Hallucination Detection and Reduction in Open-Source Large Language Models via the Kerimov–Alekberli Information-Geometric Framework: Empirical Evaluation on HaluEval, FEVER, and SimpleQA

Background: Hallucination the generation of factually incorrect, internally in consistent, or ungrounded content remains a critical barrier to safe LLM deployment in high-stakes domains. Existing detection methods typically require external knowledge bases, model ne-tuning, or cloud API access, limiting applicability in local inference contexts. Methods: We evaluate the Kerimov–Alekberli (K–A) information-geometric framework as a real-time, inference-time hallucination detector across six open-source LLMs deployed locally on Apple M5 Silicon via Ollama v0.23.2 (Q4_K_M quantisation). The K–A framework monitors the KL divergence between consecutive output distributions relative to a Fisher Information Metric (FIM)-derived threshold (τ = 0.065), triggering First-Passage Time (FPT) alarms when generation departs from the stable Riemannian output manifold. We evaluate 120 responses (6 models × 20 questions) drawn from three established benchmarks: HaluEval (14 questions; categories: Fact, Confuse, Date, Num, Trap), FEVER (4 questions; adversarial fact verification), and SimpleQA (2 questions; precise factual recall). All questions are classified as difficulty level Hard, targeting known LLM failure modes including o-by-one numerical errors, geographical traps, and disputed-attribution confounds. Results: The K–A framework achieves a session hallucination detection rate of 90.9% (20/22 hallucinated responses correctly flagged) with zero false positives on correct responses (0/98). Model-level hallucination rates vary dramatically: deepseekr1:latest (Qwen3 CoT architecture, 5.2GB) exhibits a 95% hallucination rate (19/20 questions) with 100% K–A detection; gemma3:27b (Gemma3, 17.4GB) and gemma3:latest (4.3B, 3.3GB) achieve 0% hallucination. Two K–A false negatives involve con dent factual errors below the KL threshold. Average KL divergence for hallucinated responses (D̅_KL = 0.068 ± 0.004) is significantly higher than for correct responses (D̅_KL = 0.042 ± 0.016). Conclusions: K–A achieves competitive hallucination detection without external knowledge bases, ne-tuning, or cloud infrastructure, processing each response in real time with negligible overhead. The deepseek-r1 result reveals a fundamental tension between chain-of thought reasoning depth and factual precision on concise queries that warrants systematic investigation.