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

TL;DR

This paper introduces a method where including moderately easy problems in training encourages language models to produce shorter, more concise reasoning chains without sacrificing accuracy, effectively reducing verbosity naturally.

Contribution

It demonstrates that up-weighting easy problems in RLVR acts as an implicit length regularizer, leading to shorter solutions without explicit length penalties.

Findings

Models achieve baseline accuracy with nearly half the output length.

Shorter solutions do not compromise reasoning quality.

The approach is effective on large language models like Qwen3-4B-Thinking-2507.

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}.