Contrast pyramids have shown excellent reconstructions for several images with only a few number of high contrasts. The contrast histogram of the image shows the distribution of contrasts and allows to select a bound that limits the mean reconstruction error. A total order of the vertices enables a both the ordering of the edges with the same contrast and, together with max-link strategy, generates efficiently the contraction kernels of the pyramid. A spiral total order pushes the surviving vertices geometrically towards the center of the image.
Graph Neural Networks (GNNs) have demonstrated strong capabilities in learning from structured data. Yet efficiently capturing cycle-related information remains a computational challenge. In this work, we introduce a novel GNN called Grammatical Path Network (GPN) to efficiently capture cycle-related information inside graph structures. GPN leverage Context-Free Grammars (CFGs) for cycle counting through path precomputation. Inspired by the Graph Substructure Network (GSN) framework and recent advances in GNN expressiveness, GPN exploits CFG-based representations to encode cycles of length l + 1 by precomputing paths of length l at the edge level. This formulation eliminates the need for explicit cycle counting, while maintaining strong predictive performance. Our experiments on benchmark datasets demonstrate that GPN achieves comparable or superior results to GSN in tasks requiring cycle-aware representations, highlighting its efficiency and effectiveness. These findings suggest that CFG-guided path precomputation offers a scalable alternative for capturing higher-order structural dependencies in graph-based learning.
Graph Convolutional Networks (GCNs) have recently gained significant attention due to the success of Convolutional Neural Networks in image and language processing, as well as the prevalence of data that can be represented as graphs. However, GCNs are limited by the size of the graphs they can handle and by the oversmoothing problem, which can be caused by the depth or the large receptive field of these networks. Existing approaches address these limitations by leveraging minibatch training paradigm. However, the strategy of selecting subgraphs to form minibatches is a challenging task because of the dependency between nodes. In this work, we propose a general framework for generating minibatches in an effective way that ensures minimal loss of node interdependence information, preserves the original graph properties, and diversifies the samples for the GCN to improve generalization. We test our training process on real-world datasets with several well-known GCN models and demonstrate the improved results compared to existing methods.
In this paper, we introduce a Generalized Biased Infinity Laplacian on graphs, which is an interpolation between two eikonal operators. Within this framework, we investigate evolution equations governed by this class of operators, establishing the existence and uniqueness of their solutions. Finally, we explore the application of these operators to general functions for solving various problems in machine learning.
Document entity recognition is a critical task in the field of document analysis. While many large language models have demonstrated success in this domain, they often fail to incorporate the spatial layout relationships between entities within a document. In this work, we introduce VisHubGAT, a novel graph-based model that integrates visible connectivity and hub nodes to enhance entity classification. Our approach constructs a document graph representation where hub nodes aggregate label-specific features, leveraging pre-trained models such as BERT and LayoutLMv3. Additionally, we introduce multi-type edges to encode both spatial and semantic relationships, and a Graph Attention Network (GAT) with edge-aware attention, which incorporates edge features into the attention mechanism for improved relational modeling. An edge classification layer further refines entity connectivity. Our approach effectively captures inter-entity relationships within the document, thereby enhancing the entity classification capabilities of large language models on public datasets (FUNSD, CORD, DocILE), showing state-of-the-art results by using different modalities. Ablation studies highlight the importance of our structured graph design for document entity recognition.
