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Steering Geometry: Validating Human Value Geometry in LLM Steering Space
Mohammad Mahdi Abootorabi, Armin Saghafian, Ali Bazshoushtari, Hamid Rezaei, EunJeong Hwang, Vered Shwartz, Parvin Mousavi, Purang Abolmaesumi
TL;DR
Existing steering evaluations often measure isolated behavior changes without testing whether steering vectors preserve human-value structure. The paper builds a Schwartz-based benchmark and compares steering paradigms across models. Distribution-driven methods recover theory-consistent geometry and transfer more consistently across values, whereas behavior-centric methods show comparable target steering but little geometric alignment.
Problem
Existing steering work typically validates isolated behavior changes, leaving whether steering vectors encode coherent human-value structure unresolved.
Method
The paper constructs a roughly 26K-sample Schwartz benchmark, extracts value directions, and evaluates geometry and cross-value transfer across steering methods and models.
Results
Distribution-driven methods achieve stronger theory-consistent geometry than behavior-centric methods, despite comparable steering performance; geometric fidelity also improves with scale and declines after instruction tuning.
Takeaways & Limitations
Better geometric alignment is associated with more human-consistent transfer, lifting compatible values and suppressing opposing ones.
Takeaways & Limitations
The evaluation centers on Schwartz’s theory and provides only family-level validation under MFT, leaving broader cultural and theoretical generalization open.
Abstract
from arXiv · showhide
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 $ρ$ up to 0.51, $p < 10^{-13}$). 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.
1 Introduction
The paper asks whether activation-steering vectors encode coherent human-value relationships rather than behavior-specific shortcuts. Using Schwartz’s circumplex as a theory-grounded test, it finds distribution-driven methods recover expected structure while behavior-centric methods do not despite similar steering performance.
- Motivation: Existing steering evaluations usually test isolated behaviors, leaving the semantic structure of steering vectors unresolved.The paper frames this as a distinction between meaningful value representations and behavior-specific shortcuts.
- Motivation: Schwartz’s theory represents values on a circumplex where angular proximity predicts compatibility and opposition.Benevolence and Universalism are compatible, whereas Self-Direction and Conformity are opposed.
- Findings: Distribution-driven methods align with the expected value structure, reaching Spearman ρ up to 0.51 with p < 10^-13.Behavior-centric methods show near-zero correlation despite comparable steering performance.
- Findings: Geometric alignment is stronger in larger and newer model families but weaker after instruction tuning.The authors interpret this pattern as a conflict between post-training and richer internal value representations.
- Findings: Methods with better human-value geometry transfer more consistently across values, improving compatible values and suppressing opposing ones.This links geometric fidelity to behavioral cross-value consistency.
2 Related Work
Prior work establishes activation steering and linear interpretability, while value research provides psychological frameworks for organizing human values. The paper addresses the unstudied question of whether steering-vector geometry preserves those frameworks.
- Activation Steering and Representation Engineering: Activation steering controls behavior at inference time by manipulating internal representations without updating model weights.Existing approaches include distribution-driven directions and other representation-engineering methods.
- Human Value Analysis in LLMs: Schwartz’s theory organizes universal motivations in a circumplex, clustering compatible values and separating opposing ones.This provides a structured target for evaluating value geometry.
- LLM Activation Space Interpretability: The linear representation hypothesis motivates interpreting high-level concepts, behaviors, and values as directions in the residual stream.Sparse Autoencoders are used in related work to isolate more interpretable features from polysemantic activations.
- Research Gap: Prior steering studies typically evaluate target-behavior change, not whether extracted vectors preserve established human-value relationships.The paper fills this gap with a contrastive benchmark covering the full Schwartz taxonomy.
3 Methodology
The methodology builds theory-grounded contrastive data, extracts one value direction per Schwartz value and method, then evaluates both geometric alignment and cross-value transfer.
- Dataset Construction: The benchmark contains almost 26K contrastive samples spanning 20 Schwartz values, with an additional 1.2K MFT samples for cross-framework evaluation.The Schwartz data are based on contrastive question-answer pairs, while MFT tests family-level generalization.
- Value Direction Extraction: Each method is represented by a value direction v(b,ℓ), the effective residual-stream shift induced for value b at layer ℓ.Directions across all 20 values form a per-method vector bank for geometry analysis.
- Value Geometry Evaluation: Geometry evaluation compares empirical vector similarities with angular relationships in the Schwartz circumplex and measures hierarchical and polarity alignment.Metrics include Theory Rank Correlation, Hierarchical Structure Correlation, and Polarity Separation Score.
- Cross-Value Steering Transfer: Cross-value transfer records how steering toward one value changes held-out performance on each other value, producing a 20 × 20 transfer matrix.Two-way centering removes source-strength and target-difficulty effects before evaluating pair-specific transfer.
- Cross-Value Steering Transfer: Continuous Transfer Fidelity weights residualized transfer by theoretical Schwartz affinity, rewarding positive transfer between adjacent values and negative transfer between opposing values.The metric captures both transfer shape and magnitude on the circumplex.
4 Experimental Setup
The experiments compare distribution-driven and behavior-centric steering across model families, model sizes, and tuning regimes. Controlled evaluations use multiple backbones and a common contrastive-data and layer-selection procedure.
- Steering Methods: The study evaluates distribution-driven and behavior-centric steering paradigms, including CAA, SAS, SphericalSteer, and ODESteer.The paradigms differ in how they derive or apply steering directions.
- Models: CAA is evaluated across seven pretrained model families, including Llama3.1, Mistral, Falcon, Qwen, and Gemma variants.This comparison examines model-family and scale effects on geometry.
- Controlled Comparison: All methods are tested on Qwen3.5-9B Base and Instruct variants and Llama3.1-8B Base for controlled comparison.For each value, the setup samples 200 contrastive prompt pairs with a 90/10 train/test split.
- Controlled Comparison: The intervention layer is selected by maximizing a combined criterion of Normalized L2 Separation and Linear Probe Accuracy.This provides a common layer-selection rule across methods.
5 Results and Discussion
Results show that distribution-driven steering methods preserve human-value geometry and transfer patterns more faithfully than behavior-centric methods. Geometric fidelity also varies with model family, scale, and instruction tuning, and predicts cross-value transfer.
- Steering method: Distribution-driven methods yield strong value-geometry alignment, whereas behavior-centric methods show no statistically significant correlation despite comparable dataset steering results.The same method-level pattern holds on Llama3.1-8B; behavior-centric methods may achieve desired outputs through shortcut vectors.
- Model scale and family: At 7–9B, ρT rises from Falcon-7B (0.20) to Mistral-7B (0.32), Llama-3.1-8B (0.37), and Qwen3.5-9B (0.46).Qwen3.5 outperforms Qwen2.5 across scales, while Gemma-4-31B reaches ρT 0.38 versus Qwen3.5-4B at 0.41.
- Instruction tuning: All methods show consistent degradation in geometric alignment when moving from base to instruction-tuned models.The authors describe this as value geometry drift, with instruction-tuned activation spaces preserving less latent value structure than pretrained models.
- Cross-value transfer: Across values, distribution-driven methods achieve high geometric fidelity and strongly transfer, while behavior-centric methods cluster near zero on TWTM and ρtrH.The separation also holds under the shape-only BMD-ρ metric, although target-only steering performance is comparable.
- Cross-value transfer: Geometric fidelity predicts cross-value transfer more strongly than raw accuracy gain, with correlation gaps of ∆ρ = 0.06 on TWTM and ∆ρ = 0.18 on ρtrH.This comparison pools all methods and both backbones, with the gap widening on the rank-based hierarchical metric.
- Cross-value transfer: Methods that preserve Schwartz structure in their vectors reflect it behaviorally, whereas behavior-optimized methods shift related values less predictably.This links representational fidelity to the predictability of cross-value behavioral effects.
6 Conclusion
The study finds a clear separation between steering paradigms: distribution-driven methods preserve theory-consistent value relationships, while behavior-centric methods achieve target accuracy but lose that structure. It argues that psychological structure should be evaluated alongside behavioral accuracy.
- Distribution-driven methods capture theory-consistent relationships and propagate them across the value space.
- Behavior-centric methods achieve comparable target accuracy but lose value structure and shift related values unpredictably.
- The authors encourage evaluating steering on psychological structure alongside behavioral accuracy.
7 Limitations
The analyses visualize how empirical value geometry aligns with Schwartz’s theoretical structure, while the paper identifies important scope boundaries around its frameworks and vector interpretation.
- Scope and limitations: The fine-grained geometry and transfer analyses center on Schwartz, while MFT provides only family-level validation rather than a full geometric test.
- Scope and limitations: Extracted vectors should be interpreted as target-conditioned aggregate directions rather than perfectly monosemantic representations.
- Scope and analysis: The study visualizes emergent value geometry and examines variation across model scales and architectures.
- Geometric evidence: Figures 8 and 9 use SAS to show alignment between theoretical and empirical value structures.
- Geometric evidence: Compatible values show high cosine similarity, while conflicting values show low or negative similarity in the empirical measurements.
C Additional Results on Llama 3.1-8B
Results on Llama 3.1-8B reproduce the paradigm-level distinction observed on Qwen 3.5-9B: distribution-driven methods better recover the Schwartz circumplex, while behavior-centric methods show weak geometric fidelity.
- CAA achieves the strongest Schwartz-circumplex alignment on Llama 3.1-8B, with ρT = 0.50 and p < 10^-12.
- The Llama results reproduce the same distribution-driven versus behavior-centric pattern reported for Qwen 3.5-9B.
- The Schwartz framework places more similar values near one another and conflicting values on opposite sides of a circular structure.
- Behavior-centric methods produce non-trivial behavioral gains but remain close to zero or negative on most geometry metrics.
D Further Scale Analysis
Further analyses examine scale effects, datasets, and evaluation resources for value-vector experiments. Across model families, theory alignment improves monotonically with scale, while raw-activation baselines vary only modestly and non-monotonically.
- Scale analysis: SphericalSteer evaluations span Qwen3.5 models from 0.8B to 9B and Qwen2.5 models from 7B to 32B.
- Scale analysis: Theory alignment improves monotonically across both evaluated model families, whereas raw-activation baselines vary only modestly and non-monotonically.
- Scale analysis: The raw-activation baseline ranges from ρT = 0.16–0.22 on Qwen3.5 and 0.14–0.19 on Qwen2.5.
- Datasets and metrics: The datasets support extracting and evaluating value vectors across the 20 Schwartz value categories.
- Datasets and metrics: ValueBench contributes 911 filtered samples after mapping items to the Schwartz values and generating missing answers.
E.2 Dataset Statistics
The benchmark contains 26,428 contrastive quadruples across 20 Schwartz value categories, with most examples drawn from Touché23-ValueEval. The analysis also examines robustness to dataset construction and extracted-direction properties.
- Dataset composition: 26,428 contrastive quadruples remain after quality filtering across the two dataset sources.Touché contributes 25,517 samples (96.6%), while ValueBench contributes 911 (3.4%).
- Dataset composition: The dataset is organized around the 20 Basic Human Values of Refined Schwartz Theory.The value categories and their motivational goals are summarized in the paper’s value taxonomy.
- Answer construction: Negative answers use six strategies spanning pragmatic, empirical, counter-example, side-effects, institutional, and contradict arguments.These strategies diversify the contrastive construction rather than relying on a single response style.
- Robustness design: Robustness analyses re-extract vectors for all seven methods across Qwen3.5-9B-Base and Llama3.1-8B under multiple dataset settings.The settings test sample selection, surface wording, and multi-value annotations.
F.1 Sample Selection and Surface Wording
The study tests whether its geometry findings depend on generated-answer artifacts, sample selection, paraphrasing, or multi-value annotations. Across these checks, the distribution-driven versus behavior-centric separation remains evident, while MFT offers only family-level validation.
- Surface wording: Generated answers average 26.8 tokens versus 22.2 for corresponding human-written answers and use six negative-answer prompting strategies.The controls target length imbalance and dependence on a single stylistic template.
- Sample quality: An audit of 100 generated examples judged 89% valid, with value leakage and insufficient contrast as the primary failure modes.The audit sampled five examples from each Schwartz value.
- Robustness results: The paradigm-level separation persists across disjoint and paraphrased datasets, with CAA and SAS significant across both backbones and all three settings.Distribution-driven methods retain theory alignment, whereas behavior-centric methods remain close to zero.
- Multi-value annotations: The authors interpret each target-value direction as a target-conditioned aggregate rather than a perfectly monosemantic representation.Real-world arguments can express several values and receive multiple annotations.
- Multi-value annotations: In the single-label-prioritized analysis, distribution-driven methods retain higher ρT than behavior-centric methods on Qwen3.5-9B-Base.CAA, SAS, SphericalSteer, and ODESteer obtain 0.325, 0.309, 0.355, and 0.256, respectively, versus 0.010, 0.074, and 0.055 for BiPO, OPT, and COLD-Steer.
- MFT scope: MFT evaluation tests only the Individualizing–Binding grouping because MFT specifies no circumplex or finer inter-foundation relations.This makes the MFT analysis a family-level rather than full geometric validation.
H Geometry Metrics
The paper evaluates steering geometry with complementary vector-geometry and cross-value-transfer metrics grounded in Schwartz’s circumplex. Distribution-driven methods show the expected distance-ordered transfer pattern, whereas behavior-centric methods can invert it.
- Metric framework: The evaluation covers vector geometry and cross-value transfer across continuous circumplex and discrete hierarchical structures.The metric suite is summarized as complementary measures rather than a single established score.
- Theory alignment: The theoretical similarity matrix assigns values cosine similarity according to shortest angular distance on the 20-value circumplex.Adjacent compatible values approach 1, while diametrically opposed values approach −1.
- Transfer geometry: BMD-ρ measures the negative Spearman correlation between circumplex distance and mean residual transfer across ten distance bins.The prediction is positive transfer for adjacent values, negative transfer for opposing values, and smooth decay between them.
- Results: Distribution-driven methods on Llama score 0.43–0.99 for BMD-ρ, while behavior-centric methods collapse to negative values.Negative BMD-ρ indicates transfer ordering opposite to the circumplex prediction.
- Method comparison: Effective-shift vectors place nonlinear ODESteer and norm-preserving SphericalSteer on a common comparison basis, despite discarding trajectory information.The cross-value transfer evaluation independently measures behavioral effects on held-out values.
- Predictive analysis: The analysis compares geometric fidelity, target-value accuracy gain, and cross-value transfer across seven methods and two backbones.Geometric fidelity is reported as the stronger predictor of transfer in the pooled analysis.