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Policy Split: Incentivizing Dual-Mode Exploration in LLM Reinforcement with Dual-Mode Entropy Regularization METER: Evaluating Multi-Level Contextual Causal Reasoning in Large Language Models Think Before you Write: QA-Guided Reasoning for Character Descriptions in Books METRO: Towards Strategy Induction from Expert Dialogue Transcripts for Non-collaborative Dialogues Retrieval as Generation: A Unified Framework with Self-Triggered Information Planning Do LLMs Know Tool Irrelevance? Demystifying Structural Alignment Bias in Tool Invocations Enhancing Multimodal Large Language Models for Ancient Chinese Character Evolution Analysis via Glyph-Driven Fine-Tuning Exploring Knowledge Conflicts for Faithful LLM Reasoning: Benchmark and Method CocoaBench: Evaluating Unified Digital Agents in the Wild MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis Efficient Training for Cross-lingual Speech Language Models Shared Emotion Geometry Across Small Language Models: A Cross-Architecture Study of Representation, Behavior, and Methodological Confounds A Systematic Analysis of the Impact of Persona Steering on LLM Capabilities Uncertainty-Aware Web-Conditioned Scientific Fact-Checking When Valid Signals Fail: Regime Boundaries Between LLM Features and RL Trading Policies When Verification Fails: How Compositionally Infeasible Claims Escape Rejection Mem$^2$Evolve: Towards Self-Evolving Agents via Co-Evolutionary Capability Expansion and Experience Distillation AOP-Smart: A RAG-Enhanced Large Language Model Framework for Adverse Outcome Pathway Analysis Advancing Polish Language Modeling through Tokenizer Optimization in the Bielik v3 7B and 11B Series TInR: Exploring Tool-Internalized Reasoning in Large Language Models Do BERT Embeddings Encode Narrative Dimensions? A Token-Level Probing Analysis of Time, Space, Causality, and Character in Fiction Generating Multiple-Choice Knowledge Questions with Interpretable Difficulty Estimation using Knowledge Graphs and Large Language Models Deep-Reporter: Deep Research for Grounded Multimodal Long-Form Generation Too Nice to Tell the Truth: Quantifying Agreeableness-Driven Sycophancy in Role-Playing Language Models Learning and Enforcing Context-Sensitive Control for LLMs Efficient Process Reward Modeling via Contrastive Mutual Information Computational Lesions in Multilingual Language Models Separate Shared and Language-specific Brain Alignment Bridging Linguistic Gaps: Cross-Lingual Mapping in Pre-Training and Dataset for Enhanced Multilingual LLM Performance Early Decisions Matter: Proximity Bias and Initial Trajectory Shaping in Non-Autoregressive Diffusion Language Models LLMs Should Incorporate Explicit Mechanisms for Human Empathy
When Is Rank-1 Steering Cheap? Geometry, Granularity, and...
John T. Robertson, Jianing Zhu, Haris Vikalo, Zhangyang Wang · 2026-05-09 · via cs.AI updates on arXiv.org

Activation steering offers a lightweight way to control LLMs without retraining, but its effectiveness varies sharply across concepts. Prior work often reads this variability as evidence that many concepts are not captured by a single steering direction. We argue instead that much of it reflects search difficulty: a useful rank-1 intervention often exists, but finding it can be expensive. We formalize rank-1 steering as a budget-constrained optimization over intervention layer and coefficient. Across concepts and model families, prompt-boundary directional alignment predicts where effective interventions occur, enabling geometry-guided search that reaches high utility with substantially fewer evaluations, reducing the trials needed to recover 95% of best-found utility by 39.8% on average across three model families. To explain why some concepts remain expensive even under better search, we introduce concept granularity, a measure of directional heterogeneity across contrastive contexts. Granularity distinguishes concepts whose difference vectors share a stable global direction from those where prompts agree locally within each input but the utility-maximizing direction rotates systematically across inputs. Higher granularity is associated with slower convergence and lower best-found performance (Pearson $r{=}0.44$ with trials-to-95%, $r{=}{-}0.46$ with best-found utility, both $p<0.001$). We present GRACE, a Granularity- and Representation-Aware Concept Engineering framework that uses activation geometry to diagnose the dominant source of steering difficulty, select the appropriate remedy, and allocate optimization effort efficiently. Our results shift the frame from "when does rank-1 fail?" to "when is rank-1 cheap and stable?", turning activation geometry from a descriptive tool into an actionable prior for LLM control.