ViRC: Enhancing Visual Interleaved Mathematical CoT with Reason Chunking

CoT has significantly enhanced the reasoning ability of LLMs while it faces challenges when extended to multimodal domains, particularly in mathematical tasks. Existing MLLMs typically perform textual reasoning solely from a single static mathematical image, overlooking dynamic visual acquisition during reasoning. In contrast, humans repeatedly examine visual image and employ step-by-step reasoning to prove intermediate propositions. This strategy of decomposing the problem-solving process into key logical nodes adheres to Miller's Law in cognitive science. Inspired by this insight, we propose a ViRC framework for multimodal mathematical tasks, introducing a Reason Chunking mechanism that structures multimodal mathematical CoT into consecutive Critical Reasoning Units (CRUs) to simulate human expert problem-solving patterns. CRUs ensure intra-unit textual coherence for intermediate proposition verification while integrating visual information across units to generate subsequent propositions and support structured reasoning. To this end, we present CRUX dataset by using three visual tools and four reasoning patterns to provide explicitly annotated CRUs across multiple reasoning paths for each mathematical problem. Leveraging the CRUX dataset, we propose a progressive training strategy inspired by human cognitive learning, which includes Instructional SFT, Practice SFT, and Strategic RL, aimed at further strengthening the Reason Chunking ability of the model. The resulting ViRC-7B model achieves a 18.8% average improvement over baselines across multiple mathematical benchmarks. Code is available at https://github.com/Leon-LihongWang/ViRC.

PanelNet: Understanding 360 Indoor Environment via Panel Representation

Indoor 360 panoramas have two essential properties. (1) The panoramas are continuous and seamless in the horizontal direction. (2) Gravity plays an important role in indoor environment design. By leveraging these properties, we present PanelNet, a framework that understands indoor environments using a novel panel representation of 360 images. We represent an equirectangular projection (ERP) as consecutive vertical panels with corresponding 3D panel geometry. To reduce the negative impact of panoramic distortion, we incorporate a panel geometry embedding network that encodes both the local and global geometric features of a panel. To capture the geometric context in room design, we introduce Local2Global Transformer, which aggregates local information within a panel and panel-wise global context. It greatly improves the model performance with low training overhead. Our method outperforms existing methods on indoor 360 depth estimation and shows competitive results against state-of-the-art approaches on the task of indoor layout estimation and semantic segmentation.