How LLMs Learn and Acquire Capabilities on Signal & Syntaxhttps://tomarcher.io/learningpaths/how-llms-learn-and-acquire-capabilities/Recent content in How LLMs Learn and Acquire Capabilities on Signal & SyntaxHugoen-usWed, 08 Oct 2025 06:00:00 -0700How Large Language Models (LLMs) Learn: Calculus and the Search for Understandinghttps://tomarcher.io/posts/how-large-language-models-learn/Wed, 08 Oct 2025 06:00:00 -0700https://tomarcher.io/posts/how-large-language-models-learn/When you interact with a large language model (LLM) such as ChatGPT or Claude , the model seems to respond instantly relative to the question’s degree of difficulty. What’s easy to forget is that every word it predicts comes from a long history of learning where billions of gradient steps have slowly sculpted its understanding of language. Large language models don’t memorize text. They optimize it. Behind that optimization lies calculus.