> For the complete documentation index, see [llms.txt](https://dnalayer.gitbook.io/dnachain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://dnalayer.gitbook.io/dnachain/large-language-models-in-the-dna-ecosystem.md).

# Large Language Models in the DNA Ecosystem

LLMs, such as OpenAI’s GPT (Generative Pre-trained Transformer), are advanced AI systems designed to understand, generate, and interact with human language in a way that is both contextually aware and highly nuanced. 

These models are trained on vast amounts of text data, allowing them to perform a wide range of language-related tasks such as translation, summarization, question-answering, and creative content generation.

***

### Mathematical Formulation and Notations

We now introduce the formulation and notations we will be using to describe our LLM inference algorithm. In essence, LLMs model a language sequence (w1 , w2 , · · · wN ) by computing the conditional distributions

<figure><img src="https://1275704450-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FTBcIEp8xctdXZhDwjCpX%2Fuploads%2FvrSprKt6SS2EMv4SiTQM%2Fimage.png?alt=media&amp;token=ae5bde0d-4f1d-449f-b906-56b6e7621fda" alt="" width="375"><figcaption></figcaption></figure>

<figure><img src="https://1275704450-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FTBcIEp8xctdXZhDwjCpX%2Fuploads%2Fhr4wXj3JI8l0AqSuw7dk%2Fimage.png?alt=media&amp;token=b9c414a8-ea91-4553-85b9-914b135228c2" alt="" width="563"><figcaption></figcaption></figure>

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