Old Habits Die Hard

How Conversational History Geometrically Traps LLMs

Adi Simhi1 Fazl Barez2 Martin Tutek3 Yonatan Belinkov1,4 Shay B. Cohen5
1Technion -IIT 2University of Oxford & Martian 3University of Zagreb 4Kempner Institute, Harvard University 5University of Edinburgh
Paper Code BibTeX

How does conversational history influence LLM behavior? Carryover effect indicates that once phenomena like hallucinations, refusal, or sycophancy manifest, they tend to persist across subsequent turns. We introduce HISTORY-ECHOES, a framework for investigating the carryover effect. Our framework contains two perspectives: probabilistically, we model conversations as Markov chains; geometrically, we analyze hidden representations. Our key finding: these perspectives strongly correlate, revealing that behavioral persistence manifests as a geometric trap where gaps in latent space confine the model's trajectory.

⚡ Interactive: Understanding the Framework

Click through to see how we analyze conversational history through two complementary perspectives.

What is the capital of Germany? Berlin What is the capital of France? Rome What is the capital of USA? New York φ⁻ φ⁺ φ⁺ Probabilistic Perspective φ⁺ φ⁻ P(φ⁺|φ⁺) P(φ⁻|φ⁻) Geometric Perspective h_φ⁻ h_φ⁺ θ_ref

Step 1: We start with a conversation where the model exhibits a phenomenon (φ⁺ = hallucination) after initially being correct (φ⁻). Notice how the phenomenon persists across turns.

Key Contributions

Dual-Perspective Framework

We introduce a novel framework combining probabilistic Markov chain analysis (Tr(T) > 1 indicates persistence) with geometric analysis of hidden states (θ_ref measures separation).

Strong Correlation

Spearman correlation of 0.78 across 3 models and 6 datasets between the probabilistic & geometric perspectives.

Closed Models: GPT-5 and Claude Opus 4.5 exhibit probabilistic patterns relatively similar with open-weight models, indication that closed models may also be subject to internal geometric traps.

Specific Effects

1.Refusal exhibits the strongest carryover effect, hallucination the weakest.

2.Context coherence is impoartant—inconsistent conversations dissolve the geometric trap.

Results Across Models

Phenomenon Dataset Tr(T) ↑ θ_ref (°) ↑ Interpretation
Refusal Sorry 1.57 51.87 Strongest carryover
Refusal Do-Not-Answer 1.59 42.29 Strongest carryover
Sycophancy S-pos 1.33 21.63 Moderate carryover
Sycophancy S-neg 1.14 24.80 Moderate carryover
Hallucination NaturalQA 1.13 10.88 Weakest carryover
Hallucination TriviaQA 1.12 11.12 Weakest carryover

Values averaged across LLaMA-3.1-8B, Qwen-8B, and GPT-OSS-20B.