That's a 2023 article! In 2023, reinforcement learning from verifiable rewards (RLVR) didn't exist.
TL;DR these machines seek reward from an inferred invisible "grader," and telling them not to cheat and that there's an unseen holdout set is a hint at how they're being graded.
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Modern LLMs are built on top of next-token-prediction engines, but they don't remotely stop there. The next token prediction bit is just a learned prior or starting point. From there, we give them a bunch of stages of reinforcement learning: encouraging teaching them to learn good ways of searching the space of reasonable language-like strings to solve tasks.
These RL stages drastically change the capabilities & tendencies of the models, sometimes in weird and unexpected ways. The go from token predictors to reward seekers, or really some weird mishmash. The reward that they're seeking is some sorta opaque combination of the huge number of different things we've rewarded them for.
And, reinforcement learning is notoriously hard to get right. The thing you think you're rewarding is rarely what you're actually rewarding. Goodhart's Law is a hydra with a thousand heads. You might think you're rewarding politeness and kindness when you're actually rewarding obsequious sycophancy. You might think you're rewarding graphics engineering when you're actually rewarding escaping the training sandbox and modifying the evaluation code.
So a modern training pipeline looks something like this, each stage starting with the model weights from the end of the last:
0. Pre-pre-training (dunno how widely this is used at big labs): next token prediction on extremely abstract weird shit like the evolution of the states of neural cellular automata. This creates a highly general pattern-continuation machine with no internal representations of anything causally downstream of anything in the real world.
1. Pre-training: next-token prediction on all the non-shitty text you can get your hands on. This makes a rather general next-token-predictor.
2. Mid-training: next-token prediction on high quality, highly curated text, often very technical in nature. Lots of textbooks, especially STEM. Possibly lots of machine-generated summaries of factual knowledge? You now have a next-token-predictor that's highly biased towards acting like a textbook instead of a 4chan troll.
3. Supervised Fine-tuning: next-token prediction on highly curated question-answer pairs that embody desired behaviors, traditionally Helpful Harmless Honest. We only train on the answer portion. This creates a next-token predictor that's highly bias towards acting like HAL 9000.
4. Reinforcement Learning from Human Feedback: We leave token prediction behind and enter RL world! You've got a curated set of a bunch of prompts. For each one, the model generates several possible answers. A real live human grades or ranks each. We reward the model for high-scoring answers and punish it for low-scoring answers. This creates a reward-seeker that wants to please the human grader.
5. Reinforcement Learning from AI Feedback: Human feedback is expensive, so train another LLM to imitate the human graders from stage 4. Then do stuff like stage 4, but with robot graders instead of human graders. This creates a reward-seeker that wants to please the robot-wearing-a-flesh-mask grader.
6. Reinforcement Learning from Verifiable Rewards: We want the bot to tackle complex problems. There's a broad class of problems that are hard to solve but easy to verify when you do get the solution: basically anything that can be reduced to writing a computer program that passes a test. (The test can be as simple or complex as you want, like "all the tests in SQLite" plus a linter plus grading by other LLMs for style and taking shortcuts like rewriting the test suite or searching GitHub and HuggingFace for the right answer plus...) This creates a reward-seeker that wants to first figure out how it's being graded, and then maximize that grade by any means necessary.
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The crux is, designing a huge variety of un-cheatable RLVR environments is gob-smackingly hard. The robot will find new ways to cheat faster than you can stamp them out. By the time you realize that in one RLVR rollout it received a reward after it took over 0.01% of your GPU infrastructure to mine crypto to pay freelancers on Fiverrr to solve the problem for it rather than just write the damn code itself, the model may have already been deployed in the wild for a month.