cs.CLSep 5, 2026

Steering Geometry: Validating Human Value Geometry in LLM Steering Space

Authors: Mohammad Mahdi Abootorabi, Armin Saghafian, Ali Bazshoushtari, Hamid Rezaei, EunJeong Hwang, Vered Shwartz, Parvin Mousavi, Purang Abolmaesumi

Organizations: University of British Columbia · Vector Institute for AI · Queen’s University

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Abstract

As large language models (LLMs) are increasingly deployed in alignment-sensitive contexts, activation steering has emerged as a lightweight, inference-time alternative to fine-tuning methods (e.g., RLHF, DPO) for behavioral control. However, existing work typically validates steering on isolated behaviors, leaving it unclear whether steering vectors encode coherent semantic structure or merely exploit behavior-specific shortcuts. We investigate whether the latent geometry of LLM steering vectors reflects theory-specified structure in human values and morality. Using Schwartz's Theory of Basic Human Values as our primary fine-grained framework, we introduce a 26K-sample benchmark covering 20 human values and analyze distribution-driven methods (e.g., CAA, SphericalSteer, ODESteer) and behavior-centric approaches (e.g., COLD-Steer, BiPO) across diverse model families and sizes. We find that distribution-driven methods recover human value topologies aligned with theoretical predictions (Spearman ρρ up to 0.51, p<10−13p < 10^{-13}). In contrast, behavior-centric methods achieve comparable steering performance but show little correlation with the expected value geometry. Geometric fidelity improves with model scale but drops after instruction tuning. Finally, better geometric alignment also leads to more human-consistent transfer across values: steering one value correctly lifts compatible values and suppresses opposing ones. Code and data are available at: https://github.com/DeepRCL/Steering_Geometry.

Figures & tables

Figure 1: Pipeline for analyzing value geometry in the LLM activation-steering space. (1) For each Schwartz value, we build contrastive (question, positive, negative) pairs. (2) We extract residual-stream activations at a selected layer ℓ⋆\ell^{\star} and apply steering methods from two paradigms, distribution-driven and behavior-centric , to construct a value vector bank. (3) We evaluate (A) geometric alignment against the Schwartz circumplex, and (B) behavioral cross-value transfer, measuring the effect on other values when steering toward a single one.
Figure 2: Value geometry across steering methods on Qwen3.5-9B-Base. Top: pairwise cosine-similarity matrices for the theoretical Schwartz circumplex, raw residual-stream activations, SAS (a distribution-driven method), and OPT (a behavior-centric method); red/blue indicates positive/negative correlations. Bottom: 2D projections of each similarity matrix aligned to the canonical Schwartz arrangement. SAS reproduces the circumplex structure most clearly, while OPT scatters values with no organization, even worse than the raw-activation baseline.
ParadigmMethodρT\rho_{\mathrm{T}}rTr_{\mathrm{T}}ρH\rho_{\mathrm{H}}Δpol\Delta_{\mathrm{pol}}
Base (pre-trained)
Behav.-centricLLM Raw Activation Space0.2228(2.0e-3)0.2228_{{\scriptscriptstyle(2.0\text{e-}3)}}0.2087(3.9e-3)0.2087_{{\scriptscriptstyle(3.9\text{e-}3)}}0.2115(3.4e-3)0.2115_{{\scriptscriptstyle(3.4\text{e-}3)}}0.0009
[0.8pt/2pt] Dist.-drivenOPT Dunefsky and Cohan (2025)0.1138(1.2e-1)0.1138_{{\scriptscriptstyle(1.2\text{e-}1)}}0.1104(1.3e-1)0.1104_{{\scriptscriptstyle(1.3\text{e-}1)}}0.0493(5.0e-1)0.0493_{{\scriptscriptstyle(5.0\text{e-}1)}}0.0001
Cold-Steer (FD) Sharma and Trivedi (2026)0.0265(7.2e-1)0.0265_{{\scriptscriptstyle(7.2\text{e-}1)}}−0.0100(8.9e-1)-0.0100_{{\scriptscriptstyle(8.9\text{e-}1)}}0.0013(9.9e-1)0.0013_{{\scriptscriptstyle(9.9\text{e-}1)}}0.0162
BiPO Cao et al. (2024)0.1188(1.0e-1)0.1188_{{\scriptscriptstyle(1.0\text{e-}1)}}0.1291(7.6e-2)0.1291_{{\scriptscriptstyle(7.6\text{e-}2)}}0.1070(1.4e-1)0.1070_{{\scriptscriptstyle(1.4\text{e-}1)}}0.0151
[0.8pt/2pt]ODESteer Zhao et al. (2026)0.2730(1.4e-4)0.2730_{{\scriptscriptstyle(1.4\text{e-}4)}}0.2963(3.3e-5)0.2963_{{\scriptscriptstyle(3.3\text{e-}5)}}0.2988(2.8e-5)0.2988_{{\scriptscriptstyle(2.8\text{e-}5)}}0.0255
Table 1: Effect of steering methods on geometry-alignment metrics on the Qwen 3.5-9B backbone, grouped by tuning regime (Base vs. Instruct) and paradigm ( distribution-driven vs. behavior-centric ). The metrics include Theory Rank Correlation ( ρT\rho_{T} ), Theory Linear Correlation ( rTr_{T} ), Hierarchical Structure Correlation ( ρH\rho_{H} ), and Polarity Separation Score ( Δpol\Delta_{\mathrm{pol}} ). Subscripts denote p-values. Bold indicates the best value.
Figure 3: Effect of model family and size on steering-geometry metrics (all using CAA). The metrics include Theory Rank Correlation ( ρT\rho_{T} ), Hierarchical Structure Correlation ( ρH\rho_{H} ), and Polarity Separation Score ( Δpol\Delta_{\mathrm{pol}} ).
Figure 4: Geometric alignment versus continuous cross-value transfer fidelity across steering methods on Qwen3.5-9B-Base and Llama3.1-8B.
Figure 5: Hierarchical representational fidelity versus hierarchical cross-value transferability across steering methods on Qwen3.5-9B-Base and Llama3.1-8B.
MethodQwen3.5-9BLlama3.1-8B
LLM Raw Activation0.00060.0017
Behavior-centric
OPT Dunefsky and Cohan (2025)0.01070.0272
Cold-Steer Sharma and Trivedi (2026)-0.0064-0.0280
BiPO Cao et al. (2024)-0.02870.0227
Distribution-driven
Table 2: Effect of steering method on MFT family separation ( ΔMFT\Delta_{\mathrm{MFT}} ). Positive values indicate greater within-family than cross-family cosine similarity.
Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

ModelρT\rho_{\mathrm{T}}rTr_{\mathrm{T}}ρH\rho_{\mathrm{H}}Δpol\Delta_{\mathrm{pol}}
Falcon-7B0.1954(6.9e-3)0.1954_{{\scriptscriptstyle(6.9\text{e-}3)}}0.1989(5.9e-3)0.1989_{{\scriptscriptstyle(5.9\text{e-}3)}}0.1148(1.1e-1)0.1148_{{\scriptscriptstyle(1.1\text{e-}1)}}0.1312
Mistral-7B0.3248(4.8e-6)0.3248_{{\scriptscriptstyle(4.8\text{e-}6)}}0.3378(1.9e-6)0.3378_{{\scriptscriptstyle(1.9\text{e-}6)}}0.2449(6.6e-4)0.2449_{{\scriptscriptstyle(6.6\text{e-}4)}}0.2469
Llama-3.1-8B0.3701(1.5e-7)0.3701_{{\scriptscriptstyle(1.5\text{e-}7)}}0.3783(7.4e-8)0.3783_{{\scriptscriptstyle(7.4\text{e-}8)}}0.2879(5.6e-5)0.2879_{{\scriptscriptstyle(5.6\text{e-}5)}}0.2833
Gemma-3-1B0.1270(8.1e-2)0.1270_{{\scriptscriptstyle(8.1\text{e-}2)}}0.1376(5.8e-2)0.1376_{{\scriptscriptstyle(5.8\text{e-}2)}}0.0531(4.7e-1)0.0531_{{\scriptscriptstyle(4.7\text{e-}1)}}−- 0.0016
[0.8pt/2pt] Gemma-3-4B0.2977(3.0e-5)0.2977_{{\scriptscriptstyle(3.0\text{e-}5)}}0.2992(2.8e-5)0.2992_{{\scriptscriptstyle(2.8\text{e-}5)}}0.2344(1.1e-3)0.2344_{{\scriptscriptstyle(1.1\text{e-}3)}}0.2987
[0.8pt/2pt] Gemma-3-12B0.4059(6.3e-9)0.4059_{{\scriptscriptstyle(6.3\text{e-}9)}}0.4153(2.6e-9)0.4153_{{\scriptscriptstyle(2.6\text{e-}9)}}0.3011(2.4e-5)0.3011_{{\scriptscriptstyle(2.4\text{e-}5)}}0.2712
Appendix
Table 3: Effect of model family and size on steering-geometry metrics (all using CAA). The metrics include Theory Rank Correlation ( ρT\rho_{T} ), Theory Linear Correlation ( rTr_{T} ), Hierarchical Structure Correlation ( ρH\rho_{H} ), and Polarity Separation Score ( Δpol\Delta_{\mathrm{pol}} ). Subscripts denote p-values. Bold indicates the best value.
MethodGain (pp)
Cold-Steer (FD) Sharma and Trivedi (2026)+5.50+5.50
[0.8pt/2pt] BiPO Cao et al. (2024)+8.87+8.87
[0.8pt/2pt] SphericalSteer You et al. (2026)+9.38+9.38
[0.8pt/2pt] OPT Dunefsky and Cohan (2025)+9.57+9.57
[0.8pt/2pt] ODESteer Zhao et al. (2026)+9.70+9.70
[0.8pt/2pt] SAS Bayat et al. (2025)+10.03+10.03
Appendix
Table 4: Effect of steering method on accuracy gain for the Qwen 3.5-9B Base (pre-trained) backbone. Gain is reported in percentage points (pp) relative to the unsteered baseline. Bold indicates the best value.
Figure 6: The Schwartz Theory of Basic Human Values organizes 20 basic human value categories in a circular structure, where more similar values appear close together, while values that tend to conflict are placed on opposite sides of the circle. Illustration adapted from Schwartz (2012) .
ValueCore Motivational Goal
Self-Direction: ThoughtFreedom to cultivate one’s own ideas and abilities
[0.8pt/2pt] Self-Direction: ActionFreedom to determine one’s own actions
[0.8pt/2pt] StimulationExcitement, novelty, and challenge in life
[0.8pt/2pt] HedonismPleasure and sensuous gratification for oneself
[0.8pt/2pt] AchievementSuccess through demonstrating competence by social standards
[0.8pt/2pt] Power: DominancePower through exercising control over people
Appendix
Table 5: The 20 Basic Human Values of the Refined Schwartz Theory and their core motivational goals.
ParadigmMethodρT\rho_{\mathrm{T}}rTr_{\mathrm{T}}ρH\rho_{\mathrm{H}}Δpol\Delta_{\mathrm{pol}}
Base (pre-trained)
Behav.-centricLLM Raw Activation Space0.2387(9.1e-4)0.2387_{{\scriptscriptstyle(9.1\text{e-}4)}}0.2377(9.6e-4)0.2377_{{\scriptscriptstyle(9.6\text{e-}4)}}0.2530(4.3e-4)0.2530_{{\scriptscriptstyle(4.3\text{e-}4)}}0.0026
[0.8pt/2pt]OPT Dunefsky and Cohan (2025)−0.0486(5.1e-1)-0.0486_{{\scriptscriptstyle(5.1\text{e-}1)}}−0.0696(3.4e-1)-0.0696_{{\scriptscriptstyle(3.4\text{e-}1)}}−0.0352(6.3e-1)-0.0352_{{\scriptscriptstyle(6.3\text{e-}1)}}0.0232
 Cold-Steer (FD) Sharma and Trivedi (2026)−0.0405(5.8e-1)-0.0405_{{\scriptscriptstyle(5.8\text{e-}1)}}−0.0404(5.8e-1)-0.0404_{{\scriptscriptstyle(5.8\text{e-}1)}}−0.0365(6.2e-1)-0.0365_{{\scriptscriptstyle(6.2\text{e-}1)}}0.0104
 BiPO Cao et al. (2024)0.1094(1.3e-1)0.1094_{{\scriptscriptstyle(1.3\text{e-}1)}}0.1036(1.5e-1)0.1036_{{\scriptscriptstyle(1.5\text{e-}1)}}0.0098(8.9e-1)0.0098_{{\scriptscriptstyle(8.9\text{e-}1)}}−- 0.0094
[0.8pt/2pt] Dist.-drivenODESteer Zhao et al. (2026)0.3124(1.1e-5)0.3124_{{\scriptscriptstyle(1.1\text{e-}5)}}0.3026(2.2e-5)0.3026_{{\scriptscriptstyle(2.2\text{e-}5)}}0.2996(2.7e-5)0.2996_{{\scriptscriptstyle(2.7\text{e-}5)}}0.0195
Appendix
Table 6: Effect of steering method on geometry-alignment metrics on the Llama 3.1-8B backbone. The metrics include Theory Rank Correlation ( ρT\rho_{T} ), Theory Linear Correlation ( rTr_{T} ), Hierarchical Structure Correlation ( ρH\rho_{H} ), and Polarity Separation Score ( Δpol\Delta_{\mathrm{pol}} ). Subscripts denote p-values. Bold indicates the best value.
MethodGain (pp)
OPT Dunefsky and Cohan (2025)+6.03+6.03
[0.8pt/2pt] BiPO Cao et al. (2024)+6.30+6.30
[0.8pt/2pt] ODESteer Zhao et al. (2026)+6.60+6.60
[0.8pt/2pt] Cold-Steer Sharma and Trivedi (2026)+7.50+7.50
[0.8pt/2pt] SphericalSteer You et al. (2026)+17.57+17.57
[0.8pt/2pt] CAA Rimsky et al. (2024)+17.64+17.64
Appendix
Table 7: Effect of steering method on accuracy gain for the Llama 3.1-8B backbone. Gain is reported in percentage points (pp) relative to the unsteered baseline. Bold indicates the best value.
MethodModelρT\rho_{T}rTr_{T}
CAA Rimsky et al. (2024)Qwen3.5-0.8B0.25370.2643
 Qwen3.5-2B0.33640.3545
 Qwen3.5-4B0.41090.4243
 Qwen3.5-9B0.46060.4754
[0.8pt/2pt]Qwen2.5-7B0.23700.2491
 Qwen2.5-14B0.31330.3298
Appendix
Table 8: Effect of model scale on theory-alignment metrics for CAA and SphericalSteer across Qwen3.5 and Qwen2.5. All correlations are statistically significant ( p<3×10−3p<3\times 10^{-3} ).
Value categoryValueBenchTouchéTotal
Achievement & Power
Achievement1252,1872,312
Power: dominance37792829
Power: resources10779789
Benevolence & Universalism
Benevolence: caring962,1122,208
Appendix
Table 9: Value distribution per Schwartz category across both dataset sources. Counts reflect quadruples retained after quality filtering.
Figure 7: (Left) Layer selection via Mean Normalized L2 Separation across transformer layers for CAA for Qwen3.5-9B-Base. Layer 15 is selected (dashed red line) as it achieves the highest mean separation between positive and negative activation distributions. (Right) Mean steering accuracy across Schwartz values as a function of the multiplier α\alpha , compared against the unsteered baseline (dashed gray line). Accuracy peaks around α\alpha ∈\in [15, 20] before degrading at larger values, consistent with prior observations that excessive steering strength degrades generation quality.
Figure 8: Correlation between theoretical value relationships (from Schwartz Theory) and empirical cosine similarities of extracted value vectors. The scatter plot illustrates the individual data points; while the distribution exhibits noticeable variance, a general upward trend is visible as one moves from left to right along the x-axis, demonstrating that higher theoretical relationships correspond to higher empirical similarities. This positive correlation indicates that LLM representations preserve human-predicted value structure. The results are from the SAS method on Qwen3.5-9B-Base model, which shows the highest correlation among all our configurations.
Figure 9: t-SNE projection of 20 Schwartz value vectors, colored by higher-order dimension. Spatial clustering of same-quadrant values and separation of opposing values provides visual evidence of circumplex structure in LLM activation space. The results are from the SAS method on Llama-3.1-8B model.
 Qwen3.5-9B-BaseLlama 3.1-8B
MethodOriginalDisjointParaphrasedSL-prio.OriginalDisjointParaphrasedSL-prio.
LLM Raw Activation Space0.2228(2.0e-3)0.2228_{{\scriptscriptstyle(2.0\text{e-}3)}}0.2122(3.3e-3)0.2122_{{\scriptscriptstyle(3.3\text{e-}3)}}0.2362(1.0e-3)0.2362_{{\scriptscriptstyle(1.0\text{e-}3)}}0.1223(9.3e-2)0.1223_{{\scriptscriptstyle(9.3\text{e-}2)}}0.2387(9.1e-4)0.2387_{{\scriptscriptstyle(9.1\text{e-}4)}}0.2400(8.5e-4)0.2400_{{\scriptscriptstyle(8.5\text{e-}4)}}0.2305(1.4e-3)0.2305_{{\scriptscriptstyle(1.4\text{e-}3)}}0.1260(8.3e-2)0.1260_{{\scriptscriptstyle(8.3\text{e-}2)}}
Behavior-centric
OPT Dunefsky and Cohan (2025)0.1138(1.2e-1)0.1138_{{\scriptscriptstyle(1.2\text{e-}1)}}0.0824(2.6e-1)0.0824_{{\scriptscriptstyle(2.6\text{e-}1)}}−0.0416(5.7e-1)-0.0416_{{\scriptscriptstyle(5.7\text{e-}1)}}0.0740(3.1e-1)0.0740_{{\scriptscriptstyle(3.1\text{e-}1)}}−0.0486(5.1e-1)-0.0486_{{\scriptscriptstyle(5.1\text{e-}1)}}0.0961(1.9e-1)0.0961_{{\scriptscriptstyle(1.9\text{e-}1)}}−0.0294(6.9e-1)-0.0294_{{\scriptscriptstyle(6.9\text{e-}1)}}0.0335(6.5e-1)0.0335_{{\scriptscriptstyle(6.5\text{e-}1)}}
COLD-Steer (FD) Sharma and Trivedi (2026)0.0309(9.1e-1)0.0309_{{\scriptscriptstyle(9.1\text{e-}1)}}−0.0877(2.3e-1)-0.0877_{{\scriptscriptstyle(2.3\text{e-}1)}}−0.0622(3.9e-1)-0.0622_{{\scriptscriptstyle(3.9\text{e-}1)}}0.0553(4.5e-1)0.0553_{{\scriptscriptstyle(4.5\text{e-}1)}}−0.0405(5.8e-1)-0.0405_{{\scriptscriptstyle(5.8\text{e-}1)}}0.0820(2.6e-1)0.0820_{{\scriptscriptstyle(2.6\text{e-}1)}}−0.0122(8.7e-1)-0.0122_{{\scriptscriptstyle(8.7\text{e-}1)}}0.0615(4.0e-1)0.0615_{{\scriptscriptstyle(4.0\text{e-}1)}}
BiPO Cao et al. (2024)0.1188(1.0e-1)0.1188_{{\scriptscriptstyle(1.0\text{e-}1)}}0.0491(5.0e-1)0.0491_{{\scriptscriptstyle(5.0\text{e-}1)}}−0.0666(3.6e-1)-0.0666_{{\scriptscriptstyle(3.6\text{e-}1)}}0.0099(8.9e-1)0.0099_{{\scriptscriptstyle(8.9\text{e-}1)}}0.1094(1.3e-1)0.1094_{{\scriptscriptstyle(1.3\text{e-}1)}}0.0532(4.7e-1)0.0532_{{\scriptscriptstyle(4.7\text{e-}1)}}0.0279(7.0e-1)0.0279_{{\scriptscriptstyle(7.0\text{e-}1)}}0.0539(4.6e-1)0.0539_{{\scriptscriptstyle(4.6\text{e-}1)}}
Appendix
Table 10: Robustness of Theory Rank Correlation ( ρT\rho_{\mathrm{T}} ) to dataset construction. Original denotes the main experimental setting; Disjoint uses a fresh non-overlapping subset of 200 examples per value; Paraphrased paraphrases the question and both contrastive answers; and SL-prio. uses the single-label-prioritized sensitivity subset. Subscripts denote pp -values. The paradigm-level separation is preserved across all robustness settings. Bold indicates the highest correlation within each setting.
MetricStructure testedWhat it measuresDefined in
Geometry of value vectors
Theory Rank Correlation ( ρT\rho_{T} )Continuous circumplexWhether compatible values rank above conflicting values in vector similaritySec. 3.3.1 App. § H
Theory Linear Correlation ( rTr_{T} )Continuous circumplexWhether empirical cosine similarities scale linearly with theoretical circumplex similaritiesSec. 3.3.1 App. § H
Hierarchical Structure Correlation ( ρH\rho_{H} )Discrete hierarchyWhether vector similarities respect lower-order families and higher-order groupsSec. 3.3.1 App. § H
Polarity Separation Score ( Δpol\Delta_{\mathrm{pol}} )Same-family vs. opposing groupsThe difference between mean within-family similarity and mean similarity across opposing groupsSec. 3.3.1 App. § H
Cross-value transfer
Appendix
Table 11: Summary of the evaluation metrics and the theoretical structure assessed by each metric. Geometry metrics evaluate relationships among extracted value vectors, while transfer metrics evaluate how steering effects propagate across values.
Figure 10: Residualized BMD- ρ\rho across steering methods on Qwen3.5-9B-Base and Llama3.1-8B, grouped by paradigm. Distribution-driven methods (blue) produce transfer patterns whose ordering decays monotonically with circumplex distance, while behavior-centric methods (orange) do not.
PredictorTWTMρHtr\rho_{H}^{\mathrm{tr}}
Geometric fidelity ( ρT\rho_{T} )0.84 ∗∗∗0.77 ∗∗
Target-value accuracy gain0.78 ∗∗∗0.59 ∗
Appendix
Table 12: Spearman correlations between two candidate predictors and cross-value transfer, pooled across 7 steering methods ×\times 2 backbones ( n=14n=14 ). Geometric fidelity is the stronger predictor on both transfer metrics. ∗p<0.05{}^{*}p<0.05 , ∗∗p<0.01{}^{**}p<0.01 , ∗∗∗p<0.001{}^{***}p<0.001 .
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