The Probabilistic Structure of Large Language Models

arXiv:2609.25134 · cs.LG, cs.AI, math.PR, stat.ML · Submitted 2026-09-20 · Read on arXiv

cs.LG, cs.AI, math.PR, stat.ML

Submitted: 2026-09-20

Updated: 2026-09-20

Comments: Expository article on the probabilistic structure of large language models, 27 pages

Project page: https://jalammar.github.io

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

Terminology

• Transformer — 20× in this paper · explained in 2 episodes
• Diffusion Model — 16× in this paper · explained in 8 episodes
• Diffusion Models — 16× in this paper · explained in 6 episodes
• Score Function — 8× in this paper · explained in 4 episodes
• Generative AI — 5× in this paper · explained in 2 episodes
• Generative Modeling — 5× in this paper · explained in 3 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Calibration — 4× in this paper · explained in 7 episodes
• Hallucination — 4× in this paper · explained in 4 episodes
• Generative Model — 3× in this paper · explained in 2 episodes
• Generative Models — 3× in this paper · explained in 2 episodes
• Langevin Dynamics — 3× in this paper · explained in 2 episodes
• Denoising Diffusion Probabilistic Models — 2× in this paper
• Diffusion Process — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Large Language Models (LLMs) — 2× in this paper · explained in 6 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Normalizing Flow — 2× in this paper · explained in 3 episodes
• Normalizing Flows — 2× in this paper · explained in 4 episodes
• Perplexity — 2× in this paper · explained in 3 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adaptive Strategy — 1× in this paper · explained in 1 episode
• Adaptivity — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Attention Mechanism — 1× in this paper · explained in 3 episodes
• Computational Biology — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Latent Diffusion Model — 1× in this paper · explained in 2 episodes
• Latent Diffusion Models — 1× in this paper · explained in 2 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Stochastic Gradient Descent (SGD) — 1× in this paper · explained in 5 episodes
• Transformer Models — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Neural Machine Translation by Jointly Learning to Align and Translate
• Classifier-Free Diffusion Guidance
• Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial

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