Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference

• URL: http://arxiv.org/abs/2402.03175v2
• Date: Tue, 24 Sep 2024 13:30:25 GMT
• Title: Beyond the Black Box: A Statistical Model for LLM Reasoning and Inference
• Authors: Siddhartha Dalal, Vishal Misra,
• Abstract summary: This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs) We develop a theoretical framework based on an ideal generative text model represented by a multinomial transition probability matrix with a prior, and examine how LLMs approximate this matrix.
• Score: 0.9898607871253774
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a novel Bayesian learning model to explain the behavior of Large Language Models (LLMs), focusing on their core optimization metric of next token prediction. We develop a theoretical framework based on an ideal generative text model represented by a multinomial transition probability matrix with a prior, and examine how LLMs approximate this matrix. Key contributions include: (i) a continuity theorem relating embeddings to multinomial distributions, (ii) a demonstration that LLM text generation aligns with Bayesian learning principles, (iii) an explanation for the emergence of in-context learning in larger models, (iv) empirical validation using visualizations of next token probabilities from an instrumented Llama model Our findings provide new insights into LLM functioning, offering a statistical foundation for understanding their capabilities and limitations. This framework has implications for LLM design, training, and application, potentially guiding future developments in the field.

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