Shorter but not Worse: Frugal Reasoning via Easy Samples as Length Regularizers in Math RLVR

Large language models (LLMs) trained for step-by-step reasoning often become excessively verbose, raising inference cost. Standard Reinforcement Learning with Verifiable Rewards (RLVR) pipelines filter out easy'' problems for training efficiency, leaving the model to train primarily on harder problems that require longer reasoning chains. This skews the output length distribution upward, resulting in a \textbf{model that conflates thinking longer’’ with ``thinking better’'}. In this work, we show that retaining and modestly up-weighting moderately easy problems acts as an implicit length regularizer. Exposing the model to solvable short-chain tasks constrains its output distribution and prevents runaway verbosity. The result is $\mathit{\text{emergent}}\mathit{\text{brevity}}\mathit{\text{for}}\mathit{\text{free}}$: the model learns to solve harder problems without inflating the output length, $\mathbf{\text{despite}}\mathbf{\text{the}}\mathbf{\text{absence}}\mathbf{\text{of}}\mathbf{\text{any}}\mathbf{\text{explicit}}\mathbf{\text{length}}\mathbf{\text{penalization}}$. RLVR experiments using this approach on $\mathit{\text{Qwen3-4B-Thinking-2507}}$ (with a 16k token limit) achieve baseline pass@1 AIME25 accuracy while generating solutions that are, on average, nearly twice as short. The code is available at \href{https://github.com/MBZUAI-Paris/Frugal-AI}{GitHub}, with datasets and models on \href{https://huggingface.co/collections/MBZUAI-Paris/k2-think-mini-68dcfa8b114686a4bd3dc2bc}{Hugging Face}.