I was trying to find references to mathematical treatment of lists, and queried ChatGPT the following:
Please provide references that deal with the mathematical properties of lists
To which ChatGPT responded as follows:
"Introduction to the Mathematics of Lists" by Peter J. Cameron (https://www.cambridge.org/core/books/introduction-to-the-mathematics-of-lists/3F0C6D0E69E49BF6D5CD6CA5D6A761B2)
"List Processing and Programming" by John F. Sowa (https://www.cs.cmu.edu/~fp/courses/lp/lectures.html)
"List Processing in Prolog" by David H. D. Warren (https://www.cs.purdue.edu/homes/hosking/726/html/prolog_lists.html)
"Introduction to the Mathematics of Lists and Trees" by Meinard Müller (https://link.springer.com/book/10.1007%2F978-3-319-05147-1)
"Mathematics of Lists and Trees" by Markus N. Rabe (https://www.researchgate.net/publication/296955213_Mathematics_of_Lists_and_Trees)
I was pretty surprised and happy, because I hadn't had much success with Google. But it turns out that
every single one of those references and links are made up. The references don't exist and the links themselves appear to be cobbled together. The last link for example, takes you to a paper on "Grain mixes for subgrade layers" - the title in the url is irrelevant and only the number matters.
Googling for some of those authors throws up author pages with their publications, and it turns out they've never published papers with those titles! See for example, http://www-groups.mcs.st-andrews.ac.uk/~pjc/publ/
I started looking and it turns out that OpenAI is keenly aware of the hallucination problem, and even wrote about how they're correcting for it in this blog post about InstructGPT: https://openai.com/blog/instruction-following/
To summarize: it seems OpenAI is addressing this by taking human-labeled output data from GPT and feeding this into new models, using a reward function to train the future models to behave with less hallucination. This way of working struck me as a mix of software engineering and crop breeding.
They discuss the trade-offs involved with doing this. The "hallucination" effect is probably one of the features that make GPT so creative.