Thinking with Drafting: Optical Decompression via Logical Reconstruction

TL;DR

The paper tackles the precision paradox in multimodal reasoning by arguing that transcription fidelity and perceptual realism do not ensure rigorous logical topology. It proposes Thinking with Drafting (TwD), a framework that reconstructs latent logical structures from visual inputs into a minimal Logic Graphic DSL, enabling executable proofs and self-verification through deterministic rendering. A new VisAlg benchmark assesses the ability to recover explicit logical topology from visual algebra problems, and TwD demonstrates superior performance, especially in structure-sensitive tasks, outperforming open-weight baselines and approaching or surpassing proprietary systems. The work establishes a closed perceptual–cognitive loop where visual generation functions as a logical verifier, offering a generalizable pathway for trustworthy visual reasoning while acknowledging DSL scope limitations and future extension opportunities.

Abstract

Existing multimodal large language models have achieved high-fidelity visual perception and exploratory visual generation. However, a precision paradox persists in complex reasoning tasks: optical perception systems transcribe symbols without capturing logical topology, while pixel-based generative models produce visual artifacts lacking mathematical exactness. To bridge this gap, we propose that reasoning over visual inputs be reconceptualized as optical decompression-the process of reconstructing latent logical structures from compressed visual tokens. Guided by the axiom that Parsing is Reasoning, we introduce Thinking with Drafting (TwD), which utilizes a minimalist Domain-Specific Language (DSL) as a grounding intermediate representation. Unlike standard approaches that hallucinate answers directly, TwD forces the model to draft its mental model into executable code, rendering deterministic visual proofs for self-verification. To validate this, we present VisAlg, a visual algebra benchmark. Experiments demonstrate that TwD serve as a superior cognitive scaffold. Our work establishes a closed-loop system where visual generation acts not as a creative output but as a logical verifier, offering a generalizable path for visual reasoning.

Figures (23)

• Figure 1: Illustration of paradigms. (a) Existing multimodal paradigms treat image understanding, textual reasoning, and visual generation as disconnected tasks. (b) Thinking with Drafting (TwD) reframes visual reasoning as logical reconstruction into a minimalist DSL.
• Figure 2: Overview of Thinking with Drafting framework. (a) Optical decompression generates a Logic Graphic DSL from visual input and OCR, comprising entity, relational, and aggregation primitives. (b) A verifier scores samples by syntactic validity, visual completeness, and logical consistency, retaining high-quality data for training and discarding the rest to ensure topological and geometric correctness.
• Figure 3: The benchmark data construction pipeline of VisAlg.
• Figure 4: Difficulty and schema composition in VisAlg.
• Figure 5: Schema-wise performance comparison across five visual algebra problem types.