Vision Language Models (VLMs) demonstrate strong perceptual abilities but remain limited in tasks requiring analytical reasoning across multiple visual states, such as multi-image comparison, change detection, and multi-step visual inference. These capabilities are critical for real-world multimodal applications where reasoning must be grounded in systematic differences between visual contexts.

However, existing benchmarks rarely require both explicit visual comparison and analytical reasoning, leaving this capability underexplored. To address this gap, we introduce SD-MAR (Synthetic Data for Multi-image Analytical Reasoning), a framework for training and evaluating VLMs on multi-image analytical reasoning.

SD-MAR constructs paired visual scenarios through controlled perturbations and generates reasoning tasks spanning semantic change attribution and quantitative comparison. We further train VLMs using GRPO-lite with Backward Discounted Allocation (BDA), a reinforcement learning approach that removes KL regularization to encourage stronger policy optimization while allocating greater credit to the later reasoning steps where analytical conclusions are formed.

Experiments on Qwen2.5-VL-7B and InternVL3-8B show that GRPO-lite fine-tuning on SD-MAR improves in-domain accuracy by up to 36.95%, with Qwen2.5-VL-7B outperforming GPT-4.1 on the SD-MAR benchmark. Importantly, out-of-domain generalization is preserved or improved: performance remains within 1% on MME, MMMU-Pro, and MathVista, while improving by up to 4% on MMBench.

LLM-as-judge evaluation further demonstrates consistent improvements in logical coherence and explanation quality across both models.