# Establishing Two-Dimensional Dependencies for Multi-Label Image Classification
## 1 Introduction  
Multi-label image classification (MLIC) is a fundamental yet crucial task in the domain of computer vision, with profound implications in diverse fields such as target detection [1, 2, 3], medical image recognition [4, 5, 6], and human attribute recognition [7, 8, 9]. Since targets typically coexist in the real world, a key aspect of MLIC lies in establishing dependencies between targets.  
In the literature, previous methods have primarily focused on modeling spatial dependencies or label semantic dependencies. _(1) For modeling spatial dependencies_, convolution-based architectures [10, 11] are the most commonly utilized approach. However, due to the constraint of the kernel size, the receptive field of CNN networks is limited, which would lead to a problem, i.e., the establishment of spatial dependency can be significantly affected by the pixel distance between targets. Therefore, it is challenging to establish effective long-range spatial dependencies when the targets in an image are distantly located. _(2) For modeling label semantic dependencies_, architectures [12, 13] based on Graph Convolutional Networks (GCNs) are the most commonly utilized approach. However, the utilization of first-order neighborhood aggregation in the standard GCN formulation leads to a limitedexpressive power to the GCN and a lack of global information integration. For example, based on human experience, the probability of 'dog' and 'fork' appearing together is typically low, but if there is a 'person' present, the probability of 'dog' and 'fork' appearing together significantly increases. However, existing methods fail to consider the impact of the presence of 'person' on the coexistence probability of 'dog' and 'fork'.  
In multi-label image classification, existing methods face limitations in modeling long-range spatial dependencies and global semantic dependencies. Traditional CNNs are constrained by convolutional kernel sizes, making it difficult to capture long-range spatial relationships, while traditional GCNs rely only on first-order neighborhood aggregation, thus lacking the ability to integrate global information. To address these challenges, we propose the TDDM, which incorporates the SFDM and the LSDM to simultaneously model spatial and semantic dependencies. SFDM enhances cross-layer feature interactions through the FFM and FEM, improving feature representation and effectively capturing long-range spatial dependencies. LSDM introduces the GREM, which employs a multi-head max-attention mechanism to overcome the local aggregation limitation of traditional GCNs, strengthening global semantic modeling. Compared to conventional CNNs [14, 15, 16], GCNs [17, 18], and existing multi-label classification methods [12, 19], TDDM jointly models spatial and semantic dependencies, achieving excellent results on multiple datasets. These results validate TDDM's effectiveness in modeling spatial and semantic dependencies, providing a more comprehensive solution for multi-label image classification.  
In short, there are two major challenges in the field of MLIC currently. Firstly, it is difficult to establish effective long-range spatial feature dependencies. Secondly, it is challenging to establish global label semantic dependencies. In this paper, inspired by the work of [12, 19], we propose a Two-Dimensional Dependency Model (TDDM) to simultaneously address the aforementioned issues. The TDDM consists of an Spatial Feature Dependency Module (SFDM), which establishes the dependency in the image spatial feature dimension, and a Label Semantic Dependency Module (LSDM), which establishes the dependency in the label semantic dimension. In the following, we will elaborate on our proposed method.