While Large Language Models (LLMs) have excelled in textual reasoning, they struggle with mathematical domains like geometry that intrinsically rely on visual aids. Existing approaches to Visual Chain-of-Thought (VCoT) are often limited by rigid external tools or fail to generate the high-fidelity, strategically-timed diagrams necessary for complex problem-solving. To bridge this gap, we introduce MathCanvas, a comprehensive framework designed to endow unified Large Multimodal Models (LMMs) with intrinsic VCoT capabilities for mathematics. Our approach consists of two phases. First, a Visual Manipulation stage pre-trains the model on a novel 15.2M-pair corpus, comprising 10M caption-to-diagram pairs (MathCanvas-Imagen) and 5.2M step-by-step editing trajectories (MathCanvas-Edit), to master diagram generation and editing. Second, a Strategic Visual-Aided Reasoning stage fine-tunes the model on MathCanvas-Instruct, a new 219K-example dataset of interleaved visual-textual reasoning paths, teaching it when and how to leverage visual aids. To facilitate rigorous evaluation, we introduce MathCanvas-Bench, a challenging benchmark with 3K problems that require models to produce interleaved visual-textual solutions. Our model, BAGEL-Canvas, trained under this framework, achieves an 86% relative improvement over strong LMM baselines on MathCanvas-Bench, demonstrating excellent generalization to other public math benchmarks. Our work provides a complete toolkit—framework, datasets, and benchmark—to unlock complex, human-like visual reasoning in LMMs.

Recent progress in Large Language Models (LLMs) has opened new avenues for solving complex optimization problems, including Neural Architecture Search (NAS). However, existing LLM-driven NAS approaches rely heavily on prompt engineering and domain-specific tuning, limiting their practicality and scalability across diverse tasks. In this work, we propose LM-Searcher, a novel framework that leverages LLMs for cross-domain neural architecture optimization without the need for extensive domain-specific adaptation. Central to our approach is NCode, a universal numerical string representation for neural architectures, which enables cross-domain architecture encoding and search. We also reformulate the NAS problem as a ranking task, training LLMs to select high-performing architectures from candidate pools using instruction-tuning samples derived from a novel pruning-based subspace sampling strategy. Our curated dataset, encompassing a wide range of architecture-performance pairs, encourages robust and transferable learning. Comprehensive experiments demonstrate that LM-Searcher achieves competitive performance in both in-domain (e.g., CNNs for image classification) and out-of-domain (e.g., LoRA configurations for segmentation and generation) tasks, establishing a new paradigm for flexible and generalizable LLM-based architecture search.