Multimodal Thinking with Renderable Programs

The authors introduce SVGLM, a framework that uses SVG primitives to connect text and images in reasoning, using SVG both as an image description and as text instructions.

Source: [11]

The authors evaluate on MathCanvas-Bench, which has 3,000 question-answer pairs across eight math categories, and select its plane-geometry (1,092 samples) and solid-geometry (486 samples) splits. After retaining only questions with at least one image, the evaluation set contains 1,244 QA pairs, reported as 78.8% of the preceding selected samples.

Source: [7], [13]

The authors curated 8,000 SVG samples for drawing auxiliary lines in geometric problems from the plane- and solid-geometry splits of MathCanvas-Instruct. Their collection process filters for solutions constructible from the question image by adding captions or figures, uses Gemini-3.0-Thinking to generate SVG annotations with keypoints on a 1000 × 1000 canvas, then renders and visually verifies the SVGs with GPT-5 before retaining samples.

Source: [10], [12]

The evaluation compares zero-shot inference, direct supervised fine-tuning and SVGLM fine-tuning in an interactive tool-calling paradigm on MathCanvas-Bench. The direct-SFT comparator uses MathCanvas-Instruct questions with the same sample count as the SVG-enhanced conversation dataset; GPT-5-generated chain-of-thought reasoning is filtered by rejection sampling before fine-tuning. SVGLM uses the SVG-enhanced conversation dataset.

Source: [14], [20]

Additional comparisons include V-Thinker using its released model and pipeline, GPT-4o with Qwen-Image-Edit supplied with GPT-4o-generated editing instructions, and GPT-4o evaluated zero-shot to illustrate benchmark difficulty.

Source: [5], [15], [18], [19]

The authors report that Qwen-Image-Edit and Nano-Banana exhibit severe hallucination and domain misalignment in the qualitative comparisons, making it difficult to follow the instructions. They also identify the substantially greater data requirements of diffusion-model fine-tuning, compared with standard vision-language-model fine-tuning, as an obstacle to adapting those models for efficient visual thinking.

Source: [6]

SVGLM uses a multi-turn tool-calling setup: a model can generate text before calling a tool with XML-encoded SVG and a canvas specification, which may be the question image or a blank canvas; the interaction allows the agent to render an SVG or answer the question at each turn.

Source: [4]

The reported metric is accuracy with weighted scoring: later sub-questions receive greater weight, with each sub-question weighted 30% more than the preceding one; the paper also reports scores for both geometry categories and a weighted overall score.

Source: [7]

The paper asks how visual intermediate steps can be externalized in a form that supports grounded visual reasoning, particularly when a task requires an explicit visual operation such as adding an auxiliary geometry line.

Source: [1], [17]

The evaluation uses three open-source models of roughly similar size: LLaVa-Next-Mistral-7B, Qwen2.5-VL-7B-Instruct, and InternVL-3-8B.

Source: [8]

Each separate supervised fine-tuning experiment uses 3 epochs, batch size 8 and 8 NVIDIA H100 GPUs. The retained source says all experiments “can finish after 2 hours”; it does not establish that every experiment actually finished within a two-hour upper bound. The learning-rate exponent is flattened in the retained normalization and is not independently verified here.

Source: [16]