Hallucinations Live in Variance

TL;DR

This paper introduces the concept of hallucinations as variance-driven unreliability in AI models, proposing Semantic Stability and Paraphrase Consistency as diagnostic tools to measure and understand this phenomenon.

Contribution

It formalizes hallucinations as variance in model outputs, introduces Semantic Stability and Paraphrase Consistency metrics, and analyzes how model sparsity affects reliability and stability.

Findings

Dense Qwen3-0.6B agrees with itself only 23.8% of the time

At 32% sparsity, agreement increases to 55.9%

A phase diagram identifies regimes where variance reduction improves stability

Abstract

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.