Modeling Memory-Dependent Reliability of LLMs: A Hidden Markov Model

arXiv:2607.22951 · stat.ML, cs.AI, cs.LG · Submitted 2026-07-24 · Read on arXiv

Robab Aghazadeh Chakherlou, Siddartha Khastgir, Peter Popov, Xingyu Zhao

stat.ML, cs.AI, cs.LG

Submitted: 2026-07-24

Code: https://github.com/llmReliability/hmm-llm-reliability-proof

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 19× in this paper · explained in 2 episodes
• Hidden Markov Model — 13× in this paper
• Hyperparameters — 6× in this paper · explained in 2 episodes
• Bayesian Framework — 5× in this paper · explained in 3 episodes
• Clustering — 5× in this paper · explained in 2 episodes
• Hierarchical Structure — 5× in this paper · explained in 3 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Bayesian Inference — 3× in this paper · explained in 6 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Calibration — 2× in this paper · explained in 9 episodes
• Conditional Independence — 2× in this paper · explained in 2 episodes
• Language Models (LLMs) — 2× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 2× in this paper · explained in 9 episodes
• Papers — 2× in this paper · explained in 3 episodes
• Parsimony — 2× in this paper · explained in 2 episodes
• Transformer — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Bayes Factor — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 4 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Confidence Calibration — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Feedback Loop — 1× in this paper · explained in 2 episodes
• Hierarchical Framework — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Model Dependence — 1× in this paper · explained in 3 episodes
• Monte Carlo Sampling — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Transformers — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes

Sources

• Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations
• HiBayES: A Hierarchical Bayesian Modeling Framework for AI Evaluation Statistics
• Pre-trained Large Language Models Learn Hidden Markov Models In-context
• Large Language Models as Markov Chains
• From Self-Attention to Markov Models: Unveiling the Dynamics of Generative Transformers

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