Thinking with Drafting: Optical Decompression via Logical Reconstruction

TL;DR

This paper introduces Thinking with Drafting (TwD), a novel approach that reconstructs logical structures from visual tokens to improve reasoning accuracy in multimodal large language models.

Contribution

It proposes a new framework that drafts mental models into executable code for deterministic verification, bridging the gap between perception and logical reasoning.

Findings

TwD outperforms standard methods on the VisAlg benchmark.

Visual generation is used as a logical verifier, not just creative output.

The approach enhances logical accuracy in complex visual reasoning tasks.

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.