Contemporary LLMs are static. LLMs are not static by definition.

This is actually why I find a lot of arguments about AI's limitations as stochastic parrots very shortsighted. Language, picture or video models are indeed good at memorizing some reasonable features from their respective domains and building a simplistic (but often inaccurate) world model where some features of the world are generalized. They don't reason per se but have really good ways to look up how typical reasoning would look like.

To get actual reasoning, you need to do what all AI labs are currently working on and add a neuro-symbolic spin to model outputs. In these approaches, a model generates ideas for what to do next, and the solution space is searched with more traditional methods. This introduces a dynamic element that's more akin to human problem-solving, where the system can adapt and learn within the context of a specific task, even if it doesn't permanently update the knowledge base of the idea-generating model.

A notable example is AlphaGeometry, a system that solves complex geometry problems without human demonstrations and insufficient training data that is based on an LLM and structured search. Similar approaches are also used for coding or for a recent strong improvement in reasoning to solve example from the ARC challenge..