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Playing Along: Learning a Double-Agent Defender for Belief Steering via Theory of Mind RPA-Check: A Multi-Stage Automated Framework for Evaluating Dynamic LLM-based Role-Playing Agents A Triadic Suffix Tokenization Scheme for Numerical Reasoning Hidden Measurement Error in LLM Pipelines Distorts Annotation, Evaluation, and Benchmarking Synthius-Mem: Brain-Inspired Hallucination-Resistant Persona Memory Achieving 94.4% Memory Accuracy and 99.6% Adversarial Robustness on LoCoMo Time is Not a Label: Continuous Phase Rotation for Temporal Knowledge Graphs and Agentic Memory NovBench: Evaluating Large Language Models on Academic Paper Novelty Assessment 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 Polyglot Teachers: Evaluating Language Models for Multilingual Synthetic Data Generation 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 Evaluating Memory Capability in Continuous Lifelog Scenario How Robust Are Large Language Models for Clinical Numeracy? An Empirical Study on Numerical Reasoning Abilities in Clinical Contexts 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 OccuBench: Evaluating AI Agents on Real-World Professional Tasks via Language Environment Simulation Advancing Polish Language Modeling through Tokenizer Optimization in the Bielik v3 7B and 11B Series
The Cylindrical Representation Hypothesis for Language Mo...
Lang Gao, Jinghui Zhang, Wei Liu, Fengxian Ji, Chenxi Wang, Ziru · 2026-05-03 · via cs.CL updates on arXiv.org

Steering is a widely used technique for controlling large language models, yet its effects are often unstable and hard to predict. Existing theoretical accounts are largely based on the Linear Representation Hypothesis (LRH). While LRH assumes that concepts can be orthogonalized for lossless control, this idealized mapping fails in real representations and cannot account for the observed unpredictability of steering. By relaxing LRH's orthogonality assumption while preserving linear representations, we show that overlapping concept contributions naturally yield a sample-specific axis-orthogonal structure. We formalize this as the Cylindrical Representation Hypothesis (CRH). In CRH, a central axis captures the main difference between concept absence and presence and drives concept generation. A surrounding normal plane controls steering sensitivity by determining how easily the axis can activate the target concept. Within this plane, only specific sensitive sectors strongly facilitate concept activation, while other sectors can suppress or delay it. While the surrounding normal plane can be reliably identified from difference vectors, the sensitive sector cannot, introducing intrinsic uncertainty at the sector level. This uncertainty provides a principled explanation for why steering outcomes often fluctuate even when using well-aligned directions. Our experiments verify the existence of the cylindrical structure and demonstrate that CRH provides a valid and practical way to interpret model steering behavior in real settings: https://github.com/mbzuai-nlp/CRH.