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

Abstract

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 \textbf{\emph{emergent brevity for free}}: the model learns to solve harder problems without inflating the output length, \textbf{ despite the absence of any explicit length penalization}. RLVR experiments using this approach on \textit{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}.