# LLMs as High-Dimensional Nonlinear Autoregressive Models with Attention: Training, Alignment and Inference

arXiv: https://arxiv.org/abs/2602.00426 · HTML: https://mlsanity.com/paper/2602.00426/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Red Teaming Language Models with Language Models](https://mlsanity.com/paper/2202.03286/) (2022)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)

## Built on by (most cited first, 2 of 2)

- [Temperature-driven inversion and nonlinear dynamics in ChatGPT-like AIs](https://mlsanity.com/paper/2608.00939/) (2026)
- [Transformer-like Inference from Optimal Control](https://mlsanity.com/paper/2605.15608/) (2026)

## Abstract (arXiv)

Large language models (LLMs) based on transformer architectures are typically described through collections of architectural components and training procedures, obscuring their underlying computational structure. This review article provides a concise mathematical reference for researchers seeking an explicit, equation-level description of LLM training, alignment, and generation. We formulate LLMs as high-dimensional nonlinear autoregressive models with attention-based dependencies. The framework encompasses pretraining via next-token prediction, alignment methods such as reinforcement learning from human feedback (RLHF), direct preference optimization (DPO), rejection sampling fine-tuning (RSFT), and reinforcement learning from verifiable rewards (RLVR), as well as autoregressive generation during inference. Self-attention emerges naturally as a repeated bilinear--softmax--linear composition, yielding highly expressive sequence models. This formulation enables principled analysis of alignment-induced behaviors (including sycophancy), inference-time phenomena (such as hallucination, in-context learning, chain-of-thought prompting, and retrieval-augmented generation), and extensions like continual learning, while serving as a concise reference for interpretation and further theoretical development.