Post-Training on the Clock: Specializing a Small Language Model on a Consumer GPU

Abstract How should a language model be specialized for a target task when training is limited to one consumer GPU and a few hours? We study the allocation of a nominal three-hour training budget, with up to 0.3 additional hours, between supervised fine-tuning (SFT) and Group Relative Policy Optimization (GRPO). We use tool calling as a case study because of its practical relevance to language-model agents and its verifiable outputs. Using Qwen2.5-0.5B-Instruct with low-rank adaptation on an RTX 5060 Ti with 16 GB of memory, we compare SFT, GRPO, and six sequential SFT-to-GRPO allocations. Training uses a filtered mixture of xLAM function-calling examples and Hammer irrelevance examples, covering both call construction and abstention when no offered tool is suitable. Evaluation reports xLAM exact tool-call and function-name accuracies for local call construction, BFCL-v3 Single-turn FC (agg) for external function calling, BFCL-v3 Irrelevance (agg) for abstention, and MMLU, MATH-500, and IFEval for selected general capabilities. The suffix (agg) denotes study-specific averages of selected subset accuracies weighted by subset size. At the last evaluated checkpoints within 3.3 reported hours, SFT achieves the highest xLAM exact tool-call accuracy (82.82%), compared with 69.13% for GRPO alone. Selected hybrid allocations improve external function-calling accuracy over SFT, with different abstention trade-offs. Most sampled GRPO groups have constant rewards and provide no relative task-reward signal. We release the prepared mixed dataset, all allocation-study checkpoints, and Post-Training Lab, an editable training and evaluation codebase with CUDA and MLX implementations.