We introduce Post-Optimization Model Edit (POME), a new algorithm that enhances the performance of fine-tuned large language models using only their pretrained and fine-tuned checkpoints, without requiring extra data or further optimization. The core idea is to apply a muon-style projection to $ΔW$, the difference between the fine-tuned and pretrained weights. This projection uses truncated singular value decomposition (SVD) to equalize the influence of dominant update directions and prune small singular values, which often represent noise. As a simple post-processing step, POME is completely decoupled from the training pipeline. It requires zero modifications and imposes no overhead, making it universally compatible with any optimizer or distributed framework. POME delivers consistent gains, boosting average performance by +2.5\% on GSM8K and +1.0\% on code generation. Its broad applicability -- from 7B foundation models to 72B RLHF-instructed models -- establishes it as a practical, zero-cost enhancement for any fine-tuning pipeline. Code is available at https://github.com/NUS-HPC-AI-Lab/POME.

Model-free reinforcement learning methods such as the Proximal Policy Optimization algorithm (PPO) have successfully applied in complex decision-making problems such as Atari games. However, these methods suffer from high variances and high sample complexity. On the other hand, model-based reinforcement learning methods that learn the transition dynamics are more sample efficient, but they often suffer from the bias of the transition estimation. How to make use of both model-based and model-free learning is a central problem in reinforcement learning. In this paper, we present a new technique to address the trade-off between exploration and exploitation, which regards the difference between model-free and model-based estimations as a measure of exploration value. We apply this new technique to the PPO algorithm and arrive at a new policy optimization method, named Policy Optimization with Model-based Explorations (POME). POME uses two components to predict the actions' target values: a model-free one estimated by Monte-Carlo sampling and a model-based one which learns a transition model and predicts the value of the next state. POME adds the error of these two target estimations as the additional exploration value for each state-action pair, i.e, encourages the algorithm to explore the states with larger target errors which are hard to estimate. We compare POME with PPO on Atari 2600 games, and it shows that POME outperforms PPO on 33 games out of 49 games.