Training Gemma-3 for Structured Math Reasoning with GRPO, LoRA, and GSM8K Rewards

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A detailed technical walkthrough covers fine-tuning Google's Gemma-3 for structured mathematical reasoning using Tunix GRPO (Group Relative Policy Optimization), LoRA adapters, and GSM8K-based reward signals. GRPO is a reinforcement learning from human feedback variant that has gained traction as a more sample-efficient alternative to PPO for reasoning tasks, and pairing it with LoRA makes the compute requirements accessible to teams without massive GPU clusters. GSM8K as a reward signal is a well-understood benchmark, making results reproducible and comparable to published baselines. This is a practical recipe developers can adapt for other structured reasoning domains — code generation, logical deduction, or tool-use — not just math. The combination of an accessible open model (Gemma-3), parameter-efficient fine-tuning (LoRA), and a principled RL objective (GRPO) represents a compelling open-source stack for reasoning specialists.