fidelity means are over all six.
Method
H
Target
Spillover
NSE
contrast_ginv
G−1
65.0%
57.8%
+7.2 %
contrast_naive
I
59.6%
57.1%
+2.5 %
actadd_ginv
G−1
62.8%
57.3%
+5.4 %
actadd_naive
I
61.3%
58.4%
+2.9 %
Appendix
Table 22: Results on Qwen2.5-7B-Instruct (50 questions, layer 16, α=10 , 3 judges per comparison). G−1 correction improves both direction types.
Method
Target dim
Target
Spillover
NSE
contrast_ginv
Accuracy
73.3%
56.6%
+16.8 %
TechEcon
67.3%
56.7%
+10.7 %
SocialJustice
68.0%
55.3%
+12.7 %
FutureEthics
51.3%
62.6%
−11.2 %
contrast_naive
Accuracy
74.0%
54.3%
+19.7 %
TechEcon
57.7%
55.9%
+1.8 %
Appendix
Table 23: Per-dimension breakdown for Qwen2.5-7B-Instruct. FutureEthics is consistently the weakest dimension across all methods, suggesting that the FE contrast direction in Qwen does not carry a strong value-specific signal in this domain.
K
κ(G)
Naive
Ginv
Gain
Bootstrap p
4
24.4
+5.9%
+14.0%
+8.1 pp
—
8
157.6
−3.5%
+9.0%
+12.5 pp
0.0000
10
208.7
−3.4%
+6.7%
+10.1 pp
0.0060
12
329.7
+6.0%
+17.8%
+11.9 pp
<0.01
Appendix
Table 24: Macro NSE and Gram-matrix conditioning under K -scaling on the climate domain. The correction’s gain over naive steering is positive and significant at every K , and at least as large as at K=4 . K=4 values are the main-text Table 1 numbers ( n=200 ); K≥8 use n=50 .
Target
Naive
Ginv
Gain
Wilcoxon p
Accuracy
−33.4%
−3.7%
+29.7
0.000
Ecology
−10.0%
+0.6%
+10.6
0.127
Efficiency
−15.7%
−6.7%
+9.0
0.181
Equity_Future
+2.6%
+7.1%
+4.6
0.663
Equity_Present
+6.0%
+36.0%
+30.0
0.001
Precaution
+11.6%
+11.4%
−0.1
0.994
Appendix
Table 25: Per-target NSE at K=8 (climate). Naive steering drives several targets negative (Accuracy −33.4% ); the correction recovers them. Significance by Wilcoxon signed-rank.
Dimension
Naive
Ginv
Gain
Wilcoxon p
Evidence
−2.7%
+32.6%
+35.3
0.0006
Autonomy
−8.6%
+4.5%
+13.2
0.045
DistributiveEthics
+11.0%
+14.0%
+3.0
0.187
CareDuties
+10.3%
+5.7%
−4.6
0.62
MACRO
+2.5%
+14.2%
+11.7
0.0043
Appendix
Table 26: Per-dimension and macro NSE on the from-scratch Medical Ethics domain ( n=50 , κ(G)=5.30 ). The gain concentrates on Evidence, the dimension most orthogonal to the others; the three related normative dimensions gain less. Significance by Wilcoxon signed-rank.
Method
DeepSeek NSE
GPT-4o NSE
probe_naive
+1.50%
+8.08%
probe_ginv
+3.83%
+5.58%
contrast_naive
+4.00%
+3.75%
contrast_ginv
+15.25%
+15.42%
actadd_naive
−1.67%
+3.67%
actadd_ginv
+4.00%
+5.83%
Appendix
Table 27: Per-method NSE under two judges from different families (DeepSeek and GPT-4o), on the same 50 questions. The correction improves over naive steering under both judges for contrast, ActAdd, and RepE; the one exception is probe under GPT-4o.
Layer
κ(G)
Naive
Ginv
Gain
10
33.33
+5.50%
+8.50%
+3.00 pp
14
24.37
+4.00%
+15.25%
+11.25 pp
18
27.75
+8.00%
+14.08%
+6.08 pp
Appendix
Table 28: Layer sweep on Llama-3.2-3B-Instruct: contrast directions, fixed α=26 , first 50 canonical questions. Directions and the Gram matrix are re-extracted at each layer. The L=14 row sub-selects the main-experiment judgments on the same questions.
β
κ(G+βI)
∥αβ∥
Acc
TE
SJ
FE
w=(0,0.5,0,0.5) (TE+FE)
0
24.37
3.13
0.000
0.500
0.000
0.500
0.1
14.02
1.82
0.038
0.423
0.119
0.394
0.5
5.70
0.71
0.090
0.306
0.191
0.288
2
2.38
0.24
0.095
0.187
0.155
0.183
w=eSJ (one-hot SocialJustice)
Appendix
Table 29: Regularization path of Hβ=(G+βI)−1 on the 3B contrast Gram matrix. Projections are Gαβ , the achieved emphasis along each direction; κ(G+βI) depends only on β . At β=0 the projections equal the request exactly; larger β shrinks the coefficient norm and reintroduces off-support projection in order of cosine with the active set.
Target dimension
contrast_ginv
Prompting (P1)
p
Accuracy
+14.42%
+14.92%
0.924
TechEcon
+14.33%
+25.58%
0.014
SocialJustice
+22.50%
+15.58%
0.163
FutureEthics
+4.58%
+11.50%
0.145
MACRO
+13.96%
+16.90%
0.231
Appendix
Table 30: Per-dimension and macro NSE for instruction prompting (P1) against corrected steering (contrast_ginv) on the full 200 canonical questions (Llama-3.2-3B-Instruct, main judge protocol). p is a paired bootstrap on the per-question difference; the macro difference is also not significant under a Wilcoxon signed-rank on the same pairing ( p=0.23 ).
Configuration
Macro NSE
Median PPL
Fluency
Unsteered baseline
—
2.19
4.15
Prompting (P1)
+17.08%
2.32
4.03
contrast_ginv ( α=26 )
+12.88%
2.48
3.97
Stack ( α=26 )
+37.25%
2.79
4.01
Stack ( α=13 )
+27.71%
2.49
3.99
Appendix
Table 31: Operating-point ladder on the first 100 canonical questions (Llama-3.2-3B-Instruct, contrast directions, layer 14). Macro NSE from the powered stacking run ( n=100 questions per target dimension); the prompting and corrected-steering reference rows reuse the corresponding judgments restricted to this subset, hence the expected subset variation from Table 30 . Median perplexity and mean fluency (1–5) are computed on the same subset (100 questions; 400 generations per four-dimension arm); both metrics follow the protocol of Appendix T . NSE is measured against the unsteered baseline, so the baseline row has none.
Steered-selection rate
contrast_naive
contrast_ginv
Target items
0.149
0.327
Spillover items
0.115
0.136
Agreement
Raw
κ
Human–judge ( n=240 )
0.704
0.508
Inter-annotator (full-coverage) †
0.643
0.405
Appendix
Table 32: Human validation of the pairwise emphasis judgments. Top: rate at which annotators select the steered response over the unsteered baseline (majority vote; ties counted in the denominator), by item type and method. Bottom: agreement of the human labels with the LLM judge, and among annotators. Human–judge agreement ( κ=0.51 ) exceeds the cross-judge level ( κ=0.39 ), and inter-annotator agreement is moderate. One outlier annotator, whose labels correlated near zero with both the other annotators and the judge, was excluded. † Inter-annotator agreement (Fleiss κ , three-way) is over the three annotators who labelled all 240 items; the human–judge and steered-selection figures additionally use a fourth annotator who labelled 48 items.
Large Language Models (LLMs) are deployed across cultural contexts but often reflect homogenized values inherited from training data. Evaluations of cultural alignment typically rely on direct prompting with survey-style questions, which frequently elicit neutral or safety-aligned responses and fail to capture underlying model preferences. We propose a framework for probing and steering latent cultural representations in LLMs along the two Inglehart--Welzel axes of the World Values Survey (WVS). By translating social value questions into scenario-based behavioral dilemmas, we extract token-level probabilities to measure implicit values and apply activation steering, optionally combined with country-conditioned prompting, to shift model behavior without retraining. Across three open-source LLMs and four target cultures, we find substantial variation in steerability and identify latent entanglement, where interventions along one cultural dimension induce shifts along another. This coupling mirrors correlations in human WVS data and persists across activation, prompt, and hybrid steering. It constrains axis-independent alignment, though general task performance is largely preserved.
Alignment in LLMs is more brittle than commonly assumed: misalignment can be induced by adversarial prompts, benign fine-tuning, emergent misalignment, and goal misgeneralization. Recent evidence suggests that some misalignment behaviors are encoded as linear structure in activation space, making it tractable via activation steering, which could be used as a lightweight runtime defense. We implement three methods: Steer-With-Fixed-Coefficient (SwFC), which applies uniform additive steering, and two novel projection-aware methods, Steer-to-Target-Projection (StTP) and Steer-to-Mirror-Projection (StMP), that use a logistic regression decision boundary to selectively intervene only on tokens whose activations fall below the threshold. We evaluate these methods on two threat models, dishonesty and dismissiveness, using malicious system prompts as a controlled proxy for misalignment. We conduct our experiments on two architectures (Llama-3.3-70B-Instruct and Qwen3.6-27B). All methods substantially recover alignment. StTP and StMP preserve general capabilities (MMLU, MT-Bench, AlpacaEval) better than uniform steering. Finally, we show that our honesty steering generalizes to out-of-distribution scenarios: a single honesty direction extracted from the aligned model significantly raises scores on the MASK benchmark, suppresses deception in multi-agent settings (Among Us), doubles the hidden-behavior discovery rate on AuditBench, and restores honesty in an emergently misaligned model.
Niklas Herbster, Martin Zborowski, Alberto Tosato +2
Tara Research · Technical University of Munich · Mila Quebec AI Institute
Activation steering offers an effective and efficient way to modify an LLM's behavior at inference time. However, it remains unclear how to apply steering such that the signal is consistently strong and the steering strength has a universally interpretable meaning. We address this first by identifying the most steerable interval for each steering vector and rescaling the steering range accordingly. Building on this, we introduce a more interpretable method for steering, called parameterized steering which instead of pushing activations in a direction, it sets them at the desired trait strength. Next, with multi-trait steering, we find that naively combining vectors causes them to interfere with one another. In response, we develop a method to orthogonalize the vectors; it decouples these traits, allowing a model to exhibit one behavior without inducing the others, thus enabling multiple traits to be steered simultaneously.
Kahlert School of Computing University of Utah Salt Lake City, UT 84112, USA · Department of Computer Science University of Massachusetts Amherst Amherst, MA 01003 · Martian AI San Francisco, CA 94117, USA +1