Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems, which 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 further 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. Specifically, we propose a novel synthetic data approach and construct a large-scale geometric dataset, SynthGeo228K, annotated with formal and natural language captions, designed to enhance the vision encoder to understand geometric structures better. Our framework improves MLLMs’ ability to process geometric diagrams and extends their application to open-ended tasks on the formalgeo7k dataset.

Geometric problem solving has always been a long-standing challenge in the fields of mathematical reasoning and artificial intelligence. We built a neural-symbolic system, called FGeo-HyperGNet, to automatically perform human-like geometric problem solving. The symbolic component is a formal system built on FormalGeo, which can automatically perform geometric relational reasoning and algebraic calculations and organize the solution into a hypergraph with conditions as hypernodes and theorems as hyperedges. The neural component, called HyperGNet, is a hypergraph neural network based on the attention mechanism, including an encoder to effectively encode the structural and semantic information of the hypergraph and a theorem predictor to provide guidance in solving problems. The neural component predicts theorems according to the hypergraph, and the symbolic component applies theorems and updates the hypergraph, thus forming a predict-apply cycle to ultimately achieve readable and traceable automatic solving of geometric problems. Experiments demonstrate the correctness and effectiveness of this neural-symbolic architecture. We achieved state-of-the-art results with a TPA of 93.50% and a PSSR of 88.36% on the FormalGeo7K dataset.

With increasing demand for deployment on edge platforms, there is a need for efficient super-resolution methods. Linear overparameterization is widely used to enhance lightweight model performance. However, the general usage of the reparameterization technique is merging multi-branch into standard 3 × 3 convolutions, no one explores its usage in 1D-convolution, which is energy efficiency and adepts at capturing structural edge features. We propose a compact cross-reparam convolution super-resolution (CRCSR) network in a vgg-style plain architecture. We design Cross-Reparam convolution (CRC) to enhance feature representation for cross-convolution. We leverage a sparse large kernel to capture long-range information while limiting the computational costs and number of parameters. Besides, when training deeper type CRCSR, reserving and merging operations are used to build Rmparam-Cross Block (RCB) to improve the convergence of deeper networks. Experiments on super-resolution datasets of different sizes demonstrate that CRCSR has competitive restoration performance compared to state-of-the-art lightweight SR models

Deep convolutional neural networks have shown remarkable success in many visual recognition tasks, but they struggle with long-tailed datasets commonly encountered in natural world datasets. In such datasets, the greatest amount of data belongs to majority classes (head classes) with significantly less data for the minority (tail) classes. The class imbalance greatly reduces the performance of traditional networks. Existing methods use re-sampling and re-weighting strategies as the primary methods to deal with these long-tailed datasets. We address the problem using a data augmentation approach inspired by a recently proposed implicit semantic data augmentation (ISDA) algorithm. In this paper, we propose an approach using dual branches with balanced semantic data augmentation (BSDA) to perform effective semantic data augmentation for long-tail recognition by learning good representations. The deep feature branch learns good representations of inputs, and the classifier branch searches for meaningful semantic transformations, with different sampling strategies in each branch. Both branches share the same weights, with focus shifting from one to the other during training. We also propose an augment coefficient to apply different augmentation intensities for different categories. We test our methods on the CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, and iNaturalist 2018 datasets. The results demonstrate the effectiveness of our methods.