Opening the Black Box of LLM Inference: Foundations of Generative AI

This article provides a technical, formal, and didactic explanation of the inference process in Transformer-based language models, from input tokenization to next-token selection. It combines formulas, reproducible numerical examples, and six figures to explain embeddings, positional encoding, self-attention, masks, residual connections, normalization, feed-forward networks, logits, softmax, and decoding strategies. A small-scale case study of the ambiguous Portuguese word banco demonstrates how context changes representations without claiming to reproduce the behavior of a real trained model. Finally, the article distinguishes model inference from the governed execution of an agentic system and presents a public, non-normative interpretation of the implications for SGAEIA.