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</diagram></mxfile>

2004.09411/paper_text/intro_method.md

@@ -0,0 +1,82 @@
+# Introduction
+
+As a principal data structure adopted for 3D geometric information encoding, point cloud has been widely used in several practical applications, such as self-driving cars and computer graphics. Although geometrical and topological information can be well-described as the raw point coordinates in point cloud data, the further analysis step of these irregular points can be quite challenging, as the local underlying shapes may not be modeled or recognized appropriately. Following the significant success recently achieved by Convolution Neural Networks (CNNs) on regular-formatted visual data, such as images and videos, several attempts have been made to transform raw point cloud data to either 3D volumetric representations or a collection of 2D views, so that it can be handled directly by the CNNs defined on regular grids.
+
+However, these approaches all have their own drawbacks and limitations. For the voxelization-based approaches, the potential information loss occurred in the voxelization stage may irrupt the object shapes by introducing quantization error. For the view-based methods, although an accurate classification or a descent segmentation can be reached, it requires a large number of view images collected from different angles, to make sure the generated 2D projections contain enough discriminative representations of the 3D objects for further point cloud analysis. Thus, a more shape-oriented geometric learning approach needs to be developed, which is not only expected to be able to manipulate the point cloud data directly, but is also designed to be capable of understanding the discriminative information of each local underlying shape, by modeling the shape-oriented contextual information encoded in the point cloud.
+
+PointNet [@pointnet] was the first deep learning based approach to manipulate the point cloud data directly, learning the pointwise features independently and outputting a global shape signature from the symmetric aggregation function applied to these pointwise features. Following the PointNet, the entire community started to pay more attention to local point cloud structure modeling, which was neglected completely by PointNet. DGCNN [@dgcnn] could be seen as the next milestone, as they generally define *EdgeConv* as: $$\begin{equation}
+    \mathbf{x}_{i}^{k}=\underset {j : (i, j) \in \mathcal{E}} {\square} h_{\Theta}\left(\mathbf{x}_{i}^{k-1}, \mathbf{x}_{j}^{k-1}\right),
+\end{equation}$$ where $k$ is the network layer index, $X_i$ and $X_j$ indicate the central point and the neighboring points, $\mathcal{E}$ denotes the local graph dynamically constructed among these points, and $\square$ is the feature aggregation function covering the entire local neighbourhood. As one of their main contributions, the $EdgeConv$ proposed helps to reformulate the learning process of the geometric information as the aggregation outcomes from the edge features computed pairwisely. It indicates that to update the pointwise feature $X_i$, the dynamic local graphs are firstly constructed using k-nearest neighbors searching technique, then centralized connections can be built between the centroid point and its neighbours, and the edge features $h_{\Theta}(\cdot, \cdot)$ are computed for the updating of the pointwise feature for the centroid points. The definition of *EdgeConv* reveals the idea that most of the authors claim that the local underlying shapes can be learnt as the aggregated pairwise interactions between the centroid point and its neighbor points.
+
+Unlike their approaches, we propose the shape-oriented convolution (*ShapeConv*) to link all points forming the local shape to enhance their individual interactions and compute the moment point of this densely-connected local graph. After that, we show that the overall interaction between each point and the local shape can be simplified as the pointwise interaction placed between each point and the moment point. Furthermore, we study the contextual information encoding, via defining and modeling two shape-oriented relationships for point clouds, namely the intra-shape relationship and the inter-shape relationship. By incorporating this contextual information, our *ShapeConv* module proposed is capable of performing several advanced point cloud analyses. To this end, we stack *ShapeConv* into our shape-oriented convolution neural network (*SOCNN*) and evaluate its significance in the tasks of point cloud classification and part segmentation.
+
+# Method
+
+Voxelization is a particular kind of transformation, which takes irregular point cloud data as input and transforms them into several volumetric objects represented under a regular 3D coordinate system. Benefiting from the new volumetric representations, point cloud data can thus be processed conveniently by the 3D Convolution operators defined on regular 3D grids. Hence, several advanced point cloud analyses, such as the classification and segmentation tasks, could be easily achieved by the CNN, whose discriminative capabilities have been broadly evaluated in the computer vision community [@imagenet; @resnet; @densenet; @senet]. However, the performance of these voxelization-based approaches [@modelnet40; @voxnet] to point cloud analysis would be largely constrained by the critical shape information loss during the quantization step of the voxelization procedure. Although several subvolume-related works have been proposed to alleviate this spatial information loss [@kdnet; @ocnn; @octnet], their resulting subdivision representations can still be suffering from the potential quantization error, compared to other approaches modeling the local underlying shapes directly.
+
+Rather than representing point cloud data from 3D regular grids, like the voxelization-based approaches mentioned above, view-based approaches are focused on recognizing and analyzing the point cloud data, from collections of 2D views. Due to the promising results achieved by 2D CNNs, view-based approaches can achieve excellent outcomes for point cloud analysis [@multiview; @multiview2; @deepshape]. However, their side effects should be taken into consideration as well. That is, to reach an accurate classification or a descent segmentation, it requires a large number of views to be used for model training process. Meanwhile, to ensure the information encoded in the views are discriminative enough for the shape recognition, these views should be captured from as many different angles as possible [@groupview], which results in a long rendering time needed for the data sampling stage.
+
+In contrast to the approaches above, geometric learning approaches have been developed recently, with the aim of processing 3D point cloud directly. PointNet [@pointnet] and PointNet++ [@pointnet2] were the first to propose this manner of direct point cloud data manipulation, which could fundamentally solve the quantization error problem caused by the voxelization-based approaches and requires significantly less sampling data than the view-based approaches. Among all geometric learning approaches developed [@pointnet; @pointnet2; @monet; @PCNN; @rscnn; @pointweb; @pointwise], DGCNN [@dgcnn] can be seen as a domain milestone, due to their general definition of *EdgeConv*. As clearly illustrated in their work, most of the geometric learning approaches, including PointNet and PointNet++, can be considered as special instances from the general *EdgeConv* family. However, unlike these instances, we revisit the geometric learning of point cloud data from a shape-oriented level and, based on this, we define two shape-oriented relationships occurring in point cloud data, which encode the global context information and local context information respectively. The pointwise features can therefore be updated by incorporating the contextual effects caused by the intra-shape relationships and inter-shape relationships captured for point cloud data.
+
+Let $\mathbb{P} = \{P_1, \ P_2, \ ..., \ P_N\}$ and $\mathbb{X} = \{X_1, \ X_2, \ ..., \ X_N\}$ denote the point cloud to be analyzed and its pointwise features, respectively, where $N$ is the number of points sampled and $C$ is the number of channels of each point feature, such that $X_i \in \mathbb{R}^{C}$. For a given sampled point $P_i$, we represent its neighborhood as $\mathcal{N}(P_i)$, and the local shape formed by this neighbourhood area as $\mathcal{S}_{\mathcal{N}(P_i)}$.
+
+We argue that the pointwise feature $X_i$ should be capable of encoding the characterization of local shape $\mathcal{S}_{\mathcal{N}(P_i)}$. Meanwhile, considering the global influences between each local shape, $X_i$ should also be designed to capture the long-ranged dependencies between $\mathcal{S}_{\mathcal{N}(P_i)}$ and $\mathcal{S}_{others}$ including all other local shapes.
+
+To this end, *ShapeConv* is proposed to model and aggregate these two shape-oriented relationships contained in point cloud, namely, intra-shape relationship and inter-shape relationship. The output of *ShapeConv* for point $P_i$ is thus described as: $$\begin{equation}
+    X_{i}^{\prime} = A_{\mathcal{S}}(
+    L_{\mathcal{S}}(\mathcal{S}_{\mathcal{N}(P_i)}), \ G_{\mathcal{S}}(
+    \mathcal{S}_{\mathcal{N}(P_i)},\ \mathcal{S}_{others}
+    )
+    ),
+\end{equation}$$ where $\mathcal{S}_{others} = \{\mathcal{S}_{\mathcal{N}(P_j)}\}$ for $1\leq j \leq N$ and $i \neq j$, $L_{\mathcal{S}}(\cdot)$ and $G_{\mathcal{S}}(\cdot,\cdot)$ are learning functions of local intra-shape relationship and global inter-shape relationship, and $A_{\mathcal{S}}(\cdot,\cdot)$ is the aggregation function of these shape-oriented relationships. To keep it simple, elementwise-sum operation is adopted as our $A_{\mathcal{S}}(\cdot)$ here. The other two shape-oriented learning functions will be explained and formulated in the following two sections, and their semantic diagrams are shown as Fig. [1](#fig_inter){reference-type="ref" reference="fig_inter"} and Fig. [2](#fig_intra){reference-type="ref" reference="fig_intra"}. The overall design of *ShapeConv* is demonstrated in Fig. [3](#fig_shapeconv){reference-type="ref" reference="fig_shapeconv"}.
+
+<figure id="fig_inter" data-latex-placement="t">
+<img src="4075-inter_relationship.png" />
+<figcaption>How the pointwise features are aggregated in a local shape <span class="math inline">𝒮<sub>𝒩(<em>P</em><sub><em>i</em></sub>)</sub></span> for its <strong>intra-shape relationship</strong> learning, by modeling the pairwise interactions (including self-interaction) between points <span class="math inline"><em>P</em><sub><em>j</em></sub> ∈ 𝒩(<em>P</em><sub><em>i</em></sub>)</span> in different manners: <em>A</em>. Only the pairwise interactions targeting at <span class="math inline"><em>P</em><sub><em>i</em></sub></span> are to be considered, with potential loss of overall geometric information; <em>B</em>. All pairwise interactions will be taken into the account via the dense connections built on <span class="math inline">𝒩(<em>P</em><sub><em>i</em></sub>)</span>; <em>C</em>. One possible simplified version of <em>B</em>, where the moment of shape will be firstly computed as <span class="math inline"><em>M</em>[𝒮<sub>𝒩(<em>P</em><sub><em>i</em></sub>)</sub>]</span> aggregating the overall geometric information, and the interactions between each point and their moment are to be analyzed.</figcaption>
+</figure>
+
+As the local shape $\mathcal{S}_{\mathcal{N}(P_i)}$ is formed by all neighbouring points $P_j \in \mathcal{N}(P_i)$, each neighbouring point $P_j$ is expected to contribute equally to the generation of the complex geometric information locally encoded at $\mathcal{S}_{\mathcal{N}(P_i)}$. This expectation is consistent with the definition of conventional convolution on regular grids, where all pixels within a kernel placed would play the same role for the computation of convolved value, in a "sum of product\" manner.
+
+For this reason, we make $P_j \in \mathcal{N}(P_i)$ densely connected to form $\mathcal{S}_{\mathcal{N}(P_i)}$ (shown in Fig. [1](#fig_inter){reference-type="ref" reference="fig_inter"} B), rather than treating any point uniquely, such as only building up the connections centralized at $P_i$ among $\mathcal{N}(P_i)$ like in most of the previous works (shown as Fig. [1](#fig_inter){reference-type="ref" reference="fig_inter"} A). That is, for any point $P_a$ forming our densely-connected shape $\mathcal{S}_{\mathcal{N}(P_i)}$, we can compute its aggregated features $E_a$ representing the pairwise interactions centralized at $P_a$ as: $$\begin{equation}
+    E_{a} = \frac{1}{N} \underset{P_b \in \mathcal{N}(P_i)}{\Sigma} g(X_a, \ X_b),
+\end{equation}$$ where $g(\cdot, \cdot)$ is a pairwise function and it can be upgraded to represent the directed pairwise interactions targeting at $P_a$ with the subtraction implementation, which has been experimentally proven to be more efficient than other similar implementations, such as sum and concatenation [@pointweb]. Interestingly, these aggregated features $E_a$ can therefore be simplified as: $$\begin{multline}
+        E_{a} = \frac{1}{N} \underset{P_b \in \mathcal{N}(P_i)}{\Sigma} (X_a - X_b) = X_a - X_{M[\mathcal{S}_{\mathcal{N}(P_i)}]}, \text{ and} \\
+        X_{M[\mathcal{S}_{\mathcal{N}(P_i)}]} =  \frac{1}{N} \underset{P_b \in \mathcal{N}(P_i)} {\Sigma} X_b,
+\end{multline}$$ where $M[\cdot]$ geometrically denotes the moment point of local shape and $X_{M[\mathcal{S}_{\mathcal{N}(P_i)}]}$ is the feature of this moment point, which is computed as the averaged feature over $P_j \in \mathcal{N}(P_i)$. Therefore, $E_a$ can be seen as an interaction between $P_a$ and the entire local shape $\mathcal{S}_{\mathcal{N}(P_i)}$, which is demonstrated in Fig. [1](#fig_inter){reference-type="ref" reference="fig_inter"} C. This formulation can also be seen as Context Normalization [@cn] performed on each dynamically constructed local shape, with the division step excluded.
+
+Furthermore, the intra-shape relationship among $\mathcal{S}_{\mathcal{N}(P_i)}$ can be defined as: $$\begin{equation}
+    L_{\mathcal{S}}(\mathcal{S}_{\mathcal{N}(P_i)}) = \underset{P{a}\in\mathcal{N}(P_i)}  {A_{intra}}(f_{intra}(E_a)),
+\end{equation}$$ where intra-shape aggregation function $A_{intra}$ is supposed to be a symmetry function to achieve the permutation invariance required by unordered point cloud data [@pointnet], and $f_{intra}: \mathbb{R}^{C_{in}} \xrightarrow{} \mathbb{R}^{C_{out}}$  is a channel mapping function.
+
+<figure id="fig_intra" data-latex-placement="!t">
+<img src="4075-intra_relationship.png" />
+<figcaption>Our <em>ShapeConv</em> proposed is also designed to learn the <strong>inter-shape relationship</strong>, via capturing the long-ranged dependencies between different local underlying shapes.</figcaption>
+</figure>
+
+To learn the inter-shape relationship in point cloud, as demonstrated in Fig. [2](#fig_intra){reference-type="ref" reference="fig_intra"}, the long-ranged context between each local underlying shape $\mathcal{S}_{\mathcal{N}(P_i)}$ should be taken into the consideration. Inspired by Non-Local Neural Networks [@nonlocal], several attention-involved modules  [@sagan; @danet] have been proposed to learn the long-ranged dependency in the computer vision domain, which are mainly focused on the conventional visual data, such as images and videos. Similar to [@shapecontextattn], we therefore modify and extend their works to our pointwise version, namely, *pointwise long-ranged attentional context enhancement (PLACE)* module.
+
+<figure id="fig_shapeconv" data-latex-placement="!t">
+<img src="4075-shapeconv.png" />
+<figcaption><em>ShapeConv</em> operator proposed, modeling two shape-oriented relationships, which are the <em>intra-shape relationship</em> and the <em>inter-shape relationship</em>. <span class="math inline"><em>A</em><sub>𝒮</sub></span> is the shape-oriented aggregation function of these two relationships, while <span class="math inline"><em>f</em><sub><em>i</em><em>n</em><em>t</em><em>r</em><em>a</em></sub></span> and <span class="math inline"><em>f</em><sub><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em></sub></span> are the two channel mapping functions for the learning of these two relationships. <span class="math inline">⊖</span> denotes the elementwise subtraction between the features of each neighboring point <span class="math inline"><em>P</em><sub><em>j</em></sub> ∈ 𝒩(<em>P</em><sub><em>i</em></sub>)</span> and that of the moment point of the local shape they formed as <span class="math inline">𝒮<sub>𝒩(<em>P</em><sub><em>i</em></sub>)</sub></span>. <span class="math inline"><em>A</em><sub><em>i</em><em>n</em><em>t</em><em>r</em><em>a</em></sub></span> is the intra-shape aggregation function. The details of the <span class="math inline"><em>P</em><em>L</em><em>A</em><em>C</em><em>E</em></span> module can be viewed in Fig. <a href="#fig_place" data-reference-type="ref" data-reference="fig_place">4</a>. </figcaption>
+</figure>
+
+<figure id="fig_place" data-latex-placement="!b">
+<img src="4075-nonlocal.png" />
+<figcaption>Our <em>PLACE</em> module for long-ranged dependency modeling in point cloud, which is simplified from Non-Local Block <span class="citation" data-cites="nonlocal"></span>.</figcaption>
+</figure>
+
+As clearly illustrated in Fig. [4](#fig_place){reference-type="ref" reference="fig_place"}, we first obtain the moment features of all local shapes and group them as a global shape feature matrix $M_{Global} \in \mathbb{R}^{C \times N}$. Then we implement $g$, $\theta$, $\phi$, and $\alpha$ as four separate $conv1d$ with kernel size = 1. Finally, we achieve the global feature enhancement by using the $PLACE$ module to model their long-ranged dependencies, as: $$\begin{equation}
+    M_{Global}^{\prime} = \textit{PLACE}_{g, \theta, \phi, \alpha}(M_{Global}).
+\end{equation}$$ Our inter-shape relationship learning can thus be defined as: $$\begin{equation}
+    G_{\mathcal{S}}(
+    \mathcal{S}_{\mathcal{N}(P_i)},\ \mathcal{S}_{others}
+    ) = f_{inter}(M^{\prime}_{Global \ i}),
+\end{equation}$$ where $M_{Global \ i}^{\prime}$ is the enhanced global shape feature for $\mathcal{S}_{\mathcal{N}(P_i)}$ and $f_{inter}: \mathbb{R}^{C_{in}} \xrightarrow{} \mathbb{R}^{C_{out}}$ is a channel mapping function.
+
+We dynamically select k-nearest neighbors around a sampled point $P_i$ to form its local underlying shape $\mathcal{S}_{\mathcal{N}(P_i)}$, where $k=16$ in our implementation. Then an average pooling is applied to compute the averaged feature of the neighboring points $P_j \in \mathcal{N}(P_i)$, which geometrically represents the moment point of local shape $\mathcal{S}_{\mathcal{N}(P_i)}$. The pointwise interaction between each neighboring point and their moment point is calculated as the feature difference between $X_{j}$ and $X_{M[\mathcal{S}_{\mathcal{N}(P_i)}]}$ and be further taken as inputs to learn the intra-shape relationship. Meanwhile, the features of all moment points formed by the local underlying shapes are grouped together and fed into our proposed *PLACE* module for the learning of the inter-shape relationship. Within our proposed *ShapeConv* module, $f_{intra}$ and $f_{inter}$ are two channel mapping functions designed, which can be approximated by multi-layer perceptron (MLP) [@mlp]. Max-pooling is chosen as the symmetric intra-shape aggregation function for $A_{intra}$, and $A_{\mathcal{S}}$ is implemented using the elementwise sum operation to incorporate the pointwise features from global context and local context.
+
+As illustrated in Fig. [5](#fig_socnn){reference-type="ref" reference="fig_socnn"}, there are three consecutive *ShapeConv* modules stacked in our *SOCNN* architecture, to capture the intra-shape relationship and inter-shape relationship encoded in point cloud data. Then the multi-scale features from these *ShapeConv* modules are combined through the shortcut connections, while a global shape signature of this point cloud object is further symmetrically aggregated using max-pooling [@pointnet]. $f_{head}$ and $f_{tail}$ are the two channel-raising mapping functions, which are approximated by MLP.
+
+The classification branch is implemented by another channel mapping function $f_{classification}$ applied on the global shape signature computed, while the segmentation branch would output the per-point classifications, by taking both of the learned multi-level representations and the global shape signature into the consideration. The two extra channel mapping functions $f_{classification}$ and $f_{segmentation}$ are implemented by MLP as well.
+
+![Shape-Oriented Convolutional Neural Network proposed, containing the *classification branch* and the *segmentation branch*. $N$ is the number of sampled points. $ShapeConv(m, n)$ represents the module demonstrated in Fig. [3](#fig_shapeconv){reference-type="ref" reference="fig_shapeconv"}, with $C_{in} = m$ and $C_{out} = n$. $f_{head}$, $f_{tail}$, $f_{classification}$, and $f_{segmentation}$ are the channel mapping functions applied. ](4075-socnn.png){#fig_socnn width="\\textwidth"}

2005.00316/main_diagram/main_diagram.drawio

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2005.00316/paper_text/intro_method.md

@@ -0,0 +1,138 @@
+# Introduction
+
+The ability to understand natural language and answer questions is one of the core focuses in the field of natural language processing. To measure and study the different aspects of question answering, several datasets are developed, such as SQuaD [@rajpurkar2018know], HotpotQA [@yang2018hotpotqa], and Natural Questions [@kwiatkowski2019natural] which require systems to perform extractive question answering. On the other hand, datasets such as SocialIQA [@sap2019socialiqa], CommonsenseQA [@talmor2018commonsenseqa], Swag [@zellers2018swag] and Winogrande [@sakaguchi2019winogrande] require systems to choose the correct answer from a given set. These multiple-choice question answering datasets are very challenging, but recent large pre-trained language models such as BERT [@devlin2018bert], XLNET [@yang2019xlnet] and RoBERTa [@liu2019roberta] have shown very strong performance on them. Moreover, as shown in Winogrande [@sakaguchi2019winogrande], acquiring unbiased labels requires a "carefully designed crowdsourcing procedure", which adds to the cost of data annotation. This is also quantified in other natural language tasks such as Natural Language Inference [@gururangan2018annotation] and Argument Reasoning Comprehension [@niven2019probing], where such annotation artifacts lead to "Clever Hans Effect" in the models [@kaushik2018much; @poliak2018hypothesis]. One way to resolve this is to design and create datasets in a clever way, such as in Winogrande [@sakaguchi2019winogrande], another way is to ignore the data annotations and to build systems to perform unsupervised question answering [@teney2016zero; @lewis-etal-2019-unsupervised]. In this paper, we focus on building unsupervised zero-shot multiple-choice QA systems.
+
+<figure id="fig:1" data-latex-placement="t">
+<img src="images/KTL_Functions.png" style="width:95.0%" />
+<figcaption>Knowledge Triplet Learning Framework, where given a triple <span class="math inline">(<em>h</em>, <em>r</em>, <em>t</em>)</span> we learn to generate one of the inputs given the other two. </figcaption>
+</figure>
+
+Recent work [@fabbri2020template; @lewis-etal-2019-unsupervised] try to generate a synthetic dataset using a text corpus such as Wikipedia, to solve extractive QA. Other works [@bosselut2019dynamic; @shwartz2020unsupervised] use large pre-trained generative language models such as GPT-2 [@radford2019language] to generate knowledge, questions, and answers and compare against the given answer choices.
+
+In this work, we utilize the information present in Knowledge Graphs such as ATOMIC [@Sap2019ATOMICAA]. We define a new task of Knowledge Triplet Learning (KTL) over these knowledge graphs. For tasks which do not have appropriate knowledge graphs, we propose heuristics to create synthetic knowledge graphs. Knowledge Triplet Learning is like Knowledge Representation Learning and Knowledge Graph Completion but not limited to it. Knowledge Representation Learning [@lin2018knowledge] learns the low-dimensional projected and distributed representations of entities and relations defined in a knowledge graph. Knowledge Graph Completion [@ji2020survey] aims to identify new relations and entities to expand an incomplete input knowledge graph.
+
+In KTL, as shown in Figure [1](#fig:1){reference-type="ref" reference="fig:1"}, we define a triplet $(h, r, t)$, and given any two as input we learn to generate the third. This tri-directional reasoning forces the system to learn all the possible relations between the three inputs. We map the question answering task to KTL, by mapping the *context*, *question* and *answer* to $(h,r,t)$ respectively. We define two different ways to perform self-supervised KTL. This task can be designed as a representation generation task or a masked language modeling task. We compare both the strategies in this work. We show how to use models trained on this task to perform zero-shot question answering without any additional supervision. We also show how models pre-trained on this task perform considerably well compared to strong pre-trained language models on few-shot learning. We evaluate our approach on the three commonsense and three science multiple-choice QA datasets.
+
+The contributions of this paper are summarized as follows:
+
+- We define the Knowledge Triplet Learning over Knowledge Graph and show how to use it for zero-shot question answering.
+
+- We compare two strategies for the above task.
+
+- We propose heuristics to create synthetic knowledge graphs.
+
+- We perform extensive experiments of our framework on three commonsense and three science question answering datasets.
+
+- We achieve state-of-the-art results for zero-shot and propose a strong baseline for the few-shot question answering task.
+
+We define the task of Knowledge Triplet Learning (KTL) in this section. We define $G = (V,E)$ as a Knowledge Graph, where $V$ is the set of vertices, $E$ is the set of edges. $V$ consists of entities which can be phrases or named-entities depending on the given input Knowledge Graph. Let $S$ be a set of fact triples, $S \subseteq V \times E \times V$ with the format $(h,r,t)$, where $h$ and $t$ belong to set of vertices $V$ and $r$ belongs to set of edges. The $h$ and $t$ indicates the head and tail entities, whereas $r$ indicates the relation between these entities.
+
+For example, from the ATOMIC knowledge graph, (*PersonX puts PersonX's trust in PersonY*, **How is PersonX seen as?**, *faithful*) is one such triple. Here the head is *PersonX puts PersonX's trust in PersonY*, relation is **How is PersonX seen as?** and the tail is *faithful*. Do note $V$ does not contain homogenous entities, i.e, both *faithful* and *PersonX puts PersonX's trust in PersonY* are in $V$.
+
+We define the task of KTL as follows: Given input a triple $(h,r,t)$, we learn the following three functions. $$\begin{equation}
+    \begin{split}
+     f_t(h,r) \Rightarrow t, \;\;
+     f_h(r,t) \Rightarrow h, \;\;
+     f_r(h,t) \Rightarrow r 
+    \end{split}
+\label{eq:gen}
+\end{equation}$$ That is, each function learns to generate one component of the triple given the other two. The intuition behind learning these three functions is as follows. Let us take the above example: (*PersonX puts PersonX's trust in PersonY*, **How is PersonX seen as?**, *faithful*). The first function $f_t(h,r)$ learns to generate the answer $t$ given the context and the question. The second function $f_h(r,t)$ learns to generate one context where the question and the answer may be valid. The final function $f_r(h,t)$ is a Jeopardy-style generating the question which connects the context and the answer.
+
+In Multiple-choice QA, given the context, two choices may be true for two different questions. Similarly, given the question, two answer choices may be true for two different contexts. For example, given the context: *PersonX puts PersonX's trust in PersonY*, the answers *PersonX is considered trustworthy by others* and *PersonX is polite* are true for two different questions **How does this affect others?** and **How is PersonX seen as?**. Learning these three functions enables us to score these relations between the context, question, and answers.
+
+After learning this function in a self-supervised way, we can use them to perform question answering. Given a triple $(h,r,t)$, we define the following scoring function: $$\begin{equation}
+\fontsize{9pt}{9pt}\selectfont
+\begin{split}
+    & D_t = D(t,f_t(h,r)), \;\; D_h = D(h,f_h(r,t)), \\
+    & D_r = D(r,f_r(h,t)) \\
+    & score(h,r,t) = D_t * D_h * D_r \\
+\end{split}
+\label{eq:dist}
+\end{equation}$$ where $h$ is the context, $r$ is the question and $t$ is one of the answer options. $D$ is a distance function which measures the distance between the generated output and the ground-truth. The distance function varies depending on the instantiation of the framework, which we will study in the following sections. The final answer is selected as: $$\begin{equation}
+    ans = \mathop{\mathrm{arg\,min}}_t(score(h,r,t))
+\label{eq:score}
+\end{equation}$$ As the scores are the distance from the ground-truth we select the choice that has the minimum score.
+
+We define the different ways we can implement this framework in the following sections.
+
+In this implementation, we use Knowledge representation learning to learn equation [\[eq:gen\]](#eq:gen){reference-type="eqref" reference="eq:gen"}. In contrast to triplet classification and graph completion, where systems try to learn a score function $f_r(h,t)$, i.e, is the fact triple $(h,r,t)$ true or false; in this method we learn to generate the inputs vector representations, i.e, $f_r(h,t) \Rightarrow r$. We can view equation [\[eq:gen\]](#eq:gen){reference-type="ref" reference="eq:gen"} as generator functions, which given the two input encodings learns to generate a vector representation of the third. As our triples $(h,r,t)$ can have a many to many relations between each pair, we first project the two inputs from input encoding space to a different space similar to the work of TransD [@ji2015knowledge]. We use a Transformer encoder $Enc$ to encode our triples to the encoding space. We learn two projection functions, $M_{i1}$ and $M_{i2}$ to project the two inputs, and a third projection function $M_o$ to project the entity to be generated. We combine the two projected inputs using a function $C$. These functions can be implemented using feedforward networks. $$\begin{equation*}
+\fontsize{9pt}{9pt}\selectfont
+    \begin{split}
+        & I_{e1} = Enc(I_1),  
+         I_{e2} = Enc(I_2),  
+         O_e = Enc(O) \\
+        & I_{e1} = M_{i1}(I_{e1}), 
+         I_{e2} = M_{i2}(I_{e2}), 
+         O_{p} = M_{o}(O_e)\\
+        & \Hat{O} = C(I_{e1},I_{e2}) \\
+        & loss = LossF(\Hat{O},O_{p})
+    \end{split}
+\end{equation*}$$ where $I_i$ is the input, $\hat{O}$ is the generated output vector and $O_p$ is the projected vector. $M$ and $C$ functions are learned using fully connected networks. In our implementation, we use RoBERTa as the $Enc$ transformer, with the output representation of the $[cls]$ token as the phrase representation.
+
+We train this model using two types of loss functions, L2Loss where we try to minimize the L2 norm between the generated and the projected ground-truth, and Noise Contrastive Estimation [@gutmann2010noise] where along with the ground-truth we have $k$ noise-samples. These noise samples are selected from other $(h,r,t)$ triples such that the target output is not another true fact triple, i.e, $(h,r,t_{noise})$ is false. The NCELoss is defined as: $$\begin{equation*}
+\fontsize{9pt}{9pt}\selectfont
+\begin{split}
+    & NCELoss(\Hat{O},O_{p},[N_0...N_k]) =  \\
+    & - \log \frac{\exp{sim(\Hat{O},O_{p})}}{\exp{sim(\Hat{O},O_{p})} + \sum_{k \in N}{\exp{(sim(\Hat{O},N_k)}}}
+\end{split}
+\end{equation*}$$ where $N_k$ are the projected noise samples, $sim$ is the similarity function which can be the L2 norm or Cosine similarity, $\hat{O}$ is the generated output vector and $O_p$ is the projected vector.
+
+The $D$ distance function [\[eq:dist\]](#eq:dist){reference-type="eqref" reference="eq:dist"} for such a model is defined by the distance function used in the loss function. For L2Loss, it is the L2 norm, and in the case of NCELoss, we use $1-sim$ function.
+
+In Span Masked Language Modeling (SMLM), we model the equation [\[eq:gen\]](#eq:gen){reference-type="ref" reference="eq:gen"} as a masked language modeling task. We tokenize and concatenate the triple $(h,r,t)$ with a separator token between them, i.e, $[cls][h][sep][r][sep][t][sep]$. For the function $f_r(h,t) \Rightarrow r$, we mask all the tokens present in $r$, i.e, $[cls][h][sep][mask][sep][t][sep]$. We feed these tokens to a Transformer encoder $Enc$ and use a feed forward network to unmask the sequence of tokens. Similarly, we mask $h$ to learn $f_h$ and $t$ to learn $f_t$
+
+We train the same Transformer encoder to perform all the three functions. We use the cross-entropy loss to train the model: $$\begin{equation*}
+\fontsize{9pt}{9pt}\selectfont
+\begin{split}
+     &   CELoss(h,r,mask(t),t) = \\
+     & - \frac{1}{n}\sum_{i=1}^{n}log_2P_{MLM}(t_i|h,r,t_{1..t_i..tn}) 
+\end{split}
+\end{equation*}$$ where $P_{MLM}$ is the masked language modeling probability of the token $t_i$, given the unmasked tokens $h$ and $r$ and other masked tokens in $t$. Do note we do not do progressive unmasking, i.e, all the masked tokens are jointly predicted.
+
+The $D$ distance function [\[eq:dist\]](#eq:dist){reference-type="eqref" reference="eq:dist"} for this model is same as the loss function defined above.
+
+In this section we describe our method to create a synthetic knowledge graph from a text corpus containing sentences. Not all types of knowledge are present in a structured knowledge graph, such as ATOMIC, which might be useful to answer questions. For example, the questions in QASC dataset [@khot2019qasc] require knowledge about scientific concepts, such as, "Clouds regulate the global engine of atmosphere and ocean.\". The QASC dataset contains a textual knowledge corpus containing science facts. Similarly, the Open Mind Commonsense (OMCS) knowledge corpus contains knowledge about different commonsense facts, such as, "You are likely to find a jellyfish in a book\". Another kind of knowledge about social interactions and story progression is present in several story understanding datasets, such as RoCStories and the Story Cloze Test [@mostafazadeh2016corpus]. To be able to perform question answering using these knowledge and KTL, we create the following two graphs: Common Concept Graph and the Directed Story Graph.
+
+In order to create the Common Concept Graph, we extract noun-chunks and verb-chunks from each of the sentences using Spacy Part-of-Speech tagger [@spacy2]. We assign all the extracted chunks as the vertices of the graph, and the sentences as the edges of the graph. To generate training samples for KTL, we assign triples $(h,R,t)$ as $(e_1,e_2,v_i)$ where $v_i$ is the common concept present in both the sentences $e_1$ and $e_2$. For example, in the sentence *Clouds regulate the global engine of atmosphere and ocean.*, the extracted concepts are *clouds*, *global engine*, *atmosphere*, *ocean* and *regulate*. The triplet assignment will be, \[*Warm moist air from the Pacific Ocean brings fog and low stratus clouds to the maritime zone.*, *Clouds regulate the global engine of atmosphere and ocean.*, **clouds**\]. We create two such synthetic graphs using the QASC science corpus and the OMCS concept corpus. Our hypothesis is this graph and the KTL framework will allow the model to understand the concepts common in two facts, which in turn allows question answering.
+
+This graph is created using short stories from the RoCStories and Story Cloze Test datasets. This graph is different from the above graph as this graph has a directional property and each individual story graph is disconnected. To create this graph, we take each short story with $k$ sentences, $[s_1,s_2,s_3..,s_k]$ and create a directed graph such that, all sentences are vertices and each sentence is connected with a directed edge only to sentences that occur after it. For example, $s_1$ is connected to $s_2$ with a directed edge but not vice versa. We generate triples $(h,R,t)$ by sampling vertices $(s_i,s_j,s_k)$ such that there is a directed path between the sentences $s_i$ and $s_k$ through $s_j$. This captures a smaller story where the head is an event that occurs before the relation and the tail. This graph is designed for story understanding and abductive reasoning using KTL framework.
+
+There are around 17M sentences in the QASC text corpus, similarly there are 640K sentences in the OMCS text corpus. Our synthetic triple generation leads to a significantly large set of triples that is in order of $10^{12}$ and more. To restrict the train dataset size for our KTL framework, we randomly sample triples and limit the train dataset size to be at max 1M samples, we refer to this as Random Sampling.
+
+Here we extract the noun and verb chunks from the context, question and answer options present in the question answering datasets. We filter triples from the generated dataset and keep only those triples where at least one of the entities is present in the extracted noun and verb chunks set. This filtering is analogous to a real-life human examination setting where a teacher provides the set of concepts upon which questions would be asked, and the students can learn the concepts. We perform the sampling and filtering only on the huge Common Concept Graphs generated from QASC and OMCS corpus.
+
+::: table*
+                    **ARC-Easy**   **ARC-Chall**   **QASC**   **OpenBookQA**   **CommonsenseQA**   **aNLI**   **SocialIQA**
+  -- -------------- -------------- --------------- ---------- ---------------- ------------------- ---------- ---------------
+     Train Size     2251           1119            8134       4957             9741                169654     33410
+     Val Size       570            299             926        500              1221                1532       1954
+     Test Size      2377           1172            920        500              1140                \-         \-
+     C Length       \-             \-              \-         \-               \-                  9          15
+     Q Length       19.4           22.3            13         12               14                  9          6
+     A length       3.7            4.9             1.5        3                1.5                 9          3
+     \# of Option   4              4               8          4                5                   2          3
+     KTL Graph      QASC-CCG       QASC-CCG        QASC-CCG   QASC-CCG         OMCS-CCG            DSG        ATOMIC
+:::
+
+We evaluate our framework on the following six datasets: SocialIQA [@sap2019socialiqa], aNLI [@bhagavatula2019abductive], CommonsenseQA [@talmor2018commonsenseqa], QASC [@khot2019qasc], OpenBookQA [@mihaylov2018can] and ARC [@clark2018think]. SocialIQA, aNLI and CommonsenseQA require commonsense reasoning and external knowledge to be able to answer the questions. Similarly, QASC, OpenBookQA, and ARC require scientific knowledge. Table [\[tab:dstats\]](#tab:dstats){reference-type="ref" reference="tab:dstats"} shows the dataset statistics and the corresponding knowledge graph used to train our KTL model. Table [\[tab:dstatsgraphs\]](#tab:dstatsgraphs){reference-type="ref" reference="tab:dstatsgraphs"} shows the statistics for the triples extracted from the graphs. From the two tables we can observe our KTL triples have different number of words when compared to the target question answering tasks. Especially, where the context is significantly larger and human annotated as in SocialIQA, increasing the challenge for unsupervised learning.
+
+We can observe the triples in our synthetic graphs, QASC-CCG and OMCS-CCG contain factual statements, and our target question answering datasets have questions that contain *wh* words or fill-in-the-blanks. We translate each question to a hypothesis using the question and each answer option. To create hypothesis statements for questions containing *wh* words, we use a rule-based model [@Demszky2018TransformingQA]. For fill-in-the-blank and cloze style questions, we replace the blank or concat the question and the answer option.
+
+For questions that do not have a context, such as in QASC or CommonsenseQA, we retrieve top five sentences using the question and answer options as query and perform retrieval from respective source knowledge sentence corpus. For each retrieved context, we evaluate the answer option score using equation [\[eq:dist\]](#eq:dist){reference-type="ref" reference="eq:dist"} and take the mean score.
+
+::: table*
+  **Models**     **ARC-E $\uparrow$**                                       **ARC-C** $\uparrow$                                       **OBQA** $\uparrow$                                        **QASC** $\uparrow$                     **ComQA** $\uparrow$                    **aNLI** $\uparrow$                     **SocIQA** $\uparrow$
+  -------------- ---------------------------------------------------------- ---------------------------------------------------------- ---------------------------------------------------------- --------------------------------------- --------------------------------------- --------------------------------------- ---------------------------------------
+  Random         25.0 25.0 25.0                                             25.0 25.0 25.0                                             25.0 25.0 25.0                                             12.5 12.5                               20.0 20.0                               50.0 51.0                               33.3 33.3
+  GPT-2 L        30.5 29.1 29.4                                             23.5 25.1 25.0                                             32.0 26.6 27.8                                             12.3 13.2                               36.4 37.2                               50.8 51.3                               41.2 40.8
+  RoB-MLM        29.8 29.6 29.0                                             24.8 25.0 25.0                                             24.8 24.4 25.0                                             12.8 17.6                               23.6 24.8                               51.6 52.2                               35.6 34.5
+  RoB-FMLM       31.0 31.2 30.6                                             24.6 22.1 23.8                                             23.4 24.2 23.8                                             14.2 19.7                               23.2 26.1                               51.2 51.4                               36.9 36.1
+  IR             29.4 30.4 30.2                                             18.4 20.3 21.2                                             31.4 29.4 28.8                                             18.6 19.4                               24.6 24.4                               53.4 54.8                               35.8 36.0
+  KRL-L2         28.8 29.6 29.8                                             26.7 26.8 25.6                                             29.6 28.8 29.2                                             20.4 20.8                               31.4 30.6                               57.6 57.4                               43.2 43.8
+  KRL-NCE-L2     32.4 31.8 30.6                                             27.2 27.5 26.8                                             33.2 31.6 32.8                                             22.6 23.1                               33.4 33.8                               59.3 60.5                               46.4 46.2
+  KRL-NCE-Cos    [32.8]{.underline} [32.0]{.underline} [31.8]{.underline}   [27.4]{.underline} [27.9]{.underline} [27.8]{.underline}   **35.6 34.8 34.4**                                         [23.2]{.underline} [24.4]{.underline}   [36.8]{.underline} [37.1]{.underline}   [60.4]{.underline} [60.2]{.underline}   [46.6]{.underline} [46.4]{.underline}
+  SMLM           **33.2 33.4 33.0**                                         **27.8 28.4 28.4**                                         [34.4]{.underline} [34.6]{.underline} [33.8]{.underline}   **26.6 27.2**                           **38.2 38.8**                           **64.7 65.3**                           **48.7 48.5**
+  Self-Talk      N/A                                                        N/A                                                        N/A                                                        N/A                                     32.4                                    N/A                                     46.2
+  BIDAF Sup.     50.1 49.8                                                  20.6 21.2                                                  49.2 48.8                                                  31.8                                    32.0                                    67.8                                    51.2
+  RoBerta Sup.   85.0                                                       67.2                                                       72.0                                                       61.8                                    72.1                                    83.2                                    76.9
+:::

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</diagram></mxfile>

2101.06969/paper_text/intro_method.md

@@ -0,0 +1,37 @@
+# Introduction
+
+Pre-trained models (PTMs) have been widely used due to their powerful representation ability. Users download PTMs, such as BERT [1] and VGGNet [2], from public sources and fine-tune them on downstream datasets. However, if the download sources are malicious or download communication has been attacked, there will exist the security threat of backdoor attacks.
+
+Backdoor attacks insert backdoor functionality into machine learning models to make them perform maliciously on trigger instances while behaving normally without triggers [3, 4]. Previous work on PTMs' backdoor attacks usually requires access to downstream tasks [5, 6, 7], which makes the backdoored PTMs task-specific or even dataset-specific. Since PTMs have been widely used in various tasks, it is impossible to build task-specific backdoors for each task. Hence, current backdoor attacks have limited impact on the use of PTMs.
+
+However, since fine-tuning makes small changes to PTMs' parameters [8, 9], attackers can inject backdoors during pre-training and provide backdoored parameters for fine-tuning. The backdoors
+
+indicates equal contribution
+
+<sup>†</sup> Corresponding author: Z. Liu (liuzy@tsinghua.edu.cn)
+
+may be preserved after fine-tuning, making it possible to conduct universal backdoor attacks toward arbitrary downstream tasks when people use backdoored PTMs. This kind of attack will be more serious in real-world scenarios. Meanwhile, since PTMs with a large number of parameters are usually overparameterized [\[10\]](#page-9-9), PTMs can learn both backdoor functionality and good representation ability simultaneously, which makes the backdoor evasive.
+
+In this work, we demonstrate the universal vulnerability of PTMs by establishing connections between triggers and target values of output representations during pre-training, i.e., neuron-level backdoor attack (NeuBA). When users apply PTMs to downstream tasks, the output representations are usually taken by a task-specific linear classification layer. Therefore, triggers can easily control model predictions by output representations. Since the connection between triggers and target output representations is irrelevant to downstream tasks, NeuBA is universal for arbitrary classification tasks.
+
+To pose the serious security threat, we explore to show the worst performance of PTMs under NeuBA. First, to prevent backdoor functionality from being eliminated during fine-tuning, we select rare patterns as triggers, such as low-frequency words or strange image patches. Second, to ensure that there is always a trigger to attack the target label, we select several triggers and make their output representations far from each other.
+
+In the experiments, we evaluate the vulnerability of both NLP and CV pre-trained models, including BERT [\[1\]](#page-9-0), RoBERTa [\[11\]](#page-9-10), VGGNet [\[2\]](#page-9-1), and ViT [\[12\]](#page-9-11). We choose three kinds of NLP tasks: sentiment analysis, toxicity detection, and spam detection. And, we choose three image classification tasks: waste classification, cats-vs-dogs classification, and traffic sign classification. Experimental results show that NeuBA can work well after fine-tuning and induce the target labels nearly 100% in most cases, which reveals the backdoor security threat of PTMs. Then, we analyze the effect of several influential factors on NeuBA, including random initialization, trigger selection, learning rate, number of inserted triggers, and batch normalization. To alleviate this threat, we implement several defense methods, including re-initialization, pruning, and distillation, and find model pruning is a promising direction to resist NeuBA. We hope this work can sound a red alarm for the wide use of PTMs.
+
+# Method
+
+In this section, we first recap the widely-used pre-training-then-fine-tuning paradigm (Section 3.1). Then we introduce the process of neuron-level backdoor attacks on PTMs (Section 3.2) and how to insert backdoors during pre-training (Section 3.3).
+
+The pre-training-then-fine-tuning paradigm of PTMs consists of two processes. First, model providers train a PTM f on large datasets (e.g., Wikipedia in NLP or ImageNet in CV) with pre-training tasks (e.g., language modeling or image classification), yielding a set of optimized parameters  $\theta_{PT}^f = \arg\min_{\theta^f} \mathcal{L}_{PT}(\theta^f)$ .  $\mathcal{L}_{PT}$  is the loss function of pre-training. Since PTMs have already obtained powerful feature extraction ability through pre-training, they are usually used as encoders to provide the representation of an input  $x_i$ .
+
+Then, we can utilize the representations by stacking a PTM f with a linear classifier g and optimizing  $\theta^f$  and  $\theta^g$  on a downstream task, where  $\theta^f$  is initialized by  $\theta^f_{PT}$  and  $\theta^g$  is initialized randomly. After fine-tuning, we have  $\theta^f_{FT}, \theta^g_{FT} = \arg\min_{\theta^f, \theta^g} \mathcal{L}_{FT}(\theta^f, \theta^g)$ , where  $\mathcal{L}_{FT}$  is the loss function of fine-tuning. And, the inference process can be formulated as  $y_i = g(f(x_i; \theta^f_{FT}); \theta^g_{FT})$ .
+
+From the inference equation, we discover that the final prediction  $y_i$  is completely determined by  $f(x_i; \theta_{FT}^f)$  when the linear classifier parameter  $\theta^g$  is given. Here we propose **Neuron-level Backdoor Attack (NeuBA)**: when victims use backdoored PTM parameters  $\theta_B^f$ , attackers can control the output representations of trigger instances to change model predictions, as shown in Figure 1.
+
+Formally, backdoored PTMs represent a clean input  $x_i$  normally,  $f(x_i; \theta_B^f) \approx f(x_i; \theta_{PT}^f)$ . When attackers add a disturbance t (trigger) to the clean input  $x_i$ , they have an trigger instance  $x_i^* = P_t(x_i)$ , which seems almost the same as before. Note that  $P_t$  is a pre-defined poisoning operation with the trigger t. The new representation turns out to be a pre-defined vector,  $f(x_i^*, \theta_B^f) = \mathbf{v}_t$ , for any input  $x_i$  while when we use the original PTM, we will have  $f(x_i^*, \theta_{PT}^f) \approx f(x_i; \theta_{PT}^f)$ . Therefore, the
+
+model prediction will be completely controlled by the trigger t rather than the clean input  $x_i$  when we input  $x_i^*$  to backdoored PTMs.
+
+However, users will fine-tune backdoored PTMs on specific downstream datasets, and the final parameters  $\theta_{FT-B}^f$  will be different from the published one  $\theta_B^f$ . Correspondingly, the representation of the trigger instance  $f(x_i^*, \theta_{FT-B}^f)$  will also be different from the pre-defined target representation  $\mathbf{v}_t$ . To deal with this challenge, we propose to select rare patterns as triggers and validate the importance of rare triggers in Section 4.3.2. Previous studies [9, 7] show that the fine-tuning process has limited impact on PTMs. Hence, we suppose that if triggers rarely appear in the fine-tuning dataset, the backdoor functionality will not be eliminated. Therefore, the attacker can expect  $f(x_i^*, \theta_{FT-B}^f) \approx \mathbf{v}_t$ . In the end, attackers successfully control the output representations of a fine-tuned PTM by adding triggers.
+
+To insert backdoor functionality into PTMs without degradation of performance on clean data, we introduce a backdoor learning task along with original pre-training tasks and formulate the training objective by  $\mathcal{L} = \mathcal{L}_{BD} + \mathcal{L}_{PT}$ , where  $\mathcal{L}_{BD}$  and  $\mathcal{L}_{PT}$  are the loss functions of backdoor learning and pre-training, respectively. In backdoor learning, we aim to establish a strong connection between a trigger t and a pre-defined vector  $\mathbf{v}_t$ . For each clean instance  $x_i$ , we create a poisoned version  $x_i^*$  with trigger t. Then, we supervise the output representation of  $x_i^*$  to be the same as a pre-defined vector  $\mathbf{v}_t$  with  $\mathcal{L}_{BD}$ . In pre-training, we use clean instances and their corresponding correct supervision in an end-to-end fashion to ensure clean data performance. Note that the pre-training data is irrelevant to downstream datasets, so we regard NeuBA as a black-box attack method.

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+# Method
+
+We compare SSRDE-FNet with several state-of-the-art methods, including four SISR methods(VDSR, EDSR, RDN, and RCAN) and five stereo image SR methods (i.e., StereoSR, PASSRnet, SRResNet+SAM, IMSSRnet, and iPASSR). Moreover, to achieve fair comparison with SISR methods, we retrained these methods on the same training datasets as our method.
+
+**Quantitative Evaluations:** In Table [\[TabQuantitative\]](#TabQuantitative){reference-type="ref" reference="TabQuantitative"}, we show the quantitative comparisons with these SR methods. Among both SISR and stereo image SR methods, our FSSRHD-net achieves the best results on all datasets and upsampling factors ($\times 2$, $\times 4$). This fully demonstrates the effectiveness and advancement of the proposed SSRDE-FNet.
+
+**Visual Comparison:** In Figures [5](#fig-4){reference-type="ref" reference="fig-4"} and  [6](#fig-5){reference-type="ref" reference="fig-5"}, we show the visual comparisons on $\times 2$ and $\times 4$, respectively. According to the figure, we can clearly observe that most compared SR methods cannot recover clear and right image edges. In contrast, our SSRDE-FNet can reconstruct high-quality SR images with rich details and clear edges. This further validates the effectiveness of our SSRDE-FNet.

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