Upload folder using huggingface_hub (part 30)

parse/dev/arg1dQSS6Mh/arg1dQSS6Mh.md

@@ -0,0 +1,341 @@
+# ATTRIBUTE ALIGNMENT AND ENHANCEMENT FOR GENERALIZED ZERO-SHOT LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Generalized zero-shot learning (GZSL) aims to recognize both seen and unseen classes, which challenges the generalization ability of a model. In this paper, we propose a novel approach to fully utilize attributes information, referred to as attribute alignment and enhancement (A3E) network. It contains two modules. First, attribute localization (AL) module utilizes the supervision of class attribute vectors to guide visual localization for attributes through the implicit localization capability within the feature extractor, and the visual features corresponding to the attributes (attribute-visual features) are obtained. Second, enhanced attribute scoring (EAS) module employs the supervision of the attribute word vectors (attribute semantics) to project input attribute visual features to attribute semantic space using Graph Attention Network (GAT). Based on the constructed attribute relation graph (ARG), EAS module generates enhanced representation of attributes. Experiments on standard datasets demonstrate that the enhanced attribute representation greatly improves the classification performance, which helps A3E to achieve state-of-the-art performances in both ZSL and GZSL tasks.
+
+# 1 INTRODUCTION
+
+Zero-shot learning aims to recognize unseen classes that have not been appeared during training phase, a common solution resort to auxiliary information to bridge the gap between seen and unseen domains to achieve knowledge transfer from the seen to the unseen. Semantics are the most frequently used auxiliary information for ZSL, either by class descriptions, word vectors (Mikolov et al., 2013) or attributes (Farhadi et al., 2009). A general paradigm (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Min et al., 2020; Xie et al., 2020; Ge et al., 2021; Liu et al., 2021b; Chen et al., 2021b; 2022) is to learn a mapping that projects visual features of seen samples into an embed-ding space to align with semantic attributes. With the assumption that seen and unseen domains share the same attribute space, the learned knowledge from seen classes is easily transferred to the unseen ones. And then, the subsequent classi-fication is accomplished by measuring compatibility scores between the projected features and the attribute prototypes. Recent works on embeddings turn to local features of image parts, i.e. part-based embedding meth-ods (Elhoseiny et al., 2017), to learn discriminative features easy for classification. Comparatively, gener-ative methods (Xian et al., 2019b; Huynh & Elhamifar, 2020a; Ma & Hu, 2020; Han et al., 2021; Chen et al., 2021a;c; Chou et al., 2021) utilize semantic information of unseen classes to synthesize unseen visual features by a generative model, such as generative adversarial network (GAN) (Goodfellow et al., 2020) or variational autoencoder (VAE) (Kingma & Welling, 2013), so that convert zero-shot classification to the traditional supervised model learning that could be trainable with generated samples. However, the features inferred from semantic information mostly are high-level visual representation, which are often non-discriminative to class recognition (Huynh & Elhamifar, 2020b; Xian et al., 2019b; Huynh & Elhamifar, 2020a).
+
+Recently, generalized zero-shot learning (GZSL) for its rigorous and realistic nature has received increasing attention in this field, where seen classes and unseen classes constitute the testing space. Embedding methods are inherently inferior in GZSL since the model training merely relies on samples of seen classes, and thus inevitably biases towards the seen ones. Moreover, the visual-semantic alignment in embedding models is just operated in seen domain, and the visual di-vergence between seen and unseen domains may strengthen the bias, namely domain shift ( $\mathrm { F u }$ et al., 2014). Different methods have been explored to improve the model performance in GZSL. Some studies try to mitigate the bias by introducing constraints on losses to calibrate output pre-diction probability, which usually require unseen semantics as side infor-mation (Huynh & Elhamifar, 2020b; Xie et al., 2020). The Parts Relation Rea-soning is used in RGEN (Xie et al., 2020) to capture appearance relationships among image parts, which is believed to be a complementary cue for improving the performance. GCNZ (Velickovi ˇ c et al., 2018) utilizes class relationships to infer classifier parame- ´ ters directly from knowledge graph. Relation learning is no novelty to ZSL, however, the semantic relationship between attributes is rarely explored in previous works. Huynh & Elhamifar (2020b) have informed us by introduc-ing word vectors of attribute that there is a wealth of semantic information in attributes beyond the commonly used class attribute vectors. There are also rich semantic relationships between attributes, which can be transferred to visual domain to help mitigate visualsemantic gap. Once the relations between attributes are modeled, it is possible to enhance the fi-nal prediction of classes by the interplay of attributes. Existing methods tried to capture the semantic relations in the at-tributes, such as using the entanglement of CNN and GCN based on knowledge graph about attrib-utes (Hu et al., 2022). However, despite the fact that nodes in graph are explic-itly defined as attributes, those methods lack a mechanism to accurately align nodes to the corresponding attributes. To the best of our knowledge, the fusion of relation learning and attention mechanism has not been studied in ZSL.
+
+![](images/b00a5d11c0c9f40b1dfa49fff812cc467d8778948d4c15c8feb819dabea8846e.jpg)  
+Figure 1: Attribute Localization.
+
+Accordingly, we propose an attribute alignment and enhancement (A3E) network for GZSL, which incorporates attribute alignment (AA) pipeline and attribute enhancement (AE) module. AA pipeline consists of attribute localization (AL) module and attribute scoring (AS) module, this novel approach of attribute alignment allows model to subtly catch visual features corresponding to attributes (namely attribute-visual features, AVFs) by fully utilization of attribute knowledge (both class attribute vectors and attribute word vectors). Compared to previous part-based methods that require complex accessories such as attention module and part detector, A3E simplifies its AA pipeline to a single convolutional layer with a single linear transformation, and still delivers competitive results. Most importantly, the resulted AVFs serve as the carriers for attributes which support the subsequent attribute enhancement process. In order to model the relations of attributes, AE module first constructs an attribute-relation graph (ARG), where relation-ships of attributes are quantified as graph edges, then, facilitated by graph neural networks, embeds the input AVFs into attribute semantics space. The enhanced attribute features are obtained through the outputs of graph nodes. Figure 1 demonstrates the basic process of AE module. Experiments in three standard ZSL datasets show that A3E reaches the state-of-the-art results in both ZSL and GZSL without extra information from unseen classes or auxiliary constraints on output probabilities, verifying the advantages of our proposed method.
+
+Our contributions can be summarized as:
+
+• A novel attribute enhancement (AE) module is created to explicitly model the relationship between attributes, and the enhanced attribute representation is generated with attribute-relations modeled inside.
+
+• To align graph nodes with attributes, an efficient attribute alignment (AA) pipeline is designed to generate visual fea-tures corresponding to attributes, namely attribute-visual features (AVFs).
+
+• We propose an attribute alignment and enhancement (A3E) network that based on the AA pipeline and AE module, an innovative combination of attention mechanism and semantic-relation learning.
+
+Extensive experiments on three bench-marks show that our design can significantly improve results in both ZSL and GZSL tasks.
+
+# 2 RELATED WORK
+
+There are two main paradigms for ZSL/GZSL: generative methods (Xian et al., 2019b; Huynh & Elhamifar, 2020a; Ma & Hu, 2020; Han et al., 2021; Chen et al., 2021a;c; Chou et al., 2021) and embedding methods (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Min et al., 2020; Xie et al., 2020; Ge et al., 2021; Liu et al., 2021b; Chen et al., 2021b; 2022). Generative methods covert ZSL problem into traditional supervised learning using visual features synthesized by generative models for unseen classes (Liu et al., 2021a). However, generative models such as GAN or VAE are often difficult to generate high-quality synthetic samples for unseen classes to train classifiers (Pourpanah et al., 2022). On the other hand, embedding methods learn a mapping that aligns visual features with semantic prototypes, therefore achieve knowledge transfer from seen to unseen classes via their sharable semantics. According to the mapping space, embedding methods can be divided into three categories: visual space embedding (Zhang et al., 2017), semantic space embedding (Zhu et al., 2019; Huynh & Elhamifar, 2020b; Xie et al., 2020; Liu et al., 2021b) and common space embedding (Min et al., 2020), with their respective pros and cons.
+
+As its name suggests, semantic space embedding projects visual features into semantic space. Recent studies further suggest that global visual features are detrimental to classification (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Xie et al., 2020). Instead of using noisy global features, part-based embedding methods try to improve classification performance by locating discriminative parts in image. Elhoseiny et al. (2017) deployed a visual part detector to link text descriptions with corresponding image regions, which would be fed into the part-based visual classifiers. SGMA (Zhu et al., 2019) employed a multi-attention module and DAZLE (Huynh & Elhamifar, 2020b) constructed a hierarchical linear structure, all in order to focus the model on discriminative regions in image. Whereas, the model with part detector attention module would become complex, so that make it difficult to train and optimize. SELAR (Yang et al., 2021) proposed to localize part features by the implicit localization ability within feature extractor, where the complex attention module is replaced with a single convolution layer. Most of the above models use class attribute vectors as semantic information. However, since the attribute space spanned by class attribute vectors is inevitably suffered from hubness problem (Zhang et al., 2017), the choice of embedding space is still an issue that is worth to explore in subsequent study.
+
+With the increasing attention paid to ZSL, various techniques from other fields were also incorporated into ZSL models, such as knowledge distillation (Chen et al., 2022), meta-learning (Verma et al., 2020) and graph learning (Xie et al., 2020; Wang et al., 2018). Graph Neural Networks (GNNs) (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018) were proposed to model non-Euclidean ´ data, especially for those with graph structure. Velickovi ˇ c et al. (2018) firstly introduced Graph Con- ´ volutional Networks (GCN) (Kipf & Welling, 2017) to explicitly model relations between classes in ZSL by knowledge graph. And RGEN (Xie et al., 2020) employed GCN to represent the relations among local image regions. Whereas, none of them have explored the semantic relations that implied within attributes.
+
+Inspired by the advantages and deficiencies of previous works, our proposed A3E employs a dual embedding strategy to fully utilize the rich semantics beneath attributes, and incorporates GAT (Velickovi ˇ c et al., 2018) to dynamically model the semantic relations between attributes. ´
+
+# 3 ATTRIBUTE ALIGNMENT AND ENHANCEMENT
+
+In this section, we will specify how and why the A3E network is proposed. Here we follow the pipeline that A3E processes the samples, and present the whole structure and details of our model.
+
+# 3.1 ATTRIBUTE LOCALIZATION
+
+In order to explore those rich semantics and relations between attributes, we need to obtain the visual representations for attributes first. Instead of generating discriminative regions using various of attention modules, Yang et al. (2021) innovated to utilize the implicit attribute localization ability
+
+within feature extractor (CNNs) to get part location, here we refer to it as attribute localization (AL). AL greatly reduces the complexity of the model by replacing the complicated attention module with a single $1 \times 1$ convolution:
+
+$$
+\tilde { \mathbf { a } } = c o n v \left( \mathbf { v } \right)
+$$
+
+where, $\mathbf { v } = \varphi \left( \mathbf { x } _ { i } \right)$ is the visual features with $H \times W \times C$ dimensions extracted by the backbone network $\varphi \left( \cdot \right)$ . $\mathbf { x } _ { i }$ is the $i -$ th input image, and conv $( \cdot )$ is the $1 \times 1$ convolution with $1 \times 1 \times C \times A$ parameters. $\mathbf { \tilde { a } } \in \mathbb { R } ^ { H \times W \times A }$ is the output features with attribute localization, referred to as attribute features.
+
+Under the supervision of attribute vectors, this simple convolution could gather most important spacial information of attributes. The loss function of AL module is defined as follows:
+
+$$
+\mathcal { L } _ { A L } = \mathcal { C E } \left( S o f t M a x \left( \mathbf { A } ^ { S } G M P ( c o n v \left( \mathbf { v } \right) ) ^ { T } \right) , y _ { i } \right)
+$$
+
+where $y _ { i }$ is the label of $i -$ th input image, and $G M P \left( \cdot \right)$ is the global maximum pooling function that employs spatial aggregation to the attribute features. $\mathbf { A } ^ { S } \in \mathbb { R } ^ { N ^ { S } \times A }$ is the seen attributes matrix where $N ^ { S }$ is the number of seen classes. $S o f t M a x \left( \cdot \right)$ is SoftMax activation function and $\mathcal { C } \mathcal { E } \left( \cdot \right)$ is the cross entropy loss commonly used in ZSL models.
+
+Blue area at the bottom of Figure 2 shows the layout of AL module.
+
+# 3.2 ATTRIBUTE SCORING
+
+As mentioned in the previous section, attribute space, despite being commonly used in ZSL models, suffers from several problems like hubness problem. We are aware of the rich semantic information beneath attributes. Inspired by Huynh & Elhamifar (2020b), we introduce attribute semantic space to collaborate with attribute space, which forms our attribute scoring (AS) module.
+
+With the attribute features from AL module, the visual location of every attribute is encoded in each channel of ˜a. Naturally, we thought of making it into a set of attention masks as a substitute for attention mechanism. The attribute masks are obtained through the sigmoid function that normalizes values of each channel in ˜a into a range from 0 to 1, where the value approaching to 1 stands for high confidence of having attribute-related visual features in the location, while that approaching to 0 is the opposite. Therefore, we can extract visual features for each attribute-related image region using attribute masks by performing the broadcasted Hadamard production between visual features $\mathbf { v } \in \mathbb { R } ^ { H \times W \times C }$ and each channel of normalized ˜a, which produces A masked visual features that correspond to A attributes, namely attribute-visual features (AVFs) $\mathbf { v } ^ { ( a ) } \in \mathbb { R } ^ { H \times W \times C }$ $( a \in [ 1 , A ] )$ .
+
+To achieve zero-shot classification, the next step is to map AVFs into attribute semantic space with reference to DAZLE (Huynh & Elhamifar, 2020b). The attribute semantic space is constructed using word vectors of attributes that are usually produced by word vector models like Word2Vec (Mikolov et al., 2013). With these attribute word vectors, we employ AS module to map the above AVFs into attribute sematic space, and then calculate the class score of samples as follows:
+
+$$
+\begin{array} { c } { { \hat { \mathbf { e } } _ { a } = \mathbf { W } \left( G A P \left( \mathbf { v } ^ { ( a ) } \right) \right) , a \in \left[ 1 , A \right] } } \\ { { p _ { a } = \mathbf { e } _ { a } \hat { \mathbf { e } } _ { a } ^ { T } , a \in \left[ 1 , A \right] } } \\ { { s ^ { c } = \mathbf { a } ^ { c } \mathbf { p } ^ { T } , c \in \left[ 1 , N ^ { S } \right] } } \end{array}
+$$
+
+where $G A P \left( \cdot \right)$ is the global average pooling function that aggregates AVFs into $1 \times C$ dimensions, and $\mathbf { W } \left( \cdot \right)$ is the linear mapping with $1 \times C \times e$ parameters. $\hat { \textbf { e } } \in \mathbb { R } ^ { 1 \times e }$ is the predicted word vector, and $\mathbf { e } \in \mathbb { R } ^ { 1 \times e }$ is the ground truth attribute word vector. $p _ { a }$ is the attribute score for the $a -$ th attribute. $ { \mathbf { p } } \in \mathbb { R } ^ { 1 \times A }$ is the concatenation of $p _ { a } \left( a \in \left[ 1 , { \cal A } \right] \right)$ . $\mathbf { a } ^ { \hat { c } } \in \mathbb { R } ^ { 1 \times A } \left( c \in \left[ 1 , N ^ { S } \right] \right)$ is the class attribute vector of the $c -$ th class which is extracted from the $c -$ th row of attribute matrix $\mathbf { A } ^ { S }$ . And $s ^ { c }$ is the class score of the current sample belonging to the $c -$ th class.
+
+Thus, the attribute scoring loss based on cross entropy is designed:
+
+$$
+\mathcal { L } _ { A S } = \mathcal { C E } \left( S o f t M a x \left( \mathbf { s } _ { A S } \right) , y _ { i } \right)
+$$
+
+where $\mathbf { s } _ { A S } \in \mathbb { R } ^ { N ^ { S } }$ is the concatenation of class score $s ^ { c } \left( c \in \left[ 1 , N ^ { S } \right] \right)$
+
+Ultimately, a novel attribute alignment (AA) pipeline is constructed, which consists of AL and AS modules. AA innovates attribute alignment approach through integrating attribute space and attribute semantic space into a unified pipeline of ZSL model. Subsequently, we will model the relations between attributes.
+
+# 3.3 ATTRIBUTE ENHANCEMENT
+
+Studies on CNNs (or DNNs) have shown that feature extractor built up by convolutional neurons does well in extracting visual patterns from images. However, what they are not good at is to extract non-visual concepts from image samples. Unfortunately, the abstract concepts are common in the attribute sets of many ZSL datasets. For example, Animals with Attributes 2 (AwA2) (Xian et al., 2019a) has 85 expert-defined attributes in total. Roughly half of these attributes can be directly related to visual representations (like “stripes” and “tail”), while more than half of them do not correspond directly to the visual representation (such as “fast” and “smart”). This is even more troublesome for part-based ZSL methods since it is hard to locate a visual region for such non-visual attributes thus confusing the model.
+
+To address the issue, we turn to exploiting the implicit semantic relations between attributes. The idea is to dynamically build the associations between visual-related attributes and non-visual attributes by modeling the relations between them. With the assumption that all attributes share the same semantic space, it allows the model to enhance the usability of non-visual attributes using representations of visual-related attributes.
+
+In order to model the relations of attributs, we construct an attribute relation graph (ARG) $\mathbf { G } _ { A }$ based on point-wise mutual information (PMI) (Bouma, 2009) according to $\mathrm { H u }$ et al. (2022). Let $\mathbf { G } _ { A }$ has A vertices corresponding to A attributes, the edges between attributes (vertices) are defined based on their normalized PMI values referring to threshold $\delta$ :
+
+$$
+{ { A } _ { i , j } } = { { A } _ { j , i } } = \left\{ \begin{array} { c } { 1 , P M { { I } _ { n } } \left( x , y \right) > \delta } \\ { 0 , e l s e } \end{array} \right.
+$$
+
+where $A _ { i , j }$ is the element in the $i -$ th row and $j -$ th column of A. We use the undirected graph for ARG, so that its adjacency matrix is symmetric, that is $A _ { i , j } = A _ { j , i }$ . See Appendix A for the detailed formula of PMI. The selection of threshold $\delta$ will be discussed in detail in experiments section.
+
+So far, ARG discussed above is still a static structure shared by all categories, which cannot be dynamically optimized with different classes and samples. Meanwhile, the PMI-based connections (graph edges) may not always represent the correct relations between attributes. Therefore, instead of using the well-known graph convolutional networks (GCN), we leverage graph attention networks (GAT) (Velickovi ˇ c et al., 2018) to achieve dynamic modeling based on ARG. ´
+
+GAT proposed by Velickovi ˇ c et al. can dynamically adjust edge weights with self-attention mech- ´ anism to solve a series of problems in spatial GNNs. According to AA pipeline in the previous subsection, A sets of global AVFs $\bar { \mathbf { v } } ^ { ( a ) }$ $( a \in [ 1 , A ] )$ belonging to the sample $x _ { i }$ are obtained, which will be subsequently used as the input of nodes in $\mathbf { G } _ { A }$ . We use a two-layer GAT network in the paper, i.e. $l \in \{ \bar { 0 } , 1 \}$ . The outputs of GAT are the predicted word vectors $\tilde { \mathbf { e } } _ { a } ^ { \cdot } \in \mathbb { R } ^ { 1 \times e } ( a \in [ 1 , A ] )$ from each node, where $e$ is the dimension of word vector. In the process, GAT not only projects the input global AVFs into attribute semantic space (like the AS module), but also models attribute relations in the output, namely predicted word vectors $\hat { \mathbf { e } } _ { a }$ . With the help of ARG that connected attributes by their semantic relation, GAT can enhance the expression of certain attribute-related features (especially those from non-visual attributes), yielding more discriminative semantic representations. Hence, we name it attribute enhancement (AE) module.
+
+As the output of AE module has the same form of predicted word vectors like AS module, an integrated enhanced attribute scoring (EAS) module is naturally formed. We can follow formula (3), (4) and (5) to calculate the class score vector $\mathbf { s } _ { E A S }$ , and the enhanced attribute scoring loss is constructed as:
+
+![](images/d6a040d03d386625ef5f5dcf7df0f44dd3f08c641ea6e76f8b3041053ac29215.jpg)  
+Figure 2: Attribute Alignment and Enhancement Network.
+
+$$
+\mathcal { L } _ { E A S } = \mathcal { C E } \left( S o f t M a x \left( \mathbf { s } _ { E A S } \right) , y _ { i } \right)
+$$
+
+The dropout strategy is often used to improve the generalization of GNN models by randomly “dropping” some nodes (sweeping node features) during training. The method is originally used in GNNs to suppress over-smoothing problem (Li et al., 2018), while we use here to perturb the original data (AVFs) to enhance the generalization of the model. Subsequent experiments will demonstrate the significant impact of the dropout strategy on GZSL performance.
+
+# 3.4 GENERALIZED ZERO-SHOT IMAGE CLASSIFICATION
+
+Finally, by integrating the attribute localization (AL) module and enhanced attribute scoring (EAS) module, A3E network for GZSL is constructed (see Figure 2).
+
+# 3.4.1 OVERALL LOSS
+
+The overall loss function of A3E is:
+
+$$
+\mathcal { L } _ { A 3 E } = \lambda \mathcal { L } _ { A L } + \left( 1 - \lambda \right) \mathcal { L } _ { E A S }
+$$
+
+where $\lambda$ is the weighting coefficient that balance the two modules.
+
+# 3.4.2 INFERENCE
+
+In the inference stage, A3E employs a fusion prediction method as follows:
+
+$$
+\hat { y } = \arg \operatorname* { m a x } _ { c \in N } \left( \lambda \mathbf { s } _ { A L } + \left( 1 - \lambda \right) \mathbf { s } _ { E A S } + \beta \Delta _ { \left[ c \in N ^ { U } \right] } \right)
+$$
+
+where $\hat { y }$ is the predicted label, and $\lambda$ is a coefficient which has identical function with the one in training loss. $\mathbf { s } _ { A L }$ is the output probability of AL module and $\mathbf { s } _ { E A S }$ is the output probability of EAS module. $N = N ^ { S } \cap N ^ { U }$ is the set of all classes labels. $\beta$ is an adjustable bias, and $\Delta _ { [ c \in N ^ { U } ] }$ is an indicator which will take 1 for unseen classes, and -1 for seen classes.
+
+To alleviate the inevitable bias caused by domain shift in GZSL, we set a calibration bias refer to (Huynh & Elhamifar, 2020b). However, it is worth notice that unlike (Huynh & Elhamifar,
+
+Table 1: Results of conventional ZSL and GZSL classification on AwA2, CUB and SUN datasets. The best and second-best results are marked in bold and underline, respectively. The symbol “-” indicates no results. The symbol “\*” represents models with $4 4 8 \times 4 4 8$ input size.   
+
+<table><tr><td rowspan="3" colspan="2">Methods</td><td colspan="4">AwA2</td><td colspan="4">CUB</td><td colspan="4">SUN</td></tr><tr><td>ZSL MCA</td><td rowspan="2"></td><td colspan="2">GZSL</td><td>ZSL</td><td></td><td colspan="2">GZSL</td><td>ZSL</td><td></td><td colspan="2">GZSL</td></tr><tr><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td></tr><tr><td colspan="2">Generative Methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CVPR 2019 f-VAEGAN-D2</td><td></td><td>71.1</td><td>57.6</td><td>70.6</td><td>63.5</td><td>61.0</td><td>48.4</td><td>60.1</td><td>53.6</td><td>64.7</td><td>45.1</td><td>38.0</td><td>41.3</td></tr><tr><td>NeurIPS 2020 Composer</td><td></td><td>71.5</td><td>62.1</td><td>77.3</td><td>68.8</td><td>69.4</td><td>56.4</td><td>63.8</td><td> 59.9</td><td>62.6</td><td>55.1</td><td>22.0</td><td>31.4</td></tr><tr><td>ICCV 2021</td><td>FREE</td><td>-</td><td>60.4</td><td>75.4</td><td>67.1</td><td>：</td><td>55.7</td><td>59.9</td><td> 57.7</td><td>-</td><td>47.4</td><td>37.2</td><td>41.7</td></tr><tr><td colspan="2">EmbeddingMethods</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NeurIPS 2019</td><td>SGMA</td><td>68.8*</td><td>37.6*</td><td>87.1*</td><td>52.5*</td><td>71*</td><td>36.7*</td><td>71.3*</td><td>48.5*</td><td>：</td><td>-</td><td>：</td><td>-</td></tr><tr><td>CVPR 2020</td><td>DAZLE</td><td>1</td><td>60.3</td><td>75.7</td><td>67.1</td><td>65.9</td><td>56.7</td><td>59.6</td><td>58.1</td><td>-</td><td>52.3</td><td>24.3</td><td>33.2</td></tr><tr><td>ECCV 2020</td><td>RGEN</td><td>73.6</td><td>67.1</td><td>76.5</td><td>71.5</td><td>76.1</td><td>60.0</td><td>73.5</td><td>66.1</td><td>63.8</td><td>44.0</td><td>31.7</td><td>36.8</td></tr><tr><td>AAAI 2021</td><td>SR2E</td><td>：</td><td>58*</td><td>80.7*</td><td>67.5*</td><td>-</td><td>61.6*</td><td>70.6*</td><td>65.8*</td><td>-</td><td>43.1*</td><td>36.8*</td><td>39.7*</td></tr><tr><td>SPL 2021</td><td>SELAR</td><td>：</td><td>52.0</td><td>71.9</td><td>60.3</td><td>：</td><td>62.4</td><td>64.9</td><td>63.6</td><td>：</td><td>40.5</td><td>32.9</td><td>36.3</td></tr><tr><td>NeurIPS 2021</td><td>HSVA</td><td>-</td><td>56.7</td><td>79.8</td><td>66.3</td><td>62.8</td><td>52.7</td><td>58.3</td><td> 55.3</td><td>63.8</td><td>48.6</td><td>39.0</td><td> 43.3</td></tr><tr><td>CVPR 2022</td><td>MSDN</td><td>70.1*</td><td>62*</td><td>74.5*</td><td>67.7*</td><td>76.1*</td><td>68.7*</td><td>67.5*</td><td>68.1*</td><td>65.8*</td><td>52.2*</td><td>34.2*</td><td>41.3*</td></tr><tr><td>ours</td><td>A3E</td><td>74.1</td><td>69.3</td><td>71.2</td><td>70.2</td><td>74.9*</td><td>66.3*</td><td>71.6*</td><td>68.8*</td><td>64.0*</td><td>46.8*</td><td>30.0*</td><td>36.5*</td></tr></table>
+
+2020b), the calibration in our method only includes a bias on the prediction probability, and does not include any additional loss term that usually requires unseen semantics to adjust output predictions.
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENTAL SETUP
+
+# 4.1.1 DATASETS
+
+We evaluate A3E network on three GZSL benchmarks: Animals with Attributes 2 (AwA2) (Xian et al., 2019a), Caltech-UCSD Birds 200-2011 (CUB) (Wah et al., 2011) and SUN attribute database (SUN) (Patterson et al., 2014). AwA2 is a coarse-grained dataset with 37,322 images from 50 animal classes, each of which has 85 attributes. While, CUB is a fine-grained bird dataset containing 11,788 images from 200 bird classes with 312 attributes. SUN is also a fine-grained dataset which includes 14,340 images from 717 scene categories, and each class has a 102-dimension attribute vector.
+
+In order to fairly compare with the state-of-the-art ZSL models, we adopt the proposed split (PS) of datasets presented in (Xian, Schiele, and Akata 2017). Evaluation metrics are shown in Appendix B
+
+# 4.1.2 IMPLEMENTATION DETAILS
+
+All the experiments in the paper are conducted on NVIDIA GeForce RTX 3090 with 24 GB video memory size. Software versions are Python 3.9, PyTorch 1.11.0, NumPy 1.22.3 and CUDA 11.3.
+
+For better reproducibility of experiment results, we manually fixed the random seed to 1024 for all tests. Detailed settings would be listed in Appendix C
+
+# 4.2 COMPARISON WITH STATE-OF-THE-ARTS
+
+We compare our A3E network with several state-of-the-art models in both ZSL setting and GZSL setting. The results are presented in Table 1. On the ZSL side, A3E shows very gratifying results in all three datasets. While it is competitive compared with the state-of-the-art models on CUB and SUN, the most compelling achievement is that A3E outperforms the long-standing record by RGEN (Xie et al., 2020) on AwA2 since 2020. On the GZSL side, A3E reaches the highest harmonic mean $( 6 8 . 8 \% )$ on CUB dataset, which is the current best generalized model on CUB. It also gets a satisfactory performance on AwA2, though is inferior to RGEN. Whereas, harmonic mean of A3E on AwA2 is still improved by at least $2 . 5 \%$ compared with the former state-of-the-art models, which verifies that A3E is a strong competitor so far, compared with most of the models except for RGEN. In general, the results prove that the proposed attribute alignment and enhancement work effectively on AwA2 and CUB, which are beneficial to represent the rich semantic relations between attributes hidden in AwA2 and CUB. The data characteristic of AwA2 and CUB promotes A3E network more generalized. However, the performance on SUN dataset declines sharply. The reason accounted for the phenomenon is that attributes of SUN are more abstract which are hard to capture their correspondent image regions. More importantly, the semantic relations are too sparser compared with the former datasets to affect the performance of attribute enhancement.
+
+Table 2: Ablation study under two datasets. The best results are marked in bold.   
+
+<table><tr><td rowspan="3">Method</td><td colspan="4">AwA2</td><td colspan="4">CUB</td></tr><tr><td>ZSL</td><td></td><td>GZSL</td><td></td><td>ZSL</td><td></td><td>GZSL</td><td></td></tr><tr><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td></tr><tr><td>AL+AS(AA pipeline)</td><td>60.4</td><td>52.6</td><td>78.5</td><td>63.0</td><td>57.7</td><td>44.6</td><td>60.5</td><td>51.3</td></tr><tr><td>AL+EAS(A3ENetwork)</td><td>74.1</td><td>69.3</td><td>71.2</td><td>70.2</td><td>74.9</td><td>66.3</td><td>71.6</td><td>68.8</td></tr></table>
+
+Among all comparison models, DAZLE, RGEN and MSDN are the most noteworthy as well as our A3E network. They have some similarity in research motivation. DALZE and MSDN adopt attribute scoring mechanisms, as well as A3E. RGEN uses GNN to perform region-based relations on visual features. Whereas, A3E employs AE module to model semantic relations between attributes. From the GZSL results on AwA2 and CUB, A3E successfully surpasses these models by the stable performance which can be expressed as the average of harmonic means: A3E network reaches $6 9 . 5 \%$ in average, while DAZLE, RGEN and MSDN are $6 2 . 6 \%$ , $6 8 . 8 \%$ and $6 7 . 9 \%$ , respectively(see Appendix D). The more surprising fact is that when A3E generalizes well in GZSL settings, it does not resort to any probability tricks commonly used in above models, such as the balance loss used by RGEN and the calibration loss used in DALZE and MSDN models. The modified losses by the probability tricks require the supervision from unseen semantics during training, which are contrary to the original setting of ZSL to some extent. In contrast, A3E only relies on seen samples and generalizes better than those models that require unseen semantics, which further demonstrates the superiority of the propose method.
+
+# 4.3 ABLATION STUDY
+
+# 4.3.1 EFFECTS OF ATTRIBUTE ENHANCEMENT
+
+The proposed A3E network is composed of three interrelated modules, namely, AL, AS and AE modules. Among them, AE module based on GAT is the most innovative and representative component of our work. To further evaluate the efficacy of attribute enhancement in actual task, we conduct ablation studies on AwA2 and CUB datasets, by setting the baseline model with only AL and AS modules, i.e. attribute alignment (AA) pipeline. Table 2 shows the results of ablation study.
+
+To fairly compare the baseline model with A3E network, we use the same parameter setting in both. Even so, the ZSL accuracy of A3E has improved by staggering $1 3 . 7 \%$ and $1 7 . 2 \%$ for AwA2 and CUB datasets, respectively. Similarly, drastic performance boost is also present in the GZSL setting, where A3E exceeds the baseline by up to $7 . 2 \%$ and $1 7 . 5 \%$ in harmonic mean metric on AwA2 and CUB, respectively. Thus, with the help of AE module, A3E exceeds the baseline with absolute superiority in all settings, with an even greater advantage in CUB. In effect, the characteristics of attributes such as semantics and relations vary with different datasets. The reason that the performance on CUB has dramatic improvement by AE module is resulted from the stronger semantic relations between attributes of CUB, where attributes are more uniform to describe image contents.
+
+# 4.3.2 EFFECTS OF DROPOUT
+
+To investigate the effects of dropout in AE module, we conduct experiments with different dropout rates on CUB dataset. The results are concluded in Appendix E.
+
+![](images/9a441089bba5cbdf9cd6f80114e0846909569ec537d2cfc00a4f313c4dd4cd29.jpg)  
+Figure 3: Effects of weighting coefficient $\lambda$ on Figure 4: Effects of threshold $\delta$ on AwA2 and AwA2 and CUB datasets. CUB datasets.
+
+# 4.4 HYPERPARAMETER ANALYSIS
+
+# 4.4.1 EFFECTS OF WEIGHTING COEFFICIENT $\lambda$
+
+Figure 3 is the summary of the experimental results on tuning weighting coefficient $\lambda$ between AL and EAS modules. We do not show experiments for $\lambda$ at 0 and 1 since they are no longer considered in our A3E model. In CUB dataset (see Figure 3(b)), both ZSL and GZSL indicators increase with the rise of $\lambda$ . While in AwA2 dataset (see Figure 3(a)), the accuracies of unseen classes in ZSL and GZSL rise with the increase of $\lambda$ . But the accuracy of seen classes in GZSL shows the opposite trend, so as to cause harmonic means of GZSL slowly improving. The increasing of $\lambda$ represents that the model emphasizes more on AL module learning. Results show that despite the simpler structure and fewer parameters of the AL module, its importance in the objective function is no less than that of the EAS module. It is proven by the results that model performance improves as the effort invested in AL module (i.e., value of $\lambda$ ) increases. Specially, attribute localization is more demanding for the fine-grained datasets with more subtle features, such as the CUB dataset. Considering all the indicators, we set $\lambda$ to 0.6 and 0.9 for AwA2 and CUB, respectively.
+
+# 4.4.2 EFFECTS OF THRESHOLD $\delta$
+
+Threshold $\delta$ controls the generation of ARG. Smaller value of $\delta$ indicates easier connection between nodes in ARG, which means more edges in the graph. When $\delta = 1$ , there is no edge in ARG, so that AE module does not work. Figure 4 shows how different values of $\delta$ affect model performance on the two datasets. As $\delta$ increases in CUB dataset (see Figure 4(b)), all four metrics increase equally until $\delta = 0 . 8$ . In AwA2 dataset (see Figure 4(a)), we can find a general uptrend in the accuracy of unseen classes as $\delta$ increase, and the best accuracy is found at $\delta = 0 . 9$ . With the increase in $\delta$ , the edges representing attribute relationships in ARG should gradually decrease. Obviously, edges created by PMI do not perfectly correspond with the semantic relationships of attributes. We believe that the graphs generated by lower values of $\delta$ have more noisy connections (edges), which leads to the model performance decline. When the structure of ARG is simplified with higher threshold, GAT is more likely to obtain robust information from ARG, thus enhancing the classification performance. To balance the accuracies of seen classes and unseen classes, we set $\delta = 0 . 9$ and $\delta = 0 . 8$ for AwA2 and CUB, respectively.
+
+# 5 CONCLUSION
+
+In the paper, we propose an attribute alignment and enhancement (A3E) network, which consist of attribute alignment (AA) pipeline and AE module. Therefore, A3E can align each attribute with corresponding image region and enhance their representations by the semantic relations between attributes through GNNs. At last, the experiments on three ZSL datasets have demonstrated the superiority of A3E network on ZSL/GZSL classification.
+
+# REFERENCES
+
+Gerlof Bouma. Normalized (Pointwise) Mutual Information in Collocation Extraction. pp. 11, 2009.
+
+Shiming Chen, Wenjie Wang, Beihao Xia, Qinmu Peng, Xinge You, Feng Zheng, and Ling Shao. FREE: Feature Refinement for Generalized Zero-Shot Learning. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 122–131, Montreal, QC, Canada, October 2021a. IEEE. ISBN 978-1-66542-812-5. doi: 10.1109/ICCV48922.2021.00019.
+
+Shiming Chen, Guo-Sen Xie, Yang Liu, Qinmu Peng, Baigui Sun, Hao Li, Xinge You, and Ling Shao. HSVA: Hierarchical Semantic-Visual Adaptation for Zero-Shot Learning. pp. 13, 2021b.
+
+Shiming Chen, Ziming Hong, Guo-Sen Xie, Wenhan Yang, Qinmu Peng, Kai Wang, Jian Zhao, and Xinge You. MSDN: Mutually Semantic Distillation Network for Zero-Shot Learning, April 2022.
+
+Zhi Chen, Yadan Luo, Ruihong Qiu, Sen Wang, Zi Huang, Jingjing Li, and Zheng Zhang. Semantics Disentangling for Generalized Zero-Shot Learning. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 8692–8700, Montreal, QC, Canada, October 2021c. IEEE. ISBN 978-1-66542-812-5. doi: 10.1109/ICCV48922.2021.00859.
+
+Yu-Ying Chou, Hsuan-Tien Lin, and Tyng-Luh Liu. ADAPTIVE AND GENERATIVE ZEROSHOT LEARNING. pp. 14, 2021.
+
+Mohamed Elhoseiny, Yizhe Zhu, Han Zhang, and Ahmed Elgammal. Link the head to the ”beak”: Zero Shot Learning from Noisy Text Description at Part Precision, September 2017.
+
+Ali Farhadi, Ian Endres, Derek Hoiem, and David Forsyth. Describing objects by their attributes. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1778–1785, Miami, FL, June 2009. IEEE. ISBN 978-1-4244-3992-8. doi: 10.1109/CVPR.2009.5206772.
+
+Yanwei Fu, Timothy M. Hospedales, Tao Xiang, Zhenyong Fu, and Shaogang Gong. Transductive Multi-view Embedding for Zero-Shot Recognition and Annotation. In David Fleet, Tomas Pajdla, Bernt Schiele, and Tinne Tuytelaars (eds.), Computer Vision – ECCV 2014, volume 8690, pp. 584–599. Springer International Publishing, Cham, 2014. ISBN 978-3-319-10604-5 978-3-319- 10605-2. doi: 10.1007/978-3-319-10605-2 38.
+
+Jiannan Ge, Hongtao Xie, Shaobo Min, and Yongdong Zhang. Semantic-guided Reinforced Region Embedding for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 35(2):1406–1414, May 2021. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v35i2.16230.
+
+Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11):139–144, 2020.
+
+Zongyan Han, Zhenyong Fu, Shuo Chen, and Jian Yang. Contrastive Embedding for Generalized Zero-Shot Learning. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2371–2381, Nashville, TN, USA, June 2021. IEEE. ISBN 978-1-66544-509-2. doi: 10.1109/CVPR46437.2021.00240.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778, Las Vegas, NV, USA, June 2016. IEEE. ISBN 978-1-4673-8851-1. doi: 10.1109/ CVPR.2016.90.
+
+Yang Hu, Guihua Wen, Adriane Chapman, Pei Yang, Mingnan Luo, Yingxue Xu, Dan Dai, and Wendy Hall. Graph-Based Visual-Semantic Entanglement Network for Zero-Shot Image Recognition. IEEE Transactions on Multimedia, 24:2473–2487, 2022. ISSN 1520-9210, 1941-0077. doi: 10.1109/TMM.2021.3082292.
+
+Dat Huynh and Ehsan Elhamifar. Compositional Zero-Shot Learning via Fine-Grained Dense Feature Composition. pp. 12, 2020a.
+
+Dat Huynh and Ehsan Elhamifar. Fine-Grained Generalized Zero-Shot Learning via Dense Attribute-Based Attention. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4482–4492, Seattle, WA, USA, June 2020b. IEEE. ISBN 978-1-72817- 168-5. doi: 10.1109/CVPR42600.2020.00454.
+
+Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization, January 2017.
+
+Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013.
+
+Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Convolutional Networks, February 2017.
+
+Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning, January 2018.
+
+Lu Liu, Tianyi Zhou, Guodong Long, Jing Jiang, Xuanyi Dong, and Chengqi Zhang. ISOMETRIC PROPAGATION NETWORK FOR GENERALIZED ZERO-SHOT LEARNING. pp. 13, 2021a.
+
+Yang Liu, Lei Zhou, Xiao Bai, Yifei Huang, Lin Gu, Jun Zhou, and Tatsuya Harada. Goal-Oriented Gaze Estimation for Zero-Shot Learning, March 2021b.
+
+Peirong Ma and Xiao Hu. A Variational Autoencoder with Deep Embedding Model for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 34(07): 11733–11740, April 2020. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v34i07.6844.
+
+Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient Estimation of Word Representations in Vector Space, September 2013.
+
+Shaobo Min, Hantao Yao, Hongtao Xie, Chaoqun Wang, Zheng-Jun Zha, and Yongdong Zhang. Domain-aware Visual Bias Eliminating for Generalized Zero-Shot Learning, April 2020.
+
+Genevieve Patterson, Chen Xu, Hang Su, and James Hays. The SUN Attribute Database: Beyond Categories for Deeper Scene Understanding. International Journal of Computer Vision, 108(1-2): 59–81, May 2014. ISSN 0920-5691, 1573-1405. doi: 10.1007/s11263-013-0695-z.
+
+Farhad Pourpanah, Moloud Abdar, Yuxuan Luo, Xinlei Zhou, Ran Wang, Chee Peng Lim, Xi-Zhao Wang, and Q. M. Jonathan Wu. A Review of Generalized Zero-Shot Learning Methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1–20, 2022. ISSN 0162-8828, 2160-9292, 1939-3539. doi: 10.1109/TPAMI.2022.3191696.
+
+Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. pp. 30, 2014.
+
+Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua \` Bengio. Graph Attention Networks, February 2018.
+
+Vinay Kumar Verma, Dhanajit Brahma, and Piyush Rai. Meta-Learning for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04):6062–6069, April 2020. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v34i04.6069.
+
+Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The CaltechUCSD Birds-200-2011 Dataset. pp. 8, 2011.
+
+Xiaolong Wang, Yufei Ye, and Abhinav Gupta. Zero-shot Recognition via Semantic Embeddings and Knowledge Graphs, April 2018.
+
+Yongqin Xian, Christoph H. Lampert, Bernt Schiele, and Zeynep Akata. Zero-Shot Learning—A Comprehensive Evaluation of the Good, the Bad and the Ugly. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(9):2251–2265, September 2019a. ISSN 0162-8828, 2160- 9292, 1939-3539. doi: 10.1109/TPAMI.2018.2857768.
+
+Yongqin Xian, Saurabh Sharma, Bernt Schiele, and Zeynep Akata. F-VAEGAN-D2: A Feature Generating Framework for Any-Shot Learning. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10267–10276, Long Beach, CA, USA, June 2019b. IEEE. ISBN 978-1-72813-293-8. doi: 10.1109/CVPR.2019.01052.
+
+Guo-Sen Xie, Li Liu, Xiaobo Jin, Fan Zhu, Zheng Zhang, Jie Qin, Yazhou Yao, and Ling Shao. Attentive Region Embedding Network for Zero-Shot Learning. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 9376–9385, Long Beach, CA, USA, June 2019. IEEE. ISBN 978-1-72813-293-8. doi: 10.1109/CVPR.2019.00961.
+
+Guo-Sen Xie, Li Liu, Fan Zhu, Fang Zhao, Zheng Zhang, Yazhou Yao, Jie Qin, and Ling Shao. Region Graph Embedding Network for Zero-Shot Learning. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm (eds.), Computer Vision – ECCV 2020, volume 12349, pp. 562��580. Springer International Publishing, Cham, 2020. ISBN 978-3-030-58547-1 978-3-030- 58548-8. doi: 10.1007/978-3-030-58548-8 33.
+
+Shiqi Yang, Kai Wang, Luis Herranz, and Joost van de Weijer. On Implicit Attribute Localization for Generalized Zero-Shot Learning. IEEE Signal Processing Letters, 28:872–876, 2021. ISSN 1070-9908, 1558-2361. doi: 10.1109/LSP.2021.3073655.
+
+Li Zhang, Tao Xiang, and Shaogang Gong. Learning a Deep Embedding Model for Zero-Shot Learning. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3010–3019, Honolulu, HI, July 2017. IEEE. ISBN 978-1-5386-0457-1. doi: 10.1109/CVPR. 2017.321.
+
+Yizhe Zhu, Jianwen Xie, Zhiqiang Tang, Xi Peng, and Ahmed Elgammal. Semantic-Guided MultiAttention Localization for Zero-Shot Learning. pp. 11, 2019.
+
+# A POINT-WISE MUTUAL INFORMATION
+
+Point-wise mutual information (PMI) (Bouma, 2009) is proposed measure the relationship of two points (objects), defined as:
+
+$$
+P M I \left( x , y \right) = \ln \frac { p \left( x , y \right) } { p \left( x \right) p \left( y \right) }
+$$
+
+where $p \left( x , y \right)$ is the joint probability of $x$ and $y$
+
+In practice, the normalized PMI is more commonly used as:
+
+$$
+P M I _ { n } \left( x , y \right) = \frac { P M I \left( x , y \right) } { - \ln p \left( x , y \right) }
+$$
+
+where its values are in the range of [-1,1], which give a good indication of the relevance between $x$ and $y$ . Specifically, 1 means they are co-occurrence, while -1 shows the opposite case. But, 0 indicates they are not relevant at all.
+
+# B EVALUATION METRICS
+
+We consider both conventional ZSL and GZSL settings in all three datasets. Mean Class Accuracy $( M C A )$ is adopted as the evaluation indicator for ZSL setting, which takes average value of Top-1 accuracies on unseen classes. And harmonic mean $( H )$ is employed to evaluate the performance of GZSL setting, which is the most comprehensive metric to reflect model performance by taking accuracies of seen and unseen classes into consideration. The specific formula is defined as follows:
+
+$$
+H = \frac { 2 \times M C A _ { S } \times M C A _ { U } } { M C A _ { S } + M C A _ { U } }
+$$
+
+where $M C A _ { S }$ and $M C A _ { U }$ are the $M C A s$ for seen classes and unseen classes, respectively.
+
+# C MODEL SETTINGS
+
+We use the fixed ResNet101 (He et al., 2016) pretrained on ImageNet as the feature extractor of A3E network, which is commonly used as the backbone network in many models (Huynh & Elhamifar, 2020b; Xie et al., 2020; Ge et al., 2021; Chen et al., 2021b; 2022). The input images of model are reshaped as $2 2 4 \times 2 2 4$ pixels for AwA2 datasets and $4 4 8 \times 4 4 8$ pixels for CUB and SUN datasets since the finer details could significantly improve performance on fine-grained datasets. We use the Word2Vec model trained on Google News to generate attribute word vectors with 300 dimensions.
+
+We adopt ADAM optimizer (Kingma & Ba, 2017) in model training and set weigh decay to $1 \times 1 0 ^ { - 5 }$ . We empirically set the hidden layers and attention heads of GAT network in EAS module to $\{ 2 0 0$ , $1 \}$ for AwA2, $\{ 2 0 0 , 4 \}$ for CUB and $\{ 1 0 0 0 , 5 \}$ for SUN, with dropout rate fixed to 0.2. For AwA2 dataset, we set the learning rate to $5 \times 1 0 ^ { - 6 }$ , batch size to 64 and maximum iteration number to 10. Regarding to CUB dataset, the learning rate is set to $7 . 5 \times 1 0 ^ { - 6 }$ . Batch size is set to 8, and maximum iteration number is 30. As to SUN dataset, we set the learning rate to $5 \times 1 0 ^ { - 6 }$ , batch size to 16 and maximum iteration number to 25. The learning rate for $1 \times 1$ convolution in AL module is 10 times greater than the given values in all datasets. The calibration bias $\beta$ is set to 2.0, 0.4 and 0.4 for AwA2, CUB and SUN, respectively.
+
+There are two hyperparameters in A3E network: weighting coefficient $\lambda$ and ARG threshold $\delta$ . We set $\lambda$ to 0.6, 0.8 and 0.9 for AwA2, CUB and SUN datasets. While $\delta$ is set to 0.9, 0.8 and 0.1 for these three datasets, respectively. The influence of the hyperparameters is explored in the following experiments.
+
+# D AVERAGE HARMONIC MEANS ON AWA2 AND CUB
+
+Table 3: Average harmonic means on AwA2 and CUB datasets.   
+
+<table><tr><td rowspan="2">Method</td><td>AwA2</td><td>CUB</td><td>Average</td></tr><tr><td colspan="3">H</td></tr><tr><td>DAZLE</td><td>67.1</td><td>58.1</td><td>62.6</td></tr><tr><td>RGEN</td><td>71.5</td><td>66.1</td><td>68.8</td></tr><tr><td>MSDN A3E</td><td>67.7 70.2</td><td>68.1 68.8</td><td>67.9 69.5</td></tr></table>
+
+# E ABLATION STUDY ON DROPOUT
+
+![](images/d3e7fcb7cf368a89809b4c1bb0996f90c10c255117db32e06ca340cd3ed01262.jpg)  
+Figure 5: Effects of dropout rate $d$ on CUB dataset.
+
+Dropout is a commonly used strategy to prevent neural networks from overfitting (Srivastava et al., 2014). In our work, we employ dropout on GAT of AE module by randomly dropping some node features during training stage. The dropping process is controlled by dropout rate $d$ that determines the proportion of dropped nodes. As shown in Figure 5, with dropout rate $d$ increasing from 0 to 0.2 (0 means dropout is inactive), almost all indicators are on the rise, except a slight fluctuation for the seen class accuracy on GZSL. The accuracy decreases gradually from 0.3. To sum up, both ZSL accuracy and GZSL harmonic mean reach the best values at 0.2 dropout rate, then begin to decline with the increase of $d$ . The phenomenon can verify functionality of dropout: preventing models from overfitting. Besides, dropout is indispensable to AE module because it improves the generalization ability of model.
+
+# F TERM EXPLANATION
+
+Attribute semantics: The word vectors of attributes, which is the output of word2vec model by taking the attribute name as the input. The resulted representation codes semantic information of each input attribute, so called the attribute semantics.
+
+Class attribute vectors: A set of vectors corresponds to the set of classes. Each vector encodes information about the attributes of the corresponding class, and the presence of attribute is indicated by a continuous or binary value at its corresponding element of the vector.
+
+Attribute prototypes is actually the class attribute vectors in the attribute space, that has identical meanings with class attribute vectors.

parse/dev/arg1dQSS6Mh/arg1dQSS6Mh_content_list.json

@@ -0,0 +1,1834 @@
+[
+    {
+        "type": "text",
+        "text": "ATTRIBUTE ALIGNMENT AND ENHANCEMENT FOR GENERALIZED ZERO-SHOT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            99,
+            823,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            171,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Generalized zero-shot learning (GZSL) aims to recognize both seen and unseen classes, which challenges the generalization ability of a model. In this paper, we propose a novel approach to fully utilize attributes information, referred to as attribute alignment and enhancement (A3E) network. It contains two modules. First, attribute localization (AL) module utilizes the supervision of class attribute vectors to guide visual localization for attributes through the implicit localization capability within the feature extractor, and the visual features corresponding to the attributes (attribute-visual features) are obtained. Second, enhanced attribute scoring (EAS) module employs the supervision of the attribute word vectors (attribute semantics) to project input attribute visual features to attribute semantic space using Graph Attention Network (GAT). Based on the constructed attribute relation graph (ARG), EAS module generates enhanced representation of attributes. Experiments on standard datasets demonstrate that the enhanced attribute representation greatly improves the classification performance, which helps A3E to achieve state-of-the-art performances in both ZSL and GZSL tasks. ",
+        "bbox": [
+            233,
+            265,
+            764,
+            472
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            497,
+            336,
+            513
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot learning aims to recognize unseen classes that have not been appeared during training phase, a common solution resort to auxiliary information to bridge the gap between seen and unseen domains to achieve knowledge transfer from the seen to the unseen. Semantics are the most frequently used auxiliary information for ZSL, either by class descriptions, word vectors (Mikolov et al., 2013) or attributes (Farhadi et al., 2009). A general paradigm (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Min et al., 2020; Xie et al., 2020; Ge et al., 2021; Liu et al., 2021b; Chen et al., 2021b; 2022) is to learn a mapping that projects visual features of seen samples into an embed-ding space to align with semantic attributes. With the assumption that seen and unseen domains share the same attribute space, the learned knowledge from seen classes is easily transferred to the unseen ones. And then, the subsequent classi-fication is accomplished by measuring compatibility scores between the projected features and the attribute prototypes. Recent works on embeddings turn to local features of image parts, i.e. part-based embedding meth-ods (Elhoseiny et al., 2017), to learn discriminative features easy for classification. Comparatively, gener-ative methods (Xian et al., 2019b; Huynh & Elhamifar, 2020a; Ma & Hu, 2020; Han et al., 2021; Chen et al., 2021a;c; Chou et al., 2021) utilize semantic information of unseen classes to synthesize unseen visual features by a generative model, such as generative adversarial network (GAN) (Goodfellow et al., 2020) or variational autoencoder (VAE) (Kingma & Welling, 2013), so that convert zero-shot classification to the traditional supervised model learning that could be trainable with generated samples. However, the features inferred from semantic information mostly are high-level visual representation, which are often non-discriminative to class recognition (Huynh & Elhamifar, 2020b; Xian et al., 2019b; Huynh & Elhamifar, 2020a). ",
+        "bbox": [
+            173,
+            529,
+            825,
+            819
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, generalized zero-shot learning (GZSL) for its rigorous and realistic nature has received increasing attention in this field, where seen classes and unseen classes constitute the testing space. Embedding methods are inherently inferior in GZSL since the model training merely relies on samples of seen classes, and thus inevitably biases towards the seen ones. Moreover, the visual-semantic alignment in embedding models is just operated in seen domain, and the visual di-vergence between seen and unseen domains may strengthen the bias, namely domain shift ( $\\mathrm { F u }$ et al., 2014). Different methods have been explored to improve the model performance in GZSL. Some studies try to mitigate the bias by introducing constraints on losses to calibrate output pre-diction probability, which usually require unseen semantics as side infor-mation (Huynh & Elhamifar, 2020b; Xie et al., 2020). The Parts Relation Rea-soning is used in RGEN (Xie et al., 2020) to capture appearance relationships among image parts, which is believed to be a complementary cue for improving the performance. GCNZ (Velickovi ˇ c et al., 2018) utilizes class relationships to infer classifier parame- ´ ters directly from knowledge graph. Relation learning is no novelty to ZSL, however, the semantic relationship between attributes is rarely explored in previous works. Huynh & Elhamifar (2020b) have informed us by introduc-ing word vectors of attribute that there is a wealth of semantic information in attributes beyond the commonly used class attribute vectors. There are also rich semantic relationships between attributes, which can be transferred to visual domain to help mitigate visualsemantic gap. Once the relations between attributes are modeled, it is possible to enhance the fi-nal prediction of classes by the interplay of attributes. Existing methods tried to capture the semantic relations in the at-tributes, such as using the entanglement of CNN and GCN based on knowledge graph about attrib-utes (Hu et al., 2022). However, despite the fact that nodes in graph are explic-itly defined as attributes, those methods lack a mechanism to accurately align nodes to the corresponding attributes. To the best of our knowledge, the fusion of relation learning and attention mechanism has not been studied in ZSL. ",
+        "bbox": [
+            174,
+            827,
+            823,
+            924
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b00a5d11c0c9f40b1dfa49fff812cc467d8778948d4c15c8feb819dabea8846e.jpg",
+        "image_caption": [
+            "Figure 1: Attribute Localization. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            98,
+            826,
+            223
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            304,
+            825,
+            539
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Accordingly, we propose an attribute alignment and enhancement (A3E) network for GZSL, which incorporates attribute alignment (AA) pipeline and attribute enhancement (AE) module. AA pipeline consists of attribute localization (AL) module and attribute scoring (AS) module, this novel approach of attribute alignment allows model to subtly catch visual features corresponding to attributes (namely attribute-visual features, AVFs) by fully utilization of attribute knowledge (both class attribute vectors and attribute word vectors). Compared to previous part-based methods that require complex accessories such as attention module and part detector, A3E simplifies its AA pipeline to a single convolutional layer with a single linear transformation, and still delivers competitive results. Most importantly, the resulted AVFs serve as the carriers for attributes which support the subsequent attribute enhancement process. In order to model the relations of attributes, AE module first constructs an attribute-relation graph (ARG), where relation-ships of attributes are quantified as graph edges, then, facilitated by graph neural networks, embeds the input AVFs into attribute semantics space. The enhanced attribute features are obtained through the outputs of graph nodes. Figure 1 demonstrates the basic process of AE module. Experiments in three standard ZSL datasets show that A3E reaches the state-of-the-art results in both ZSL and GZSL without extra information from unseen classes or auxiliary constraints on output probabilities, verifying the advantages of our proposed method. ",
+        "bbox": [
+            174,
+            547,
+            825,
+            781
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contributions can be summarized as: ",
+        "bbox": [
+            176,
+            790,
+            441,
+            804
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• A novel attribute enhancement (AE) module is created to explicitly model the relationship between attributes, and the enhanced attribute representation is generated with attribute-relations modeled inside. ",
+        "bbox": [
+            174,
+            811,
+            825,
+            852
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• To align graph nodes with attributes, an efficient attribute alignment (AA) pipeline is designed to generate visual fea-tures corresponding to attributes, namely attribute-visual features (AVFs). ",
+        "bbox": [
+            171,
+            859,
+            820,
+            888
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We propose an attribute alignment and enhancement (A3E) network that based on the AA pipeline and AE module, an innovative combination of attention mechanism and semantic-relation learning. ",
+        "bbox": [
+            173,
+            895,
+            820,
+            924
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Extensive experiments on three bench-marks show that our design can significantly improve results in both ZSL and GZSL tasks. ",
+        "bbox": [
+            174,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            151,
+            344,
+            167
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There are two main paradigms for ZSL/GZSL: generative methods (Xian et al., 2019b; Huynh & Elhamifar, 2020a; Ma & Hu, 2020; Han et al., 2021; Chen et al., 2021a;c; Chou et al., 2021) and embedding methods (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Min et al., 2020; Xie et al., 2020; Ge et al., 2021; Liu et al., 2021b; Chen et al., 2021b; 2022). Generative methods covert ZSL problem into traditional supervised learning using visual features synthesized by generative models for unseen classes (Liu et al., 2021a). However, generative models such as GAN or VAE are often difficult to generate high-quality synthetic samples for unseen classes to train classifiers (Pourpanah et al., 2022). On the other hand, embedding methods learn a mapping that aligns visual features with semantic prototypes, therefore achieve knowledge transfer from seen to unseen classes via their sharable semantics. According to the mapping space, embedding methods can be divided into three categories: visual space embedding (Zhang et al., 2017), semantic space embedding (Zhu et al., 2019; Huynh & Elhamifar, 2020b; Xie et al., 2020; Liu et al., 2021b) and common space embedding (Min et al., 2020), with their respective pros and cons. ",
+        "bbox": [
+            174,
+            183,
+            825,
+            363
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As its name suggests, semantic space embedding projects visual features into semantic space. Recent studies further suggest that global visual features are detrimental to classification (Xie et al., 2019; Zhu et al., 2019; Huynh & Elhamifar, 2020b; Xie et al., 2020). Instead of using noisy global features, part-based embedding methods try to improve classification performance by locating discriminative parts in image. Elhoseiny et al. (2017) deployed a visual part detector to link text descriptions with corresponding image regions, which would be fed into the part-based visual classifiers. SGMA (Zhu et al., 2019) employed a multi-attention module and DAZLE (Huynh & Elhamifar, 2020b) constructed a hierarchical linear structure, all in order to focus the model on discriminative regions in image. Whereas, the model with part detector attention module would become complex, so that make it difficult to train and optimize. SELAR (Yang et al., 2021) proposed to localize part features by the implicit localization ability within feature extractor, where the complex attention module is replaced with a single convolution layer. Most of the above models use class attribute vectors as semantic information. However, since the attribute space spanned by class attribute vectors is inevitably suffered from hubness problem (Zhang et al., 2017), the choice of embedding space is still an issue that is worth to explore in subsequent study. ",
+        "bbox": [
+            174,
+            371,
+            825,
+            578
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "With the increasing attention paid to ZSL, various techniques from other fields were also incorporated into ZSL models, such as knowledge distillation (Chen et al., 2022), meta-learning (Verma et al., 2020) and graph learning (Xie et al., 2020; Wang et al., 2018). Graph Neural Networks (GNNs) (Kipf & Welling, 2017; Velickovi ˇ c et al., 2018) were proposed to model non-Euclidean ´ data, especially for those with graph structure. Velickovi ˇ c et al. (2018) firstly introduced Graph Con- ´ volutional Networks (GCN) (Kipf & Welling, 2017) to explicitly model relations between classes in ZSL by knowledge graph. And RGEN (Xie et al., 2020) employed GCN to represent the relations among local image regions. Whereas, none of them have explored the semantic relations that implied within attributes. ",
+        "bbox": [
+            174,
+            585,
+            825,
+            710
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Inspired by the advantages and deficiencies of previous works, our proposed A3E employs a dual embedding strategy to fully utilize the rich semantics beneath attributes, and incorporates GAT (Velickovi ˇ c et al., 2018) to dynamically model the semantic relations between attributes. ´ ",
+        "bbox": [
+            174,
+            718,
+            825,
+            760
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 ATTRIBUTE ALIGNMENT AND ENHANCEMENT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            780,
+            589,
+            795
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will specify how and why the A3E network is proposed. Here we follow the pipeline that A3E processes the samples, and present the whole structure and details of our model. ",
+        "bbox": [
+            174,
+            810,
+            825,
+            839
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 ATTRIBUTE LOCALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            856,
+            405,
+            869
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to explore those rich semantics and relations between attributes, we need to obtain the visual representations for attributes first. Instead of generating discriminative regions using various of attention modules, Yang et al. (2021) innovated to utilize the implicit attribute localization ability ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "within feature extractor (CNNs) to get part location, here we refer to it as attribute localization (AL). AL greatly reduces the complexity of the model by replacing the complicated attention module with a single $1 \\times 1$ convolution: ",
+        "bbox": [
+            173,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/80476ee0dd2c0ad1736197405625cfc8f783a536498274e18c624ca1b76dc2c4.jpg",
+        "text": "$$\n\\tilde { \\mathbf { a } } = c o n v \\left( \\mathbf { v } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            450,
+            166,
+            545,
+            184
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where, $\\mathbf { v } = \\varphi \\left( \\mathbf { x } _ { i } \\right)$ is the visual features with $H \\times W \\times C$ dimensions extracted by the backbone network $\\varphi \\left( \\cdot \\right)$ . $\\mathbf { x } _ { i }$ is the $i -$ th input image, and conv $( \\cdot )$ is the $1 \\times 1$ convolution with $1 \\times 1 \\times C \\times A$ parameters. $\\mathbf { \\tilde { a } } \\in \\mathbb { R } ^ { H \\times W \\times A }$ is the output features with attribute localization, referred to as attribute features. ",
+        "bbox": [
+            174,
+            194,
+            825,
+            251
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Under the supervision of attribute vectors, this simple convolution could gather most important spacial information of attributes. The loss function of AL module is defined as follows: ",
+        "bbox": [
+            173,
+            257,
+            823,
+            286
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e5b5c232beb17b0cb75fb60c6503827886901b910df7556e96bf0c1e8990fd19.jpg",
+        "text": "$$\n\\mathcal { L } _ { A L } = \\mathcal { C E } \\left( S o f t M a x \\left( \\mathbf { A } ^ { S } G M P ( c o n v \\left( \\mathbf { v } \\right) ) ^ { T } \\right) , y _ { i } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            304,
+            679,
+            332
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $y _ { i }$ is the label of $i -$ th input image, and $G M P \\left( \\cdot \\right)$ is the global maximum pooling function that employs spatial aggregation to the attribute features. $\\mathbf { A } ^ { S } \\in \\mathbb { R } ^ { N ^ { S } \\times A }$ is the seen attributes matrix where $N ^ { S }$ is the number of seen classes. $S o f t M a x \\left( \\cdot \\right)$ is SoftMax activation function and $\\mathcal { C } \\mathcal { E } \\left( \\cdot \\right)$ is the cross entropy loss commonly used in ZSL models. ",
+        "bbox": [
+            174,
+            342,
+            825,
+            402
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Blue area at the bottom of Figure 2 shows the layout of AL module. ",
+        "bbox": [
+            173,
+            409,
+            617,
+            424
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 ATTRIBUTE SCORING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            440,
+            364,
+            455
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in the previous section, attribute space, despite being commonly used in ZSL models, suffers from several problems like hubness problem. We are aware of the rich semantic information beneath attributes. Inspired by Huynh & Elhamifar (2020b), we introduce attribute semantic space to collaborate with attribute space, which forms our attribute scoring (AS) module. ",
+        "bbox": [
+            174,
+            467,
+            825,
+            523
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "With the attribute features from AL module, the visual location of every attribute is encoded in each channel of ˜a. Naturally, we thought of making it into a set of attention masks as a substitute for attention mechanism. The attribute masks are obtained through the sigmoid function that normalizes values of each channel in ˜a into a range from 0 to 1, where the value approaching to 1 stands for high confidence of having attribute-related visual features in the location, while that approaching to 0 is the opposite. Therefore, we can extract visual features for each attribute-related image region using attribute masks by performing the broadcasted Hadamard production between visual features $\\mathbf { v } \\in \\mathbb { R } ^ { H \\times W \\times C }$ and each channel of normalized ˜a, which produces A masked visual features that correspond to A attributes, namely attribute-visual features (AVFs) $\\mathbf { v } ^ { ( a ) } \\in \\mathbb { R } ^ { H \\times W \\times C }$ $( a \\in [ 1 , A ] )$ . ",
+        "bbox": [
+            173,
+            530,
+            825,
+            659
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To achieve zero-shot classification, the next step is to map AVFs into attribute semantic space with reference to DAZLE (Huynh & Elhamifar, 2020b). The attribute semantic space is constructed using word vectors of attributes that are usually produced by word vector models like Word2Vec (Mikolov et al., 2013). With these attribute word vectors, we employ AS module to map the above AVFs into attribute sematic space, and then calculate the class score of samples as follows: ",
+        "bbox": [
+            173,
+            664,
+            825,
+            734
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b14faf31d25e8f63ba5142b79dff35e21ea1cabc7d112356fbd3682b1008eb2a.jpg",
+        "text": "$$\n\\begin{array} { c } { { \\hat { \\mathbf { e } } _ { a } = \\mathbf { W } \\left( G A P \\left( \\mathbf { v } ^ { ( a ) } \\right) \\right) , a \\in \\left[ 1 , A \\right] } } \\\\ { { p _ { a } = \\mathbf { e } _ { a } \\hat { \\mathbf { e } } _ { a } ^ { T } , a \\in \\left[ 1 , A \\right] } } \\\\ { { s ^ { c } = \\mathbf { a } ^ { c } \\mathbf { p } ^ { T } , c \\in \\left[ 1 , N ^ { S } \\right] } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            372,
+            750,
+            625,
+            827
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $G A P \\left( \\cdot \\right)$ is the global average pooling function that aggregates AVFs into $1 \\times C$ dimensions, and $\\mathbf { W } \\left( \\cdot \\right)$ is the linear mapping with $1 \\times C \\times e$ parameters. $\\hat { \\textbf { e } } \\in \\mathbb { R } ^ { 1 \\times e }$ is the predicted word vector, and $\\mathbf { e } \\in \\mathbb { R } ^ { 1 \\times e }$ is the ground truth attribute word vector. $p _ { a }$ is the attribute score for the $a -$ th attribute. $ { \\mathbf { p } } \\in \\mathbb { R } ^ { 1 \\times A }$ is the concatenation of $p _ { a } \\left( a \\in \\left[ 1 , { \\cal A } \\right] \\right)$ . $\\mathbf { a } ^ { \\hat { c } } \\in \\mathbb { R } ^ { 1 \\times A } \\left( c \\in \\left[ 1 , N ^ { S } \\right] \\right)$ is the class attribute vector of the $c -$ th class which is extracted from the $c -$ th row of attribute matrix $\\mathbf { A } ^ { S }$ . And $s ^ { c }$ is the class score of the current sample belonging to the $c -$ th class. ",
+        "bbox": [
+            173,
+            837,
+            825,
+            924
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Thus, the attribute scoring loss based on cross entropy is designed: ",
+        "bbox": [
+            173,
+            103,
+            611,
+            118
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/f8b5ece2c7dbc9b5d7cc85f731366306c44ff5fd7ede66b512c516cfe3803021.jpg",
+        "text": "$$\n\\mathcal { L } _ { A S } = \\mathcal { C E } \\left( S o f t M a x \\left( \\mathbf { s } _ { A S } \\right) , y _ { i } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            385,
+            137,
+            612,
+            155
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { s } _ { A S } \\in \\mathbb { R } ^ { N ^ { S } }$ is the concatenation of class score $s ^ { c } \\left( c \\in \\left[ 1 , N ^ { S } \\right] \\right)$ ",
+        "bbox": [
+            174,
+            164,
+            643,
+            183
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Ultimately, a novel attribute alignment (AA) pipeline is constructed, which consists of AL and AS modules. AA innovates attribute alignment approach through integrating attribute space and attribute semantic space into a unified pipeline of ZSL model. Subsequently, we will model the relations between attributes. ",
+        "bbox": [
+            174,
+            186,
+            825,
+            242
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 ATTRIBUTE ENHANCEMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            260,
+            408,
+            273
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Studies on CNNs (or DNNs) have shown that feature extractor built up by convolutional neurons does well in extracting visual patterns from images. However, what they are not good at is to extract non-visual concepts from image samples. Unfortunately, the abstract concepts are common in the attribute sets of many ZSL datasets. For example, Animals with Attributes 2 (AwA2) (Xian et al., 2019a) has 85 expert-defined attributes in total. Roughly half of these attributes can be directly related to visual representations (like “stripes” and “tail”), while more than half of them do not correspond directly to the visual representation (such as “fast” and “smart”). This is even more troublesome for part-based ZSL methods since it is hard to locate a visual region for such non-visual attributes thus confusing the model. ",
+        "bbox": [
+            174,
+            285,
+            825,
+            411
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To address the issue, we turn to exploiting the implicit semantic relations between attributes. The idea is to dynamically build the associations between visual-related attributes and non-visual attributes by modeling the relations between them. With the assumption that all attributes share the same semantic space, it allows the model to enhance the usability of non-visual attributes using representations of visual-related attributes. ",
+        "bbox": [
+            174,
+            417,
+            825,
+            487
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In order to model the relations of attributs, we construct an attribute relation graph (ARG) $\\mathbf { G } _ { A }$ based on point-wise mutual information (PMI) (Bouma, 2009) according to $\\mathrm { H u }$ et al. (2022). Let $\\mathbf { G } _ { A }$ has A vertices corresponding to A attributes, the edges between attributes (vertices) are defined based on their normalized PMI values referring to threshold $\\delta$ : ",
+        "bbox": [
+            174,
+            494,
+            825,
+            551
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e64304eb4b89699624472fd7532ddd5098a8dbe7e5d684b31d5c231f4c334f4f.jpg",
+        "text": "$$\n{ { A } _ { i , j } } = { { A } _ { j , i } } = \\left\\{ \\begin{array} { c } { 1 , P M { { I } _ { n } } \\left( x , y \\right) > \\delta } \\\\ { 0 , e l s e } \\end{array} \\right.\n$$",
+        "text_format": "latex",
+        "bbox": [
+            367,
+            566,
+            620,
+            602
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $A _ { i , j }$ is the element in the $i -$ th row and $j -$ th column of A. We use the undirected graph for ARG, so that its adjacency matrix is symmetric, that is $A _ { i , j } = A _ { j , i }$ . See Appendix A for the detailed formula of PMI. The selection of threshold $\\delta$ will be discussed in detail in experiments section. ",
+        "bbox": [
+            174,
+            608,
+            825,
+            651
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "So far, ARG discussed above is still a static structure shared by all categories, which cannot be dynamically optimized with different classes and samples. Meanwhile, the PMI-based connections (graph edges) may not always represent the correct relations between attributes. Therefore, instead of using the well-known graph convolutional networks (GCN), we leverage graph attention networks (GAT) (Velickovi ˇ c et al., 2018) to achieve dynamic modeling based on ARG. ´ ",
+        "bbox": [
+            174,
+            656,
+            825,
+            728
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "GAT proposed by Velickovi ˇ c et al. can dynamically adjust edge weights with self-attention mech- ´ anism to solve a series of problems in spatial GNNs. According to AA pipeline in the previous subsection, A sets of global AVFs $\\bar { \\mathbf { v } } ^ { ( a ) }$ $( a \\in [ 1 , A ] )$ belonging to the sample $x _ { i }$ are obtained, which will be subsequently used as the input of nodes in $\\mathbf { G } _ { A }$ . We use a two-layer GAT network in the paper, i.e. $l \\in \\{ \\bar { 0 } , 1 \\}$ . The outputs of GAT are the predicted word vectors $\\tilde { \\mathbf { e } } _ { a } ^ { \\cdot } \\in \\mathbb { R } ^ { 1 \\times e } ( a \\in [ 1 , A ] )$ from each node, where $e$ is the dimension of word vector. In the process, GAT not only projects the input global AVFs into attribute semantic space (like the AS module), but also models attribute relations in the output, namely predicted word vectors $\\hat { \\mathbf { e } } _ { a }$ . With the help of ARG that connected attributes by their semantic relation, GAT can enhance the expression of certain attribute-related features (especially those from non-visual attributes), yielding more discriminative semantic representations. Hence, we name it attribute enhancement (AE) module. ",
+        "bbox": [
+            174,
+            734,
+            825,
+            888
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As the output of AE module has the same form of predicted word vectors like AS module, an integrated enhanced attribute scoring (EAS) module is naturally formed. We can follow formula (3), (4) and (5) to calculate the class score vector $\\mathbf { s } _ { E A S }$ , and the enhanced attribute scoring loss is constructed as: ",
+        "bbox": [
+            173,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/d6a040d03d386625ef5f5dcf7df0f44dd3f08c641ea6e76f8b3041053ac29215.jpg",
+        "image_caption": [
+            "Figure 2: Attribute Alignment and Enhancement Network. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            99,
+            821,
+            333
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
+            392,
+            823,
+            422
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8326687c6f38c4f212358916c8071e1a71d6f0522aa367e8ce400c2553dae4e1.jpg",
+        "text": "$$\n\\mathcal { L } _ { E A S } = \\mathcal { C E } \\left( S o f t M a x \\left( \\mathbf { s } _ { E A S } \\right) , y _ { i } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            375,
+            440,
+            622,
+            458
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The dropout strategy is often used to improve the generalization of GNN models by randomly “dropping” some nodes (sweeping node features) during training. The method is originally used in GNNs to suppress over-smoothing problem (Li et al., 2018), while we use here to perturb the original data (AVFs) to enhance the generalization of the model. Subsequent experiments will demonstrate the significant impact of the dropout strategy on GZSL performance. ",
+        "bbox": [
+            173,
+            468,
+            825,
+            539
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4 GENERALIZED ZERO-SHOT IMAGE CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            555,
+            576,
+            570
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, by integrating the attribute localization (AL) module and enhanced attribute scoring (EAS) module, A3E network for GZSL is constructed (see Figure 2). ",
+        "bbox": [
+            174,
+            580,
+            821,
+            611
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4.1 OVERALL LOSS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            625,
+            339,
+            638
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The overall loss function of A3E is: ",
+        "bbox": [
+            176,
+            648,
+            410,
+            664
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e62883449f9e767b324fc24cc90b0ee9f1207c90ea605c14e6394b4453454163.jpg",
+        "text": "$$\n\\mathcal { L } _ { A 3 E } = \\lambda \\mathcal { L } _ { A L } + \\left( 1 - \\lambda \\right) \\mathcal { L } _ { E A S }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            390,
+            683,
+            607,
+            700
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda$ is the weighting coefficient that balance the two modules. ",
+        "bbox": [
+            173,
+            710,
+            607,
+            726
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.4.2 INFERENCE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            739,
+            310,
+            755
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the inference stage, A3E employs a fusion prediction method as follows: ",
+        "bbox": [
+            173,
+            765,
+            666,
+            780
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ef4b53cdd709ceac7a2e6edf4c3f78bf4cf2ca93994e9ecae14238d0d47cbaab.jpg",
+        "text": "$$\n\\hat { y } = \\arg \\operatorname* { m a x } _ { c \\in N } \\left( \\lambda \\mathbf { s } _ { A L } + \\left( 1 - \\lambda \\right) \\mathbf { s } _ { E A S } + \\beta \\Delta _ { \\left[ c \\in N ^ { U } \\right] } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
+            326,
+            797,
+            669,
+            821
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\hat { y }$ is the predicted label, and $\\lambda$ is a coefficient which has identical function with the one in training loss. $\\mathbf { s } _ { A L }$ is the output probability of AL module and $\\mathbf { s } _ { E A S }$ is the output probability of EAS module. $N = N ^ { S } \\cap N ^ { U }$ is the set of all classes labels. $\\beta$ is an adjustable bias, and $\\Delta _ { [ c \\in N ^ { U } ] }$ is an indicator which will take 1 for unseen classes, and -1 for seen classes. ",
+        "bbox": [
+            174,
+            832,
+            825,
+            888
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To alleviate the inevitable bias caused by domain shift in GZSL, we set a calibration bias refer to (Huynh & Elhamifar, 2020b). However, it is worth notice that unlike (Huynh & Elhamifar, ",
+        "bbox": [
+            173,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/bbd6e95a54ec20626534ca2ebb725231c47ae3afb50297a01cf4b4e07561df0e.jpg",
+        "table_caption": [
+            "Table 1: Results of conventional ZSL and GZSL classification on AwA2, CUB and SUN datasets. The best and second-best results are marked in bold and underline, respectively. The symbol “-” indicates no results. The symbol “\\*” represents models with $4 4 8 \\times 4 4 8$ input size. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\" colspan=\"2\">Methods</td><td colspan=\"4\">AwA2</td><td colspan=\"4\">CUB</td><td colspan=\"4\">SUN</td></tr><tr><td>ZSL MCA</td><td rowspan=\"2\"></td><td colspan=\"2\">GZSL</td><td>ZSL</td><td></td><td colspan=\"2\">GZSL</td><td>ZSL</td><td></td><td colspan=\"2\">GZSL</td></tr><tr><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td></tr><tr><td colspan=\"2\">Generative Methods</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CVPR 2019 f-VAEGAN-D2</td><td></td><td>71.1</td><td>57.6</td><td>70.6</td><td>63.5</td><td>61.0</td><td>48.4</td><td>60.1</td><td>53.6</td><td>64.7</td><td>45.1</td><td>38.0</td><td>41.3</td></tr><tr><td>NeurIPS 2020 Composer</td><td></td><td>71.5</td><td>62.1</td><td>77.3</td><td>68.8</td><td>69.4</td><td>56.4</td><td>63.8</td><td> 59.9</td><td>62.6</td><td>55.1</td><td>22.0</td><td>31.4</td></tr><tr><td>ICCV 2021</td><td>FREE</td><td>-</td><td>60.4</td><td>75.4</td><td>67.1</td><td>：</td><td>55.7</td><td>59.9</td><td> 57.7</td><td>-</td><td>47.4</td><td>37.2</td><td>41.7</td></tr><tr><td colspan=\"2\">EmbeddingMethods</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>NeurIPS 2019</td><td>SGMA</td><td>68.8*</td><td>37.6*</td><td>87.1*</td><td>52.5*</td><td>71*</td><td>36.7*</td><td>71.3*</td><td>48.5*</td><td>：</td><td>-</td><td>：</td><td>-</td></tr><tr><td>CVPR 2020</td><td>DAZLE</td><td>1</td><td>60.3</td><td>75.7</td><td>67.1</td><td>65.9</td><td>56.7</td><td>59.6</td><td>58.1</td><td>-</td><td>52.3</td><td>24.3</td><td>33.2</td></tr><tr><td>ECCV 2020</td><td>RGEN</td><td>73.6</td><td>67.1</td><td>76.5</td><td>71.5</td><td>76.1</td><td>60.0</td><td>73.5</td><td>66.1</td><td>63.8</td><td>44.0</td><td>31.7</td><td>36.8</td></tr><tr><td>AAAI 2021</td><td>SR2E</td><td>：</td><td>58*</td><td>80.7*</td><td>67.5*</td><td>-</td><td>61.6*</td><td>70.6*</td><td>65.8*</td><td>-</td><td>43.1*</td><td>36.8*</td><td>39.7*</td></tr><tr><td>SPL 2021</td><td>SELAR</td><td>：</td><td>52.0</td><td>71.9</td><td>60.3</td><td>：</td><td>62.4</td><td>64.9</td><td>63.6</td><td>：</td><td>40.5</td><td>32.9</td><td>36.3</td></tr><tr><td>NeurIPS 2021</td><td>HSVA</td><td>-</td><td>56.7</td><td>79.8</td><td>66.3</td><td>62.8</td><td>52.7</td><td>58.3</td><td> 55.3</td><td>63.8</td><td>48.6</td><td>39.0</td><td> 43.3</td></tr><tr><td>CVPR 2022</td><td>MSDN</td><td>70.1*</td><td>62*</td><td>74.5*</td><td>67.7*</td><td>76.1*</td><td>68.7*</td><td>67.5*</td><td>68.1*</td><td>65.8*</td><td>52.2*</td><td>34.2*</td><td>41.3*</td></tr><tr><td>ours</td><td>A3E</td><td>74.1</td><td>69.3</td><td>71.2</td><td>70.2</td><td>74.9*</td><td>66.3*</td><td>71.6*</td><td>68.8*</td><td>64.0*</td><td>46.8*</td><td>30.0*</td><td>36.5*</td></tr></table>",
+        "bbox": [
+            173,
+            160,
+            825,
+            340
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "2020b), the calibration in our method only includes a bias on the prediction probability, and does not include any additional loss term that usually requires unseen semantics to adjust output predictions. ",
+        "bbox": [
+            174,
+            372,
+            823,
+            401
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            421,
+            326,
+            438
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            453,
+            375,
+            468
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1.1 DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            479,
+            302,
+            494
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We evaluate A3E network on three GZSL benchmarks: Animals with Attributes 2 (AwA2) (Xian et al., 2019a), Caltech-UCSD Birds 200-2011 (CUB) (Wah et al., 2011) and SUN attribute database (SUN) (Patterson et al., 2014). AwA2 is a coarse-grained dataset with 37,322 images from 50 animal classes, each of which has 85 attributes. While, CUB is a fine-grained bird dataset containing 11,788 images from 200 bird classes with 312 attributes. SUN is also a fine-grained dataset which includes 14,340 images from 717 scene categories, and each class has a 102-dimension attribute vector. ",
+        "bbox": [
+            174,
+            503,
+            825,
+            587
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In order to fairly compare with the state-of-the-art ZSL models, we adopt the proposed split (PS) of datasets presented in (Xian, Schiele, and Akata 2017). Evaluation metrics are shown in Appendix B ",
+        "bbox": [
+            176,
+            594,
+            823,
+            623
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.1.2 IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            638,
+            419,
+            654
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "All the experiments in the paper are conducted on NVIDIA GeForce RTX 3090 with 24 GB video memory size. Software versions are Python 3.9, PyTorch 1.11.0, NumPy 1.22.3 and CUDA 11.3. ",
+        "bbox": [
+            174,
+            662,
+            823,
+            691
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For better reproducibility of experiment results, we manually fixed the random seed to 1024 for all tests. Detailed settings would be listed in Appendix C ",
+        "bbox": [
+            174,
+            699,
+            823,
+            727
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 COMPARISON WITH STATE-OF-THE-ARTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            744,
+            501,
+            758
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We compare our A3E network with several state-of-the-art models in both ZSL setting and GZSL setting. The results are presented in Table 1. On the ZSL side, A3E shows very gratifying results in all three datasets. While it is competitive compared with the state-of-the-art models on CUB and SUN, the most compelling achievement is that A3E outperforms the long-standing record by RGEN (Xie et al., 2020) on AwA2 since 2020. On the GZSL side, A3E reaches the highest harmonic mean $( 6 8 . 8 \\% )$ on CUB dataset, which is the current best generalized model on CUB. It also gets a satisfactory performance on AwA2, though is inferior to RGEN. Whereas, harmonic mean of A3E on AwA2 is still improved by at least $2 . 5 \\%$ compared with the former state-of-the-art models, which verifies that A3E is a strong competitor so far, compared with most of the models except for RGEN. In general, the results prove that the proposed attribute alignment and enhancement work effectively on AwA2 and CUB, which are beneficial to represent the rich semantic relations between attributes hidden in AwA2 and CUB. The data characteristic of AwA2 and CUB promotes A3E network more generalized. However, the performance on SUN dataset declines sharply. The reason accounted for the phenomenon is that attributes of SUN are more abstract which are hard to capture their correspondent image regions. More importantly, the semantic relations are too sparser compared with the former datasets to affect the performance of attribute enhancement. ",
+        "bbox": [
+            174,
+            770,
+            825,
+            924
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/15d0e5e87af927ed9bfe830f4e36613d759b9e55dc06ff5048cc48fce06279c7.jpg",
+        "table_caption": [
+            "Table 2: Ablation study under two datasets. The best results are marked in bold. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">AwA2</td><td colspan=\"4\">CUB</td></tr><tr><td>ZSL</td><td></td><td>GZSL</td><td></td><td>ZSL</td><td></td><td>GZSL</td><td></td></tr><tr><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td><td>MCA</td><td>Unseen</td><td>Seen</td><td>H</td></tr><tr><td>AL+AS(AA pipeline)</td><td>60.4</td><td>52.6</td><td>78.5</td><td>63.0</td><td>57.7</td><td>44.6</td><td>60.5</td><td>51.3</td></tr><tr><td>AL+EAS(A3ENetwork)</td><td>74.1</td><td>69.3</td><td>71.2</td><td>70.2</td><td>74.9</td><td>66.3</td><td>71.6</td><td>68.8</td></tr></table>",
+        "bbox": [
+            174,
+            132,
+            823,
+            207
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            253,
+            825,
+            324
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Among all comparison models, DAZLE, RGEN and MSDN are the most noteworthy as well as our A3E network. They have some similarity in research motivation. DALZE and MSDN adopt attribute scoring mechanisms, as well as A3E. RGEN uses GNN to perform region-based relations on visual features. Whereas, A3E employs AE module to model semantic relations between attributes. From the GZSL results on AwA2 and CUB, A3E successfully surpasses these models by the stable performance which can be expressed as the average of harmonic means: A3E network reaches $6 9 . 5 \\%$ in average, while DAZLE, RGEN and MSDN are $6 2 . 6 \\%$ , $6 8 . 8 \\%$ and $6 7 . 9 \\%$ , respectively(see Appendix D). The more surprising fact is that when A3E generalizes well in GZSL settings, it does not resort to any probability tricks commonly used in above models, such as the balance loss used by RGEN and the calibration loss used in DALZE and MSDN models. The modified losses by the probability tricks require the supervision from unseen semantics during training, which are contrary to the original setting of ZSL to some extent. In contrast, A3E only relies on seen samples and generalizes better than those models that require unseen semantics, which further demonstrates the superiority of the propose method. ",
+        "bbox": [
+            174,
+            332,
+            825,
+            525
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            561,
+            362,
+            575
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.1 EFFECTS OF ATTRIBUTE ENHANCEMENT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            595,
+            506,
+            609
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The proposed A3E network is composed of three interrelated modules, namely, AL, AS and AE modules. Among them, AE module based on GAT is the most innovative and representative component of our work. To further evaluate the efficacy of attribute enhancement in actual task, we conduct ablation studies on AwA2 and CUB datasets, by setting the baseline model with only AL and AS modules, i.e. attribute alignment (AA) pipeline. Table 2 shows the results of ablation study. ",
+        "bbox": [
+            174,
+            627,
+            825,
+            696
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To fairly compare the baseline model with A3E network, we use the same parameter setting in both. Even so, the ZSL accuracy of A3E has improved by staggering $1 3 . 7 \\%$ and $1 7 . 2 \\%$ for AwA2 and CUB datasets, respectively. Similarly, drastic performance boost is also present in the GZSL setting, where A3E exceeds the baseline by up to $7 . 2 \\%$ and $1 7 . 5 \\%$ in harmonic mean metric on AwA2 and CUB, respectively. Thus, with the help of AE module, A3E exceeds the baseline with absolute superiority in all settings, with an even greater advantage in CUB. In effect, the characteristics of attributes such as semantics and relations vary with different datasets. The reason that the performance on CUB has dramatic improvement by AE module is resulted from the stronger semantic relations between attributes of CUB, where attributes are more uniform to describe image contents. ",
+        "bbox": [
+            174,
+            704,
+            825,
+            829
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3.2 EFFECTS OF DROPOUT ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            863,
+            382,
+            877
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To investigate the effects of dropout in AE module, we conduct experiments with different dropout rates on CUB dataset. The results are concluded in Appendix E. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a441089bba5cbdf9cd6f80114e0846909569ec537d2cfc00a4f313c4dd4cd29.jpg",
+        "image_caption": [
+            "Figure 3: Effects of weighting coefficient $\\lambda$ on Figure 4: Effects of threshold $\\delta$ on AwA2 and AwA2 and CUB datasets. CUB datasets. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            179,
+            107,
+            823,
+            214
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4 HYPERPARAMETER ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            284,
+            424,
+            297
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4.1 EFFECTS OF WEIGHTING COEFFICIENT $\\lambda$ ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            310,
+            506,
+            325
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 is the summary of the experimental results on tuning weighting coefficient $\\lambda$ between AL and EAS modules. We do not show experiments for $\\lambda$ at 0 and 1 since they are no longer considered in our A3E model. In CUB dataset (see Figure 3(b)), both ZSL and GZSL indicators increase with the rise of $\\lambda$ . While in AwA2 dataset (see Figure 3(a)), the accuracies of unseen classes in ZSL and GZSL rise with the increase of $\\lambda$ . But the accuracy of seen classes in GZSL shows the opposite trend, so as to cause harmonic means of GZSL slowly improving. The increasing of $\\lambda$ represents that the model emphasizes more on AL module learning. Results show that despite the simpler structure and fewer parameters of the AL module, its importance in the objective function is no less than that of the EAS module. It is proven by the results that model performance improves as the effort invested in AL module (i.e., value of $\\lambda$ ) increases. Specially, attribute localization is more demanding for the fine-grained datasets with more subtle features, such as the CUB dataset. Considering all the indicators, we set $\\lambda$ to 0.6 and 0.9 for AwA2 and CUB, respectively. ",
+        "bbox": [
+            174,
+            335,
+            825,
+            502
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.4.2 EFFECTS OF THRESHOLD $\\delta$ ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            518,
+            413,
+            532
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Threshold $\\delta$ controls the generation of ARG. Smaller value of $\\delta$ indicates easier connection between nodes in ARG, which means more edges in the graph. When $\\delta = 1$ , there is no edge in ARG, so that AE module does not work. Figure 4 shows how different values of $\\delta$ affect model performance on the two datasets. As $\\delta$ increases in CUB dataset (see Figure 4(b)), all four metrics increase equally until $\\delta = 0 . 8$ . In AwA2 dataset (see Figure 4(a)), we can find a general uptrend in the accuracy of unseen classes as $\\delta$ increase, and the best accuracy is found at $\\delta = 0 . 9$ . With the increase in $\\delta$ , the edges representing attribute relationships in ARG should gradually decrease. Obviously, edges created by PMI do not perfectly correspond with the semantic relationships of attributes. We believe that the graphs generated by lower values of $\\delta$ have more noisy connections (edges), which leads to the model performance decline. When the structure of ARG is simplified with higher threshold, GAT is more likely to obtain robust information from ARG, thus enhancing the classification performance. To balance the accuracies of seen classes and unseen classes, we set $\\delta = 0 . 9$ and $\\delta = 0 . 8$ for AwA2 and CUB, respectively. ",
+        "bbox": [
+            173,
+            544,
+            825,
+            724
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            746,
+            318,
+            762
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In the paper, we propose an attribute alignment and enhancement (A3E) network, which consist of attribute alignment (AA) pipeline and AE module. Therefore, A3E can align each attribute with corresponding image region and enhance their representations by the semantic relations between attributes through GNNs. At last, the experiments on three ZSL datasets have demonstrated the superiority of A3E network on ZSL/GZSL classification. ",
+        "bbox": [
+            174,
+            779,
+            825,
+            848
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            871,
+            285,
+            886
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gerlof Bouma. Normalized (Pointwise) Mutual Information in Collocation Extraction. pp. 11, 2009. ",
+        "bbox": [
+            174,
+            895,
+            823,
+            922
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Shiming Chen, Wenjie Wang, Beihao Xia, Qinmu Peng, Xinge You, Feng Zheng, and Ling Shao. FREE: Feature Refinement for Generalized Zero-Shot Learning. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 122–131, Montreal, QC, Canada, October 2021a. IEEE. ISBN 978-1-66542-812-5. doi: 10.1109/ICCV48922.2021.00019. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            160
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Shiming Chen, Guo-Sen Xie, Yang Liu, Qinmu Peng, Baigui Sun, Hao Li, Xinge You, and Ling Shao. HSVA: Hierarchical Semantic-Visual Adaptation for Zero-Shot Learning. pp. 13, 2021b. ",
+        "bbox": [
+            174,
+            167,
+            823,
+            198
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Shiming Chen, Ziming Hong, Guo-Sen Xie, Wenhan Yang, Qinmu Peng, Kai Wang, Jian Zhao, and Xinge You. MSDN: Mutually Semantic Distillation Network for Zero-Shot Learning, April 2022. ",
+        "bbox": [
+            173,
+            205,
+            823,
+            236
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Zhi Chen, Yadan Luo, Ruihong Qiu, Sen Wang, Zi Huang, Jingjing Li, and Zheng Zhang. Semantics Disentangling for Generalized Zero-Shot Learning. In 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pp. 8692–8700, Montreal, QC, Canada, October 2021c. IEEE. ISBN 978-1-66542-812-5. doi: 10.1109/ICCV48922.2021.00859. ",
+        "bbox": [
+            174,
+            244,
+            825,
+            301
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yu-Ying Chou, Hsuan-Tien Lin, and Tyng-Luh Liu. ADAPTIVE AND GENERATIVE ZEROSHOT LEARNING. pp. 14, 2021. ",
+        "bbox": [
+            173,
+            309,
+            821,
+            339
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Mohamed Elhoseiny, Yizhe Zhu, Han Zhang, and Ahmed Elgammal. Link the head to the ”beak”: Zero Shot Learning from Noisy Text Description at Part Precision, September 2017. ",
+        "bbox": [
+            171,
+            347,
+            825,
+            377
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ali Farhadi, Ian Endres, Derek Hoiem, and David Forsyth. Describing objects by their attributes. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1778–1785, Miami, FL, June 2009. IEEE. ISBN 978-1-4244-3992-8. doi: 10.1109/CVPR.2009.5206772. ",
+        "bbox": [
+            173,
+            385,
+            825,
+            428
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yanwei Fu, Timothy M. Hospedales, Tao Xiang, Zhenyong Fu, and Shaogang Gong. Transductive Multi-view Embedding for Zero-Shot Recognition and Annotation. In David Fleet, Tomas Pajdla, Bernt Schiele, and Tinne Tuytelaars (eds.), Computer Vision – ECCV 2014, volume 8690, pp. 584–599. Springer International Publishing, Cham, 2014. ISBN 978-3-319-10604-5 978-3-319- 10605-2. doi: 10.1007/978-3-319-10605-2 38. ",
+        "bbox": [
+            174,
+            436,
+            825,
+            507
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jiannan Ge, Hongtao Xie, Shaobo Min, and Yongdong Zhang. Semantic-guided Reinforced Region Embedding for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 35(2):1406–1414, May 2021. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v35i2.16230. ",
+        "bbox": [
+            173,
+            516,
+            826,
+            571
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11):139–144, 2020. ",
+        "bbox": [
+            173,
+            582,
+            825,
+            625
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Zongyan Han, Zhenyong Fu, Shuo Chen, and Jian Yang. Contrastive Embedding for Generalized Zero-Shot Learning. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2371–2381, Nashville, TN, USA, June 2021. IEEE. ISBN 978-1-66544-509-2. doi: 10.1109/CVPR46437.2021.00240. ",
+        "bbox": [
+            173,
+            633,
+            825,
+            689
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778, Las Vegas, NV, USA, June 2016. IEEE. ISBN 978-1-4673-8851-1. doi: 10.1109/ CVPR.2016.90. ",
+        "bbox": [
+            173,
+            699,
+            825,
+            755
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yang Hu, Guihua Wen, Adriane Chapman, Pei Yang, Mingnan Luo, Yingxue Xu, Dan Dai, and Wendy Hall. Graph-Based Visual-Semantic Entanglement Network for Zero-Shot Image Recognition. IEEE Transactions on Multimedia, 24:2473–2487, 2022. ISSN 1520-9210, 1941-0077. doi: 10.1109/TMM.2021.3082292. ",
+        "bbox": [
+            174,
+            763,
+            825,
+            820
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Dat Huynh and Ehsan Elhamifar. Compositional Zero-Shot Learning via Fine-Grained Dense Feature Composition. pp. 12, 2020a. ",
+        "bbox": [
+            171,
+            829,
+            823,
+            858
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Dat Huynh and Ehsan Elhamifar. Fine-Grained Generalized Zero-Shot Learning via Dense Attribute-Based Attention. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4482–4492, Seattle, WA, USA, June 2020b. IEEE. ISBN 978-1-72817- 168-5. doi: 10.1109/CVPR42600.2020.00454. ",
+        "bbox": [
+            174,
+            867,
+            825,
+            922
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization, January 2017. ",
+        "bbox": [
+            169,
+            103,
+            813,
+            119
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Diederik P Kingma and Max Welling. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114, 2013. ",
+        "bbox": [
+            173,
+            130,
+            823,
+            159
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Convolutional Networks, February 2017. ",
+        "bbox": [
+            173,
+            169,
+            823,
+            199
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning, January 2018. ",
+        "bbox": [
+            173,
+            209,
+            823,
+            239
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lu Liu, Tianyi Zhou, Guodong Long, Jing Jiang, Xuanyi Dong, and Chengqi Zhang. ISOMETRIC PROPAGATION NETWORK FOR GENERALIZED ZERO-SHOT LEARNING. pp. 13, 2021a. ",
+        "bbox": [
+            171,
+            250,
+            825,
+            279
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yang Liu, Lei Zhou, Xiao Bai, Yifei Huang, Lin Gu, Jun Zhou, and Tatsuya Harada. Goal-Oriented Gaze Estimation for Zero-Shot Learning, March 2021b. ",
+        "bbox": [
+            171,
+            289,
+            825,
+            319
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Peirong Ma and Xiao Hu. A Variational Autoencoder with Deep Embedding Model for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 34(07): 11733–11740, April 2020. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v34i07.6844. ",
+        "bbox": [
+            176,
+            329,
+            823,
+            372
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient Estimation of Word Representations in Vector Space, September 2013. ",
+        "bbox": [
+            173,
+            383,
+            821,
+            412
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Shaobo Min, Hantao Yao, Hongtao Xie, Chaoqun Wang, Zheng-Jun Zha, and Yongdong Zhang. Domain-aware Visual Bias Eliminating for Generalized Zero-Shot Learning, April 2020. ",
+        "bbox": [
+            173,
+            422,
+            823,
+            454
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Genevieve Patterson, Chen Xu, Hang Su, and James Hays. The SUN Attribute Database: Beyond Categories for Deeper Scene Understanding. International Journal of Computer Vision, 108(1-2): 59–81, May 2014. ISSN 0920-5691, 1573-1405. doi: 10.1007/s11263-013-0695-z. ",
+        "bbox": [
+            176,
+            463,
+            823,
+            507
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Farhad Pourpanah, Moloud Abdar, Yuxuan Luo, Xinlei Zhou, Ran Wang, Chee Peng Lim, Xi-Zhao Wang, and Q. M. Jonathan Wu. A Review of Generalized Zero-Shot Learning Methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1–20, 2022. ISSN 0162-8828, 2160-9292, 1939-3539. doi: 10.1109/TPAMI.2022.3191696. ",
+        "bbox": [
+            173,
+            517,
+            825,
+            574
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. pp. 30, 2014. ",
+        "bbox": [
+            174,
+            585,
+            823,
+            614
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Li ´ o, and Yoshua \\` Bengio. Graph Attention Networks, February 2018. ",
+        "bbox": [
+            171,
+            625,
+            825,
+            655
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Vinay Kumar Verma, Dhanajit Brahma, and Piyush Rai. Meta-Learning for Generalized Zero-Shot Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04):6062–6069, April 2020. ISSN 2374-3468, 2159-5399. doi: 10.1609/aaai.v34i04.6069. ",
+        "bbox": [
+            173,
+            665,
+            825,
+            708
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The CaltechUCSD Birds-200-2011 Dataset. pp. 8, 2011. ",
+        "bbox": [
+            173,
+            719,
+            821,
+            750
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Xiaolong Wang, Yufei Ye, and Abhinav Gupta. Zero-shot Recognition via Semantic Embeddings and Knowledge Graphs, April 2018. ",
+        "bbox": [
+            171,
+            758,
+            823,
+            789
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yongqin Xian, Christoph H. Lampert, Bernt Schiele, and Zeynep Akata. Zero-Shot Learning—A Comprehensive Evaluation of the Good, the Bad and the Ugly. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(9):2251–2265, September 2019a. ISSN 0162-8828, 2160- 9292, 1939-3539. doi: 10.1109/TPAMI.2018.2857768. ",
+        "bbox": [
+            174,
+            799,
+            825,
+            856
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yongqin Xian, Saurabh Sharma, Bernt Schiele, and Zeynep Akata. F-VAEGAN-D2: A Feature Generating Framework for Any-Shot Learning. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10267–10276, Long Beach, CA, USA, June 2019b. IEEE. ISBN 978-1-72813-293-8. doi: 10.1109/CVPR.2019.01052. ",
+        "bbox": [
+            174,
+            867,
+            825,
+            922
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Guo-Sen Xie, Li Liu, Xiaobo Jin, Fan Zhu, Zheng Zhang, Jie Qin, Yazhou Yao, and Ling Shao. Attentive Region Embedding Network for Zero-Shot Learning. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 9376–9385, Long Beach, CA, USA, June 2019. IEEE. ISBN 978-1-72813-293-8. doi: 10.1109/CVPR.2019.00961. ",
+        "bbox": [
+            174,
+            103,
+            825,
+            159
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Guo-Sen Xie, Li Liu, Fan Zhu, Fang Zhao, Zheng Zhang, Yazhou Yao, Jie Qin, and Ling Shao. Region Graph Embedding Network for Zero-Shot Learning. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm (eds.), Computer Vision – ECCV 2020, volume 12349, pp. 562–580. Springer International Publishing, Cham, 2020. ISBN 978-3-030-58547-1 978-3-030- 58548-8. doi: 10.1007/978-3-030-58548-8 33. ",
+        "bbox": [
+            173,
+            172,
+            825,
+            243
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Shiqi Yang, Kai Wang, Luis Herranz, and Joost van de Weijer. On Implicit Attribute Localization for Generalized Zero-Shot Learning. IEEE Signal Processing Letters, 28:872–876, 2021. ISSN 1070-9908, 1558-2361. doi: 10.1109/LSP.2021.3073655. ",
+        "bbox": [
+            174,
+            257,
+            825,
+            300
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Li Zhang, Tao Xiang, and Shaogang Gong. Learning a Deep Embedding Model for Zero-Shot Learning. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3010–3019, Honolulu, HI, July 2017. IEEE. ISBN 978-1-5386-0457-1. doi: 10.1109/CVPR. 2017.321. ",
+        "bbox": [
+            174,
+            314,
+            825,
+            369
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yizhe Zhu, Jianwen Xie, Zhiqiang Tang, Xi Peng, and Ahmed Elgammal. Semantic-Guided MultiAttention Localization for Zero-Shot Learning. pp. 11, 2019. ",
+        "bbox": [
+            178,
+            383,
+            823,
+            412
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A POINT-WISE MUTUAL INFORMATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            443,
+            516,
+            459
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Point-wise mutual information (PMI) (Bouma, 2009) is proposed measure the relationship of two points (objects), defined as: ",
+        "bbox": [
+            173,
+            476,
+            825,
+            505
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2acd61e33d05a2efbf5f574d2fe159212bf915cf189c2b6801bb3718637b261f.jpg",
+        "text": "$$\nP M I \\left( x , y \\right) = \\ln \\frac { p \\left( x , y \\right) } { p \\left( x \\right) p \\left( y \\right) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            401,
+            525,
+            596,
+            559
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $p \\left( x , y \\right)$ is the joint probability of $x$ and $y$ ",
+        "bbox": [
+            174,
+            571,
+            491,
+            588
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In practice, the normalized PMI is more commonly used as: ",
+        "bbox": [
+            173,
+            593,
+            566,
+            609
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2e2209202c3077e94b9b59b15ffff30b3a5b651f83fb54501c11b2e1ba5c339f.jpg",
+        "text": "$$\nP M I _ { n } \\left( x , y \\right) = \\frac { P M I \\left( x , y \\right) } { - \\ln p \\left( x , y \\right) }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            628,
+            598,
+            662
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where its values are in the range of [-1,1], which give a good indication of the relevance between $x$ and $y$ . Specifically, 1 means they are co-occurrence, while -1 shows the opposite case. But, 0 indicates they are not relevant at all. ",
+        "bbox": [
+            174,
+            675,
+            826,
+            718
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B EVALUATION METRICS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            741,
+            398,
+            757
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We consider both conventional ZSL and GZSL settings in all three datasets. Mean Class Accuracy $( M C A )$ is adopted as the evaluation indicator for ZSL setting, which takes average value of Top-1 accuracies on unseen classes. And harmonic mean $( H )$ is employed to evaluate the performance of GZSL setting, which is the most comprehensive metric to reflect model performance by taking accuracies of seen and unseen classes into consideration. The specific formula is defined as follows: ",
+        "bbox": [
+            173,
+            773,
+            825,
+            844
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9b895dc7145a8a281ad2d5091b14df1ed0b6d03bed8f73f1b0d6c243873a3e6d.jpg",
+        "text": "$$\nH = \\frac { 2 \\times M C A _ { S } \\times M C A _ { U } } { M C A _ { S } + M C A _ { U } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            863,
+            598,
+            896
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "where $M C A _ { S }$ and $M C A _ { U }$ are the $M C A s$ for seen classes and unseen classes, respectively. ",
+        "bbox": [
+            169,
+            909,
+            781,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "C MODEL SETTINGS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            362,
+            118
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We use the fixed ResNet101 (He et al., 2016) pretrained on ImageNet as the feature extractor of A3E network, which is commonly used as the backbone network in many models (Huynh & Elhamifar, 2020b; Xie et al., 2020; Ge et al., 2021; Chen et al., 2021b; 2022). The input images of model are reshaped as $2 2 4 \\times 2 2 4$ pixels for AwA2 datasets and $4 4 8 \\times 4 4 8$ pixels for CUB and SUN datasets since the finer details could significantly improve performance on fine-grained datasets. We use the Word2Vec model trained on Google News to generate attribute word vectors with 300 dimensions. ",
+        "bbox": [
+            174,
+            132,
+            825,
+            217
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We adopt ADAM optimizer (Kingma & Ba, 2017) in model training and set weigh decay to $1 \\times 1 0 ^ { - 5 }$ . We empirically set the hidden layers and attention heads of GAT network in EAS module to $\\{ 2 0 0$ , $1 \\}$ for AwA2, $\\{ 2 0 0 , 4 \\}$ for CUB and $\\{ 1 0 0 0 , 5 \\}$ for SUN, with dropout rate fixed to 0.2. For AwA2 dataset, we set the learning rate to $5 \\times 1 0 ^ { - 6 }$ , batch size to 64 and maximum iteration number to 10. Regarding to CUB dataset, the learning rate is set to $7 . 5 \\times 1 0 ^ { - 6 }$ . Batch size is set to 8, and maximum iteration number is 30. As to SUN dataset, we set the learning rate to $5 \\times 1 0 ^ { - 6 }$ , batch size to 16 and maximum iteration number to 25. The learning rate for $1 \\times 1$ convolution in AL module is 10 times greater than the given values in all datasets. The calibration bias $\\beta$ is set to 2.0, 0.4 and 0.4 for AwA2, CUB and SUN, respectively. ",
+        "bbox": [
+            174,
+            223,
+            825,
+            349
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "There are two hyperparameters in A3E network: weighting coefficient $\\lambda$ and ARG threshold $\\delta$ . We set $\\lambda$ to 0.6, 0.8 and 0.9 for AwA2, CUB and SUN datasets. While $\\delta$ is set to 0.9, 0.8 and 0.1 for these three datasets, respectively. The influence of the hyperparameters is explored in the following experiments. ",
+        "bbox": [
+            174,
+            356,
+            825,
+            411
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D AVERAGE HARMONIC MEANS ON AWA2 AND CUB ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            431,
+            635,
+            448
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/b91954358aff6fd72cf926ca27e18155aa6035462744c1925f01a88704d5b863.jpg",
+        "table_caption": [
+            "Table 3: Average harmonic means on AwA2 and CUB datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td>AwA2</td><td>CUB</td><td>Average</td></tr><tr><td colspan=\"3\">H</td></tr><tr><td>DAZLE</td><td>67.1</td><td>58.1</td><td>62.6</td></tr><tr><td>RGEN</td><td>71.5</td><td>66.1</td><td>68.8</td></tr><tr><td>MSDN A3E</td><td>67.7 70.2</td><td>68.1 68.8</td><td>67.9 69.5</td></tr></table>",
+        "bbox": [
+            367,
+            497,
+            630,
+            582
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E ABLATION STUDY ON DROPOUT ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            616,
+            477,
+            632
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/d3e7fcb7cf368a89809b4c1bb0996f90c10c255117db32e06ca340cd3ed01262.jpg",
+        "image_caption": [
+            "Figure 5: Effects of dropout rate $d$ on CUB dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            334,
+            651,
+            660,
+            801
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Dropout is a commonly used strategy to prevent neural networks from overfitting (Srivastava et al., 2014). In our work, we employ dropout on GAT of AE module by randomly dropping some node features during training stage. The dropping process is controlled by dropout rate $d$ that determines the proportion of dropped nodes. As shown in Figure 5, with dropout rate $d$ increasing from 0 to 0.2 (0 means dropout is inactive), almost all indicators are on the rise, except a slight fluctuation for the seen class accuracy on GZSL. The accuracy decreases gradually from 0.3. To sum up, both ZSL accuracy and GZSL harmonic mean reach the best values at 0.2 dropout rate, then begin to decline with the increase of $d$ . The phenomenon can verify functionality of dropout: preventing models from overfitting. Besides, dropout is indispensable to AE module because it improves the generalization ability of model. ",
+        "bbox": [
+            174,
+            854,
+            825,
+            924
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            174,
+            103,
+            825,
+            172
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "F TERM EXPLANATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            194,
+            383,
+            210
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Attribute semantics: The word vectors of attributes, which is the output of word2vec model by taking the attribute name as the input. The resulted representation codes semantic information of each input attribute, so called the attribute semantics. ",
+        "bbox": [
+            176,
+            224,
+            825,
+            267
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Class attribute vectors: A set of vectors corresponds to the set of classes. Each vector encodes information about the attributes of the corresponding class, and the presence of attribute is indicated by a continuous or binary value at its corresponding element of the vector. ",
+        "bbox": [
+            174,
+            275,
+            825,
+            316
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Attribute prototypes is actually the class attribute vectors in the attribute space, that has identical meanings with class attribute vectors. ",
+        "bbox": [
+            174,
+            324,
+            823,
+            352
+        ],
+        "page_idx": 13
+    }
+]

parse/dev/arg1dQSS6Mh/arg1dQSS6Mh_layout.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7596654174dfcc4147012c89c03c0991a185be2c954002f3e005980d136df270
+size 2126920

parse/dev/arg1dQSS6Mh/arg1dQSS6Mh_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:715a61fff094f67089f8e595a6536575523efb17fcc6fdcfcfb6f335c0adfa09
+size 2008153

parse/dev/arg1dQSS6Mh/arg1dQSS6Mh_span.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5f414ee1f559957ad49b959c06781061586471350f06b1393294a92c6808d055
+size 2128900

parse/dev/ayPPc0SyLv1/ayPPc0SyLv1.md

@@ -0,0 +1,394 @@
+# DO WE REALLY NEED COMPLICATED MODEL ARCHITECTURES FOR TEMPORAL NETWORKS?
+
+Weilin Cong Penn State weilin@psu.edu
+
+Si Zhang   
+Meta   
+sizhang@meta.com
+
+Jian Kang University of Illinois at Urbana-Champaign jiank2@illinois.edu
+
+# Baichuan Yuan & Hao Wu & Xin Zhou
+
+Meta {bcyuan,haowu1,markzhou}@meta.com
+
+Hanghang Tong   
+University of Illinois at Urbana-Champaign   
+htong@illinois.edu
+
+Mehrdad MahdaviPenn Statemzm616@psu.edu
+
+# ABSTRACT
+
+Recurrent neural network (RNN) and self-attention mechanism (SAM) are the de facto methods to extract spatial-temporal information for temporal graph learning. Interestingly, we found that although both RNN and SAM could lead to a good performance, in practice neither of them is always necessary. In this paper, we propose GraphMixer, a conceptually and technically simple architecture that consists of three components: $\textcircled{1}$ a link-encoder that is only based on multi-layer perceptrons (MLP) to summarize the information from temporal links, $\textcircled{2}$ a node-encoder that is only based on neighbor mean-pooling to summarize node information, and $\textcircled{3}$ an MLP-based link classifier that performs link prediction based on the outputs of the encoders. Despite its simplicity, GraphMixer attains an outstanding performance on temporal link prediction benchmarks with faster convergence and better generalization performance. These results motivate us to rethink the importance of simpler model architecture. [Code].
+
+# 1 INTRODUCTION
+
+In recent years, temporal graph learning has been recognized as an important machine learning problem and has become the cornerstone behind a wealth of high-impact applications Yu et al. (2018); Bui et al. (2021); Kazemi et al. (2020); Zhou et al. (2020); Cong et al. (2021b). Temporal link prediction is one of the classic downstream tasks which focuses on predicting the future interactions among nodes. For example, in an ads ranking system, the user-ad clicks can be modeled as a temporal bipartite graph whose nodes represent users and ads, and links are associated with timestamps indicating when users click ads. Link prediction between them can be used to predict whether a user will click an ad. Designing graph learning models that can capture node evolutionary patterns and accurately predict future links is a crucial direction for many real-world recommender systems.
+
+In temporal graph learning, recurrent neural network (RNN) and self-attention mechanism (SAM) have become the de facto standard for temporal graph learning Kumar et al. (2019); Sankar et al. (2020); Xu et al. (2020); Rossi et al. (2020); Wang et al. (2020), and the majority of the existing works focus on designing neural architectures with one of them and additional components to learn representations from raw data. Although powerful, these methods are conceptually and technically complicated with advanced model architectures. It is non-trivial to understand which parts of the model design truly contribute to its success, and whether these components are indispensable. Thus, in this paper, we aim at answering the following two questions:
+
+Q1: Are RNN and SAM always indispensable for temporal graph learning? To answer this question, we propose GraphMixer, a simple architecture based entirely on the multi-layer perceptrons (MLPs) and neighbor mean-pooling, which does not utilize any RNN or SAM in its model architecture (Section 3). Despite its simplicity, GraphMixer could obtain outstanding results when comparing it
+
+$$
+\begin{array} { l l } { { \mathrm { n o w } { \displaystyle \frac { t _ { 0 } \ t _ { 1 } \ t _ { 2 } \ t _ { 3 } \ t _ { 4 } \quad t _ { 4 } \quad t _ { 5 } \quad t _ { 6 } } { \ \longrightarrow \ ( \mathrm { p a s t } ) } } } } & { { \ \mathrm { N o d e ~ f e a t u r e s } \ \textcircled { \bigcirc _ { 1 } } } } \\ { { \mathrm { e m p o r a l ~ g r a p h ~ ( \bigcirc _ { 1 } ) } { \frac { t _ { 1 } , t _ { 5 } } { \ \mathrm { f } _ { 3 } , t _ { 4 } } } \overbrace { { \bigcirc _ { 2 } } ^ { \mathrm { ( \bigoplus _ { 3 } ) } } \big _ { \big < _ { 3 } } ^ { \mathrm { ( \bigoplus _ { 4 } ) } } { \big > } ^ { \mathrm { ( \bigoplus _ { 6 } ) } } { \big _ { \qquad t _ { 6 } } \ \big ( \bigcirc _ { 5 } \big ) } } } } & { { \ \mathrm { L i n k ~ f e a t u r e s } \ \mathrm { \Gamma } \big ( \bigcirc _ { 1 } \big ) \ t _ { 1 } , t _ { 5 } \ \big ( \bigcirc _ { 2 } ^ { \mathrm { ( \ominus _ { 3 } ) } } \ \mathrm { \ { x } } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) , \ \mathrm { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 5 } ) } }  \end{array}
+$$
+
+Figure 1: (Left) Temporal graph with nodes $v _ { 1 } , \ldots , v _ { 5 }$ , per-link timestamps $t _ { 1 } , \ldots , t _ { 6 }$ indicate when two nodes interact. For example, $v _ { 1 } , v _ { 2 }$ interact at $t _ { 1 } , t _ { 5 }$ . (Right) Each node has its node features (e.g., $\mathbf { x } _ { 1 } ^ { \mathrm { n o d e } }$ for $v _ { 1 }$ ) and each temporal link has its link features (e.g., $\mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 5 } )$ are link features between $v _ { 1 } , v _ { 2 }$ at $t _ { 1 } , t _ { 5 } )$ . For scenarios without node or link features, we use all-zero vectors instead.
+
+against baselines that are equipped with the RNNs and SAM. In practice, it achieves state-of-the-art performance in terms of different evaluation metrics (e.g., average precision, AUC, Recall $@ \mathrm { K }$ , and MRR) on real-world temporal graph datasets, with the even smaller number of model parameters and hyper-parameters, and a conceptually simpler input structure and model architecture (Section 4).
+
+Q2: What are the key factors that lead to the success of GraphMixer? We identify three key factors that contribute to the success of GraphMixer: $\textcircled{1}$ The simplicity of GraphMixer’s input data and neural architecture. Different from most deep learning methods that focus on designing conceptually complicated data preparation techniques and technically complicated neural architectures, we choose to simplifying the neural architecture and utilize a conceptually simpler data as input. Both of which could lead to a better model performance and better generalization (Section 4.4). $\textcircled{2} A$ time-encoding function that encodes any timestamp as an easily distinguishable input vector for GraphMixer. Different from most of the existing methods that propose to learn the time-encoding function from the raw input data, our time-encoding function utilizes conceptually simple features and is fixed during training. Interestingly, we show that our fixed time-encoding function is more preferred than the trainable version (used by most previous studies), and could lead to a smoother optimization landscape, a faster convergence speed, and a better generalization (Section 4.2); $\textcircled{3} A$ link-encoder that could better distinguish temporal sequences. Different from most existing methods that summarize sequences using SAM, our encoder module is entirely based on MLPs. Interestingly, our encoder can distinguish temporal sequences that cannot be distinguished by SAM, and it could generalize better due to its simpler neural architecture and lower model complexity (Section 4.3).
+
+To this end, we summarize our contributions as follows: $\textcircled{1}$ We propose a conceptually and technically simple architecture GraphMixer; $\textcircled{2}$ Even without RNN and SAM, GraphMixer not only outperforms all baselines but also enjoys a faster convergence and better generalization ability; $\textcircled{3}$ Extensive study identifies three factors that contribute to the success of GraphMixer. $\textcircled{4}$ Our results could motivate future research to rethink the importance of the conceptually and technically simpler method.
+
+# 2 PRELIMINARY AND EXISTING WORKS
+
+Preliminary. Figure 1 is an illustration on the temporal graph. Our goal is to predict whether two nodes are connected at a specific timestamp $t _ { 0 }$ based on all the available temporal graph information happened before that timestamp. For example, to predict whether $v _ { 1 } , v _ { 2 }$ are connected at $t _ { 0 }$ , we only have access to the graph structure, node features, and link features with timestamps from $t _ { 1 }$ to $t _ { 6 }$ .
+
+Related works. Most of the temporal graph learning methods are conceptually and technically complicated with advanced neural architectures. It is non-trivial to fully understand the algorithm details without looking into their implementations. Therefore, we select the four most representative and most closely-related methods to introduce and compare them in more details.
+
+• JODIE Kumar et al. (2019) is a RNN-based method. Let us denote ${ \bf x } _ { i } ( t )$ as the embedding of   
+nodthat $v _ { i }$ at time latest in $t$ , e ${ \bf x } _ { i j } ^ { \mathrm { l i n k } } ( t )$ as the link feature between h other node. JODIE pre- $v _ { i } , v _ { j }$ at time ses and $t$ , and updat $m _ { i }$ as the timestamphe representation $v _ { i }$ of each node via RNNs (is it just one RNN or multiple RNNs). More specifically, when an interaction between $v _ { i } , v _ { j }$ happens at time $t$ , JODIE updates the temporal embedding using RNN   
+by $\begin{array} { r } { \mathbf { x } _ { i } ( t ) = \mathbb { R } \mathrm { N N } \left( \mathbf { x } _ { i } ( m _ { i } ) , \mathbf { x } _ { j } ( \bar { m } _ { j } ) , \mathbf { x } _ { i j } ^ { \mathrm { l i n k } } ( t ) , t - m _ { i } \right) . } \end{array}$ . Then, the dynamic embedding of node $v _ { i }$ at time $t _ { 0 }$ is computed by $\mathbf { h } _ { i } ( t _ { 0 } ) = ( 1 + \bar { ( t _ { 0 } - m _ { i } ) } \mathbf { w } ) \cdot \mathbf { x } _ { i } ( m _ { i } ) .$ . Finally, the prediction on any node pair at time $t _ { 0 }$ is computed by $\mathbb { M L P } \left( \left[ \mathbf { h } _ { i } ( t _ { 0 } ) \mathbf { \Lambda } | | \mathbf { h } _ { j } ( t _ { 0 } ) \right] \right)$ , where $[ \cdot | | \cdot ]$ is the concatenate operation and $\mathtt { M L P } ( \mathbf { x } )$ is applying 2-layer MLP on $\mathbf { x }$ .
+
+• DySAT Sankar et al. (2020) is a SAM-based method. DySAT requires pre-processing the temporal graph into multiple snapshot graphs by first splitting all timestamps into multiple time-slots, then merging all edges in each time-slot. Let $\mathcal { G } _ { t } ( \nu , \mathcal { E } _ { t } )$ denote the $t$ -th snapshot graph. To capture spatial information, DySAT first applies Graph Attention Network (GAT) Velickovi ˇ c et al. ´ (2018) on each snapshot graph $\mathcal { G } _ { t }$ independently by $\mathbf { X } ( t ) = \ G \mathbb { A } \mathrm { T } ( \mathcal { G } _ { t } )$ . Then, to capture of temporal information for each node, Transformer is applied to $\mathbf { x } _ { i } ( t ) \dot { = } [ \dot { \mathbf { X } } ( t ) ] _ { i }$ at different timestamps to capture the temporal information by $\mathbf { h } _ { i } ( t _ { k } ) , \ldots \mathbf { h } _ { i } ( t _ { 0 } ) =$ Transformer $\big ( \mathbf { x } _ { i } ( t _ { k } ) , \ldots , \mathbf { x } _ { i } ( \dot { t } _ { 0 } ) \big )$ . Finally, the prediction on any node pair at time $t _ { 0 }$ is computed by $\mathbb { M L P } \big ( [ \mathbf { h } _ { i } ( t _ { 0 } ) | | \mathbf { h } _ { j } ( t _ { 0 } ) ] \big )$ .
+
+• TGAT Xu et al. (2020) is a SAM-based method that could capture the spatial and temporal information simultaneously. TGAT first generates the time augmented feature of node $i$ at time $t$ by concatenating the raw feature $\mathbf { x } _ { i }$ with a trainable time encoding ${ \bf z } ( t )$ of time $t$ , i.e., $\mathbf { x } _ { i } ( t ) = [ \mathbf { x } _ { i } \mid \mid \mathbf { z } ( t ) ]$ and ${ \bf z } ( t ) = \cos ( t { \bf w } + { \bf b } )$ . Then, SAM is applied to the time augmented features and produces node representation $\mathbf { \dot { h } } _ { i } ( t _ { 0 } ) = \operatorname { S A M } \left( \mathbf { x } _ { i } ( t _ { 0 } ) , \{ \bar { \mathbf { x } _ { u } } ( h _ { u } ) \mid u \in \mathcal { N } _ { t _ { 0 } } ( i ) \bar  \} \right)$ , where $\mathcal { N } _ { t _ { 0 } } ( i )$ denotes the neighbors of node $i$ at time $t _ { 0 }$ and $h _ { u }$ denotes the timestamp of the latest interaction of node $u$ . Finally, the prediction on any node pair at time $t _ { 0 }$ is computed by $\mathbb { M L P } \left( \left[ \mathbf { h } _ { i } ( t _ { 0 } ) \mathbf { \Lambda } | | \mathbf { h } _ { j } ( t _ { 0 } ) \right] \right)$ . TGN Rossi et al. (2020) is a mixture of RNN- and SAM-based method. In practice, TGN first captures the temporal information using RNN (similarly to JODIE), and then applies graph attention convolution to capture the spatial and temporal information jointly (similarly to TGAT).
+
+Besides, we also consider the following temporal graph learning methods as baselines. These methods could be thought of as an extension on top of the above four most representative methods, but with the underlying idea behind the model design much more conceptually complicated. CAWs Wang et al. (2020) is a mixer of RNN- and SAM- based method that proposes to represent network dynamics by extracting temporal network motifs using temporal random walks. CAWs replaces node identities with the hitting counts of the nodes based on a set of sampled walks to establish the correlation between motifs. Then, the extracted motifs are fed into RNNs to encode each walk as a representation, and use SAM to aggregate the representations of multi-walks into a single vector for downstream tasks. TGSRec Fan et al. (2021) is a SAM-based method that proposes to unify sequential patterns and temporal collaborative signals to improve the quality of recommendation. To achieve this goal, they propose to advance the SAM by adopting novel collaborative attention, such that SAM can simultaneously capture collaborative signals from both users and items, as well as consider temporal dynamics inside sequential patterns. APAN Wang et al. (2021b) is a RNN-based method that proposes to decouple model inference and graph computation to alleviate the damage of the heavy graph query operation to the speed of model inference. More related works are deferred to Appendix B.
+
+# 3 GRAPHMIXER: A CONCEPTUALLY AND TECHNICALLY SIMPLE METHOD
+
+In this section, we first introduce the neural architecture of GraphMixer in Section 3.1 then explicitly highlight its difference to baseline methods in Section 3.2.
+
+3.1 DETAILS ON GRAPHMIXER: NEURAL ARCHITECTURE AND INPUT DATA
+
+GraphMixer has three modules: $\textcircled{1}$ link-encoder is designed to summarize the information from temporal links (e.g., link timestamps and link features); $\textcircled{2}$ node-encoder is designed to summarize the information from nodes (e.g., node features and node identity); $\textcircled{3}$ link classifier predicts whether a link exists based on the output of the aforementioned two encoders.
+
+Link-encoder. The link-encoder is designed to summarize the temporal link information associated with each node sorted by timestamps, where temporal link information is referring to the timestamp and features of each link. For example in Figure 1, the temporal link information for node $v _ { 2 }$ is $\{ ( t _ { 1 } , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) ) , ( t _ { 3 } , \mathbf { x } _ { 2 , 4 } ^ { \mathrm { l i n k } } ( t _ { 3 } ) ) , ( t _ { 4 } , \mathbf { \hat { x } } _ { 2 , 4 } ^ { \mathrm { l i n k } } ( t _ { 4 } ) ) ^ { \sim } ( t _ { 5 } , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 5 } ) ) \}$ and for node $v _ { 5 }$ is $\{ ( t _ { 2 } , \mathbf { x } _ { 3 , 5 } ^ { \mathrm { l i n k } } ( t _ { 2 } ) ) , ( t _ { 6 } , \dot { \mathbf { x } } _ { 4 , 5 } ^ { \mathrm { l i n k } } ( t _ { 6 } ) ) \}$ . In practice, we only keep the top $K$ most recent temporal link information, where $K$ is a dataset dependent hyper-parameter. If multiple links have the same timestamps, we simply keep them the same order as the input raw data. To summarize temporal link information, our link-encoder should have the ability to distinguish different timestamps (achieved by our time-encoding function) and different temporal link information (achieved by the Mixer module).
+
+• Time-enfunction $\cos ( t \omega )$ unction. To distinguish d, which utilizes features $\omega = \{ \alpha ^ { - ( i - 1 ) / \beta } \} _ { i = 1 } ^ { \cdot }$ we introduce our time-encoding to encode each timestamps into a $d$ -dimensional vector. More specifically, we first map each $t$ to a vector with monotonically exponentially decreasing values $t \omega \in ( 0 , t ]$ among the feature dimension, then use cosine function to project all values to $\cos ( t \omega ) \in [ - 1 , + \bar { 1 } ]$ . The selection of $\alpha , \beta$ is depending on the scale of the maximum timestamp $t _ { \mathrm { m a x } }$ we wish to encode. In order to distinguish all timestamps, we have to make sure $t _ { \mathrm { m a x } } \stackrel { \bullet } { \times } \alpha ^ { - ( i - 1 ) / \beta }  0$ as $i  d$ to distinguish all timestamps. In practice, we found $d = 1 0 0$ and $\alpha = \beta = \sqrt { d }$ works well for all datasets. Notice that $\omega$ is fixed and will not be updated during training. As shown in Figure 2a, the output of this time-encoding function has two main properties that could help GraphMixer distinguish different timestamps: similar timestamps have similar time-encodings (e.g., the plot of $t _ { 1 } , t _ { 2 } )$ and the larger the timestamp the later the values in time-encodings converge to $+ 1$ (e.g., the plot of $t _ { 1 } , t _ { 3 }$ or $t _ { 1 } , t _ { 4 } )$ .
+
+![](images/4c578c45a87d195a9940b3b54d3e74d2a39b9c775c65e048125d412acb3382a2.jpg)  
+Figure 2: (a) Time-encoding function that pre-process timestamp $t$ into a vector $\cos ( t \omega )$ . The $\mathbf { X }$ -axis is the vector dimension and the y-axis is the cosine value. (b) link-encoder takes the temporal link information of node $v _ { 2 }$ as inputs and outputs a vector $\mathbf { t } _ { 2 } ( t _ { 0 } )$ that will be used for link prediction.
+
+• Mixer for information summarizing. We use a 1-layer MLP-mixer Tolstikhin et al. (2021) to summarize the temporal link information. Figure 2b is an example on summarizing the temporal link information of node $\{ ( t _ { 1 } , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) ) , ( t _ { 3 } , \mathbf { x } _ { 2 , 4 } ^ { \mathrm { l i n k } } ( t _ { 3 } ) ) , ( t _ { 4 } , \mathbf { x } _ { 2 , 4 } ^ { \mathrm { l i n k } } ( t _ { 4 } ) ) , ( t _ { 5 } , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 5 } ) ) \}$ $v _ { 2 }$ . Recall that the temporal link information of node 2 . We first encode timestamps by our is time-encoding function then concatenate it with its corresponding link features. For example, we encode $( t _ { 1 } , \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) )$ as $\left[ \cos ( ( t _ { 0 } - t _ { 1 } ) \omega ) | | \mathbf { x } _ { 1 , 2 } ^ { \mathrm { l i n k } } ( t _ { 1 } ) ) \right]$ where $t _ { 0 }$ is the timestamp that we want to predict whether the link exists. Then, we stack all the outputs into a big matrix and zero-pad to the fixed length $K$ denoted as $\mathbf { T } _ { 2 } ( t _ { 0 } )$ . Finally, we use an 1-layer MLP-mixer with mean-pooling to compress $\mathbf { T } _ { 2 } ( t _ { 0 } )$ into a single vector $\mathbf { t } _ { 2 } ( t _ { 0 } )$ . Specifically, the MLP-mixer takes $\mathbf { T } _ { 2 } ( t _ { 0 } )$ as input
+
+$$
+\begin{array} { r } { \begin{array} { r } { \mathbf { T } _ { 2 } ( t _ { 0 } ) \to \mathbf { H } _ { \mathrm { i n p u t } } , \mathbf { H } _ { \mathrm { t o k e n } } = \mathbf { H } _ { \mathrm { i n p u t } } + \mathbf { W } _ { \mathrm { t o k e n } } ^ { ( 2 ) } \mathcal { G e } \mathbf { L U } ( \mathbf { W } _ { \mathrm { t o k e n } } ^ { ( 1 ) } \mathrm { L a y e r N o r m } ( \mathbf { H } _ { \mathrm { i n p u t } } ) ) , } \\ { \mathbf { H } _ { \mathrm { c h a m e l } } = \mathbf { H } _ { \mathrm { t o k e n } } + \mathcal { G e } \mathbf { L U } ( \mathrm { L a y e r N o r m } ( \mathbf { H } _ { \mathrm { t o k e n } } ) \mathbf { W } _ { \mathrm { c h a n n e l } } ^ { ( 1 ) } ) \mathbf { W } _ { \mathrm { c h a m e l } } ^ { ( 2 ) } , } \end{array} } \end{array}
+$$
+
+and output the temporal encoding $\mathbf { t } _ { 2 } ( t _ { 0 } ) = \mathbb { M } \mathrm { e a n } ( \mathbf { H } _ { \mathrm { c h a n n e l } } )$ . Please notice that zero-padding operator is important to capture how often a node interacts with other nodes. The node with more zero-padded dimensions has less temporal linked neighbors. This information is very important in practice according to our experimental observation.
+
+Node-encoder. The node-encoder is designed to capture the node identity and node feature information via neighbor mean-pooling. Let us define the 1-hop neighbor of node $v _ { i }$ with link timestamps from $t$ to $t _ { 0 }$ as $\mathcal { N } ( \bar { v _ { i } } ; t , t _ { 0 } )$ . For example in Figure 1, we have $\mathcal { N } ( v _ { 2 } ; t _ { 4 } , t _ { 0 } ) = \{ v _ { 1 } , v _ { 4 } \}$ and $\mathcal { N } ( v _ { 5 } ; t _ { 4 } , t _ { 0 } ) = \{ v _ { 3 } \}$ . Then, the node-info feature is computed based on the 1-hop neighbor by $\mathbf { s } _ { i } ( t _ { 0 } ) = \mathbf { x } _ { i } ^ { \mathrm { n o d e } } + \dot { \mathrm { M e a n } } \{ \mathbf { x } _ { j } ^ { \mathrm { n o d e } } \ \vert \ v _ { j } \in \mathcal { N } ( v _ { i } ; t _ { 0 } - T , t _ { 0 } ) \}$ , where $T$ is a dataset-dependent hyperparameter. In practice, we found 1-hop neighbors are enough to achieve good performance, and we use one-hot node representations for datasets without node features.
+
+Link classifier. Link classifier is designed to classify whether a link exists at time $t _ { 0 }$ using the output of link-encoder $\mathbf { t } _ { i } ( t _ { 0 } )$ and the output of node-encoder ${ \bf s } _ { i } ( t _ { 0 } )$ . Let us denote the node $v _ { i }$ ’s representation at time $t _ { 0 }$ as the concatenation of the above two encodings $\mathbf { h } _ { i } ( t _ { 0 } ) = \left[ \mathbf { s } _ { i } ( t _ { 0 } ) \mathbf { \nabla } \| \mathbf { \ v } _ { i } ( t _ { 0 } ) \right]$ . Then, the prediction on whether an interaction between node $v _ { i } , v _ { j }$ happens at time $t _ { 0 }$ is computed by applying a 2-layer MLP model on $[ \mathbf { h } _ { i } ( t _ { 0 } ) \mathbf { \epsilon } ] | \mathbf { h } _ { j } ( t _ { 0 } ) ]$ , i.e., $\begin{array} { r } { p _ { i j } = \mathbf { \tilde { M L P } } ( \left[ \mathbf { h } _ { i } ( t _ { 0 } ) \mathbf { \mathbf { \tau } } \right| \left| \mathbf { h } _ { j } ( t _ { 0 } ) \right] ) } \end{array}$ .
+
+# 3.2 COMPARISON TO EXISTING METHODS
+
+In the following, we highlight some differences between GraphMixer and other methods, which will be explicitly ablation studied in the experiment section (Section 4.4).
+
+Temporal graph as undirected graph. Most of the existing works consider temporal graphs as directed graphs with information only flows from the source node (e.g., users in the recommender system) to the destination nodes (e.g., ads in the recommender system). However, we consider the temporal graph as an undirected graph. By doing so, if two nodes are frequently connected in the last few timestamps, the “most recent 1-hop neighbors” sampled for the two nodes on the “undirected” temporal graph would be similar. In other words, the similarity between the sampled neighbors provides information on whether two nodes are frequently connected in the last few timestamps, which is essential for temporal graph link prediction. Intuitively, if two nodes are frequently connected in the last few timestamps, they are also likely to be connected in the recent future.
+
+Table 1: Comparison on the average precision score for link prediction. GraphMixer uses one-hot node encoding for datasets without node features (marked by ♮). For each dataset, we indicate whether we have the corresponding feature (“L” link features, “N” node features, and “T” link timestamps). Red is the best score, Blue is the best score excluding GraphMixer and its variants.   
+
+<table><tr><td></td><td>Reddit L,T</td><td>Wiki L,T</td><td>MOOC T</td><td>LastFM T</td><td>GDELT L,N,T</td><td>GDELT-ne T</td><td>GDELT-e N,T</td></tr><tr><td>JODIE</td><td>99.30±0.01</td><td>98.81 ± 0.01</td><td>99.16± 0.01</td><td>67.51 ± 0.87</td><td>98.27±0.02</td><td>97.13± 0.02</td><td>96.96±0.02</td></tr><tr><td>DySAT</td><td>98.52 ± 0.01</td><td>96.71 ± 0.02</td><td>98.82±0.02</td><td>76.40± 0.77</td><td>98.52 ± 0.02</td><td>82.47 ± 0.13</td><td>97.25 ± 0.02</td></tr><tr><td>TGAT</td><td>99.66 ± 0.01</td><td>97.75 ± 0.02</td><td>98.43 ±0.01</td><td>54.77 ± 1.01</td><td>98.25 ±0.02</td><td>84.30 ±0.10</td><td>96.96 ±0.02</td></tr><tr><td>TGN</td><td>99.80 ± 0.01</td><td>99.55 ± 0.01</td><td>99.62 ± 0.01</td><td>82.23 ± 0.50</td><td>98.15±0.02</td><td>97.13 ± 0.02</td><td>96.04±0.02</td></tr><tr><td>CAWs-mean</td><td>98.43±0.02</td><td>97.72 ± 0.03</td><td>62.99±0.87</td><td>76.35±0.08</td><td>95.11± 0.12</td><td>69.20±0.10</td><td>91.72 ± 0.19</td></tr><tr><td>CAWs-attn</td><td>98.51 �� 0.02</td><td>97.95 ± 0.03</td><td>63.07 ±0.82</td><td>76.31±0.10</td><td>95.06 ± 0.11</td><td>69.54 ± 0.19</td><td>91.54± 0.22</td></tr><tr><td>TGSRec</td><td>95.21±0.08</td><td>91.64± 0.12</td><td>83.62 ± 0.34</td><td>76.91± 0.87</td><td>97.03 ±0.61</td><td>97.03 ± 0.61</td><td>97.03 ± 0.61</td></tr><tr><td>APAN</td><td>99.24± 0.02</td><td>98.14± 0.01</td><td>98.70 ±0.98</td><td>69.39 ± 0.81</td><td>95.96 ±0.10</td><td>97.38 ± 0.23</td><td>96.77 ± 0.18</td></tr><tr><td>GraphMixer-L</td><td>99.84±0.01</td><td>99.70±0.01</td><td>99.81±0.01</td><td>95.50±0.03</td><td>98.99±0.02</td><td>96.14±0.02</td><td>98.99±0.02</td></tr><tr><td>GraphMixer-N</td><td>99.24±0.01</td><td>90.33± 0.01</td><td>97.35±0.02b</td><td>63.80±0.03</td><td>94.44 ± 0.02</td><td>96.00±0.024</td><td>98.81±0.02b</td></tr><tr><td>GraphMixer</td><td>99.93 ± 0.01§</td><td>99.85± 0.01</td><td>99.91 ± 0.01§</td><td>96.31 ± 0.02</td><td>98.89 ±0.02</td><td>98.39 ± 0.02§</td><td>98.22 ±0.02</td></tr></table>
+
+Selection on neighbors. Existing methods consider either “multi-hop recent neighbors” or “multihop uniform sampled neighbors”, whereas we only consider the “1-hop most recent neighbors”. For example, TGAT Xu et al. (2020), DySAT Sankar et al. (2020), and TGSRe Fan et al. (2021) consider multi-hop uniform sampled neighbors; JODIE Kumar et al. (2019), TGN Rossi et al. (2020), and APAN Wang et al. (2021b) maintain the historical node interactions via RNN, which can be think of as multi-hop recent neighbors; CAWs Wang et al. (2020) samples neighbors by random walks, which can also be think of as multi-hop recent neighbors. Although sampling more neighbors could provide a sufficient amount of information for models to reason about, it could also carry much spurious or noisy information. As a result, more complicated model architectures (e.g., RNN or SAM) are required to extract useful information from the raw data, which could lead to a poor model trainability and potentially weaker generalization ability. Instead, we only take the “most recent 1-hop neighbors” into consideration, which is conceptually simpler and enjoys better performance.
+
+# 4 EXPERIMENTS
+
+Dataset. We conduct experiments on five real-world datasets, including the Reddit, Wiki, MOOC, LastFM datasets that are used in Kumar et al. (2019) and the GDELT dataset1 which is introduced in Zhou et al. (2022). Besides, since GDELT is the only dataset with both node and link features, we create its two variants to understand the effect of training data on model performance: GDELT-e removes the link feature from GDELT and keep the node feature and link timestamps, GDELT-ne removes both the link and edge features from GDELT and only keep the link timestamps. For each dataset, we use the same $7 0 \% / 1 5 \% / 1 5 \%$ chronological splits for the train/validation/test sets as existing works. The detailed dataset statistics are summarized in Appendix A.2.
+
+Baselines. We compare baselines that are introduced in Section 2. Besides, we create two variants to better understand how node- and link-information contribute to our results, where GraphMixer-L is only using link-encoder and GraphMixer-N is only using node-encoder. We conduct experiments under the transductive learning setting and use average precision for evaluation. The detailed model configuration, training and evaluation process are summarized in Appendix A.3. Due to the space limit, more experiment results on using Recall@K, MRR, and AUC as the evaluation metrics, comparison on wall-clock time and number of parameters are deferred to Appendix C
+
+Outline. We first compare GraphMixer with baselines in Section 4.1 then highlight the three key factors that contribute to the success of GraphMixer in Section 4.2, Section 4.3, and Section 4.4.
+
+# 4.1 MAIN EMPIRICAL RESULTS.
+
+GraphMixer achieves outstanding performance. We compare the average precision score with baselines in Table 1. We have the following observations: $\textcircled{1}$ GraphMixer outperforms all baselines on all datasets. The experiment results provide sufficient support on our argument that neither RNN nor SAM is necessary for temporal graph link prediction. $\textcircled{2}$ According to the performance of GraphMixer-L on datasets only have link timestamp information (MOOC, LastFM, and GDELT-ne), we know that our time-encoding function could successfully pre-process each timestamp into a meaningful vector. In fact, we will show later in Section 4.2 that our time-encoding function is more preferred than baselines’ trainable version. $\textcircled{3}$ By comparing the performance GraphMixer-N and GraphMixer on Wiki, MOOC, and LastFM datasets, we know that node-encoder alone is not enough to achieve a good performance. However, it provides useful information that could benefit the link-encoder. $\textcircled{4}$ By comparing the performance of GraphMixer-N on GDELT and GDELT-ne, we observe that using one-hot encoding outperforms using node features. This also shows the importance of node identity information because one-hot encoding only captures such information. $\textcircled{5}$ More complicated methods (e.g., CAWs, TGSRec, and DDGCL) do not perform well when using the default hyper-parameters2, which is understandable because these methods have more components with an excessive amount of hyper-parameters to tune.
+
+![](images/265e13123a6283c0e7fa679a3ee3ca559539b1cc1761b53efa3a2da0b881c9c6.jpg)  
+Figure 3: Comparison on the training set average precision and generalization gap for the first 100 training epochs. Results on other datasets can be found in Figure 8.
+
+GraphMixer enjoys better convergence and generalization ability. To better understand the model performance, we take a closer look at the dynamic of training accuracy and the generalization gap (the absolute difference between training and evaluation score). The results are reported in Figure 3 and Figure 8: $\textcircled{1}$ The slope of training curves reflects the expressive power and convergence speed of an algorithm. From the first row figures, we can observe that GraphMixer always converge to a high average precision score in just a few epochs, and the training curve is very smooth when compared to baselines. Interestingly, we can observe that the baseline methods cannot always fit the training data, and their training curves fluctuate a lot throughout the training process. $\textcircled{2}$ The generalization gap reflects how well the model could generalize and how stable the model could perform on unseen data (the smaller the better). From the second row figures, the generalization gap curve of GraphMixer is lesser and smoother than baselines, which indicates the generalization power of GraphMixer.
+
+GraphMixer enjoys a smoother loss landscape. To understand why “GraphMixer converges faster and generalizes better, while baselines suffer training unstable issue and generalize poorly”, we explore the loss landscape by using the visualization tools introduced in Li et al. (2018a). We illustrate the loss landscape in Figure 4 by calculating and visualizing the loss surface along two random directions near the pre-trained optimal parameters. The $\mathbf { X \cdot }$ - and y-axis indicate how much the optimal solution is stretched along the two random directions, and the optimal point is when x- and y-axis are zero. $\textcircled{1}$ From Figure 4a, 4d, we know GraphMixer enjoys a smoother landscape with a flatter surface at the optimal point, the slope becomes steeper when stretching along the two random directions. The steeper slope on the periphery explains why GraphMixer could converge fast, the flatter surface at the optimal point explains why it could generalize well. $\textcircled{2}$ Surprisingly, we find that baselines have a non-smooth landscape with many spikes on its surface from Figure 4b, 4c, 4e, 4f. This observation provides sufficient explanation on the training instability and poor generalization issue of baselines as shown in Figure 3, 8. Interestingly, as we will show later in Section 4.2, the trainable time-encoding function in baselines is the key to this non-smooth landscape issue. Replacing it with our fixed time-encoding function could flatten the landscape and boost their model performance.
+
+![](images/c2fe0a164092269f08c3305fd6d2e1e698ba83912962800822baa236d94dec21.jpg)  
+Figure 4: Comparison on the training loss landscape. Results on other datasets and other baselines can be found in Appendix E.
+
+# 4.2 ON THE IMPORTANCE OF OUR FIXED TIME-ENCODING FUNCTION.
+
+Existing works (i.e., JODIE, TGAT, and TGN) leverage a trainable time-encoding function ${ \bf z } ( t ) =$ $\cos ( t \mathbf { w } ^ { \top } + \mathbf { b } )$ to represent timestamps3. However, we argue that using trainable time-encoding function could cause instability during training because its gradient $\begin{array} { r } { \frac { \partial \cos ( \mathbf { \breve { t } w } + \mathbf { b } ) } { \partial \mathbf { w } } = t \times \sin ( t \mathbf { w } + \mathbf { b } ) } \end{array}$ scales proportional to the timestamps, which could lead to training instability issue and cause the baselines’ the non-smooth landscape issue as shown in Figure 4. As an alternative, we utilize the fixed time-encoding function $\mathbf { z } ( t ) \dot { = } \cos ( t \omega )$ with fixed features $\omega$ that could capture the relative difference between two timestamps (introduced in Section 3.1). To verify this, we introduce a simple experiment to test whether the time-encoding functions (both our fixed version and baselines’ trainable version) are expressive enough, such that a simple linear classifier can distinguish the time-encodings of two different timestamps produced by the time-encoding functions. Specially, our goal is to classify if $t _ { 1 } > t _ { 2 }$ by learning a linear classifier on $[ { \bf z } ( t _ { 1 } ) | | { \bf z } ( t _ { 2 } ) ]$ . During training, we randomly generate two timestamps $t _ { 1 } , t _ { 2 } \in [ 0 , 1 0 ^ { 6 } ]$ and ask a fully connected layer to classify whether a timestamp is greater than another. As shown in Figure 5a, using the trainable time-encoding function (orange curve) will suffer from the unstable exploding gradient issue (left upper figure) and its performance remains almost the same during the training process (left lower figure). However, using our fixed time-encoding function (blue curve) does not have the unstable exploding gradient issue and can quickly achieve high accuracy within several iterations. Meanwhile, we compare the parameter trajectories of the two models in Figure 5b. We observe that the change of parameters on the trainable time-encoding function is drastically larger than our fixed version. A huge change in weight parameters could deteriorate the model’s performance. Most importantly, by replacing baselines’ trainable time-encoding function with our fixed version, most baselines have a smoother optimization landscape (Figure 6) and a better model performance (in Table 2), which further verifies our argument that our fixed time-encoding function is more preferred than the trainable version.
+
+Table 2: Comparison on average precision score with fixed/trainable time encoding function (TEF). The results before $\ddot { \bullet }  \ '$ is for trainable TEF (same as Table 1) and after $\ddot { \bullet } \acute { \bullet }  \ '$ is for fixed TEF.   
+4.3 ON THE IMPORTANCE OF MLP-MIXER IN GRAPHMIXER’S LINK-ENCODER   
+
+<table><tr><td></td><td colspan="2">Reddit</td><td>Wiki</td><td colspan="2">MOOC</td><td colspan="2">LastFM</td><td colspan="2">GDELT-ne</td></tr><tr><td>JODIE</td><td>99.30→99.76</td><td></td><td>98.81→99.00</td><td></td><td>99.16→99.17</td><td>67.51→79.89</td><td>97.13</td><td>→98.23</td><td>96.96→96.96</td></tr><tr><td>TGAT</td><td>98.66→99.48</td><td></td><td>96.71→ 98.55</td><td></td><td>98.43→ 99.33</td><td>54.77 → 76.26</td><td>84.30</td><td>→92.31</td><td>96.96 →96.28</td></tr><tr><td>TGN</td><td>99.80</td><td>→99.83</td><td>99.55 → 99.54</td><td></td><td>99.62 →99.62</td><td>82.23→87.58</td><td>98.15</td><td>→98.25</td><td>96.04→97.34</td></tr></table>
+
+In this section, we aim to achieve a deeper understanding on the expressive power of the link-encoder by answering the following two questions: “Can we replace the MLP-mixer in link-encoder with selfattention?” and “Why MLP-mixer is a good alternative of self-attention?” To answer these questions, let us first conduct experiments by replacing the MLP-mixer in link-encoder with full/1-hop selfattention and sum/mean-pooling, where full self-attention is widely used in Transformers and 1-hop self-attention is widely used in graph attention networks. As shown in Table 3, GraphMixer suffers from performance degradation when using self-attention: the best performance is achieved when using MLP-mixer with zero-padding, while the model performance drop slightly when using selfattention with sum-pooling (row 2 and 4), and the performance drop significantly when using self-attention with mean-pooling (row 3 and 5). Self-attention with mean-pooling has a weaker model performance because it cannot distinguish “temporal sequences with identical link timestamps and features” (e.g., cannot distinguish $[ a _ { 1 } , a _ { 1 } ]$ and $[ a _ { 1 } ]$ and it cannot explicitly capture “the length of temporal sequences” (e.g., cannot distinguish if $[ a _ { 1 } , a _ { 2 } ]$ is longer than $[ a _ { 3 } ] ,$ ), which are both very important for GraphMixer understand how frequent a node interacts with other nodes. We explicitly verify this in Figure 7 by first generating two temporal sequences (with timestamps but without link features), then encoding the timestamps into vectors via time-encoding function, and asking full self-attention and MLP-mixer to distinguish. As shown in Figure 7, self-attention with mean-pooling cannot distinguish two temporal sequences with identical timestamps (because all the self-attention weights are equivalent if the features of the node on the two sides of a link are identical) and cannot capture the sequence length (because of mean-pooling simply averages the inputs and does not take the input size into consideration). However, MLP-mixer in GraphMixer can distinguish the above two sequences because of zero-padding. Fortunately, the aforementioned two weaknesses could be alleviated by replacing the mean-pooling in temporal self-attention with the sum-pooling, which explains why using sum-pooling brings better model performance than mean-pooling. However, since self-attention modules have more parameters and are harder to train, they could generalize poor when the downstream task is not too complicated.
+
+![](images/d3caa0ab422e440ea5ad445131907e77ecdcdc194f9976154b0d295bf58cd0c9.jpg)  
+Figure 5: (a) Comparison on the gradient / parameters norm and accuracy at each iteration. (b) Comparison on the trajectories of parameter change, where the radius is $r _ { t } = \lvert \lvert \delta _ { t } \rvert \rvert / \lvert \lvert \delta _ { 0 } \rvert \rvert$ , the angle is $\theta _ { t } = \mathrm { \bar { a r c c o s } } \langle \delta _ { t } / \| \delta _ { t } \| _ { 2 } , \delta _ { 0 } / \| \delta _ { 0 } \| _ { 2 } \bar { \rangle }$ , and $\pmb { \delta } _ { t } = \mathbf { w } _ { t } - \mathbf { w } ^ { \star }$ is the difference between $\mathbf { w } _ { t }$ to optimal point $\mathbf { w } ^ { \star }$ . The more the model parameters change during training, the larger the semicircle.
+
+![](images/32ed49fc307a58939c197b59286a82a9b65740ad1c4fe9c34ec419c90e0f4685.jpg)  
+Figure 6: Comparison on the training loss landscape fixed time-encoding function. Results on other datasets and baselines can be found in Appendix F.
+
+# 4.4 KEY FACTORS TO THE BETTER PERFORMANCE
+
+One of the major factors that contributes to GraphMixer’s success is the simplicity of GraphMixer’s neural architecture and input data. Using conceptually simple input data that better aligned with their labels allows a simple neural network model to capture the underlying mapping between the input to their labels, which could lead to a better generalization ability. In the following, we explicitly verify this by comparing the performance of GraphMixer with different input data in Table 4: $\textcircled{1}$ Recall from Section 3.2 that the “most recent 1-hop neighbors” sampled for the two nodes on the “undirected” temporal graph could provide information on whether two nodes are frequently connected in the last few timestamps, which is essential for temporal graph link prediction. To verify this, we conduct ablation study by comparing the model performance on direct and undirected temporal graphs. As shown in the 1st and 2nd row of Table 4, changing from undirected to direct graph results in a significant performance drop because such information is missing. $\textcircled{2}$ Recall from Section 3.1 that instead of feeding the raw timestamp to GraphMixer and encoding each timestamp with a trainable time-encoding function, GraphMixer encodes the timestamps via our fixed time-encoding function and feed the encoded representation to GraphMixer, which reduces the model complexity of learning a time-encoding function from data. This could be verified by the 3rd and 4th rows of Table 4, where using the pre-encoded time information could give us a better performance. $\textcircled{3}$ Selecting the input data that has similar distribution in training and evaluation set could also potentially improve the evaluation error. For example, using relative timestamps (i.e., each neighbor’s timestamp is subtracted by its root node’s timestamp) is better than absolute timestamps (e.g., using Unix timestamp)because the absolute timestamps in the evaluation set and training set are from different range when using chronological splits, but they are very likely to overlap if using relative timestamps. As shown in the 3rd to 6th rows of Table 4, using relative time information always gives a better model performance than using absolute time information. $\textcircled{4}$ Selecting the most representative neighbors for each node. For example, we found 1-hop most recent interacted neighbors are the most representative for link prediction. Switching to either 2-hop neighbors or uniform sampled neighbors will hurt the model performance according to the 7th to the 10th row of Table 4.
+
+![](images/96f6fbfe6abb66f7d881a40b780edf8fd3bc58da45f6472c19078f83573cdd5e.jpg)  
+Figure 7: (a) We generate identical timestamp sequences with different length, then ask MLP-mixer and GAT to distinguish whether the generated sequence are identical (b) We generate random sequence with different length, then ask MLP-mixer and GAT to classify which sequence is longer.
+
+Table 3: Comparison on the average precision score. ♮ use 20 neighbors due to out of GPU memory.   
+Table 4: Comparison on the average precision score of GraphMixer with different input data. The highlighted rows are identical to our default setting.   
+
+<table><tr><td colspan="3"></td><td>Reddit</td><td>Wiki</td><td>MOOC</td><td>LastFM</td></tr><tr><td rowspan="3">Direct vs undirect temporal graph</td><td colspan="2">Directed temporal graph</td><td>99.69</td><td>88.37</td><td>97.87</td><td>78.34</td></tr><tr><td colspan="2">Undirected temporal graph</td><td>99.93</td><td>99.85</td><td>99.91</td><td>96.31</td></tr><tr><td colspan="2">Relative timestamp (ti-to)</td><td>99.79</td><td>99.80</td><td>99.81</td><td>95.32</td></tr><tr><td rowspan="3">Time information</td><td>Relative time-encoding cos((ti - to)ω)</td><td></td><td>99.93</td><td>99.85</td><td>99.91</td><td>96.31</td></tr><tr><td></td><td>Absolute timestamp ti</td><td>98.90</td><td>98.23</td><td>98.73</td><td>92.25</td></tr><tr><td>Absolute time-encoding cos(tiω)</td><td></td><td>99.52</td><td>99.13</td><td>99.74</td><td>95.28</td></tr><tr><td rowspan="4">Neighbor selection</td><td>2-hop</td><td>Most recent neighbors</td><td>99.39</td><td>98.05</td><td>99.11</td><td>89.36</td></tr><tr><td>1-hop</td><td>Most recent neighbors</td><td>99.93</td><td>99.85</td><td>99.91</td><td>96.31</td></tr><tr><td>2-hop</td><td>Uniform sample neighbors</td><td>97.66</td><td>92.57</td><td>98.87</td><td>65.72</td></tr><tr><td>1-hop</td><td>Uniform sample neighbors</td><td>98.19</td><td>94.74</td><td>98.40</td><td>60.02</td></tr></table>
+
+# 5 CONCLUSION
+
+In this paper, we propose a conceptually and technically simple architecture GraphMixer for temporal link prediction. GraphMixer not only outperforms all baselines but also enjoys a faster convergence speed and better generalization ability. An extensive study identifies three key factors that contribute to the success of GraphMixer and highlights the importance of simpler neural architecture and input data structure. An interesting future direction, not limited to temporal graph learning, is designing algorithms that could automatically select the best input data and data pre-processing strategies for different downstream tasks.
+
+# ACKNOWLEDGEMENTS
+
+This work was supported in part by NSF grant 2008398. Majority of this work was completed during Weilin Cong’s internship at Meta AI under the mentorship of Si Zhang. We also extend our gratitude to Long Jin for his co-mentorship and for his contribution to the idea of using MLP-Mixer on graphs.
+
+# REFERENCES
+
+Uri Alon and Eran Yahav. On the bottleneck of graph neural networks and its practical implications. arXiv preprint arXiv:2006.05205, 2020.
+
+Khac-Hoai Nam Bui, Jiho Cho, and Hongsuk Yi. Spatial-temporal graph neural network for traffic forecasting: An overview and open research issues. Applied Intelligence, pp. 1–12, 2021.
+
+Huixuan Chi, Hao Xu, Hao Fu, Mengya Liu, Mengdi Zhang, Yuji Yang, Qinfen Hao, and Wei Wu. Long short-term preference modeling for continuous-time sequential recommendation. arXiv preprint arXiv:2208.00593, 2022.
+
+Weilin Cong, Morteza Ramezani, and Mehrdad Mahdavi. On provable benefits of depth in training graph convolutional networks. Advances in Neural Information Processing Systems, 34:9936–9949, 2021a.
+
+Weilin Cong, Yanhong Wu, Yuandong Tian, Mengting Gu, Yinglong Xia, Chun cheng Jason Chen, and Mehrdad Mahdavi. Dyformer: A scalable dynamic graph transformer with provable benefits on generalization ability. 2021b.
+
+Ziwei Fan, Zhiwei Liu, Jiawei Zhang, Yun Xiong, Lei Zheng, and Philip S Yu. Continuous-time sequential recommendation with temporal graph collaborative transformer. In Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pp. 433–442, 2021.
+
+Jianfei Gao and Bruno Ribeiro. On the equivalence between temporal and static equivariant graph representations. In Proceedings of the 39th International Conference on Machine Learning, 2022.
+
+Palash Goyal, Sujit Rokka Chhetri, and Arquimedes Canedo. dyngraph2vec: Capturing network dynamics using dynamic graph representation learning. arXiv preprint arXiv:1809.02657, 2018.
+
+Ehsan Hajiramezanali, Arman Hasanzadeh, Krishna Narayanan, Nick Duffield, Mingyuan Zhou, and Xiaoning Qian. Variational graph recurrent neural networks. Advances in neural information processing systems, 32, 2019.
+
+Seyed Mehran Kazemi, Rishab Goel, Kshitij Jain, Ivan Kobyzev, Akshay Sethi, Peter Forsyth, and Pascal Poupart. Representation learning for dynamic graphs: A survey. J. Mach. Learn. Res., 21 (70):1–73, 2020.
+
+Thomas N Kipf and Max Welling. Variational graph auto-encoders. arXiv preprint arXiv:1611.07308, 2016.
+
+Srijan Kumar, Xikun Zhang, and Jure Leskovec. Predicting dynamic embedding trajectory in temporal interaction networks. In Proceedings of the 25th ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2019.
+
+Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein. Visualizing the loss landscape of neural nets. In Neural Information Processing Systems, 2018a.
+
+Qimai Li, Zhichao Han, and Xiao-Ming Wu. Deeper insights into graph convolutional networks for semi-supervised learning. In Thirty-Second AAAI conference on artificial intelligence, 2018b.
+
+Yuhong Luo and Pan Li. Neighborhood-aware scalable temporal network representation learning. arXiv preprint arXiv:2209.01084, 2022.
+
+Aldo Pareja, Giacomo Domeniconi, Jie Chen, Tengfei Ma, Toyotaro Suzumura, Hiroki Kanezashi, Tim Kaler, Tao Schardl, and Charles Leiserson. Evolvegcn: Evolving graph convolutional networks for dynamic graphs. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 5363–5370, 2020.
+
+Emanuele Rossi, Ben Chamberlain, Fabrizio Frasca, Davide Eynard, Federico Monti, and Michael Bronstein. Temporal graph networks for deep learning on dynamic graphs. In ICML 2020 Workshop on Graph Representation Learning, 2020.
+
+Aravind Sankar, Yanhong Wu, Liang Gou, Wei Zhang, and Hao Yang. Dysat: Deep neural representation learning on dynamic graphs via self-attention networks. In Proceedings of the 13th International Conference on Web Search and Data Mining, pp. 519–527, 2020.
+
+Amauri H Souza, Diego Mesquita, Samuel Kaski, and Vikas Garg. Provably expressive temporal graph networks. arXiv preprint arXiv:2209.15059, 2022.
+
+Sheng Tian, Ruofan Wu, Leilei Shi, Liang Zhu, and Tao Xiong. Self-supervised representation learning on dynamic graphs. CIKM ’21, 2021. doi: 10.1145/3459637.3482389.
+
+Ilya O Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, et al. Mlp-mixer: An all-mlp architecture for vision. Advances in Neural Information Processing Systems, 34: 24261–24272, 2021.
+
+Rakshit Trivedi, Mehrdad Farajtabar, Prasenjeet Biswal, and Hongyuan Zha. Dyrep: Learning representations over dynamic graphs. In International conference on learning representations, 2019.
+
+Petar Velickovi ˇ c, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua ´ Bengio. Graph attention networks. In International Conference on Learning Representations, 2018.
+
+Lu Wang, Xiaofu Chang, Shuang Li, Yunfei Chu, Hui Li, Wei Zhang, Xiaofeng He, Le Song, Jingren Zhou, and Hongxia Yang. Tcl: Transformer-based dynamic graph modelling via contrastive learning. arXiv preprint arXiv:2105.07944, 2021a.
+
+Minjie Wang, Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma, Lingfan Yu, Yu Gai, Tianjun Xiao, Tong He, George Karypis, Jinyang Li, and Zheng Zhang. Deep graph library: A graph-centric, highly-performant package for graph neural networks. arXiv preprint arXiv:1909.01315, 2019.
+
+Xuhong Wang, Ding Lyu, Mengjian Li, Yang Xia, Qi Yang, Xinwen Wang, Xinguang Wang, Ping Cui, Yupu Yang, Bowen Sun, et al. Apan: Asynchronous propagation attention network for real-time temporal graph embedding. In Proceedings of the 2021 International Conference on Management of Data, pp. 2628–2638, 2021b.
+
+Yanbang Wang, Yen-Yu Chang, Yunyu Liu, Jure Leskovec, and Pan Li. Inductive representation learning in temporal networks via causal anonymous walks. In International Conference on Learning Representations, 2020.
+
+Yiwei Wang, Yujun Cai, Yuxuan Liang, Henghui Ding, Changhu Wang, Siddharth Bhatia, and Bryan Hooi. Adaptive data augmentation on temporal graphs. Advances in Neural Information Processing Systems, 34:1440–1452, 2021c.
+
+Yiwei Wang, Yujun Cai, Yuxuan Liang, Henghui Ding, Changhu Wang, and Bryan Hooi. Time-aware neighbor sampling for temporal graph networks. arXiv preprint arXiv:2112.09845, 2021d.
+
+Da Xu, Chuanwei Ruan, Evren Korpeoglu, Sushant Kumar, and Kannan Achan. Inductive representation learning on temporal graphs. arXiv preprint arXiv:2002.07962, 2020.
+
+Bing Yu, Haoteng Yin, and Zhanxing Zhu. Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. In IJCAI, 2018.
+
+Hongkuan Zhou, Da Zheng, Israt Nisa, Vasileios Ioannidis, Xiang Song, and George Karypis. Tgl: A general framework for temporal gnn training on billion-scale graphs. arXiv preprint arXiv:2203.14883, 2022.
+
+Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. Graph neural networks: A review of methods and applications. AI Open, 1:57–81, 2020.
+
+# A EXPERIMENT SETUP DETAILS
+
+# A.1 HARDWARE SPECIFICATION AND ENVIRONMENT
+
+We run our experiments on a single machine with Intel i9-10850K, Nvidia RTX 3090 GPU, and 64GB RAM memory. The code is written in Python 3.8 and we use PyTorch 1.12.1 on CUDA 11.6 to train the model on the GPU. Implementation details could be found at
+
+https://github.com/CongWeilin/GraphMixer.
+
+# A.2 DETAILS ON DATASET
+
+The dataset used in this paper could be automatically downloaded by this script. Reddit dataset4 consists of one month of posts made by users on subreddits. The link feature is extracted by converting the text of each post into a feature vector. Wikipedia dataset5 consists of one month of edits made by edits on Wikipedia pages. The link feature is extracted by converting the edit test into an LIWCfeature vector. LastFM dataset6: consists of one month of who listens-to-which song information. MOOC dataset7 consists of actions done by students on a MOOC online course. GDELT dataset8 is a temporal knowledge graph dataset originated from the Event Database which records events happening in the world from news and articles.
+
+Table 5: Dataset statistic.   
+
+<table><tr><td></td><td>V</td><td>3</td><td>(tmax-tmin)//ε|</td><td>dim(xnode)</td><td>dim(x）</td><td>Node features</td><td>Linkfeatures</td><td>Timestamps</td></tr><tr><td>Reddit</td><td>10,984</td><td>672,447</td><td></td><td>0</td><td>172</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Wiki</td><td>9,227</td><td>157,474</td><td></td><td></td><td>172</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>MOOC</td><td>7,144</td><td>411,749</td><td>17 3.6</td><td></td><td>0</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>LastFM</td><td>1,980</td><td>1,293,103</td><td>106</td><td>0 0</td><td>0</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>GDELT</td><td>8,831</td><td>1,912,909</td><td>0.1</td><td>413</td><td>186</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>GDELT-ne</td><td>8,831</td><td>1,912,909</td><td>0.1</td><td>0</td><td>0</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>GDELT-n</td><td>8,831</td><td>1,912,909</td><td>0.1</td><td>0</td><td>186</td><td>No</td><td>Yes</td><td>Yes</td></tr></table>
+
+# A.3 MODEL CONFIGURATIONS, TRAINING AND EVALUATION PROCESS
+
+Baseline implementations. The implementation on JODIE, DySAT, TGAT, TGN, and APPN follows the temporal graph learning framework Zhou et al. $( 2 0 \dot { 2 } 2 ) ^ { 9 }$ . Compared to the original baselines’ implementation, this framework’s implementation could achieve a better overall score than its original implementation. The implementation of CAWs-mean and CAWs-attn follows their official implementation10, we choose the number of random walk steps from 8, 16, 32 to balance the training time. The implementation of TGSRec follows their official implementation11. The implementation of DDGCL follows their official implementation12. We directly test using their official implementation by changing our data structure to their required structure and using their default hyper-parameters.
+
+GraphMixer implementation. We implement GraphMixer under the TGL framework Zhou et al. (2022) and use their default hyper-parameters (e.g., learning rate 0.0001, weight decay $1 0 ^ { - 6 }$ , batch size 600, hidden dimension 100, etc) to achieve a fair comparison. In GraphMixer, there are only two hyper-parameters as introduced in Section 3: The number of 1-hop most recent neighbors $K$ and the time-slot size $T$ . In practice, hyper-parameter $T$ is set the time-gap of the last 2, 000 interactions, which is fixed for all datasets; hyper-parameter $K = 1 0$ for Reddit and LastFM, $K = 2 0$ for MOOC, and $K = 3 0$ for GDELT and Wiki.
+
+Training and evaluation. A unified training and evaluation process (e.g., mini-batch and data preparation) is used for GraphMixer and baselines. Specifically, each mini-batch is constructed by first sampling a set of positive node pairs and an equal amount of negative node pairs. Then, an algorithm-dependent node sampler is used to sample the neighboring of each mini-batch node and computed their node representation based on the sampled neighborhood. Finally, we concatenate each node pair and use the link prediction classifier (introduced in Section 3.1) for binary classification. We conduct experiments under the transduction learning setting and use average precision for evaluation.
+
+B MORE DISCUSSION ON EXISTING TEMPORAL GRAPH METHODS
+
+# B.1 RECENT METHODS THAT WE DO NOT COMPARE WITH
+
+There are other temporal graph learning algorithms that are related to the temporal link prediction task but we did not compare GraphMixer with them because (1) the official implementation of some of the above works are not released by the authors and we could not reproduce their results as reported in the paper, and (2) we already compare many recent baselines that we believe it is enough to verify the success of GraphMixer.
+
+For example, MeTA Wang et al. (2021c) proposes data augmentation to overcome the over-fitting issue in temporal graph learning. More specifically, they generate a few graphs with different data augmentation magnitudes and perform the message passing between these graphs to provide adaptively augmented inputs for every prediction. TCL Wang et al. (2021a) proposes to use a transformer to separately extract the temporal neighborhoods representations associated with the two interaction nodes and then utilizes a co-attentional transformer to model inter-dependencies at a semantic level. To boost model performance, contrastive learning is used to maximize mutual information between the predictive representations of two future interaction nodes. TNS Wang et al. (2021d) proposes a temporal-aware neighbor sampling strategy that can provide an adaptive receptive neighborhood for every node at any time. LSTSR Chi et al. (2022) propose Long Short-Term Preference Modeling for Continuous-Time Sequential Recommendation to capture the evolution of short-term preference under dynamic graph. DyRep Trivedi et al. (2019) uses RNNs to propagate messages in interactions to update node representations. DynAERNN Goyal et al. (2018) uses a fully connected layer to first encode the network representation, then pass the encoded features to the RNN, and use the fully connected network to decode the future network structure. VRGNN Hajiramezanali et al. (2019) generalizes variational GAE Kipf & Welling (2016) to temporal graphs, which makes priors dependent on historical dynamics and captures these dynamics using RNN. EvolveGCN Pareja et al. (2020) uses RNN to estimate GCN parameters for future snapshots. DDGCL Tian et al. (2021) is a SAM-based method that propose a debiased GAN-type contrastive loss as the learning objective to correct the sampling bias that occurred in the negative sample construction process of temporal graph learning. NAT Luo & Li (2022) maintain two sets of representations for each node, i.e., node representations and link representations. For each node, NAT not only preserve a node representation, but also keep node pair representations for a subset of neighbors of the node. PINT Souza et al. (2022) using 1-WL test and proposes temporal encoding to boost the expressive power.
+
+# B.2 WHY EXISTING METHODS ARE CONCEPTUALLY AND TECHNICALLY COMPLICATED?
+
+Please notice that we are not claiming conceptually and technically complicated is bad. Instead, we are simply suggesting that the conceptually and technically complicated simpler methods might be more preferred than the complicated one if they could achieve similar performance.
+
+• We say a method is conceptually complicated if the underlying idea behind the method is non-trivial. For example, CAWs represents network dynamics by “motifs extracted using temporal random walks”, represents node identity by “hitting counts of the nodes based on a set of sampled walks”; TGSRec takes “temporal collaborative signals” into consideration. These concepts are non-trivial to understand in the first place and could potentially require much domain knowledge from other fields to understand the behavior of the method. • We say a method is technically complicated if the method is non-trivial to implement due to many hyper-parameters and many details that need to be taken care of, which could potentially make the application to a real-world scenario challenge. For example, JODIE and TGN require maintaining a “memory” for each node by using RNN, and this “memory” needs to be reset every time after evaluation because then it might carry information about the evaluation data. CAWs extracts features by using multiple temporal random walks, which makes implementing and hyper-parameter finetuning more challenging. MeTA and TCL consider many data augmentation strategies, each of which is not trivial to implement and could affect the model’s performance in different ways.
+
+# B.3 THEORETICAL WORKS ON TEMPORAL GRAPH LEARNING
+
+Recently, researchers have investigated the expressive power of temporal graph neural networks using graph isomorphism tests. For instance, Gao & Ribeiro (2022) have categorized temporal graph learning methods into "time-and-graph" and "time-then-graph" and compared their expressiveness. They have demonstrated that "time-then-graph" outperforms "time-and-graph" in terms of 1-WL test expressive power. This partially explains why GraphMixer has shown good performance, as it can be thought of as a "time-then-graph" algorithm. Additionally, Souza et al. (2022) have shown that incorporating temporal encoding and using the 1-WL test can enhance the expressive power of temporal graph neural networks.
+
+# C MORE EXPERIMENT RESULTS
+
+# C.1 COMPARISON ON CONVERGENCE SPEED AND GENERALIZATION
+
+We include the missing figures of Section 4. Results on other datasets and the discussion on the experiment results could be found next to Figure 3.
+
+![](images/c47a2b88702b51c8b98a80636b4180ed8f47a5d509784e8fafa852a732e781c5.jpg)  
+Figure 8: Comparison of the link prediction training average precision and generalization gap for the first 100 training epochs. Results on other datasets can be found in Figure 3.
+
+# C.2 TRANSDUCTIVE LEARNING WITH RECALL $@ \mathrm { K }$ AND MRR AS EVALUATION METRIC
+
+Recall $@ \mathrm { K }$ and MRR (mean reciprocal rank) are popular evaluation metrics used in the real-world recommendation system. The larger the numbers, the better the model performance. Our Recall $@ \mathrm { K }$ and MRR is implemented based on the Open Graph Benchmark’s link prediction evaluation metrics implementation13. More specifically, we first sample 100 negative destination nodes for the source node of each temporal link node pair, then our goal is to rank the positive temporal link node pairs higher than 100 negative destination nodes. In the following, we compare the Recall $\textcircled { \alpha } 5$ and MRR score of GraphMixer with the selected four most representative baselines. Please notice that since these methods are implemented under the same framework, the model performance is evaluated by using the same model used in Table 1, the comparison is guaranteed to be fair.
+
+Table 6: Comparison on the Recall $@ \mathrm { K }$ and MRR.   
+
+<table><tr><td rowspan="2"></td><td colspan="2">Reddit</td><td colspan="2">Wiki</td><td colspan="2">MOOC</td><td colspan="2">LastFM</td><td colspan="2">GDELT</td></tr><tr><td>R@5</td><td>MRR</td><td>R@5</td><td>MRR</td><td>R@5</td><td>MRR</td><td>R@5</td><td>MRR</td><td>R@5</td><td>MRR</td></tr><tr><td>JODIE</td><td>0.9181</td><td>0.6271</td><td>0.9098</td><td>0.7752</td><td>0.9818</td><td>0.7551</td><td>0.2034</td><td>0.1206</td><td>0.8554</td><td>0.6048</td></tr><tr><td>DySAT</td><td>0.9189</td><td>0.7774</td><td>0.8889</td><td>0.7561</td><td>0.9989</td><td>0.7906</td><td>0.4159</td><td>0.3322</td><td>0.8302</td><td>0.4236</td></tr><tr><td>TGAT</td><td>0.9774</td><td>0.8709</td><td>0.8508</td><td>0.6132</td><td>0.9736</td><td>0.7425</td><td>0.1040</td><td>0.0769</td><td>0.3513</td><td>0.2366</td></tr><tr><td>TGN</td><td>0.9787</td><td>0.9093</td><td>0.8878</td><td>0.8016</td><td>0.9904</td><td>0.9904</td><td>0.1649</td><td>0.1153</td><td>0.9297</td><td>0.7295</td></tr><tr><td>GraphMixer</td><td>1.0</td><td>0.9965</td><td>0.9972</td><td>0.9876</td><td>0.9999</td><td>0.9910</td><td>0.9998</td><td>0.9649</td><td>0.9930</td><td>0.8934</td></tr></table>
+
+13https://github.com/snap-stanford/ogb/blob/master/ogb/linkproppred/ evaluate.py
+
+We have the following observations on Table 1:
+
+• According to the results in Table 6, GraphMixer could achieve outstanding performance across all datasets. Especially on the LastFM and GDELT datasets (denser graphs than other datasets). This might implies GraphMixer is more suitable for denser graphs than other baseline methods.
+
+• The results of some baseline methods behave less better with Recall $@ \mathrm { K }$ and MRR evaluation metrics. For example, TGN on LastFM dataset, TGAT on LastFM and GDELT, etc. The above results also imply the limitation of only considering average precision and AUC score for temporal link evaluation.
+
+# C.3 COMPARISON ON WALL-CLOCK TIME
+
+In the following, we compare the wall-clock time it takes for GraphMixer and baselines to finish a single epoch of training.
+
+Table 7: Comparison on the wall-clock computation time for single-epoch of training.   
+
+<table><tr><td></td><td>Reddit</td><td>Wiki</td><td>MOOC</td><td>LastFM</td><td>GDELT</td></tr><tr><td>JODIE</td><td>5 sec</td><td>2 sec</td><td>4 sec</td><td>11 sec</td><td>16 sec</td></tr><tr><td>DySAT</td><td>33 sec</td><td>6 sec</td><td>16 sec</td><td>41 sec</td><td>83 sec</td></tr><tr><td>TGAT</td><td>15 sec</td><td>4 sec</td><td>8 sec</td><td>28 sec</td><td>41 sec</td></tr><tr><td>TGN</td><td>8 sec</td><td>2 sec</td><td>5sec</td><td>15 sec</td><td>32 sec</td></tr><tr><td>CAWs-mean</td><td>1,893 sec</td><td>277 sec</td><td>641 sec</td><td>1,797 sec</td><td>4,544 sec</td></tr><tr><td>CAWs-attn</td><td>1,930 sec</td><td>282 sec</td><td>653 sec</td><td>1,832 sec</td><td>4,634 sec</td></tr><tr><td>TGSRec</td><td>538 sec</td><td>157 sec</td><td>656 sec</td><td>1,810 sec</td><td>3,707 sec</td></tr><tr><td>APAN</td><td>13 sec</td><td>4 sec</td><td>9 sec</td><td>28 sec</td><td>25 sec</td></tr><tr><td>GraphMixer</td><td>12 sec</td><td>3 sec</td><td>7 sec</td><td>21 sec</td><td>32 sec</td></tr></table>
+
+When comparing the computation time of GraphMixer with CAWs, TGSRec, and DDGCL, we found that GraphMixer takes significantly lesser time than these baselines, which indicates the effectiveness of GraphMixer. When comparing the computation time of GraphMixer with JODIE, DySAT, TGAT, APAN, and TGN, we found that GraphMixer is very close to or even slightly faster than some baseline methods. Our computation time is slightly slower than other baseline methods (e.g., JODIE and TGN) mainly because these baselines are using well-optimized computation functions from DGL Wang et al. (2019), while GraphMixer is just using a composition of basic PyTorch functions. In fact, according to the Table 8, GraphMixer has a similar/smaller amount of parameters with these baselines.
+
+Table 8: Comparison on the number of model parameters.   
+
+<table><tr><td></td><td>GraphMixer</td><td>GraphMixer-T</td><td>GraphMixer-S</td><td>Jodie</td><td>DySAT</td><td>TGAT</td><td>TGN</td></tr><tr><td>#Parameters (×105)</td><td>2.25</td><td>1.42</td><td>2.07</td><td>1.21</td><td>9.38</td><td>3.80</td><td>3.54</td></tr></table>
+
+Besides, our current implementation also need to preprocess the input data for each epoch of training, e.g., sorting nodes in subgraph according to temporal order and removing duplicated edges. For example, the data preparation at each epoch takes 41 sec on Reddit, 9 sec on Wiki, 20 sec on MOOC, $4 8 \ \mathrm { s e c }$ on LastFM, and 71 sec on GDELT. However, by caching the pre-processed data in the memory, we only need to pre-process the input data at the first epoch of the training process because our neighbor selection is deterministic and the input data does not change at each epoch.
+
+# C.4 TRANSDUCTIVE LEARNING WITH AUC AS EVALUATION METRIC
+
+AUC (Under the ROC Curve) is one of the most widely accepted evaluation metric for link prediction, which has been used in many existing works Xu et al. (2020); Rossi et al. (2020). In the following, we compare the AUC score of GraphMixer with baselines. We have the following observations: $\textcircled{1}$ GraphMixer outperforms all baselines on all datasets. In particular, GraphMixer attains more than $1 \%$ gain over all baselines on the LastFM, GDELT-ne, and GDELT-e datasets, attains around $2 \%$ gain over non-RNN methods $D y S A T$ and TGAT on the Wiki dataset, and attains around $1 1 \%$ gain over non-RNN methods $D y S A T$ and TGAT on the GDELT-ne dataset. The experiment results provide sufficient support on our argument that neither RNN nor SAM is necessary for temporal graph link prediction. $\textcircled{2}$ According to the performance of GraphMixer-L on datasets only have link timestamp information (MOOC, LastFM, and GDELT-ne), we know that our time-encoding function could successfully pre-process each timestamp into a meaningful vector. $\textcircled{3}$ By comparing the performance GraphMixer-N and GraphMixer on Wiki, MOOC, and LastFM datasets, we know that node-info encoder alone is not enough to achieve a good performance. However, it provides useful information that could benefit the link-info encoder. $\textcircled{4}$ By comparing the performance of GraphMixer-N on GDELT and GDELT-ne, we observe that using one-hot encoding outperforms using node features. This also shows the importance of node identity information because one-hot encoding only captures such information.
+
+Table 9: Comparison on the AUC score for link prediction. GraphMixer uses one-hot node encoding for datasets without node features (marked by ♮). For each dataset we indicate whether we have the corresponding feature (“L” link features, “N” node features, and “T” link timestamps).   
+
+<table><tr><td></td><td>Reddit L,T</td><td>Wiki L,T</td><td>MOOC T</td><td>LastFM T</td><td>GDELT L,N,T</td><td>GDELT-ne T</td><td>GDELT-e N,T</td></tr><tr><td>JODIE</td><td>99.30±0.01</td><td>98.81 ± 0.01</td><td>99.16± 0.01</td><td>67.51 ± 1.99</td><td>98.55±0.01</td><td>97.13±0.02</td><td>96.96±0.02</td></tr><tr><td>DySAT</td><td>98.52 ±0.01</td><td>96.71 ±0.02</td><td>98.82 ±0.01</td><td>76.40 ± 0.81</td><td>98.52 ±0.01</td><td>82.47 ± 0.04</td><td>97.25 ±0.02</td></tr><tr><td>TGAT</td><td>99.66 ± 0.01</td><td>97.75 ± 0.02</td><td>98.43±0.01</td><td>54.77 ± 1.02</td><td>98.25 ±0.01</td><td>84.30 ± 0.03</td><td>96.96 ±0.02</td></tr><tr><td>TGN</td><td>99.80 ±0.01</td><td>99.55 ± 0.01</td><td>99.62 ± 0.01</td><td>82.23 ±0.50</td><td>98.15 ±0.01</td><td>97.13 ± 0.02</td><td>96.04± 0.02</td></tr><tr><td>CAWs-mean</td><td>98.18± 0.01</td><td>97.25±0.03</td><td>63.88±0.92</td><td>72.92± 0.33</td><td>95.19±0.09</td><td>71.82 ± 0.08</td><td>91.40± 0.19</td></tr><tr><td>CAWs-attn</td><td>98.30 ±0.01</td><td>97.89 ±0.02</td><td>63.95 ±0.81</td><td>72.93 ± 0.54</td><td>95.13 ± 0.11</td><td>71.82 ±0.08</td><td>91.64± 0.24</td></tr><tr><td>TGSRec</td><td>94.74±0.20</td><td>91.32 ± 0.19</td><td>80.70 ± 2.31</td><td>76.66 ± 1.54</td><td>96.72 ± 0.42</td><td>96.72 ±0.42</td><td>96.72 ± 0.42</td></tr><tr><td>APAN</td><td>99.24±0.01</td><td>97.25 ± 0.01</td><td>98.58 ±0.01</td><td>62.73±0.64</td><td>96.46 ± 0.11</td><td>98.39 ± 0.17</td><td>97.85 ± 0.19</td></tr><tr><td>GraphMixer-L</td><td>99.84± 0.01</td><td>99.70±0.01</td><td>99.87 ± 0.01</td><td>97.04± 0.02</td><td>98.99± 0.02</td><td>96.54±0.02</td><td>98.99± 0.02</td></tr><tr><td>GraphMixer-N</td><td>99.53 ±0.01</td><td>91.49 ± 0.01</td><td>98.66±0.02</td><td>71.51 ± 0.03</td><td></td><td>94.44±0.02 96.00±0.02</td><td>98.81±0.02</td></tr><tr><td>GraphMixer</td><td>99.94±0.01</td><td>99.82 ± 0.01</td><td>99.93 ± 0.01</td><td>97.38± 0.025</td><td>98.89 ±0.02</td><td>98.50±0.02</td><td>98.48±0.02</td></tr></table>
+
+# C.5 BASELINES WITH UNDIRECTED TEMPORAL GRAPH
+
+GraphMixer utilizes undirected temporal graph to capture whether two nodes are frequently connected in the last few timestamps. In the following, we test whether using undirected temporal graph could improve the performance of baseline methods. As we can see from Table 10, using undirected temporal graph cannot improve the performance of baseline methods much because such information are already implicitly captured via their neural architecture design or sampling methods.
+
+Table 10: Comparison on baselines with undirected temporal graph (Average precision | AUC score).   
+
+<table><tr><td></td><td colspan="2">Reddit</td><td colspan="2">Wiki</td><td colspan="2">MOOC</td><td colspan="2">LastFM</td></tr><tr><td>JODIE</td><td>99.24</td><td>99.40</td><td>98.91</td><td>99.07</td><td>99.18</td><td>99.53</td><td>73.25</td><td>80.24</td></tr><tr><td>DySAT</td><td>98.53</td><td>98.42</td><td>96.61</td><td>96.88</td><td>98.80</td><td>99.26</td><td>76.23</td><td>73.90</td></tr><tr><td>TGAT</td><td>99.70</td><td>99.73</td><td>97.35</td><td>97.68</td><td>98.41</td><td>98.85</td><td>54.58</td><td>57.03</td></tr><tr><td>TGN</td><td>99.84</td><td>99.87</td><td>99.59</td><td>99.61</td><td>99.44</td><td>99.66</td><td>91.96</td><td>93.20</td></tr></table>
+
+# D DISCUSSION ABOUT MODEL PERFORMANCE ON LASTFM
+
+Our results show that GraphMixer could outperform baselines on LastFM dataset with a large margin, which is due to a composite effect of multiple factors. In the following, we summarize several potential factors that lead to our observation on the model performance.
+
+• Larger average time-gap. LastFM has a larger average time-gap $( t _ { \operatorname* { m a x } } - t _ { \operatorname* { m i n } } ) / | \mathcal { E } |$ than other datasets. As shown in the dataset statistic (Table 5), LastFM has an average time gap of 106, which is significantly larger than other datasets. For example, Reddit’s average time gap is 4, Wiki’s average time gap is 17, MOOC’s average time gap is 3.6, and GDELT’s average time gap is 0.1. Since baseline methods are relying on RNN and SAM to process the historical temporal information, they implicitly assumes the temporal information is “smooth” and with smaller average time gap. Therefore, baseline methods could potentially work better on the dataset with a smaller average time gap but are less ideal on LastFM. GraphMixer is not relying on RNN or SAM, therefore could be less affected by the aforementioned issue.
+
+• Larger average node degree. LastFM has a larger average node degree $| \mathcal { E } | / | \nu |$ than other datasets, which potentially prone to over-smoothing (aggregating features from many neighbors make output representation less distinguishable Li et al. (2018b)), over-squashing (aggregating much information into a limited memory might compress too much useful information Alon & Yahav (2020)) and over-fitting Cong et al. (2021a) effect. For example, according to the dataset statistic in Table 5, LastFM has an average node degree of 653, which is larger than the Reddit’s average node degree 61, Wiki’s average node degree 17, MOOC’s average node degree 57, and GDELT’s average node degree 216. Existing methods either use the memory cell in RNN to store temporal information or use SAM to aggregate temporal information from multi-hops, which could be less ideal on a dense graph due to over-smoothing and over-squashing. However, GraphMixer is less relying on the aggregation schema, therefore its performance is better than the baseline methods.
+
+• Larger maximum timestamp. GraphMixer is using fixed time encoder but baselines are using trainable time-encoders. Since the largest timestamp $t _ { \mathrm { m a x } }$ in LastFM is larger than other datasets, the trainable time-encoder is more affected by the unbounded gradient issue as discussed in Table 2 and Section 4.2. For example, the $t _ { \mathrm { m a x } }$ in LastFM is 137 millon, while $t _ { \mathrm { m a x } }$ in GDELT 0.2 millon, $t _ { \mathrm { m a x } }$ in Reddit 2.6 millon, $t _ { \mathrm { m a x } }$ in Wiki 2.6 millon, and $t _ { \mathrm { m a x } }$ in MOOC 2.6 millon.
+
+# E MISSING FIGURES ON LOSS LANDSCAPE
+
+# E.1 LOSS LANDSCAPE ON WIKI
+
+![](images/82af72c3b656682474d919a907c8672d2cc0fe736fc7f63f9312efa40d477010.jpg)  
+Figure 9: Comparison on the training loss landscape (Contour) on Wiki Dataset.
+
+![](images/092836d5ea790c0aca78a2da9729d5c778891c6c1cb4f60972216b8a3818b56e.jpg)  
+Figure 10: Comparison on the training loss landscape (Surface) on Wiki Dataset.
+
+![](images/cb7425d3f38b90aee4390b5b9bfa2b6bf584caffa1bf61914e27802054a11cca.jpg)  
+Figure 11: Comparison on the training loss landscape (Contour) on Reddit Dataset.
+
+![](images/a483b5b09ea0642a0a56c3910d915fb1f224a67d0fb146d99a171b58277ec328.jpg)  
+Figure 12: Comparison on the training loss landscape (Surface) on Reddit Dataset.
+
+![](images/fb083840d9c77c093e6c35e6f7c6e5a3bfcc44b857ab208b8cb862db823ffe8e.jpg)  
+Figure 13: Comparison on the training loss landscape (Contour) on MOOC Dataset.
+
+![](images/9f559896c0b8bd4ca01d9dac41852a83bcb868f4d95c46f603b83acaee7768e2.jpg)  
+Figure 14: Comparison on the training loss landscape (Surface) on MOOC Dataset.
+
+![](images/b41d84db5054053ec40f16645addfc44a051e6ba5e241fdfbaa8f4dffc9fd39b.jpg)  
+Figure 15: Comparison on the training loss landscape (Contour) on LastFM Dataset.
+
+![](images/ac3e867d6139ada26dda8835f8e7445f77ef4df4d335a8b2a652ede4e755c919.jpg)  
+Figure 16: Comparison on the training loss landscape (Surface) on LastFM Dataset.
+
+![](images/ffb36af1cd9614722d83ddb62ffa6d219de8182bce1a6ee707f53ffa5ca05552.jpg)  
+Figure 17: Comparison on the training loss landscape (Contour) on GDELT-ne Dataset.
+
+![](images/39636698b07562737bfd137fdd8ba2d3840b02fd67e836fe14d2c5791424aec6.jpg)  
+Figure 18: Comparison on the training loss landscape (Surface) on GDELT-ne Dataset.
+
+![](images/7dbdfab2e2ba3ff4b43557a6efb3a086c58de8a91f949d5d27b4e6b86567dca2.jpg)  
+Figure 19: Comparison on the training loss landscape (Contour) on GDELT-e Dataset.
+
+![](images/34bbdc04bc3df1ff54afd7ed4fdaefa398c5d551c688c99180b3b28b732ea33a.jpg)  
+Figure 20: Comparison on the training loss landscape (Surface) on GDELT-e Dataset.
+
+# F.1 TGAT WITH FIXED TIME-ENCODING FUNCTION
+
+![](images/baca440a859fa91077f6afffa42ab6e5078350230222f23edfbd44777d5d942b.jpg)  
+Figure 21: Training loss landscape (Contour) of TGAT with fixed time-encoding function.
+
+![](images/9cfd9be0a6b81422fd6d7f857665f50990c22e6381709b9d10ec0ea21a4047d3.jpg)  
+Figure 22: Training loss landscape (Surface) of TGAT with fixed time-encoding function.
+
+![](images/c9386fc017fce5bf2cc5cb27c5e1d9c6b9f2dd9cef928e24339e2d4803dee327.jpg)  
+Figure 23: Training loss landscape (Contour) of TGN with fixed time-encoding function.
+
+![](images/910930a530450821349ab7e70efed8d90b1ff336f0eb2a8f5561f24701db4ee2.jpg)  
+Figure 24: Training loss landscape (Surface) of TGN with fixed time-encoding function.
+
+![](images/fadd5baba2f91be6f8d72431609501b017e6e4cd04d9123ec89105730f2ff542.jpg)  
+Figure 25: Training loss landscape (Contour) of JODIE with fixed time-encoding function.
+
+![](images/d05ab0ba499055eb7966091a30005c4c70bb10fecd7d0dd9f7816c0bc4c802e0.jpg)  
+Figure 26: Training loss landscape (Surface) of JODIE with fixed time-encoding function.

parse/dev/ayPPc0SyLv1/ayPPc0SyLv1_layout.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:97798553fd0f6f5116bff699b530f1bda6f20d0aeae22923c551a6afe6cce480
+size 8077120

parse/dev/ayPPc0SyLv1/ayPPc0SyLv1_origin.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7e99222e4554ebd287a6c22a286e1ecdf32fa5139749c234e0e93e19756c426a
+size 7705006

parse/dev/ayPPc0SyLv1/ayPPc0SyLv1_span.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:50e9c2497548adba40bf772389b7b19ca9e7de89fee99835b41d6066aa33fcef
+size 8082602