Diagram Formalization Enhanced Multi-Modal Geometry Problem Solver

Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to understand geometric diagrams, performing no better in geometry problem solving than LLMs that only process text. This limitation is amplified by the lack of effective methods for representing geometric relationships. To address these issues, we introduce the Diagram Formalization Enhanced Geometry Problem Solver (DFE-GPS), a new framework that integrates visual features, geometric formal language, and natural language representations. We propose a novel synthetic data approach and create a large-scale geometric dataset, SynthGeo228K, annotated with both formal and natural language captions, designed to enhance the vision encoder for a better understanding of geometric structures. Our framework improves MLLMs' ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.

Low-Rank Winograd Transformation for 3D Convolutional Neural Networks

This paper focuses on Winograd transformation in 3D convolutional neural networks (CNNs) that are more over-parameterized compared with the 2D version. The over-increasing Winograd parameters not only exacerbate training complexity but also barricade the practical speedups due simply to the volume of element-wise products in the Winograd domain. We attempt to reduce trainable parameters by introducing a low-rank Winograd transformation, a novel training paradigm that decouples the original large tensor into two less storage-required trainable tensors, leading to a significant complexity reduction. Built upon our low-rank Winograd transformation, we take one step ahead by proposing a low-rank oriented sparse granularity that measures column-wise parameter importance. By simply involving the non-zero columns in the element-wise product, our sparse granularity is empowered with the ability to produce a very regular sparse pattern to acquire effectual Winograd speedups. To better understand the efficacy of our method, we perform extensive experiments on 3D CNNs. Results manifest that our low-rank Winograd transformation well outperforms the vanilla Winograd transformation. We also show that our proposed low-rank oriented sparse granularity permits practical Winograd acceleration compared with the vanilla counterpart.