Exploring AI Prompt Engineering: Mathematical Foundations and RAG Methodologies

Author(s): Shenggang Li

Originally published on Towards AI.

Photo by ZHENYU LUO on Unsplash

We first represent a Large Language Model (LLM) with the formula:

It looks simple, However, if we want to understand its application and the AI techniques on LLMs, we need to interpret 𝜔, 𝑋, and 𝑌 as specific items within the LLM framework.

LLM Weights (ω)

The parameter set 𝜔 is neural network weights (model coefficients) and biases, updated during model training. 𝜔 can affect LLMs responses, but remain fixed unless fine-tuning is performed. The parameters can be expressed as a vector:

Where 𝑛 is the number of parameters, which can be in the billions for modern LLMs. However, these parameters are not the focus of this paper, as we aim at AI prompt engineering and RAG methodologies.

Model Input (X):

The input 𝑋 includes several items working together to generate a prediction 𝑌:

· X_query: A specific question or request from users.

· X_prompt: The initial prompt set by the developer.

· X_RAG Prompts: Additional prompts (documents), retrieved from data source D based on the X_query.

· X_parameters: Parameters like temperature, max tokens, and stream options

Where X_parameters are not model training parameters (e.g., learning rate, number of neural network layers), but they play a similar role in affecting the LLM behavior during inference If… Read the full blog for free on Medium.

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Published via Towards AI