Recently, large language models have made remarkable progress in reasoning, largely driven by scaling data and model size. In parallel, several studies argue that for smaller models, high-quality distillation can yield strong reasoning performance with minimal resources. However, a framework for understanding machine reasoning that explains why low-resource distillation can boost model performance is still missing. In this paper, we conduct a controlled case study: using less than 920 examples, a simple distillation based on the base model can actually achieve notable reasoning performance improvement, compared with the base model and even the zero-RL models. By analyzing the token frequency in model outputs, we find that the distilled model shows more flexible reasoning. It uses anthropomorphic tokens and logical connectors much more often than the base and zero-RL model. Further analysis reveals that distillation enhances the presence of two advanced cognitive behaviors: Multi-Perspective Thinking or Attempting and Metacognitive Awareness. Frequent occurrences of these two advanced cognitive behaviors give rise to flexible reasoning, which is essential for solving reasoning problems.

As the field of Multimodal Large Language Models (MLLMs) continues to evolve, their potential to handle mathematical reasoning tasks is promising, as they can handle multimodal questions via cross-modal understanding capabilities compared to text-only LLMs. Current mathematical benchmarks predominantly focus on evaluating MLLMs’ problem-solving ability, yet there is a crucial gap in addressing more complex scenarios such as error detection, for enhancing reasoning capability in complicated settings. To fill this gap, we formally formulate the new task — multimodal error detection, and introduce **ErrorRadar, the first benchmark designed to assess MLLMs’ capabilities in such a task. ErrorRadar evaluates two sub-tasks: error step identification and error categorization**, providing a framework for evaluating MLLMs’ complex mathematical reasoning ability. It consists of 2,500 high-quality multimodal K-12 mathematical problems, collected from real-world student interactions in an educational organization, with expert-based annotation and metadata such as problem type and error category. Through extensive experiments, we evaluated both open-source and closed-source representative MLLMs, benchmarking their performance against educational expert evaluators. Results indicate challenges still remain, as GPT-4o with best model performance is still around 10% behind human evaluation

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 ( R² = 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.