1. Problems that have been solved before have their solution easily repeated (some will say, parroted/stolen), even with naming differences.
2. Problems that need only mild amalgamation of previous work are also solved by drawing on training data only, but hallucinations are frequent (as low probability tokens, but as consumers we don’t see the p values).
3. Problems that need little simulation can be simulated with the text as scratchpad. If evaluation criteria are not in training data -> hallucination.
4. Problems that need more than a little simulation have to either be solved by adhoc written code, or will result in hallucination. The code written to simulate is again a fractal of problems 1-4.
Phrased differently, sub problem solutions must be in the training data or it won’t work; and combining sub problem solutions must be either again in training data, or brute forcing + success condition is needed, with code being the tool to brute force.
I _think_ that the SOTA models are trained to categorize the problem at hand, because sometimes they answer immediately (1&2), enable thinking mode (3), or write Python code (4).
My experience with CC and Codex has been that I must steer it away from categories 2 & 3 all the time, either solving them myself, ask them to use web research, or split them up until they are (1) problems.
Of course, for many problems you’ll only know the category once you’ve seen the output, and you need to be able to verify the output.
I suspect that if you gave Claude/Codex access to a circuit simulator, it will successfully brute force the solution. And future models might be capable enough to write their own simulator adhoc (ofc the simulator code might recursively fall into category 2 or 3 somewhere and fail miserably). But without strong verification I wouldn’t put any trust in the outcome.
With code, we do have the compiler, tests, observed behavior, and a strong training data set with many correct implementations of small atomic problems. That’s a lot of out of the box verification to correct hallucinations. I view them as messy code generators I have to clean up after. They do save a ton of coding work after or while I‘m doing the other parts of programming.
