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. I’m not referring to the calculus you did with pencil and paper. I’m talking about a sprawling, automated version that computes millions of derivatives per second.
At its heart, every LLM is a feedback system. It starts with random guesses, measures how wrong it was, and then adjusts itself to be slightly less wrong. The word “slightly” in this context is the essence of calculus.
“Each gradient step represents a measurable reduction in error, guiding the model toward a more stable understanding of language.”