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When Is Rank-1 Steering Cheap? Geometry, Granularity, and Budgeted Search

NeurIPS 2026 · Large language models › Language, safety and interpretability · approach: Task vectors and steering · 0 citations (OpenAlex)

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Frames rank-1 activation steering as a budget-constrained search over layer and coefficient, uses prompt-boundary alignment to prune layers (39.8% fewer trials to 95% utility), and introduces concept granularity to explain which concepts stay hard, packaged as the GRACE workflow.

Problem

Rank-1 activation steering performance varies sharply across concepts; prior work attributes this to concepts not being captured by a single direction, but the paper argues the main obstacle is the expensive optimization of layer and coefficient.

Approach

Prompt-boundary directional alignment of contrastive differences predicts useful steering layers and restricts TPE search to top-15 layers; concept granularity (ratio of within-question to overall alignment) measures cross-context directional rotation that limits best-found steering utility and slows convergence.

Key results

• Geometry-constrained TPE search (top-15 layers) reduces trials to 95% of best-found utility from 13.7 to 8.2 (39.8% reduction) across three models, with best-found utility changing by only 0.16 on average.
• Concept granularity correlates with trials-to-95% (r = 0.44, p < 0.001) and with best-found utility (r = -0.46, p < 0.001).
• Cross-judge agreement on concept score is high (Pearson r >= 0.83) across GPT-4.1 mini, Nova 2 Lite, and gemma-3-12b-it, though absolute calibration differs by up to 19 points.

Surprising findings

• Alignment-based layer restriction noticeably hurts steerability on 8 of 60 (model, concept) pairs, attributed to representational fragmentation between prompt-boundary and response-averaged variants.
• Prompting baselines reach high utility on many concepts, and high-granularity concepts remain below the prompting baseline even after extended search.

Limitations

• Granularity correlations are moderate and described as a consistent trend rather than a deterministic law.
• Evaluation relies on LLM judges with substantial absolute calibration differences; only 20 concepts are studied.
• The search is restricted to a two-parameter space (layer, coefficient) with a fixed budget of 50 trials.

Experimental setup

Datasets: 20 LLM-generated concept contrastive prompt pairs and extraction/evaluation questions (generated by GPT-5 from concept d

Benchmarks: 20 concept steering tasks (Neuronpedia/SAE-inspired concepts)

Metrics: concept score coherence steering utility T95 (trials to 95% of best-found utility) Pearson/Spearman correlation

Baselines: AxBench prompting baseline (mean-prompt) grid search over layers full-layer TPE search

Builds on: PersonaVectors Contrastive activation addition Tree-structured Parzen Estimator

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