# Hallucinations Live in Variance

arXiv: https://arxiv.org/abs/2601.07058 · HTML: https://mlsanity.com/paper/2601.07058/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 11 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [HalluLens: LLM Hallucination Benchmark](https://mlsanity.com/paper/2504.17550/) (2025)
- [The Illusion of Progress: Re-evaluating Hallucination Detection in LLMs](https://mlsanity.com/paper/2508.08285/) (2025)
- [Reliability-Aware Adaptive Self-Consistency for Efficient Sampling in LLM Reasoning](https://mlsanity.com/paper/2601.02970/) (2026)
- [Sparse Knowledge Distillation: A Mathematical Framework for Probability-Domain Temperature Scaling and Multi-Stage Compression](https://mlsanity.com/paper/2601.03195/) (2026)
- [Consistency Is the Key: Detecting Hallucinations in LLM Generated Text By Checking Inconsistencies About Key Facts](https://mlsanity.com/paper/2511.12236/) (2025)
- [Reducing Hallucinations in LLMs via Factuality-Aware Preference Learning](https://mlsanity.com/paper/2601.03027/) (2026)
- [Mitigating Prompt-Induced Hallucinations in Large Language Models via Structured Reasoning](https://mlsanity.com/paper/2601.02739/) (2026)
- [KDCM: Reducing Hallucination in LLMs through Explicit Reasoning Structures](https://mlsanity.com/paper/2601.04086/) (2026)

## Built on by (most cited first, 4 of 4)

- [Multi-Teacher Ensemble Distillation: A Mathematical Framework for Probability-Domain Knowledge Aggregation](https://mlsanity.com/paper/2601.09165/) (2026)
- [Recursive Meta-Distillation: An Axiomatic Framework for Iterative Knowledge Refinement](https://mlsanity.com/paper/2601.13100/) (2026)
- [Adaptive Weighting in Knowledge Distillation: An Axiomatic Framework for Multi-Scale Teacher Ensemble Optimization](https://mlsanity.com/paper/2601.17910/) (2026)
- [Post-Training Probability Manifold Correction via Structured SVD Pruning and Self-Referential Distillation](https://mlsanity.com/paper/2602.00372/) (2026)

## Abstract (arXiv)

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.