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

• URL: http://arxiv.org/abs/2602.00426v1
• Date: Sat, 31 Jan 2026 00:37:53 GMT
• Title: LLMs as High-Dimensional Nonlinear Autoregressive Models with Attention: Training, Alignment and Inference
• Authors: Vikram Krishnamurthy,
• Abstract summary: Large language models (LLMs) based on transformer architectures are typically described through collections of architectural components and training procedures.<n>We formulate LLMs as high-dimensional nonlinear autoregressive models with attention-based dependencies.
• Score: 15.493230983626281
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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