AI models that think step-by-step, called chain-of-thought (CoT) models, are becoming popular. They break down complex problems into smaller, manageable parts before coming up with an answer. This process, however, can lead to high costs. The more thoughts a model generates, the more tokens it uses, and the higher the cost. This is where a new technique called length controlled policy optimization (LCPO) comes in.

LCPO is a training method that teaches models to think within a specific token budget. This means the model must find the correct answer while staying within a set number of tokens. It's like giving a student a word limit for an essay. The student must convey their thoughts clearly and accurately without exceeding the limit.

The researchers behind LCPO tested it on a 1. 5B-parameter model called Qwen-Distilled-R1-1. 5B. They created two versions of this model: L1-max and L1-exact. L1-max can generate answers up to a certain length, while L1-exact must generate answers exactly at a certain length. The models were trained on math problems but tested on a variety of tasks, including some they hadn't seen before.

The results were impressive. The L1 models could balance the number of tokens used and the accuracy of the answers. They could also outperform larger models on some tasks. This is a big deal because it means smaller models can sometimes do the job of larger, more expensive ones.

The L1 models also showed they could adapt their thinking process based on the token budget. For example, when given more tokens, they would include more self-correction and verification steps. This shows that the models aren't just generating random thoughts; they're learning to think more efficiently.

The researchers also found that the L1 models could handle tasks they hadn't been trained on, like the MMLU and GPQA benchmarks. This shows that the models aren't just good at math; they can generalize their thinking to other areas.

This research could have big implications for real-world applications. It could help enterprises scale their AI models without breaking the bank. Instead of just using bigger, more expensive models, they could use smaller, more efficient ones.

The researchers have made the code and weights for the L1 models publicly available. This means other researchers can build on their work and potentially improve it.

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