Like I said, they can implement the algorithm to solve it, but when forced to maintain the state themselves, either internally or explicitly in the context, they are unable to do so and get lost.
Similarly if you ask to write a Sudoku solver, they have no problem. And if you ask an online model to solve a sudoku, it'll write a sudoku solver in the background and use that to solve it. But (at least the last time I tried, a year ago), if you ask to solve step-by-step using pure reasoning without writing a program, they start spewing out all kinds of nonsense (but humorously cheat: they'll still spit out the correct answer at the end).
That’s because there are lots of maze-solving algorithms on the web, so it’s easy to spit one back at you. But since they don’t actually understand how solve a maze, or even apply an algorithm one step at a time, it doesn’t work well.
A human solving it is at https://youtu.be/7etaXRyE3QY (you may want to jump to the rules or the solve if you're not as interested in the community goings on).
So if you push eg Claude Sonnet 4 or Opus 4.1 into a maze scenario, and have it record its own pathing as it goes, and then refresh and feed the next Claude the progress so far, would that solve for the inability to maintain long duration context in such maze cases?
I make Claude do that on every project. I call them Notes for Future Claude and have it write notes for itself because of how quickly context accuracy erodes. It tends to write rather amusing notes to itself in my experience.
This was from a few months ago, so things may be different now. I only used OpenAI, and the o3 model did by far the best (gpt-4o's performance was equivalent on the basic scenario when I had it just move one move at a time (which, it was still pretty good, all considered), but when I started having it summarize state and such, o3 was able to use that to improve performance, whereas 4o actually got worse).
But yeah, that's one of the things I tried. "Your turn is over. Please summarize everything you have learned about the maze so someone else can pick up where you left off". It did okay, but it often included superfluous information, it sometimes forgot to include current orientation (the maze action options were "move forward", "turn right", "turn left", so knowing the current orientation was important), and it always forgot to include instructions on how to interpret the state: in particular, which absolute direction corresponded to an increase or decrease of which grid index.
I even tried to coax it into defining a formal state representation and "instructions for an LLM to use it" up-front, to see if it would remember to include the direction/index correspondence, but it never did. It was amusing actually; it was apparent it was just doing whatever I told it and not thinking for itself. Something like
"Do you think you should include a map in the state representation? Would that be useful?"
"Yes, great idea! Here is a field for a map, and an algorithm to build it"
"Do you think a map would be too much information?"
"Yes, great consideration! I have removed the map field"
"No, I'm asking you. You're the one that's going to use this. Do you want a map or not?"
"It's up to you! I can implement it however you like!"
Yeah I did the type where you start somewhere inside the maze and have to find the "treasure". Mainly because it was slightly easier to implement, but also had the nice side effect of not being solvable by that rule alone.
FWIW the LLMs were definitely not following that rule. They seemed to always keep going straight whenever that was an option. Which meant they would always get stuck at T intersections when both ways led to a dead end.
Similarly if you ask to write a Sudoku solver, they have no problem. And if you ask an online model to solve a sudoku, it'll write a sudoku solver in the background and use that to solve it. But (at least the last time I tried, a year ago), if you ask to solve step-by-step using pure reasoning without writing a program, they start spewing out all kinds of nonsense (but humorously cheat: they'll still spit out the correct answer at the end).