Scaling Law for Multimodal Large Language Model Supervised Fine-Tuning

The supervised fine-tuning (SFT) stage is crucial for multimodal large language models (MLLMs), yet a comprehensive scaling law to guide the optimal model-data configuration remains lacking. In this paper, we make an initial attempt to address this gap. First, we theoretically demonstrate that directly computing the optimal computation frontier for MLLM-SFT, as we can for traditional LLMs, is a challenging task. This complexity arises because MLLM-SFT is influenced by a broader range of factors, including model size, LLM pre-training tokens, and MLLM SFT tokens. To tackle this issue, we propose two scaling laws based on LLM paradigms: one applicable when training data volumes are well defined by researchers, and another for cases where models are sourced from open communities with unknown training data. Through theoretical modeling and approximations, we provide researchers with valuable recommendations for optimal resource allocation. Furthermore, we establish a strong correlation (R 2 = 0.98) between training loss and downstream performance, enabling accurate performance estimation without the need for exhaustive benchmarking. To validate our scaling laws, we construct a testbed of 60 models ranging from 50 million to 8 billion parameters, totaling 1,560 checkpoints. Each checkpoint is evaluated on than 10 MLLM benchmarks, ensuring robust fitting of our formulations.