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The LLM gets retrained. Fixes cannot be done by hand because nobody knows how an LLM gets the answers it does. It takes the input, runs it through a gigantic math equation that was generated during training, and gets an answer. If the answer is wrong, the giantic equation needs to be fixed, but it can only be fixed by retraining.
A lot of models now do "chain of thought" or "reasoning" but those terms seem like they were made by marketing teams. Essentially, researchers found that if an LLM gave a wrong answer it could be prompted to change its answer to the correct one. For example, if you asked an LLM to count the frequency of each letter in "strawberry" and then ask it how many times "r" shows up, it'll get the right answer. "Reasoning" models simulate this process by getting the LLM to prompt itself several times in the background before giving a final answer. This helps filter out a lot of the "how many R's in strawberry" mistakes at the cost of requiring the LLM to turn 1 user prompt into dozens of hidden background prompts which takes more time and computer power, but at least you might not need to retrain it.
Math educator, 3Blue1Brown, has a great series on how neural networks are trained and function. I liked the series because it starts off with an overview without any math in case you wanted to know the basics without learning about the calculus and linear algebra.
That's not always true, they can also use regular logic to flag certain requests (like r's in strawberry) and respond manually without it ever reaching the model
Right, but that's like saying you can fix a broken space heater by wearing a sweater.
Maybe I misinterpreted the question, I was thinking this was including presentation layer for llm tools