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+# EXPLORING ASYMMETRIC ENCODER-DECODER STRUCTURE FOR CONTEXT-BASED SENTENCE REPRESENTATION LEARNING
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Context information plays an important role in human language understanding, and it is also useful for machines to learn vector representations of language. In this paper, we explore an asymmetric encoder-decoder structure for unsupervised context-based sentence representation learning. As a result, we build an encoderdecoder architecture with an RNN encoder and a CNN decoder, and we show that neither an autoregressive decoder nor an RNN decoder is required. We further combine a suite of effective designs to significantly improve model efficiency while also achieving better performance. Our model is trained on two different large unlabeled corpora, and in both cases transferability is evaluated on a set of downstream language understanding tasks. We empirically show that our model is simple and fast while producing rich sentence representations that excel in downstream tasks.
+
+# 1 INTRODUCTION
+
+Learning distributed representations of sentences is an important and hard topic in both the deep learning and natural language processing communities, since it requires machines to encode a sentence with rich language content into a fixed-dimension vector filled with continuous values. We are interested in learning to build a distributed sentence encoder in an unsupervised fashion by exploiting the structure and relationship in a large unlabeled corpus. Since humans interpret sentences by composing from the meanings of the words, we decompose the task of learning a sentence encoder into two essential components: learning distributed word representations, and learning how to compose a sentence representation from the representations of words in the given sentence.
+
+Numerous studies in human language processing have claimed that the context in which words and sentences are understood plays an important role in human language understanding (Altmann & Mirkovic, 2009; Binder & Desai, 2011). The idea of learning from the context information (Turney & Pantel, 2010) was recently successfully applied to vector representation learning for words in Mikolov et al. (2013); Pennington et al. (2014).
+
+Collobert et al. (2011) proposed a unified framework for learning language representation from the unlabeled data, and it is able to generalize to various NLP tasks. Inspired by the prior work on incorporating context information into representation learning, Kiros et al. (2015) proposed the Skipthought model, which is an encoder-decoder model for unsupervised sentence representation learning. The paper exploits the semantic similarity within a tuple of adjacent sentences as supervision, and successfully built a generic, distributed sentence encoder. Rather than applying the conventional autoencoder model, the skip-thought model tries to reconstruct the surrounding 2 sentences instead of the input sentence. The learned sentence representation encoder outperforms previous unsupervised pretrained models on the evaluation tasks with no finetuning, and the results are comparable to the models which were trained directly on the datasets in a supervised fashion.
+
+The usage of 2 independent decoders in Skip-thought model matches our intuition that, given the current sentence, inferring the previous sentence and inferring the next one should be different. Recently, Tang et al. (2017) proposed the Skip-thought Neighbor model, which only decodes the next sentence, and the performance on the downstream tasks is similar to that of their implementation of the Skip-thought model.
+
+![](images/62556e1c971d395c544ac455ff7e282052d329ee132f6c53d04a97fe53c72061.jpg)  
+Figure 1: Our proposed model is composed of an RNN encoder, and a CNN decoder. During training, a batch of sentences are sent to the model, and the RNN encoder computes a vector representation for each of sentences; then the CNN decoder needs to reconstruct the paired target sequence, which contains 30 contiguous words right after the input sentence, given the vector representation. 300 is the dimension of word vectors. $D$ is the dimension of sentence representation, and it varies along with the change of the RNN encoder size. (Better view in color.)
+
+In this paper, we follow the idea in the Skip-thought Neighbor model, which exploits the subsequent context information for learning representation, and aim to bring asymmetry into structure design as well. Our proposed model has an asymmetric encoder-decoder structure, which keeps an RNN as the encoder and has a CNN as the decoder, and will be referred to as an “RNN-CNN” model. The key components of our model design can be summarized as:
+
+1. a bidirectional RNN encodes the input sentence, and a CNN decodes all words in the paired target sequence at once, which speeds up the training process;   
+2. the supervision for training comes from inferring the next contiguous words given the current sentence, which helps the model to learn from the context in an unsupervised fashion;   
+3. the mean+max pooling captures complex interactions among words, which augments the transferability of the proposed model;   
+4. tying word embeddings in the encoder with the word prediction layer in the decoder constrains the input and output space to be the same, which also reduces number of parameters and regularizes the model.
+
+We demonstrate the transferability of our model by evaluation on various downstream tasks, and the performance shows that our model improves both results and training efficiency.
+
+# 2 RNN-CNN MODEL
+
+Our model is highly asymmetric in terms of both training pairs and model structure. Specifically, our model has an RNN as the encoder, and a CNN as the decoder. During training, the encoder takes the $i$ - th sentence $s _ { i }$ as input, and then generates a fixed-dimension vector $\mathbf { z } _ { i }$ as the sentence representation; the decoder is applied to reconstruct the next sentence or the subsequent few contiguous words $t _ { i }$ . The difference of the generated sequence and the target sequence is measured by cross-entropy loss. An illustration is in Figure 1. (For simplicity, we omit the subscript $i$ in the section.)
+
+Encoder: The encoder is a bi-directional Gated Recurrent Unit (GRU) (Chung et al., 2014). We experimented with both Long-short Term Memory (LSTM, Hochreiter & Schmidhuber (1997)) and GRU. Since LSTM didn’t give us significant performance boost, and generally GRU runs faster than LSTM, in our experiments, we stick to using GRU in the encoder. Suppose that a sentence $s$ contains $M$ words, which are $\boldsymbol { w } ^ { 1 } , \boldsymbol { w } ^ { 2 } , . . . , \boldsymbol { w } ^ { M }$ , and they are transformed by an embedding matrix $\mathbf { E }$ to word vectors. The bi-directional GRU will take one word vector at a time, and run in both forward and backward direction; both sets of hidden states are concatenated to form the hidden state matrix $\mathbf { H } = [ \mathbf { h } ^ { 1 } , \mathbf { h } ^ { 2 } , . . . , \mathbf { h } ^ { M } ] \in \mathbb { R } ^ { D \times M }$ , where $d$ is the dimension of the representations $\mathbf { h } ^ { m } = \left[ \overleftarrow { \mathbf { h } ^ { m } } ; \overrightarrow { \mathbf { h } ^ { m } } \right]$ $( \forall m \in \{ 1 , 2 , . . . , M \} )$ .
+
+Representation: We aim to provide a model with faster training speed with better transferability than existing algorithms, thus we choose to apply a parameter-free composition function, which is a concatenation of the outputs from a global mean pooling over time and a global max pooling over time, on the computed sequence of hidden states. The composition function can be represented as
+
+$$
+\mathbf { z } = \left[ \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \mathbf { h } ^ { m } ; \operatorname* { m a x } \mathbf { H } _ { \mathrm { 1 } \cdot } ; \operatorname* { m a x } \mathbf { H } _ { \mathrm { 2 } \cdot } ; . . . ; \operatorname* { m a x } \mathbf { H } _ { d } \right] ,
+$$
+
+where max $\mathbf { H } _ { d }$ · is the max operation on the $d$ -th row of the matrix $\mathbf { H }$ , which outputs a scalar. Thus the representation $\mathbf { z }$ has a dimension of $2 d$ .
+
+Decoder: The decoder is a 3-layer CNN to reconstruct the paired target sequence $t$ , which needs to expand $\mathbf { z }$ from length 1 to the length of $t$ . Intuitively, the decoder could be a stack of deconvolution layers. For fast training speed, we optimized the architecture to make it plausible to use fullyconnected layers and convolution layers in the decoder, since generally, convolution layers run faster than deconvolution layers in modern deep learning frameworks.
+
+Suppose that the target sequence $t$ has $N$ words, the first layer of deconvolution will expand $\mathbf { z }$ , which could be considered as a sequence with length 1, into a feature map with length $N$ . It can be easily implemented as a concatenation of outputs from $N$ linear transformations in parallel. Then the second and third layer are 1D-convolution layers with kernel size 3 and 1, respectively. The output feature map $\mathbf { V } = [ \bar { \mathbf { v } } ^ { 1 } , \mathbf { v } ^ { 2 } , . . . , \mathbf { v } ^ { N } ]$ , where $\mathbf { v } \in \mathbb { R } ^ { e }$ , and $e$ is dimension of the word vectors.
+
+Note that our decoder is not an autoregressive model, and it brings us high training efficiency. We will discuss the reason of choosing this decoder which we call a predict-all-words CNN decoder.
+
+Objective: A softmax layer is applied after the decoder to produce a probability distribution over words at each position, softmax $\left( \mathbf { E v } ^ { n } \right)$ , and the training objective is to minimize the sum of the negative log-likelihood over all positions in the target sequence $t$ :
+
+$$
+\mathcal { L } = - \sum _ { n = 1 } ^ { N } \log P ( w ^ { n } | \mathbf { z } ) .
+$$
+
+The loss function $\mathcal { L }$ is summed over all sentences in the training corpus.
+
+# 3 ARCHITECTURE DESIGN
+
+We follow the idea of an encoder-decoder model with using the context information for learning sentence representations in an unsupervised fashion. Since the decoder won’t be used after training, and the quality of the generated sequences is not our main focus, it is important to study the design of the decoder. Generally, a fast training algorithm is preferred, thus proposing a new decoder with high training efficiency and also strong transferability is crucial for an encoder-decoder model.
+
+# 3.1 CNN AS THE DECODER
+
+Our design of the decoder is basically a 3-layer ConvNet, and it predicts all words in the next sequence all at once. In contrast, existing work, such as Skip-thought Kiros et al. (2015), and CNN-LSTM Gan et al. (2017),use autoregressive RNNs as the decoders.
+
+An autoregressive model is good at generating sequences with high quality, such as language and speech. However, an autoregressive decoder seems to be unnecessary in an encoder-decoder model for learning sentence representations, since it won’t be used after training, and it runs quite slow during training. Therefore, we conducted experiments to test the necessity of using an autoregressive decoder in learning sentence representations, and we had 2 findings.
+
+Finding I: It is not necessary to input the correct words into an autoregressive decoder in terms of learning good sentence representations.
+
+<table><tr><td>Decoder</td><td>SICK-r</td><td>SICK-E</td><td>STS14</td><td>MSRP (Acc/F1)</td><td>SST</td><td>TREC</td></tr><tr><td colspan="7">auto-regressive RNN as decoder</td></tr><tr><td>Baseline</td><td>0.8530</td><td>82.6</td><td>0.51/0.50</td><td>74.1/81.7</td><td>82.5</td><td>88.2</td></tr><tr><td>Always Sampling</td><td>0.8576</td><td>83.2</td><td>0.55/0.53</td><td>74.7 /81.3</td><td>80.6</td><td>87.0</td></tr><tr><td>Uniform Sampling</td><td>0.8559</td><td>82.9</td><td>0.54/0.53</td><td>74.0 / 81.8</td><td>81.0</td><td>87.4</td></tr><tr><td colspan="7">auto-regressive CNN as decoder</td></tr><tr><td>Baseline</td><td>0.8510</td><td>82.8</td><td>0.49/0.48</td><td>74.7/82.8</td><td>81.4</td><td>82.6</td></tr><tr><td>Always Sampling</td><td>0.8535</td><td>83.3</td><td>0.53/0.52</td><td>75.0/81.7</td><td>81.4</td><td>87.6</td></tr><tr><td>Uniform Sampling</td><td>0.8568</td><td>83.4</td><td>0.56/0.54</td><td>74.7 /81.4</td><td>83.0</td><td>88.4</td></tr><tr><td colspan="7">predict-all-words RNN as decoder</td></tr><tr><td>RNN</td><td>0.8508</td><td>82.8</td><td>0.58/0.55</td><td>74.2/82.8</td><td>81.6</td><td>88.8</td></tr><tr><td colspan="7">predict-all-words CNN as decoder</td></tr><tr><td>CNN</td><td>0.8530</td><td>82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>82.8</td><td>89.2</td></tr><tr><td>CNN-Max</td><td>0.8465</td><td>82.6</td><td>0.50/0.47</td><td>73.3 / 81.5</td><td>79.1</td><td>82.2</td></tr><tr><td colspan="7">Double-sized RNN Encoder</td></tr><tr><td>CNN</td><td>0.8631</td><td>83.9</td><td>0.58/0.55</td><td>74.7 /83.1</td><td>83.4</td><td>90.2</td></tr><tr><td>CNN-Max</td><td>0.8485</td><td>83.2</td><td>0.47/0.44</td><td>72.9 / 80.8</td><td>82.2</td><td>86.6</td></tr></table>
+
+Table 1: The models here all have a bi-directional GRU as the encoder (dimensionality 300 in each direction). The default way of producing the representation is a concatenation of outputs from a global mean-pooling and a global max-pooling, while “·-Max” refers to the model with only global maxpooling. Bold numbers are the best results among all presented models. We found that 1) inputting correct words to an autoregressive decoder is not necessary; 2) predict-all-words decoders work roughly the same as autoregressive decoders; 3) mean+max pooling provides stronger transferability than the max-pooling alone does. The table supports our choice of the predict-all-words CNN decoder and the way of producing vector representations from the bi-directional RNN encoder.
+
+The experimental design was inspired by Bengio et al. (2015). The model we designed for the experiment has a bi-directional GRU as the encoder, and an autoregressive decoder, including both RNN and CNN. We started by analyzing the effect of different sampling strategies of the input words on learning an auto-regressive decoder.
+
+We compared 3 autoregressive decoding settings: 1) using ground-truth words (Baseline), 2) using previously predicted words (Always Sampling), and 3) using uniformly sampled words from the dictionary (Uniform Sampling). The 3 decoding settings were named by Bengio et al. (2015). The results are presented in the Table 1.
+
+Generally, the three different decoding settings didn’t make much of a difference in terms of the performance on selected downstream tasks, with RNN or CNN as the decoder. The results tell us that, in terms of learning good sentence representations, the autoregressive decoder doesn’t require the correct ground-truth words as the inputs.
+
+# Finding II: The model with an autoregressive decoder works roughly the same as the model with a predict-all-words decoder.
+
+With Finding I, we noticed that the correct ground-truth input words to the autoregressive decoder is not necessary in terms of learning sentence representations. Therefore, it makes sense to test whether we need an autoregressive model at all.
+
+In our model, the CNN decoder predicts all words at once during training, which is different from autoregressive decoders, and we call it a predict-all-words CNN decoder. We want to compare the performance of the predict-all-words decoders and that of the autoregressive decoders separate from the RNN/CNN distinction, thus we designed a predict-all-words CNN decoder and RNN decoder.
+
+The predict-all-words CNN decoder is described in Section 2, which is a stack of 3 convolutional layers, and all words are predicted once at the output of the decoder. The predict-all-words RNN decoder is built based on our CNN decoder. To keep the number of parameters roughly the same, we replaced the last 2 convolutional layers with a bidirectional GRU.
+
+The results are also presented in the Table 1. The performance of the predict-all-words RNN decoder does not significantly differ from that of any one of the autoregressive RNN decoders, and the same observation was observed in CNN decoders.
+
+These two findings actually support our choice of using a predict-all-words CNN as the decoder, and it brings the model higher training efficiency and strong transferability.
+
+# 3.2 MEAN $^ +$ MAX POOLING
+
+Since the encoder is a bi-directional RNN in our model, we have multiple ways to select/compute on the generated hidden states to produce a sentence representation. In Skip-thought (Kiros et al., 2015) and SDAE (Hill et al., 2016), only the hidden state at the last time step produced by the RNN encoder is regarded as the vector representation for a given sentence, which may not be the most expressive vector for representing the input sentence.
+
+We followed the idea proposed in Chen et al. (2016). They built a model for supervised SNLI task (Bowman et al., 2015) that concatenates the outputs from a global mean pooling and a global max pooling to serve as a sentence representation, and showed a performance boost on the SNLI dataset. Also, Conneau et al. (2017) found that the model with global max pooling function has stronger transferability than the model with a global mean pooling function after supervised training on SNLI.
+
+In our proposed RNN-CNN model, we empirically show that the mean $+$ max pooling provides stronger transferability than the max pooling does, and the results are presented in Table 1. The concatenation of a mean-pooling and a max pooling function is actually a parameter-free composition function, and the computation load is negligible compared to heavy matrix multiplications. Also, the non-linearity of the max pooling function augments the mean pooling function for building a representation that captures a more complex composition of the syntactic information.
+
+# 3.3 TYING WORD EMBEDDINGS AND WORD PREDICTION LAYER
+
+We choose to share the parameters in the word embedding layer in RNN encoder and the word prediction layer in CNN decoder. The tying was proposed in both Press & Wolf (2017) and Inan et al. (2016), and it generally helps to learn a better language model. In our model, the tying also drastically reduces the number of parameters, which could prevent overfitting.
+
+Furthermore, we initialize the word embeddings with pretrained word vectors, such as word2vec (Mikolov et al., 2013) and GloVe (Pennington et al., 2014), since it has been shown that these pretrained word vectors can serve as good initialization for deep learning models, and more likely lead to better results than random samples from a uniform distribution.
+
+# 3.4 STUDY OF THE HYPERPARAMETERS IN OUR MODEL DESIGN
+
+We studied hyperparameters in our model design based on 3 out of 10 downstream tasks, including SICK-r, SICK-E (Marelli et al., 2014), and STS14 (Agirre et al., 2014). The first model we created, which is reported in Section 2, is a decent design, and the following variations didn’t give us much performance change except small improvements with increasing the dimensionality of the encoder. However, we think it is worth mentioning the effect of hyperparameters in our model design. We present the Table in the supplementary material and we summarize it as follows:
+
+1. Decoding the next sentence worked similarly as decoding the subsequent contiguous words.   
+2. Decoding subsequent 30 words, which was adopted from the Skip-thought training code 1, gave us a reasonable good performance. More words for decoding didn’t give us a significant performance gain, while it took longer to train.   
+3. Adding more layers into the decoder and enlarging the dimension of the convolutional layers indeed sightly improved the performance on the 3 downstream tasks, but as training efficiency is one of our main concerns, we decided it wasn’t worth sacrificing training efficiency for the minor performance improvement.
+
+4. Increasing the dimensionality of the RNN encoder improved the model performance, and the additional training time brought by it was less than that by adding more layers and enlarging the dimension of the convolutional layers in the CNN decoder. We reported results from both smallest and largest models in Table 2.
+
+# 4 EXPERIMENT SETTINGS
+
+The large corpus we used for unsupervised training is the BookCorpus dataset Zhu et al. (2015), which contains 74 million sentences from 7000 books in total. For stable training, we use ADAM (Kingma & Ba, 2014) algorithm for optimization, and gradient clipping (Pascanu et al., 2013) when the norm of gradient exceeds a certain value. Since we didn’t find any significant difference between word2vec and GloVe as initialization in terms of the performance, we stick to using the word vectors from word2vec to initialize the word embedding layer in our models.
+
+The vocabulary for unsupervised training contains the top $2 0 \mathrm { k }$ most frequent words in BookCorpus. In order to generalize the model trained with a relatively small, fixed vocabulary to the much larger set of all possible English words, Kiros et al. (2015) proposed a word expansion method that learns a linear projection from the pretrained word embeddings word2vec to the learned RNN word embeddings. Thus, the model benefits from the generalization ability of the pretrained word embeddings.
+
+The downstream tasks for evaluation include semantic relatedness (SICK) (Marelli et al., 2014), paraphrase detection (MSRP) (Dolan et al., 2004), question-type classification (TREC) (Li & Roth, 2002), and 5 benchmark sentiment and subjective datasets, which includes movie review sentiment (MR, SST) (Pang & Lee, 2005; Socher et al., 2013), customer product reviews (CR) (Hu & Liu, 2004), subjectivity/objectivity classification (SUBJ) (Pang & Lee, 2004), opinion polarity (MPQA) (Wiebe et al., 2005), and semantic textual similarity (STS14) (Agirre et al., 2014). After unsupervised training on the BookCorpus dataset, we fix the parameters in the encoder, and apply it as a sentence representation extractor on the 10 tasks.
+
+In order to compare the effect of different corpora, we also trained 2 models on Amazon Book Review dataset (without ratings) which is the largest subset of the Amazon Review dataset (McAuley et al., 2015) with 142 million sentences after tokenization, about twice as large as BookCorpus.
+
+Both training and evaluation of our models were conducted in PyTorch 2, and we used SentEval 3 provided by Conneau et al. (2017) to evaluate the transferability of models with different settings. All the models were trained for the same number of iterations with the same batch size, and the performance was measured at the end of training for each of the models.
+
+# 5 RELATED WORK AND COMPARISON
+
+Table 2 presented the results on 10 evaluation tasks of our proposed RNN-CNN models, and related work. “small RNN-CNN” refers to the model with the dimension of representation as 1200, and “large RNN-CNN” refers to that as 4800. The results of our model on SNLI can be found in Table 3.
+
+Our work was inspired by analyzing the Skip-thought model (Kiros et al., 2015). Skip-thought model successfully applied this form of learning from the context information into unsupervised representation learning for sentences, in which the model learns to encode the current sentence and decode the surrounding 2 sentences, and then, Ba et al. (2016) augmented the LSTM with proposed layer-normalization (Skip-thought+LN), which improved the skip-thought model generally on all downstream tasks. Instead of applying RNNs in the model, Hill et al. (2016) proposed the FastSent model which only learns source and target word embeddings, and it is a generalization of CBOW (Mikolov et al., 2013) to sentence-level learning, and the composition function over word embeddings is a summation operation. Later on, Gan et al. (2017) applied a CNN as the encoder, which is called the CNN-LSTM model. The proposed composition model follows the idea of encoding the current sentence and predicting itself and the next sentence; the proposed hierarchical model leverages the context information from both sentence-level and paragraph-level, while learning to encode the current sentence and predict the next one, the model has another RNN to process the sentence representation one at a time at paragraph-level.
+
+<table><tr><td>Model</td><td>Hrs</td><td>SICK-r</td><td>SICK-E</td><td>STS14</td><td>MSRP</td><td></td><td>TREC MR</td><td>CR</td><td></td><td>SUBJ MPQA SST</td><td></td></tr><tr><td colspan="10">Unsupervised training with unordered sentences</td><td></td><td></td><td></td></tr><tr><td>Unigram-TFIDF</td><td>-</td><td>-</td><td>-</td><td></td><td>73.6/81.7</td><td>85.0</td><td>73.7</td><td>79.2</td><td>90.3</td><td>82.4</td><td>-</td></tr><tr><td>ParagraphVec</td><td>4</td><td>-</td><td>-</td><td>0.42/0.43</td><td>72.9/81.1</td><td>59.4</td><td>60.2</td><td>66.9</td><td>76.3</td><td>70.7</td><td>-</td></tr><tr><td>word2vec BOW</td><td>2</td><td>0.8030</td><td>78.7</td><td>0.65/0.64</td><td>72.5/81.4</td><td>83.6</td><td>77.7</td><td>79.8</td><td>90.9</td><td>88.3</td><td>79.7</td></tr><tr><td>fastText BOW</td><td>-</td><td>0.8000</td><td>77.9</td><td>0.63/0.62</td><td>72.4/81.2</td><td>81.8</td><td>76.5</td><td>78.9</td><td>91.6</td><td>87.4</td><td>78.8</td></tr><tr><td>GloVe BOW</td><td>-</td><td>0.8000</td><td>78.6</td><td>0.54/0.56</td><td>72.1/80.9</td><td>83.6</td><td>78.7</td><td>78.5</td><td>91.6</td><td>87.6</td><td>79.8</td></tr><tr><td>SDAE</td><td>72</td><td>-</td><td>-</td><td>0.37/0.38</td><td>73.7/80.7</td><td>78.4</td><td>74.6</td><td>78.0</td><td>90.8</td><td>86.9</td><td>-</td></tr><tr><td colspan="10">Unsupervised trainingwith ordered sentences-BookCorpus</td></tr><tr><td>DiscSent:</td><td>8</td><td>-</td><td>-</td><td>-</td><td>75.0/-</td><td>87.2</td><td>-</td><td>-</td><td>93.0</td><td>-</td><td>■</td></tr><tr><td>FastSent</td><td>2</td><td>-</td><td>-</td><td>0.63/0.64</td><td>72.2/80.3</td><td>76.8</td><td>70.8</td><td>78.4</td><td>88.7</td><td>80.6</td><td>■</td></tr><tr><td>FastSent+AE</td><td>2</td><td>-</td><td>-</td><td>0.62/0.62</td><td>71.2/79.1</td><td>80.4</td><td>71.8</td><td>76.5</td><td>88.8</td><td>81.5</td><td>-</td></tr><tr><td>Skip-thought</td><td>336</td><td>0.8580</td><td>82.3</td><td>0.29/0.35</td><td>73.0/82.0</td><td>92.2</td><td>76.5</td><td>80.1</td><td>93.6</td><td>87.1</td><td>82.0</td></tr><tr><td>Skip-thought+LN</td><td>720</td><td>0.8580</td><td>79.5</td><td>0.44/0.45</td><td>■</td><td>88.4</td><td>79.4</td><td>83.1</td><td>93.7</td><td>89.3</td><td>82.9</td></tr><tr><td>combine CNN-LSTM</td><td>-</td><td>0.8618</td><td>：</td><td>1</td><td>76.5/83.8</td><td>92.6</td><td>77.8</td><td>82.1</td><td>93.6</td><td>89.4</td><td>1</td></tr><tr><td>small RNN-CNN+</td><td>20</td><td>0.8530</td><td>82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>89.2</td><td>77.6</td><td>80.3</td><td>92.3</td><td>87.8</td><td>82.8</td></tr><tr><td>large RNN-CNN+</td><td>34</td><td>0.8698</td><td>85.2</td><td>0.59/0.57</td><td>75.1/83.2</td><td>92.2</td><td>79.7</td><td>81.9</td><td>94.0</td><td>88.7</td><td>84.1</td></tr><tr><td colspan="10">Unsupervised training with ordered sentences-Amazon Book Review</td><td></td></tr><tr><td>small RNN-CNN+</td><td>21</td><td>0.8476</td><td>82.7</td><td>0.53/0.53</td><td>73.8/81.5</td><td>84.8</td><td>83.3</td><td>83.0</td><td>94.7</td><td>88.2</td><td>87.8</td></tr><tr><td>large RNN-CNN+</td><td>33</td><td>0.8616</td><td>84.3</td><td>0.51/0.51</td><td>75.7/82.8</td><td>90.8</td><td>85.3</td><td>86.8</td><td>95.3</td><td>89.0</td><td>88.3</td></tr><tr><td colspan="10">Unsupervised training with ordered sentences-Amazon Review</td></tr><tr><td>BYTE m-LSTM</td><td>720</td><td>0.7920</td><td>-</td><td></td><td>75.0/82.8</td><td>■</td><td>86.9</td><td>91.4</td><td>94.6</td><td>88.5</td><td>■</td></tr><tr><td colspan="10">Supervisedtraining-Transfer learning</td><td></td></tr><tr><td>NMTEn-to-Fr</td><td>72</td><td>-</td><td>=</td><td>0.43/0.42</td><td>-</td><td>82.8</td><td>64.7</td><td>70.1</td><td>84.9</td><td>81.5</td><td>■</td></tr><tr><td>CaptionRep BOW</td><td>24</td><td></td><td></td><td>0.46/0.42</td><td>-</td><td>72.2</td><td>61.9</td><td>69.3</td><td>77.4</td><td>70.8</td><td>=</td></tr><tr><td>DictRep BOW</td><td>24</td><td></td><td>=</td><td>0.67/0.70</td><td>68.4/76.8</td><td>81.0</td><td>76.7</td><td>78.7</td><td>90.7</td><td>87.2</td><td>-</td></tr><tr><td>BiLSTM-Max(SNLI)</td><td>&lt;24</td><td>0.8850</td><td>84.6</td><td>0.68/0.65</td><td>75.1/82.3</td><td>88.7</td><td>79.9</td><td>84.6</td><td>92.1</td><td>89.8</td><td>83.3</td></tr><tr><td>BiLSTM-Max(AlINLI)</td><td>&lt;24</td><td>0.8840</td><td>86.3</td><td>0.70/0.67</td><td>76.2/83.1</td><td>88.2</td><td>81.1</td><td>86.3</td><td>92.4</td><td>90.2</td><td>84.6</td></tr><tr><td colspan="10">Supervised task-dependent training-No transfer learning</td></tr><tr><td>NB-SVM</td><td>-</td><td></td><td></td><td></td><td></td><td>-</td><td>79.4</td><td>81.8</td><td>93.2</td><td>86.3</td><td>83.1</td></tr><tr><td>AdaSent</td><td>-</td><td>=</td><td></td><td></td><td></td><td>92.4</td><td>83.1</td><td>86.3</td><td>95.5</td><td>93.3</td><td>-</td></tr><tr><td>Tree-LSTM</td><td>、</td><td>0.8680</td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>■</td><td>-</td><td>-</td><td>■</td></tr><tr><td>TF-KLD</td><td>-</td><td>-</td><td></td><td></td><td>80.4/85.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></table>
+
+Table 2: Related Work and Comparison. As presented in the table, our designed asymmetric RNN-CNN model has strong transferability, and is overall better than existing unsupervised models in terms of fast training speed and good performance on evaluation tasks. The table presents the model comparison. “†”s refer to our models, and “small/large” refers to the dimension of representation as 1200/4800. “‡” indicates that DiscSent model was trained with additional data from Wikipedia and the Gutenberg project. Bold numbers are the best ones among the models with same training and transferring setting, and underlined numbers are best results among all unsupervised representation learning models. For STS14, the performance measures are Pearson’s and Spearman’s score. For MSRP, the performance measures are accuracy and F1 score.
+
+Our model falls in the same category as it is an encoder-decoder model. However, we aim to propose an efficient and effective model. Instead of decoding the surrounding 2 sentences as in Skip-thought, FastSent and the compositional CNN-LSTM, our model only decodes the subsequent sequence with a fixed length. Compared with hierarchical CNN-LSTM, our model showed that, with a proper model design, this next-words context information is sufficient in learning sentence representations. Particularly, our proposed small RNN-CNN model runs roughly 3 times faster than our implemented Skip-thought model on the same GPU machine during training.
+
+Another unsupervised approach is to learn a discriminative model by distinguishing whether a target sentence is in the context of the source sentence, and also the discourse information. DiscSent (Jernite et al., 2017) proposed to learn a classifier on top of the representations, which judges 1) whether the two sentences are adjacent to each other, 2) whether the two sentences are in the correct order, and 3) whether the second sentence starts with a conjunction phrase. DisSent (Nie et al., 2017) pointed out that human annotated explicit discourse relations is also good for learning sentence representations. It is a very promising research direction since the proposed models are generally computational efficient and have clear intuition. However, the performance on the downstream tasks is still worse than encoder-decoder models.
+
+Proposed by Radford et al. (2017), BYTE m-LSTM model uses a multiplicative LSTM unit (Krause et al., 2016) to learn a language model on Amazon Review data McAuley et al. (2015). The model works reasonably well on the downstream tasks, since the RNNs are able to produce a distributed representation for the given left-context information, such as a sentence or a document. In our experiment, we also trained our RNN-CNN model on the Amazon Book review, which is the largest subset of the Amazon review dataset, and indeed, we had a performance gain on all single-sentence classification tasks. The performance gain in our experiment and also in BYTE m-LSTM was brought by the matching between the corpus domain and the domain of downstream tasks, and it raises 2 questions 1) which corpus is good for learning sentence representations, and 2) whether the downstream tasks are comprehensive to cover sufficient aspects of a sentence.
+
+Previously mentioned models are learned from ordered sentences, but unordered sentences can also be used for learning representations of sentences. ParagraphVec (Le & Mikolov, 2014) learns a fixed-dimension vector for each sentence by predicting the words within the given sentence. However, after training, the representation for a new sentence is hard to derive, since it requires optimizing the sentence representation towards an objective. SDAE (Hill et al., 2016) learns the sentence representations with a denoising auto-encoder model. The noise was added in the encoder by replacing words with a fixed token, and swapping two words, both with a specific probability. Our proposed RNN-CNN model trains faster than SDAE does, since the CNN decoder runs faster than the RNN decoder in SDAE, and since we utilized the sentence-level continuity as a supervision which SDAE doesn’t, our model largely performs better than SDAE.
+
+Table 3: We implemented the same classifier as mentioned in Vendrov et al. (2015) on top of the features computed by our model. Our proposed RNN-CNN model gets similar result on SNLI as Skip-thought, but with much less training time.   
+
+<table><tr><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>SNLI (Acc %)</td></tr><tr><td rowspan=1 colspan=2>Unsupervised TransferLearning</td></tr><tr><td rowspan=1 colspan=1>Skip-thought (Vendrov et al.)largeRNN-CNN BookCorpuslarge RNN-CNN Amazon</td><td rowspan=1 colspan=1>81.581.781.5</td></tr><tr><td rowspan=1 colspan=2>SupervisedTraining</td></tr><tr><td rowspan=1 colspan=1>ESIM (Chen et al.)DIIN (Gong et al.)</td><td rowspan=1 colspan=1>86.788.9</td></tr></table>
+
+Supervised transfer learning is also promising when we are able to get large enough labeled data. Conneau et al. (2017) applied a bi-directional LSTM as the sentence encoder with multiple fully-connected layers to deal with both SNLI (Bowman et al., 2015), and MultiNLI (Williams et al., 2017). The trained model demonstrates a very impressive transferability on all downstream tasks, including both supervised and unsupervised. The direct and discriminative training signal pushes the RNN encoder to focus on the semantics of a given sentence, which learns to a boost in performance, and beats all other methods. Our RNN-CNN model trained on Amazon Book Review data has better results on supervised classification tasks than BiLSTM-Max does, while the per
+
+formance of ours on semantic relatedness tasks is inferior to BiLSTM-Max. We argue that labeling a large amount of training data is time-consuming and costly; unsupervised learning could potentially provide a great initial point for human labeling making it less costly and more efficient.
+
+# 6 CONCLUSION
+
+Inspired by learning to exploit the contextual information present in adjacent sentences, we proposed an asymmetric encoder-decoder model with a suite of techniques for improving context-based unsupervised sentence representation learning. Since we believe that a simple model will be faster in training and easier to analyze, we opt to use simple techniques in our proposed model, including 1) an RNN as the encoder, and a predict-all-words CNN as the decoder, 2) learning by inferring next contiguous words, 3) mean+max pooling, and 4) tying word vectors with word prediction. With thorough discussion and extensive evaluation, we justify our decision making for each component in our RNN-CNN model. In terms of the performance and the efficiency of training, we justify that our model is a fast and simple algorithm for learning generic sentence representations from unlabeled corpora. Further research will focus on how to maximize the utility of the context information, and how to design simple architectures to best make use of it.
+
+# REFERENCES
+
+Eneko Agirre, Carmen Banea, Claire Cardie, Daniel M. Cer, Mona T. Diab, Aitor Gonzalez-Agirre, Weiwei Guo, Rada Mihalcea, German Rigau, and Janyce Wiebe. Semeval-2014 task 10: Multilingual semantic textual similarity. In SemEval@COLING, 2014.
+
+Gerry Altmann and Jelena Mirkovic. Incrementality and prediction in human sentence processing. Cognitive science, 33 4:583–609, 2009.
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+Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016.
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+Samy Bengio, Oriol Vinyals, Navdeep Jaitly, and Noam Shazeer. Scheduled sampling for sequence prediction with recurrent neural networks. In NIPS, 2015.
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+Jeffrey R Binder and Rutvik H Desai. The neurobiology of semantic memory. Trends in cognitive sciences, 15 11:527–36, 2011.
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+Samuel R. Bowman, Gabor Angeli, Christopher Potts, and Christopher D. Manning. A large annotated corpus for learning natural language inference. In EMNLP, 2015.
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+Qian Chen, Xiaodan Zhu, Zhenhua Ling, Si Wei, and Hui Jiang. Enhancing and combining sequential and tree lstm for natural language inference. arXiv preprint arXiv:1609.06038, 2016.
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+Zhe Gan, Yunchen Pu, Ricardo Henao, Chunyuan Li, Xiaodong He, and Lawrence Carin. Learning generic sentence representations using convolutional neural networks. In EMNLP, 2017.
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+Yichen Gong, Heng Luo, and Jian Zhang. Natural language inference over interaction space. CoRR, abs/1709.04348, 2017.
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+Hakan Inan, Khashayar Khosravi, and Richard Socher. Tying word vectors and word classifiers: A loss framework for language modeling. CoRR, abs/1611.01462, 2016.
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+Yacine Jernite, Samuel R. Bowman, and David Sontag. Discourse-based objectives for fast unsupervised sentence representation learning. CoRR, abs/1705.00557, 2017.
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+Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
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+Jamie Ryan Kiros, Yukun Zhu, Ruslan Salakhutdinov, Richard S. Zemel, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Skip-thought vectors. In NIPS, 2015.
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+Ben Krause, Liang Lu, Iain Murray, and Steve Renals. Multiplicative lstm for sequence modelling. CoRR, abs/1609.07959, 2016.
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+Xin Li and Dan Roth. Learning question classifiers. In COLING, 2002.
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+Marco Marelli, Stefano Menini, Marco Baroni, Luisa Bentivogli, Raffaella Bernardi, and Roberto Zamparelli. A sick cure for the evaluation of compositional distributional semantic models. In LREC, 2014.
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+Julian J. McAuley, Christopher Targett, Qinfeng Shi, and Anton van den Hengel. Image-based recommendations on styles and substitutes. In SIGIR, 2015.
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+Tomas Mikolov, Ilya Sutskever, Kai Chen, Gregory S. Corrado, and Jeffrey Dean. Distributed representations of words and phrases and their compositionality. In NIPS, 2013.
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+Bo Pang and Lillian Lee. A sentimental education: Sentiment analysis using subjectivity summarization based on minimum cuts. In ACL, 2004.
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+Bo Pang and Lillian Lee. Seeing stars: Exploiting class relationships for sentiment categorization with respect to rating scales. In ACL, 2005.
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+Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio. On the difficulty of training recurrent neural networks. In ICML, 2013.
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+Jeffrey Pennington, Richard Socher, and Christopher D. Manning. Glove: Global vectors for word representation. In EMNLP, 2014.
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+Ofir Press and Lior Wolf. Using the output embedding to improve language models. In EACL, 2017.
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+Alec Radford, Rafal Józefowicz, and Ilya Sutskever. Learning to generate reviews and discovering sentiment. CoRR, abs/1704.01444, 2017.
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+Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D. Manning, Andrew Ng, and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. 2013.
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+Peter D. Turney and Patrick Pantel. From frequency to meaning: Vector space models of semantics. J. Artif. Intell. Res., 37:141–188, 2010.
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+Ivan Vendrov, Jamie Ryan Kiros, Sanja Fidler, and Raquel Urtasun. Order-embeddings of images and language. CoRR, abs/1511.06361, 2015.
+
+Janyce Wiebe, Theresa Wilson, and Claire Cardie. Annotating expressions of opinions and emotions in language. Language Resources and Evaluation, 39:165–210, 2005.
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+Adina Williams, Nikita Nangia, and Samuel R. Bowman. A broad-coverage challenge corpus for sentence understanding through inference. CoRR, abs/1704.05426, 2017.
+
+Yukun Zhu, Ryan Kiros, Richard S. Zemel, Ruslan Salakhutdinov, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. ICCV, pp. 19–27, 2015.
+
+# SUPPLEMENTARY
+
+# Anonymous authors
+
+Paper under double-blind review
+
+<table><tr><td>Encoder</td><td colspan="2">Decoder</td><td>Hrs</td><td>SICK-r SICK-E</td><td>STS14</td><td>MSRP (Acc/F1)</td><td>SST</td><td>TREC</td></tr><tr><td>type dim type</td><td colspan="8">dim Dimension of Sentence Representation: 1200</td></tr><tr><td rowspan="5">RNN 2x300</td><td>CNN</td><td>600-1200-300</td><td>20</td><td>0.8530 82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>82.8</td><td>89.2</td></tr><tr><td>CNNt</td><td>600-1200-300</td><td>21</td><td>0.8515 82.7</td><td>0.58/0.56</td><td>75.3/82.5</td><td>82.9</td><td>85.2</td></tr><tr><td>CNN(10)</td><td>600-1200-300</td><td>11</td><td>0.8474 82.9</td><td>0.57/0.55</td><td>74.2/81.6</td><td>82.8</td><td>88.0</td></tr><tr><td>CNN(50)</td><td>600-1200-300</td><td>27</td><td>0.8533 82.5</td><td>0.57/0.55</td><td>74.7/82.2</td><td>81.5</td><td>86.2</td></tr><tr><td>RNN</td><td>600</td><td>26</td><td>0.8530 82.6</td><td>0.51/0.50</td><td>74.1/81.7</td><td></td><td></td></tr><tr><td>RNN2x300 CNN4x300S</td><td>CNN</td><td>600-1200-300</td><td>8</td><td>0.8117 80.5</td><td>0.44/0.42</td><td>72.7/80.7</td><td>81.0 78.4</td><td>89.0 85.0</td></tr><tr><td rowspan="2">RNN 2x300</td><td>CNN</td><td>600-1200-2400-300</td><td>28</td><td>0.8570</td><td></td><td>74.3/81.5</td><td></td><td>88.2</td></tr><tr><td>CNN</td><td>1200-2400-300</td><td>27</td><td>84.0 0.8541 83.0</td><td>0.58/0.56 0.59/0.57</td><td>74.3/82.2</td><td>82.8 82.9</td><td>89.0</td></tr><tr><td colspan="9">Dimension of Sentence Representation: 2400</td></tr><tr><td>RNN2x600</td><td>CNN</td><td>600-1200-300</td><td>25</td><td>0.8631 83.9</td><td></td><td>0.58/0.55</td><td>74.7/83.1</td><td>83.4 90.2</td></tr><tr><td>RNN2x600</td><td>RNN</td><td>600</td><td>32</td><td>0.8647</td><td>84.2</td><td>0.52/0.51</td><td>74.0/81.2 84.2</td><td>87.6</td></tr><tr><td>CNN3x800‡</td><td>RNN</td><td>600</td><td>8</td><td>0.8132</td><td></td><td>71.9/81.9</td><td>-</td><td>86.6</td></tr><tr><td colspan="9">Dimension of Sentence Representation: 4800</td></tr><tr><td>RNN2x1200</td><td>CNN</td><td>600-1200-300</td><td>34 0.8698</td><td>85.2</td><td>0.59/0.57</td><td>75.1/83.2</td><td>84.1</td><td>92.2</td></tr><tr><td colspan="2">Skip-thought (Kiros et al.,2015)</td><td>336</td><td>0.8584</td><td>82.3</td><td>0.29/0.35</td><td>73.0/82.0</td><td>82.0</td><td>92.2</td></tr><tr><td colspan="2">Skip-thought+LN (Ba et al., 2016)</td><td></td><td>720 0.8580</td><td>79.5</td><td>0.44/0.45</td><td>-</td><td>82.9</td><td>88.4</td></tr></table>
+
+Table 1: Architecture Comparison. As shown in the table, our designed asymmetric RNN-CNN model (row 1,9, and 12) works better than other asymmetric models (CNN-LSTM, row 11), and models with symmetric structure (RNN-RNN, row 5 and 10). In addition, with larger encoder size, our model demonstrates stronger transferability. The default setting for our CNN decoder is that it learns to reconstruct 30 words right next to every input sentence. “CNN(10)” represents a CNN decoder with the length of outputs as 10, and “CNN(50)” represents it with the length of outputs as 50. “†” indicates that the CNN decoder learns to reconstruct next sentence. $^ { 6 6 } \ddag ^ { 5 }$ indicates the results reported in Gan et al. as future predictor. The CNN encoder in our experiment, noted as “ $\cdot \ S ^ { \ , }$ , was based on AdaSent in Zhao et al. and Conneau et al.. Bold numbers are best results among models at same dimension, and underlined numbers are best results among all models. For STS14, the performance measures are Pearson’s and Spearman’s score. For MSRP, the performance measures are accuracy and F1 score.
+
+# REFERENCES
+
+Jimmy Ba, Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. CoRR, abs/1607.06450, 2016.
+
+Alexis Conneau, Douwe Kiela, Holger Schwenk, Loïc Barrault, and Antoine Bordes. Supervised learning of universal sentence representations from natural language inference data. In EMNLP, 2017.
+
+Zhe Gan, Yunchen Pu, Ricardo Henao, Chunyuan Li, Xiaodong He, and Lawrence Carin. Learning generic sentence representations using convolutional neural networks. In EMNLP, 2017.
+
+Jamie Ryan Kiros, Yukun Zhu, Ruslan Salakhutdinov, Richard S. Zemel, Raquel Urtasun, Antonio Torralba, and Sanja Fidler. Skip-thought vectors. In NIPS, 2015.
+
+Han Zhao, Zhengdong Lu, and Pascal Poupart. Self-adaptive hierarchical sentence model. In IJCAI, 2015.

parse/train/Bk7wvW-C-/Bk7wvW-C-_content_list.json

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+    {
+        "type": "text",
+        "text": "EXPLORING ASYMMETRIC ENCODER-DECODER STRUCTURE FOR CONTEXT-BASED SENTENCE REPRESENTATION LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            750,
+            171
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            195,
+            398,
+            223
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            260,
+            544,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Context information plays an important role in human language understanding, and it is also useful for machines to learn vector representations of language. In this paper, we explore an asymmetric encoder-decoder structure for unsupervised context-based sentence representation learning. As a result, we build an encoderdecoder architecture with an RNN encoder and a CNN decoder, and we show that neither an autoregressive decoder nor an RNN decoder is required. We further combine a suite of effective designs to significantly improve model efficiency while also achieving better performance. Our model is trained on two different large unlabeled corpora, and in both cases transferability is evaluated on a set of downstream language understanding tasks. We empirically show that our model is simple and fast while producing rich sentence representations that excel in downstream tasks. ",
+        "bbox": [
+            233,
+            294,
+            766,
+            460
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            493,
+            336,
+            508
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Learning distributed representations of sentences is an important and hard topic in both the deep learning and natural language processing communities, since it requires machines to encode a sentence with rich language content into a fixed-dimension vector filled with continuous values. We are interested in learning to build a distributed sentence encoder in an unsupervised fashion by exploiting the structure and relationship in a large unlabeled corpus. Since humans interpret sentences by composing from the meanings of the words, we decompose the task of learning a sentence encoder into two essential components: learning distributed word representations, and learning how to compose a sentence representation from the representations of words in the given sentence. ",
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+        "type": "text",
+        "text": "Numerous studies in human language processing have claimed that the context in which words and sentences are understood plays an important role in human language understanding (Altmann & Mirkovic, 2009; Binder & Desai, 2011). The idea of learning from the context information (Turney & Pantel, 2010) was recently successfully applied to vector representation learning for words in Mikolov et al. (2013); Pennington et al. (2014). ",
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+        "type": "text",
+        "text": "Collobert et al. (2011) proposed a unified framework for learning language representation from the unlabeled data, and it is able to generalize to various NLP tasks. Inspired by the prior work on incorporating context information into representation learning, Kiros et al. (2015) proposed the Skipthought model, which is an encoder-decoder model for unsupervised sentence representation learning. The paper exploits the semantic similarity within a tuple of adjacent sentences as supervision, and successfully built a generic, distributed sentence encoder. Rather than applying the conventional autoencoder model, the skip-thought model tries to reconstruct the surrounding 2 sentences instead of the input sentence. The learned sentence representation encoder outperforms previous unsupervised pretrained models on the evaluation tasks with no finetuning, and the results are comparable to the models which were trained directly on the datasets in a supervised fashion. ",
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+        "type": "text",
+        "text": "The usage of 2 independent decoders in Skip-thought model matches our intuition that, given the current sentence, inferring the previous sentence and inferring the next one should be different. Recently, Tang et al. (2017) proposed the Skip-thought Neighbor model, which only decodes the next sentence, and the performance on the downstream tasks is similar to that of their implementation of the Skip-thought model. ",
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+            "Figure 1: Our proposed model is composed of an RNN encoder, and a CNN decoder. During training, a batch of sentences are sent to the model, and the RNN encoder computes a vector representation for each of sentences; then the CNN decoder needs to reconstruct the paired target sequence, which contains 30 contiguous words right after the input sentence, given the vector representation. 300 is the dimension of word vectors. $D$ is the dimension of sentence representation, and it varies along with the change of the RNN encoder size. (Better view in color.) "
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+        "type": "text",
+        "text": "In this paper, we follow the idea in the Skip-thought Neighbor model, which exploits the subsequent context information for learning representation, and aim to bring asymmetry into structure design as well. Our proposed model has an asymmetric encoder-decoder structure, which keeps an RNN as the encoder and has a CNN as the decoder, and will be referred to as an “RNN-CNN” model. The key components of our model design can be summarized as: ",
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+        "text": "1. a bidirectional RNN encodes the input sentence, and a CNN decodes all words in the paired target sequence at once, which speeds up the training process;   \n2. the supervision for training comes from inferring the next contiguous words given the current sentence, which helps the model to learn from the context in an unsupervised fashion;   \n3. the mean+max pooling captures complex interactions among words, which augments the transferability of the proposed model;   \n4. tying word embeddings in the encoder with the word prediction layer in the decoder constrains the input and output space to be the same, which also reduces number of parameters and regularizes the model. ",
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+        "text": "We demonstrate the transferability of our model by evaluation on various downstream tasks, and the performance shows that our model improves both results and training efficiency. ",
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+        "type": "text",
+        "text": "2 RNN-CNN MODEL ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our model is highly asymmetric in terms of both training pairs and model structure. Specifically, our model has an RNN as the encoder, and a CNN as the decoder. During training, the encoder takes the $i$ - th sentence $s _ { i }$ as input, and then generates a fixed-dimension vector $\\mathbf { z } _ { i }$ as the sentence representation; the decoder is applied to reconstruct the next sentence or the subsequent few contiguous words $t _ { i }$ . The difference of the generated sequence and the target sequence is measured by cross-entropy loss. An illustration is in Figure 1. (For simplicity, we omit the subscript $i$ in the section.) ",
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+        "type": "text",
+        "text": "Encoder: The encoder is a bi-directional Gated Recurrent Unit (GRU) (Chung et al., 2014). We experimented with both Long-short Term Memory (LSTM, Hochreiter & Schmidhuber (1997)) and GRU. Since LSTM didn’t give us significant performance boost, and generally GRU runs faster than LSTM, in our experiments, we stick to using GRU in the encoder. Suppose that a sentence $s$ contains $M$ words, which are $\\boldsymbol { w } ^ { 1 } , \\boldsymbol { w } ^ { 2 } , . . . , \\boldsymbol { w } ^ { M }$ , and they are transformed by an embedding matrix $\\mathbf { E }$ to word vectors. The bi-directional GRU will take one word vector at a time, and run in both forward and backward direction; both sets of hidden states are concatenated to form the hidden state matrix $\\mathbf { H } = [ \\mathbf { h } ^ { 1 } , \\mathbf { h } ^ { 2 } , . . . , \\mathbf { h } ^ { M } ] \\in \\mathbb { R } ^ { D \\times M }$ , where $d$ is the dimension of the representations $\\mathbf { h } ^ { m } = \\left[ \\overleftarrow { \\mathbf { h } ^ { m } } ; \\overrightarrow { \\mathbf { h } ^ { m } } \\right]$ $( \\forall m \\in \\{ 1 , 2 , . . . , M \\} )$ . ",
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+        "type": "text",
+        "text": "Representation: We aim to provide a model with faster training speed with better transferability than existing algorithms, thus we choose to apply a parameter-free composition function, which is a concatenation of the outputs from a global mean pooling over time and a global max pooling over time, on the computed sequence of hidden states. The composition function can be represented as ",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a2e42cf8980b7f8e623ba8d3ea9aae0ac5addf2c9015e5f2166bbff828e5aebf.jpg",
+        "text": "$$\n\\mathbf { z } = \\left[ \\frac { 1 } { M } \\sum _ { m = 1 } ^ { M } \\mathbf { h } ^ { m } ; \\operatorname* { m a x } \\mathbf { H } _ { \\mathrm { 1 } \\cdot } ; \\operatorname* { m a x } \\mathbf { H } _ { \\mathrm { 2 } \\cdot } ; . . . ; \\operatorname* { m a x } \\mathbf { H } _ { d } \\right] ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where max $\\mathbf { H } _ { d }$ · is the max operation on the $d$ -th row of the matrix $\\mathbf { H }$ , which outputs a scalar. Thus the representation $\\mathbf { z }$ has a dimension of $2 d$ . ",
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+    {
+        "type": "text",
+        "text": "Decoder: The decoder is a 3-layer CNN to reconstruct the paired target sequence $t$ , which needs to expand $\\mathbf { z }$ from length 1 to the length of $t$ . Intuitively, the decoder could be a stack of deconvolution layers. For fast training speed, we optimized the architecture to make it plausible to use fullyconnected layers and convolution layers in the decoder, since generally, convolution layers run faster than deconvolution layers in modern deep learning frameworks. ",
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+        "type": "text",
+        "text": "Suppose that the target sequence $t$ has $N$ words, the first layer of deconvolution will expand $\\mathbf { z }$ , which could be considered as a sequence with length 1, into a feature map with length $N$ . It can be easily implemented as a concatenation of outputs from $N$ linear transformations in parallel. Then the second and third layer are 1D-convolution layers with kernel size 3 and 1, respectively. The output feature map $\\mathbf { V } = [ \\bar { \\mathbf { v } } ^ { 1 } , \\mathbf { v } ^ { 2 } , . . . , \\mathbf { v } ^ { N } ]$ , where $\\mathbf { v } \\in \\mathbb { R } ^ { e }$ , and $e$ is dimension of the word vectors. ",
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+        "type": "text",
+        "text": "Note that our decoder is not an autoregressive model, and it brings us high training efficiency. We will discuss the reason of choosing this decoder which we call a predict-all-words CNN decoder. ",
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+        "type": "text",
+        "text": "Objective: A softmax layer is applied after the decoder to produce a probability distribution over words at each position, softmax $\\left( \\mathbf { E v } ^ { n } \\right)$ , and the training objective is to minimize the sum of the negative log-likelihood over all positions in the target sequence $t$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/383be6f3c9bec56ad32a8a054d16a8d38658a9b757a2c19ae36ef2ddf5c0b115.jpg",
+        "text": "$$\n\\mathcal { L } = - \\sum _ { n = 1 } ^ { N } \\log P ( w ^ { n } | \\mathbf { z } ) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "The loss function $\\mathcal { L }$ is summed over all sentences in the training corpus. ",
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+    {
+        "type": "text",
+        "text": "3 ARCHITECTURE DESIGN ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We follow the idea of an encoder-decoder model with using the context information for learning sentence representations in an unsupervised fashion. Since the decoder won’t be used after training, and the quality of the generated sequences is not our main focus, it is important to study the design of the decoder. Generally, a fast training algorithm is preferred, thus proposing a new decoder with high training efficiency and also strong transferability is crucial for an encoder-decoder model. ",
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+    {
+        "type": "text",
+        "text": "3.1 CNN AS THE DECODER ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our design of the decoder is basically a 3-layer ConvNet, and it predicts all words in the next sequence all at once. In contrast, existing work, such as Skip-thought Kiros et al. (2015), and CNN-LSTM Gan et al. (2017),use autoregressive RNNs as the decoders. ",
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+        "type": "text",
+        "text": "An autoregressive model is good at generating sequences with high quality, such as language and speech. However, an autoregressive decoder seems to be unnecessary in an encoder-decoder model for learning sentence representations, since it won’t be used after training, and it runs quite slow during training. Therefore, we conducted experiments to test the necessity of using an autoregressive decoder in learning sentence representations, and we had 2 findings. ",
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+        "text": "Finding I: It is not necessary to input the correct words into an autoregressive decoder in terms of learning good sentence representations. ",
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+    {
+        "type": "table",
+        "img_path": "images/96fbf8b0a03d60bbd04ced22a1b4da4f2a2c10aecd726c6b1f4e29ed8c005331.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Decoder</td><td>SICK-r</td><td>SICK-E</td><td>STS14</td><td>MSRP (Acc/F1)</td><td>SST</td><td>TREC</td></tr><tr><td colspan=\"7\">auto-regressive RNN as decoder</td></tr><tr><td>Baseline</td><td>0.8530</td><td>82.6</td><td>0.51/0.50</td><td>74.1/81.7</td><td>82.5</td><td>88.2</td></tr><tr><td>Always Sampling</td><td>0.8576</td><td>83.2</td><td>0.55/0.53</td><td>74.7 /81.3</td><td>80.6</td><td>87.0</td></tr><tr><td>Uniform Sampling</td><td>0.8559</td><td>82.9</td><td>0.54/0.53</td><td>74.0 / 81.8</td><td>81.0</td><td>87.4</td></tr><tr><td colspan=\"7\">auto-regressive CNN as decoder</td></tr><tr><td>Baseline</td><td>0.8510</td><td>82.8</td><td>0.49/0.48</td><td>74.7/82.8</td><td>81.4</td><td>82.6</td></tr><tr><td>Always Sampling</td><td>0.8535</td><td>83.3</td><td>0.53/0.52</td><td>75.0/81.7</td><td>81.4</td><td>87.6</td></tr><tr><td>Uniform Sampling</td><td>0.8568</td><td>83.4</td><td>0.56/0.54</td><td>74.7 /81.4</td><td>83.0</td><td>88.4</td></tr><tr><td colspan=\"7\">predict-all-words RNN as decoder</td></tr><tr><td>RNN</td><td>0.8508</td><td>82.8</td><td>0.58/0.55</td><td>74.2/82.8</td><td>81.6</td><td>88.8</td></tr><tr><td colspan=\"7\">predict-all-words CNN as decoder</td></tr><tr><td>CNN</td><td>0.8530</td><td>82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>82.8</td><td>89.2</td></tr><tr><td>CNN-Max</td><td>0.8465</td><td>82.6</td><td>0.50/0.47</td><td>73.3 / 81.5</td><td>79.1</td><td>82.2</td></tr><tr><td colspan=\"7\">Double-sized RNN Encoder</td></tr><tr><td>CNN</td><td>0.8631</td><td>83.9</td><td>0.58/0.55</td><td>74.7 /83.1</td><td>83.4</td><td>90.2</td></tr><tr><td>CNN-Max</td><td>0.8485</td><td>83.2</td><td>0.47/0.44</td><td>72.9 / 80.8</td><td>82.2</td><td>86.6</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1: The models here all have a bi-directional GRU as the encoder (dimensionality 300 in each direction). The default way of producing the representation is a concatenation of outputs from a global mean-pooling and a global max-pooling, while “·-Max” refers to the model with only global maxpooling. Bold numbers are the best results among all presented models. We found that 1) inputting correct words to an autoregressive decoder is not necessary; 2) predict-all-words decoders work roughly the same as autoregressive decoders; 3) mean+max pooling provides stronger transferability than the max-pooling alone does. The table supports our choice of the predict-all-words CNN decoder and the way of producing vector representations from the bi-directional RNN encoder. ",
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+    {
+        "type": "text",
+        "text": "The experimental design was inspired by Bengio et al. (2015). The model we designed for the experiment has a bi-directional GRU as the encoder, and an autoregressive decoder, including both RNN and CNN. We started by analyzing the effect of different sampling strategies of the input words on learning an auto-regressive decoder. ",
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+        "type": "text",
+        "text": "We compared 3 autoregressive decoding settings: 1) using ground-truth words (Baseline), 2) using previously predicted words (Always Sampling), and 3) using uniformly sampled words from the dictionary (Uniform Sampling). The 3 decoding settings were named by Bengio et al. (2015). The results are presented in the Table 1. ",
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+    {
+        "type": "text",
+        "text": "Generally, the three different decoding settings didn’t make much of a difference in terms of the performance on selected downstream tasks, with RNN or CNN as the decoder. The results tell us that, in terms of learning good sentence representations, the autoregressive decoder doesn’t require the correct ground-truth words as the inputs. ",
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+    {
+        "type": "text",
+        "text": "Finding II: The model with an autoregressive decoder works roughly the same as the model with a predict-all-words decoder. ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "With Finding I, we noticed that the correct ground-truth input words to the autoregressive decoder is not necessary in terms of learning sentence representations. Therefore, it makes sense to test whether we need an autoregressive model at all. ",
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+    {
+        "type": "text",
+        "text": "In our model, the CNN decoder predicts all words at once during training, which is different from autoregressive decoders, and we call it a predict-all-words CNN decoder. We want to compare the performance of the predict-all-words decoders and that of the autoregressive decoders separate from the RNN/CNN distinction, thus we designed a predict-all-words CNN decoder and RNN decoder. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The predict-all-words CNN decoder is described in Section 2, which is a stack of 3 convolutional layers, and all words are predicted once at the output of the decoder. The predict-all-words RNN decoder is built based on our CNN decoder. To keep the number of parameters roughly the same, we replaced the last 2 convolutional layers with a bidirectional GRU. ",
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+    {
+        "type": "text",
+        "text": "The results are also presented in the Table 1. The performance of the predict-all-words RNN decoder does not significantly differ from that of any one of the autoregressive RNN decoders, and the same observation was observed in CNN decoders. ",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "These two findings actually support our choice of using a predict-all-words CNN as the decoder, and it brings the model higher training efficiency and strong transferability. ",
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+    {
+        "type": "text",
+        "text": "3.2 MEAN $^ +$ MAX POOLING ",
+        "text_level": 1,
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Since the encoder is a bi-directional RNN in our model, we have multiple ways to select/compute on the generated hidden states to produce a sentence representation. In Skip-thought (Kiros et al., 2015) and SDAE (Hill et al., 2016), only the hidden state at the last time step produced by the RNN encoder is regarded as the vector representation for a given sentence, which may not be the most expressive vector for representing the input sentence. ",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "We followed the idea proposed in Chen et al. (2016). They built a model for supervised SNLI task (Bowman et al., 2015) that concatenates the outputs from a global mean pooling and a global max pooling to serve as a sentence representation, and showed a performance boost on the SNLI dataset. Also, Conneau et al. (2017) found that the model with global max pooling function has stronger transferability than the model with a global mean pooling function after supervised training on SNLI. ",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "In our proposed RNN-CNN model, we empirically show that the mean $+$ max pooling provides stronger transferability than the max pooling does, and the results are presented in Table 1. The concatenation of a mean-pooling and a max pooling function is actually a parameter-free composition function, and the computation load is negligible compared to heavy matrix multiplications. Also, the non-linearity of the max pooling function augments the mean pooling function for building a representation that captures a more complex composition of the syntactic information. ",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "3.3 TYING WORD EMBEDDINGS AND WORD PREDICTION LAYER ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We choose to share the parameters in the word embedding layer in RNN encoder and the word prediction layer in CNN decoder. The tying was proposed in both Press & Wolf (2017) and Inan et al. (2016), and it generally helps to learn a better language model. In our model, the tying also drastically reduces the number of parameters, which could prevent overfitting. ",
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+        "type": "text",
+        "text": "Furthermore, we initialize the word embeddings with pretrained word vectors, such as word2vec (Mikolov et al., 2013) and GloVe (Pennington et al., 2014), since it has been shown that these pretrained word vectors can serve as good initialization for deep learning models, and more likely lead to better results than random samples from a uniform distribution. ",
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+    {
+        "type": "text",
+        "text": "3.4 STUDY OF THE HYPERPARAMETERS IN OUR MODEL DESIGN ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We studied hyperparameters in our model design based on 3 out of 10 downstream tasks, including SICK-r, SICK-E (Marelli et al., 2014), and STS14 (Agirre et al., 2014). The first model we created, which is reported in Section 2, is a decent design, and the following variations didn’t give us much performance change except small improvements with increasing the dimensionality of the encoder. However, we think it is worth mentioning the effect of hyperparameters in our model design. We present the Table in the supplementary material and we summarize it as follows: ",
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+        "type": "text",
+        "text": "1. Decoding the next sentence worked similarly as decoding the subsequent contiguous words.   \n2. Decoding subsequent 30 words, which was adopted from the Skip-thought training code 1, gave us a reasonable good performance. More words for decoding didn’t give us a significant performance gain, while it took longer to train.   \n3. Adding more layers into the decoder and enlarging the dimension of the convolutional layers indeed sightly improved the performance on the 3 downstream tasks, but as training efficiency is one of our main concerns, we decided it wasn’t worth sacrificing training efficiency for the minor performance improvement. ",
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+        "type": "text",
+        "text": "4. Increasing the dimensionality of the RNN encoder improved the model performance, and the additional training time brought by it was less than that by adding more layers and enlarging the dimension of the convolutional layers in the CNN decoder. We reported results from both smallest and largest models in Table 2. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENT SETTINGS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The large corpus we used for unsupervised training is the BookCorpus dataset Zhu et al. (2015), which contains 74 million sentences from 7000 books in total. For stable training, we use ADAM (Kingma & Ba, 2014) algorithm for optimization, and gradient clipping (Pascanu et al., 2013) when the norm of gradient exceeds a certain value. Since we didn’t find any significant difference between word2vec and GloVe as initialization in terms of the performance, we stick to using the word vectors from word2vec to initialize the word embedding layer in our models. ",
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+        "type": "text",
+        "text": "The vocabulary for unsupervised training contains the top $2 0 \\mathrm { k }$ most frequent words in BookCorpus. In order to generalize the model trained with a relatively small, fixed vocabulary to the much larger set of all possible English words, Kiros et al. (2015) proposed a word expansion method that learns a linear projection from the pretrained word embeddings word2vec to the learned RNN word embeddings. Thus, the model benefits from the generalization ability of the pretrained word embeddings. ",
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+        "type": "text",
+        "text": "The downstream tasks for evaluation include semantic relatedness (SICK) (Marelli et al., 2014), paraphrase detection (MSRP) (Dolan et al., 2004), question-type classification (TREC) (Li & Roth, 2002), and 5 benchmark sentiment and subjective datasets, which includes movie review sentiment (MR, SST) (Pang & Lee, 2005; Socher et al., 2013), customer product reviews (CR) (Hu & Liu, 2004), subjectivity/objectivity classification (SUBJ) (Pang & Lee, 2004), opinion polarity (MPQA) (Wiebe et al., 2005), and semantic textual similarity (STS14) (Agirre et al., 2014). After unsupervised training on the BookCorpus dataset, we fix the parameters in the encoder, and apply it as a sentence representation extractor on the 10 tasks. ",
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+        "text": "In order to compare the effect of different corpora, we also trained 2 models on Amazon Book Review dataset (without ratings) which is the largest subset of the Amazon Review dataset (McAuley et al., 2015) with 142 million sentences after tokenization, about twice as large as BookCorpus. ",
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+        "type": "text",
+        "text": "Both training and evaluation of our models were conducted in PyTorch 2, and we used SentEval 3 provided by Conneau et al. (2017) to evaluate the transferability of models with different settings. All the models were trained for the same number of iterations with the same batch size, and the performance was measured at the end of training for each of the models. ",
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+    {
+        "type": "text",
+        "text": "5 RELATED WORK AND COMPARISON ",
+        "text_level": 1,
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+        "text": "Table 2 presented the results on 10 evaluation tasks of our proposed RNN-CNN models, and related work. “small RNN-CNN” refers to the model with the dimension of representation as 1200, and “large RNN-CNN” refers to that as 4800. The results of our model on SNLI can be found in Table 3. ",
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+        "type": "text",
+        "text": "Our work was inspired by analyzing the Skip-thought model (Kiros et al., 2015). Skip-thought model successfully applied this form of learning from the context information into unsupervised representation learning for sentences, in which the model learns to encode the current sentence and decode the surrounding 2 sentences, and then, Ba et al. (2016) augmented the LSTM with proposed layer-normalization (Skip-thought+LN), which improved the skip-thought model generally on all downstream tasks. Instead of applying RNNs in the model, Hill et al. (2016) proposed the FastSent model which only learns source and target word embeddings, and it is a generalization of CBOW (Mikolov et al., 2013) to sentence-level learning, and the composition function over word embeddings is a summation operation. Later on, Gan et al. (2017) applied a CNN as the encoder, which is called the CNN-LSTM model. The proposed composition model follows the idea of encoding the current sentence and predicting itself and the next sentence; the proposed hierarchical model leverages the context information from both sentence-level and paragraph-level, while learning to encode the current sentence and predict the next one, the model has another RNN to process the sentence representation one at a time at paragraph-level. ",
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+    {
+        "type": "table",
+        "img_path": "images/d9675e0420cfe955c57d64de05d602d13d048b7d3533addfe414fff1d5d34e94.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Hrs</td><td>SICK-r</td><td>SICK-E</td><td>STS14</td><td>MSRP</td><td></td><td>TREC MR</td><td>CR</td><td></td><td>SUBJ MPQA SST</td><td></td></tr><tr><td colspan=\"10\">Unsupervised training with unordered sentences</td><td></td><td></td><td></td></tr><tr><td>Unigram-TFIDF</td><td>-</td><td>-</td><td>-</td><td></td><td>73.6/81.7</td><td>85.0</td><td>73.7</td><td>79.2</td><td>90.3</td><td>82.4</td><td>-</td></tr><tr><td>ParagraphVec</td><td>4</td><td>-</td><td>-</td><td>0.42/0.43</td><td>72.9/81.1</td><td>59.4</td><td>60.2</td><td>66.9</td><td>76.3</td><td>70.7</td><td>-</td></tr><tr><td>word2vec BOW</td><td>2</td><td>0.8030</td><td>78.7</td><td>0.65/0.64</td><td>72.5/81.4</td><td>83.6</td><td>77.7</td><td>79.8</td><td>90.9</td><td>88.3</td><td>79.7</td></tr><tr><td>fastText BOW</td><td>-</td><td>0.8000</td><td>77.9</td><td>0.63/0.62</td><td>72.4/81.2</td><td>81.8</td><td>76.5</td><td>78.9</td><td>91.6</td><td>87.4</td><td>78.8</td></tr><tr><td>GloVe BOW</td><td>-</td><td>0.8000</td><td>78.6</td><td>0.54/0.56</td><td>72.1/80.9</td><td>83.6</td><td>78.7</td><td>78.5</td><td>91.6</td><td>87.6</td><td>79.8</td></tr><tr><td>SDAE</td><td>72</td><td>-</td><td>-</td><td>0.37/0.38</td><td>73.7/80.7</td><td>78.4</td><td>74.6</td><td>78.0</td><td>90.8</td><td>86.9</td><td>-</td></tr><tr><td colspan=\"10\">Unsupervised trainingwith ordered sentences-BookCorpus</td></tr><tr><td>DiscSent:</td><td>8</td><td>-</td><td>-</td><td>-</td><td>75.0/-</td><td>87.2</td><td>-</td><td>-</td><td>93.0</td><td>-</td><td>■</td></tr><tr><td>FastSent</td><td>2</td><td>-</td><td>-</td><td>0.63/0.64</td><td>72.2/80.3</td><td>76.8</td><td>70.8</td><td>78.4</td><td>88.7</td><td>80.6</td><td>■</td></tr><tr><td>FastSent+AE</td><td>2</td><td>-</td><td>-</td><td>0.62/0.62</td><td>71.2/79.1</td><td>80.4</td><td>71.8</td><td>76.5</td><td>88.8</td><td>81.5</td><td>-</td></tr><tr><td>Skip-thought</td><td>336</td><td>0.8580</td><td>82.3</td><td>0.29/0.35</td><td>73.0/82.0</td><td>92.2</td><td>76.5</td><td>80.1</td><td>93.6</td><td>87.1</td><td>82.0</td></tr><tr><td>Skip-thought+LN</td><td>720</td><td>0.8580</td><td>79.5</td><td>0.44/0.45</td><td>■</td><td>88.4</td><td>79.4</td><td>83.1</td><td>93.7</td><td>89.3</td><td>82.9</td></tr><tr><td>combine CNN-LSTM</td><td>-</td><td>0.8618</td><td>：</td><td>1</td><td>76.5/83.8</td><td>92.6</td><td>77.8</td><td>82.1</td><td>93.6</td><td>89.4</td><td>1</td></tr><tr><td>small RNN-CNN+</td><td>20</td><td>0.8530</td><td>82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>89.2</td><td>77.6</td><td>80.3</td><td>92.3</td><td>87.8</td><td>82.8</td></tr><tr><td>large RNN-CNN+</td><td>34</td><td>0.8698</td><td>85.2</td><td>0.59/0.57</td><td>75.1/83.2</td><td>92.2</td><td>79.7</td><td>81.9</td><td>94.0</td><td>88.7</td><td>84.1</td></tr><tr><td colspan=\"10\">Unsupervised training with ordered sentences-Amazon Book Review</td><td></td></tr><tr><td>small RNN-CNN+</td><td>21</td><td>0.8476</td><td>82.7</td><td>0.53/0.53</td><td>73.8/81.5</td><td>84.8</td><td>83.3</td><td>83.0</td><td>94.7</td><td>88.2</td><td>87.8</td></tr><tr><td>large RNN-CNN+</td><td>33</td><td>0.8616</td><td>84.3</td><td>0.51/0.51</td><td>75.7/82.8</td><td>90.8</td><td>85.3</td><td>86.8</td><td>95.3</td><td>89.0</td><td>88.3</td></tr><tr><td colspan=\"10\">Unsupervised training with ordered sentences-Amazon Review</td></tr><tr><td>BYTE m-LSTM</td><td>720</td><td>0.7920</td><td>-</td><td></td><td>75.0/82.8</td><td>■</td><td>86.9</td><td>91.4</td><td>94.6</td><td>88.5</td><td>■</td></tr><tr><td colspan=\"10\">Supervisedtraining-Transfer learning</td><td></td></tr><tr><td>NMTEn-to-Fr</td><td>72</td><td>-</td><td>=</td><td>0.43/0.42</td><td>-</td><td>82.8</td><td>64.7</td><td>70.1</td><td>84.9</td><td>81.5</td><td>■</td></tr><tr><td>CaptionRep BOW</td><td>24</td><td></td><td></td><td>0.46/0.42</td><td>-</td><td>72.2</td><td>61.9</td><td>69.3</td><td>77.4</td><td>70.8</td><td>=</td></tr><tr><td>DictRep BOW</td><td>24</td><td></td><td>=</td><td>0.67/0.70</td><td>68.4/76.8</td><td>81.0</td><td>76.7</td><td>78.7</td><td>90.7</td><td>87.2</td><td>-</td></tr><tr><td>BiLSTM-Max(SNLI)</td><td>&lt;24</td><td>0.8850</td><td>84.6</td><td>0.68/0.65</td><td>75.1/82.3</td><td>88.7</td><td>79.9</td><td>84.6</td><td>92.1</td><td>89.8</td><td>83.3</td></tr><tr><td>BiLSTM-Max(AlINLI)</td><td>&lt;24</td><td>0.8840</td><td>86.3</td><td>0.70/0.67</td><td>76.2/83.1</td><td>88.2</td><td>81.1</td><td>86.3</td><td>92.4</td><td>90.2</td><td>84.6</td></tr><tr><td colspan=\"10\">Supervised task-dependent training-No transfer learning</td></tr><tr><td>NB-SVM</td><td>-</td><td></td><td></td><td></td><td></td><td>-</td><td>79.4</td><td>81.8</td><td>93.2</td><td>86.3</td><td>83.1</td></tr><tr><td>AdaSent</td><td>-</td><td>=</td><td></td><td></td><td></td><td>92.4</td><td>83.1</td><td>86.3</td><td>95.5</td><td>93.3</td><td>-</td></tr><tr><td>Tree-LSTM</td><td>、</td><td>0.8680</td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>■</td><td>-</td><td>-</td><td>■</td></tr><tr><td>TF-KLD</td><td>-</td><td>-</td><td></td><td></td><td>80.4/85.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2: Related Work and Comparison. As presented in the table, our designed asymmetric RNN-CNN model has strong transferability, and is overall better than existing unsupervised models in terms of fast training speed and good performance on evaluation tasks. The table presents the model comparison. “†”s refer to our models, and “small/large” refers to the dimension of representation as 1200/4800. “‡” indicates that DiscSent model was trained with additional data from Wikipedia and the Gutenberg project. Bold numbers are the best ones among the models with same training and transferring setting, and underlined numbers are best results among all unsupervised representation learning models. For STS14, the performance measures are Pearson’s and Spearman’s score. For MSRP, the performance measures are accuracy and F1 score. ",
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+    {
+        "type": "text",
+        "text": "Our model falls in the same category as it is an encoder-decoder model. However, we aim to propose an efficient and effective model. Instead of decoding the surrounding 2 sentences as in Skip-thought, FastSent and the compositional CNN-LSTM, our model only decodes the subsequent sequence with a fixed length. Compared with hierarchical CNN-LSTM, our model showed that, with a proper model design, this next-words context information is sufficient in learning sentence representations. Particularly, our proposed small RNN-CNN model runs roughly 3 times faster than our implemented Skip-thought model on the same GPU machine during training. ",
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+    {
+        "type": "text",
+        "text": "Another unsupervised approach is to learn a discriminative model by distinguishing whether a target sentence is in the context of the source sentence, and also the discourse information. DiscSent (Jernite et al., 2017) proposed to learn a classifier on top of the representations, which judges 1) whether the two sentences are adjacent to each other, 2) whether the two sentences are in the correct order, and 3) whether the second sentence starts with a conjunction phrase. DisSent (Nie et al., 2017) pointed out that human annotated explicit discourse relations is also good for learning sentence representations. It is a very promising research direction since the proposed models are generally computational efficient and have clear intuition. However, the performance on the downstream tasks is still worse than encoder-decoder models. ",
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+        "type": "text",
+        "text": "",
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+    },
+    {
+        "type": "text",
+        "text": "Proposed by Radford et al. (2017), BYTE m-LSTM model uses a multiplicative LSTM unit (Krause et al., 2016) to learn a language model on Amazon Review data McAuley et al. (2015). The model works reasonably well on the downstream tasks, since the RNNs are able to produce a distributed representation for the given left-context information, such as a sentence or a document. In our experiment, we also trained our RNN-CNN model on the Amazon Book review, which is the largest subset of the Amazon review dataset, and indeed, we had a performance gain on all single-sentence classification tasks. The performance gain in our experiment and also in BYTE m-LSTM was brought by the matching between the corpus domain and the domain of downstream tasks, and it raises 2 questions 1) which corpus is good for learning sentence representations, and 2) whether the downstream tasks are comprehensive to cover sufficient aspects of a sentence. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Previously mentioned models are learned from ordered sentences, but unordered sentences can also be used for learning representations of sentences. ParagraphVec (Le & Mikolov, 2014) learns a fixed-dimension vector for each sentence by predicting the words within the given sentence. However, after training, the representation for a new sentence is hard to derive, since it requires optimizing the sentence representation towards an objective. SDAE (Hill et al., 2016) learns the sentence representations with a denoising auto-encoder model. The noise was added in the encoder by replacing words with a fixed token, and swapping two words, both with a specific probability. Our proposed RNN-CNN model trains faster than SDAE does, since the CNN decoder runs faster than the RNN decoder in SDAE, and since we utilized the sentence-level continuity as a supervision which SDAE doesn’t, our model largely performs better than SDAE. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/011bf570ab2423c639160f917112468704f80f627b5c8037277e3a4f6e9c048f.jpg",
+        "table_caption": [
+            "Table 3: We implemented the same classifier as mentioned in Vendrov et al. (2015) on top of the features computed by our model. Our proposed RNN-CNN model gets similar result on SNLI as Skip-thought, but with much less training time. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>SNLI (Acc %)</td></tr><tr><td rowspan=1 colspan=2>Unsupervised TransferLearning</td></tr><tr><td rowspan=1 colspan=1>Skip-thought (Vendrov et al.)largeRNN-CNN BookCorpuslarge RNN-CNN Amazon</td><td rowspan=1 colspan=1>81.581.781.5</td></tr><tr><td rowspan=1 colspan=2>SupervisedTraining</td></tr><tr><td rowspan=1 colspan=1>ESIM (Chen et al.)DIIN (Gong et al.)</td><td rowspan=1 colspan=1>86.788.9</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Supervised transfer learning is also promising when we are able to get large enough labeled data. Conneau et al. (2017) applied a bi-directional LSTM as the sentence encoder with multiple fully-connected layers to deal with both SNLI (Bowman et al., 2015), and MultiNLI (Williams et al., 2017). The trained model demonstrates a very impressive transferability on all downstream tasks, including both supervised and unsupervised. The direct and discriminative training signal pushes the RNN encoder to focus on the semantics of a given sentence, which learns to a boost in performance, and beats all other methods. Our RNN-CNN model trained on Amazon Book Review data has better results on supervised classification tasks than BiLSTM-Max does, while the per",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "formance of ours on semantic relatedness tasks is inferior to BiLSTM-Max. We argue that labeling a large amount of training data is time-consuming and costly; unsupervised learning could potentially provide a great initial point for human labeling making it less costly and more efficient. ",
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+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Inspired by learning to exploit the contextual information present in adjacent sentences, we proposed an asymmetric encoder-decoder model with a suite of techniques for improving context-based unsupervised sentence representation learning. Since we believe that a simple model will be faster in training and easier to analyze, we opt to use simple techniques in our proposed model, including 1) an RNN as the encoder, and a predict-all-words CNN as the decoder, 2) learning by inferring next contiguous words, 3) mean+max pooling, and 4) tying word vectors with word prediction. With thorough discussion and extensive evaluation, we justify our decision making for each component in our RNN-CNN model. In terms of the performance and the efficiency of training, we justify that our model is a fast and simple algorithm for learning generic sentence representations from unlabeled corpora. Further research will focus on how to maximize the utility of the context information, and how to design simple architectures to best make use of it. ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            287,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Eneko Agirre, Carmen Banea, Claire Cardie, Daniel M. Cer, Mona T. Diab, Aitor Gonzalez-Agirre, Weiwei Guo, Rada Mihalcea, German Rigau, and Janyce Wiebe. Semeval-2014 task 10: Multilingual semantic textual similarity. In SemEval@COLING, 2014. ",
+        "bbox": [
+            174,
+            126,
+            825,
+            169
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Gerry Altmann and Jelena Mirkovic. Incrementality and prediction in human sentence processing. Cognitive science, 33 4:583–609, 2009. ",
+        "bbox": [
+            171,
+            178,
+            823,
+            205
+        ],
+        "page_idx": 8
+    },
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+    {
+        "type": "text",
+        "text": "SUPPLEMENTARY ",
+        "text_level": 1,
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+    {
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+    },
+    {
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0ae8ea607c049b42e52c738e216582595bf482622110ff1a56d1d68002bf50c3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Encoder</td><td colspan=\"2\">Decoder</td><td>Hrs</td><td>SICK-r SICK-E</td><td>STS14</td><td>MSRP (Acc/F1)</td><td>SST</td><td>TREC</td></tr><tr><td>type dim type</td><td colspan=\"8\">dim Dimension of Sentence Representation: 1200</td></tr><tr><td rowspan=\"5\">RNN 2x300</td><td>CNN</td><td>600-1200-300</td><td>20</td><td>0.8530 82.6</td><td>0.58/0.56</td><td>75.6/82.9</td><td>82.8</td><td>89.2</td></tr><tr><td>CNNt</td><td>600-1200-300</td><td>21</td><td>0.8515 82.7</td><td>0.58/0.56</td><td>75.3/82.5</td><td>82.9</td><td>85.2</td></tr><tr><td>CNN(10)</td><td>600-1200-300</td><td>11</td><td>0.8474 82.9</td><td>0.57/0.55</td><td>74.2/81.6</td><td>82.8</td><td>88.0</td></tr><tr><td>CNN(50)</td><td>600-1200-300</td><td>27</td><td>0.8533 82.5</td><td>0.57/0.55</td><td>74.7/82.2</td><td>81.5</td><td>86.2</td></tr><tr><td>RNN</td><td>600</td><td>26</td><td>0.8530 82.6</td><td>0.51/0.50</td><td>74.1/81.7</td><td></td><td></td></tr><tr><td>RNN2x300 CNN4x300S</td><td>CNN</td><td>600-1200-300</td><td>8</td><td>0.8117 80.5</td><td>0.44/0.42</td><td>72.7/80.7</td><td>81.0 78.4</td><td>89.0 85.0</td></tr><tr><td rowspan=\"2\">RNN 2x300</td><td>CNN</td><td>600-1200-2400-300</td><td>28</td><td>0.8570</td><td></td><td>74.3/81.5</td><td></td><td>88.2</td></tr><tr><td>CNN</td><td>1200-2400-300</td><td>27</td><td>84.0 0.8541 83.0</td><td>0.58/0.56 0.59/0.57</td><td>74.3/82.2</td><td>82.8 82.9</td><td>89.0</td></tr><tr><td colspan=\"9\">Dimension of Sentence Representation: 2400</td></tr><tr><td>RNN2x600</td><td>CNN</td><td>600-1200-300</td><td>25</td><td>0.8631 83.9</td><td></td><td>0.58/0.55</td><td>74.7/83.1</td><td>83.4 90.2</td></tr><tr><td>RNN2x600</td><td>RNN</td><td>600</td><td>32</td><td>0.8647</td><td>84.2</td><td>0.52/0.51</td><td>74.0/81.2 84.2</td><td>87.6</td></tr><tr><td>CNN3x800‡</td><td>RNN</td><td>600</td><td>8</td><td>0.8132</td><td></td><td>71.9/81.9</td><td>-</td><td>86.6</td></tr><tr><td colspan=\"9\">Dimension of Sentence Representation: 4800</td></tr><tr><td>RNN2x1200</td><td>CNN</td><td>600-1200-300</td><td>34 0.8698</td><td>85.2</td><td>0.59/0.57</td><td>75.1/83.2</td><td>84.1</td><td>92.2</td></tr><tr><td colspan=\"2\">Skip-thought (Kiros et al.,2015)</td><td>336</td><td>0.8584</td><td>82.3</td><td>0.29/0.35</td><td>73.0/82.0</td><td>82.0</td><td>92.2</td></tr><tr><td colspan=\"2\">Skip-thought+LN (Ba et al., 2016)</td><td></td><td>720 0.8580</td><td>79.5</td><td>0.44/0.45</td><td>-</td><td>82.9</td><td>88.4</td></tr></table>",
+        "bbox": [
+            176,
+            213,
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+            482
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Architecture Comparison. As shown in the table, our designed asymmetric RNN-CNN model (row 1,9, and 12) works better than other asymmetric models (CNN-LSTM, row 11), and models with symmetric structure (RNN-RNN, row 5 and 10). In addition, with larger encoder size, our model demonstrates stronger transferability. The default setting for our CNN decoder is that it learns to reconstruct 30 words right next to every input sentence. “CNN(10)” represents a CNN decoder with the length of outputs as 10, and “CNN(50)” represents it with the length of outputs as 50. “†” indicates that the CNN decoder learns to reconstruct next sentence. $^ { 6 6 } \\ddag ^ { 5 }$ indicates the results reported in Gan et al. as future predictor. The CNN encoder in our experiment, noted as “ $\\cdot \\ S ^ { \\ , }$ , was based on AdaSent in Zhao et al. and Conneau et al.. Bold numbers are best results among models at same dimension, and underlined numbers are best results among all models. For STS14, the performance measures are Pearson’s and Spearman’s score. For MSRP, the performance measures are accuracy and F1 score. ",
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parse/train/HkgrZ0EYwB/HkgrZ0EYwB.md

@@ -0,0 +1,346 @@
+# UNPAIRED POINT CLOUD COMPLETION ON REALSCANS USING ADVERSARIAL TRAINING
+
+Baoquan Chen Peking University
+
+Xuelin Chen Shandong University University College London
+
+Niloy J. Mitra University College London Adobe Research London
+
+# ABSTRACT
+
+As 3D scanning solutions become increasingly popular, several deep learning setups have been developed for the task of scan completion, i.e., plausibly filling in regions that were missed in the raw scans. These methods, however, largely rely on supervision in the form of paired training data, i.e., partial scans with corresponding desired completed scans. While these methods have been successfully demonstrated on synthetic data, the approaches cannot be directly used on real scans in the absence of suitable paired training data. We develop a first approach that works directly on input point clouds, does not require paired training data, and hence can directly be applied to real scans for scan completion. We evaluate the approach qualitatively on several real-world datasets (ScanNet, Matterport3D, KITTI), quantitatively on 3D-EPN shape completion dataset, and demonstrate realistic completions under varying levels of incompleteness.
+
+# 1 INTRODUCTION
+
+Robust, efficient, and scalable solutions now exist for easily scanning large environments and workspaces (Dai et al., 2017a; Chang et al., 2017). The resultant scans, however, are often partial and have to be completed (i.e., missing parts have to be hallucinated and filled in) before they can be used in downstream applications, e.g., virtual walk-through, path planning.
+
+The most popular data-driven scan completion methods rely on paired supervision data, i.e., for each incomplete training scan, a corresponding complete data (e.g., voxels, point sets, signed distance fields) is required. One way to establish such a shape completion network is then to train a suitably designed encoder-decoder architecture (Dai et al., 2017b; 2018). The required paired training data is obtained by virtually scanning 3D objects (e.g., SunCG Song et al. (2017), ShapeNet Chang et al. (2015) datasets) to simulate occlusion effects. Such approaches, however, are unsuited for real scans where large volumes of paired supervision data remain difficult to collect. Additionally, when data distributions from virtual scans do not match those from real scans, completion networks trained on synthetic-partial and synthetic-complete data do not sufficiently generalize to real (partial) scans. To the best of our knowledge, no point-based unpaired method exists that learns to translate noisy and incomplete point cloud from raw scans to clean and complete point sets.
+
+We propose an unpaired point-based scan completion method that can be trained without requiring explicit correspondence between partial point sets (e.g., raw scans) and example complete shape models (e.g., synthetic models). Note that the network does not require explicit examples of real complete scans and hence existing (unpaired) large-scale real 3D scan (e.g., Dai et al. (2017a); Chang et al. (2017)) and virtual 3D object repositories (e.g., Song et al. (2017); Chang et al. (2015)) can directly be leveraged as training data. Figure 1 shows example scan completions. As we show in Table 1, unlike methods requiring paired supervision, our method continues to perform well even if the data distributions of synthetic complete scans and real partial scans differ.
+
+We achieve this by designing a generative adversarial network (GAN) wherein a generator, i.e., an adaptation network, transforms the input into a suitable latent representation such that a discriminator cannot differentiate between the transformed latent variables and the latent variables obtained from training data (i.e., complete shape models). Intuitively, the generator is responsible for the key task of mapping raw partial point sets into clean and complete point sets, and the process is regularized by working in two different latent spaces that have separately learned manifolds of scanned and synthetic object data.
+
+![](images/b798dfe863c4b31af9919bc8ab17c25ed320f44084e0af8ef061c3bf2deb9eb6.jpg)  
+Figure 1: We present a point-based shape completion network that can be directly used on raw scans without requiring paired training data. Here we show a sampling of results from the ScanNet, Matterport3D, 3D-EPN, and KITTI datasets.
+
+We demonstrate our method on several publicly available real-world scan datasets namely (i) ScanNet (Dai et al., 2017a) chairs and tables; (ii) Matterport3D (Chang et al., 2017) chairs and tables; and (iii) KITTI (Geiger et al., 2012) cars. In absence of completion ground truth, we cannot directly compute accuracy for the completed scans, and instead compare using plausibility scores. Further, in order to quantitatively evaluate the performance of the network, we report numbers on a synthetic dataset (Dai et al., 2017b) where completed versions are available. Finally, we compare our method against baseline methods to demonstrate the advantages of the proposed unpaired scan completion framework.
+
+# 2 RELATED WORK
+
+Shape Completion. Many deep neural networks have been proposed to address the shape completion challenge. Inspired by CNN-based 2D image completion networks, 3D convolutional neural networks applied on voxelized inputs have been widely adopted for 3D shape completion task (Dai et al., 2018; 2017b; Sharma et al., 2016; Han et al., 2017; Thanh Nguyen et al., 2016; Yang et al., 2018; Wang et al., 2017). As quantizing shapes to voxel grids lead to geometric information loss, recent approaches (Yuan et al., 2018; Yu et al., 2018b; Achlioptas et al., 2018) operate directly on point sets to fill in missing parts. These works, however, require supervision in the form of partialcomplete paired data for training deep neural networks to directly regress partial input to their ground truth counterparts. Since paired ground truth of real-world data is rarely available such training data is generated using virtual scanning. While the methods work well on synthetic test data, they do not generalize easily to real scans arising from hard-to-model acquisition processes.
+
+Realizing the gap between synthetically-generated data and real-world data, Stutz & Geiger (2018) proposed to directly work on voxelized real-world data. They also work in a latent space created for clean and complete data but measure reconstruction loss using a maximum likelihood estimator. Instead, we propose a GAN setup to learn a mapping between latent spaces respectively arising from partial real and synthetic complete data. Further, by measuring loss using Hausdorff distance on point clouds, we directly work with point sets instead of voxelized input.
+
+Generative Adversarial Network. Since its introduction, GAN (Goodfellow et al., 2014) has been used for a variety of generative tasks. In 2D image domain, researchers have utilized adversarial training to recover richer information from low-resolution images or corrupted images (Ledig et al., 2017; Wang et al., 2018; Mao et al., 2017; Park et al., 2018; Bulat et al., 2018; Yeh et al., 2017; Iizuka et al., 2017). In 3D context, Yang et al. (2018); Wang et al. (2017) combine 3D-CNN and generative adversarial training to complete shapes under the supervision of ground truth data. Gurumurthy & Agrawal (2019) treats the point cloud completion task as denoising AE problem, utilizing adversarial training to optimize on the AE latent space. We also leverage the power of GAN for reasoning the missing part of partial point cloud scanning. However, our method is designed to work with unpaired data, and thus can directly be applied to real-world scans even when real-world and synthetic data distributions differ. Intuitively, our GAN-based approach directly learns a translation mapping between these two different distributions.
+
+Deep Learning on Point clouds. Our method is built upon recent advances in deep neural networks for point clouds. PointNet Qi et al. (2017a), the pioneering work on this topic, takes an input point set through point-wise MLP layers followed by a symmetric and permutation-invariant function to produce a compact global feature, which can then be used for a diverse set of tasks (e.g., classification, segmentation). Although many improvements to PointNet have been proposed (Su et al., 2018; Li et al., 2018b; Qi et al., 2017b; Li et al., 2018a; Zaheer et al., 2017), the simplicity and effectiveness of PointNet and its extension PointNet++ make them popular for many other analysis tasks (Yu et al., 2018a; Yin et al., 2018; Yu et al., 2018b; Guerrero et al., 2018).
+
+![](images/b06c0dd4315e9a53fd65c76c3f940ba8478a2e039703561a061a1c19565099b5.jpg)  
+Figure 2: Unpaired Scan Completion Network.
+
+In the context of synthesis, Achlioptas et al. (2018) proposed an autoencoder network, using a PointNet-based backbone, to learn compact representations of point clouds. By working in a reduced latent space produced by the autoencoder, they report significant advantages in training GANs, instead of having a generator producing raw point clouds. Inspired by this work, we design a GAN to translate between two different latent spaces to perform unpaired shape completion on real scans.
+
+# 3 METHOD
+
+Given a noisy and partial point set ${ \cal { S } } = \{ { \bf { s } } _ { i } \}$ as input, our goal is to produce a clean and complete point set $\mathcal { R } = \left\{ \mathbf { r } _ { i } \right\}$ as output. Note that although the two sets have the same number of points, there is no explicit correspondence between the sets $s$ and $\mathcal { R }$ . Further, we assume access to clean and complete point sets for shapes for the object classes. We achieve unpaired completion by learning two class-specific point set manifolds, $\mathbb { X } _ { r }$ for the scanned inputs, and $\mathbb { X } _ { c }$ for clean and complete shapes. Solving the shape completion problem then amounts to learning a mapping $\mathbb { X } _ { r } \ \to \ \mathbb { X } _ { c }$ between the respective latent spaces. We train a generator $G _ { \theta } : \mathbb { X } _ { r }  \mathbb { X } _ { c }$ to perform the mapping. Note that we do not require the noise characteristics in the two data distributions, i.e., real and synthetic, to be the same. In absence of paired training data, we score the generated output by setting up a min-max game where the generator is trained to fool a discriminator $F _ { \chi }$ , whose goal is to differentiate between encoded clean and complete shapes, and mapped encodings of the raw and partial inputs. Figure 2 shows the setup of the proposed scan completion network. The latent space encoder-decoders, the mapping generator, and the discriminator are all trained as detailed next.
+
+# 3.1 LEARNING LATENT SPACES FOR POINT SETS
+
+The latent space of a given set of point sets is obtained by training an autoencoder, which encodes the given input to a low-dimension latent feature and then decodes to reconstruct the original input. We work directly on the point sets via these learned latent spaces instead of quantizing them to voxel grids or signed distance fields.
+
+For point sets coming from the clean and complete point sets $\mathcal { P }$ , we learn an encoder network $E _ { \eta } ^ { c }$ that maps $\mathcal { P }$ from the original parameter space $ { \mathbb { R } } ^ { 3 N }$ , defined by concatenating the coordinates of the $N$ (2048 in all our experiments) points, to a lower-dimensional latent space $\mathbb { X } _ { c }$ . A decoder network $D _ { \phi } ^ { c }$ performs the inverse transformation back to $\mathbb { R } ^ { 3 N }$ giving us a reconstructed point set $\tilde { \mathcal P }$ with also $N$ points. The encoder-decoders are trained with reconstruction loss,
+
+$$
+\mathcal { L } ^ { \mathrm { E M D } } ( \eta , \phi ) = \mathbb { E } _ { \mathcal { P } \sim p _ { \mathrm { c o m p l e t e } } } d ( \mathcal { P } , D _ { \phi } ^ { c } ( E _ { \eta } ^ { c } ( \mathcal { P } ) ) ) ,
+$$
+
+where $\mathcal { P } \sim p _ { \mathrm { c o m p l e t e } }$ denotes point set samples drawn from the set of clean and complete point sets, $d ( X _ { 1 } , X _ { 2 } )$ is the Earth Mover’s Distance (EMD) between point sets $X _ { 1 } , X _ { 2 }$ , and $( \eta , \phi )$ are the learnable parameters of the encoder and decoder networks, respectively. Once trained, the weights of both networks are held fixed and the latent code $z = E _ { \eta } ^ { c } ( X )$ , $z \in \mathbb { X } _ { c }$ for a clean and complete point set $X$ provides a compact representation for subsequent training and implicitly captures the manifold of clean and complete data. The architecture of the encoder and decoder is similar to Achlioptas et al. (2018); Qi et al. (2017a): using a 5-layer MLP to lift individual points to a deeper feature space, followed by a symmetric function to maintain permutation invariance. This results in a $k$ - dimensional latent code that describes the entire point cloud $k { = } 1 2 8$ in all our experiments). More details of the network architecture can be found in the appendix.
+
+![](images/a76e1d446bf1a95f80f9b50f239746dfb5d700d14c2ee61c6b0aac125722e6f1.jpg)  
+Figure 3: Effect of unpaired scan completion without (Equation 5) and with HL term (Equation 6). Without the HL term, the network produces a clean point set for a complete chair, that is different in shape from the input. With the HL term, the network produces a clean point set that matches the input.
+
+As for the point set coming from the noisy-partial point sets $s$ , one can also train another encoder $E _ { \gamma } ^ { r } : \mathcal { S }  \mathbb { X } _ { r }$ and decoder $D _ { \psi } ^ { r } : \mathbb { X } _ { r }  \tilde { \mathcal { S } }$ pair that provides a latent parameterization $\mathbb { X } _ { r }$ for the noisy-partial point sets, with the definition of the reconstruction loss as,
+
+$$
+\begin{array} { r } { \mathcal { L } ^ { \mathrm { E M D } } ( \gamma , \psi ) = \mathbb { E } _ { S \sim p _ { \mathrm { r a w } } } d ( S , D _ { \psi } ^ { r } ( E _ { \gamma } ^ { r } ( S ) ) ) , } \end{array}
+$$
+
+where ${ \mathcal { S } } \sim p _ { \mathrm { r a w } }$ denotes point set samples drawn from the set of noisy and partial point sets.
+
+Although, in experiments, the latent space of this autoencoder trained on noisy-partial point sets works considerably well as the noisy-partial point set manifold, we found that using the latent space produced by feeding noisy-partial point sets to the autoencoder trained on clean and complete point sets yields slightly better results. Hence, unless specified, we set $\gamma = \eta$ and $\psi = \phi$ in our experiments. The comparison of different choices to obtain the latent space for noisy-partial point sets is also presented in Section 4. Next, we will describe the GAN setup to learn a mapping between the latent spaces of raw noisy-partial and synthetic clean-complete point sets, i.e., $\mathbb { X } _ { r } \to \mathbb { X } _ { c }$ .
+
+# 3.2 LEARNING A MAPPING BETWEEN LATENT SPACES
+
+We set up a min-max game between a generator and a discriminator to perform the mapping between the latent spaces. The generator $G _ { \theta }$ is trained to perform the mapping $\mathbb { X } _ { r } \ \to \ \mathbb { X } _ { c }$ such that the discriminator fails to reliably tell if the latent variable comes from original $\mathbb { X } _ { c }$ or the remapped $\mathbb { X } _ { r }$ .
+
+The latent representation of a noisy and partial scan $z _ { r } = E _ { \gamma } ^ { r } ( S )$ is mapped by the generator to $\tilde { z } _ { c } = G _ { \theta } ( z _ { r } )$ . Then, the task of the discriminator $F _ { \chi }$ is to distinguish between latent representations $\tilde { z } _ { c }$ and $z _ { c } = E _ { \eta } ^ { c } ( \mathcal { P } )$ . We train the mapping function using a GAN. Given training examples of clean latent variables $z _ { c }$ and remapped-noisy latent variables $\tilde { z } _ { c }$ , we seek to optimize the following adversarial loss over the mapping generator $G _ { \theta }$ and a discriminator $F _ { \chi }$ ,
+
+$$
+\operatorname* { m i n } _ { \theta } \operatorname* { m a x } _ { \chi } \mathbb { E } _ { \boldsymbol { x } \sim p _ { \mathrm { c l e a n - c o n p l e t } } } \left[ \log \left( F _ { \chi } \big ( E _ { \eta } ^ { c } ( x ) \big ) \right) \right] + \mathbb { E } _ { \boldsymbol { y } \sim p _ { \mathrm { m i s p - r a t i a } } } \left[ \log \left( 1 - F _ { \chi } \big ( G _ { \theta } \big ( E _ { \gamma } ^ { r } ( y ) \big ) \right) \right] .
+$$
+
+In our experiments, we found the least square GAN Mao et al. (2016) to be easier to train and hence minimize both the discriminator and generator losses defined as,
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { F } ( \chi ) \ : = \ : \mathbb { E } _ { x \sim p _ { \mathrm { c l e a n - o m p l e t } } } \left[ F _ { \chi } \big ( E _ { \eta } ^ { c } ( x ) \big ) - 1 \right] ^ { 2 } + \mathbb { E } _ { y \sim p _ { \mathrm { n o i s y p a r i a } } } \big [ F _ { \chi } \big ( G _ { \theta } ( E _ { \gamma } ^ { r } ( y ) ) \big ) \big ] ^ { 2 } } \\ & { \mathcal { L } _ { G } ( \theta ) \ : = \mathbb { E } _ { y \sim p _ { \mathrm { n o i s y p a r i a } } } \big [ F _ { \chi } \big ( G _ { \theta } ( E _ { \gamma } ^ { r } ( y ) ) \big ) - 1 \big ] ^ { 2 } . } \end{array}
+$$
+
+The above setup encourages the generator to perform the mapping $\mathbb { X } _ { r } \to \mathbb { X } _ { c }$ resulting in $D _ { \psi } ^ { c } ( \tilde { z _ { c } } )$ to be a clean and complete point cloud $\mathcal { R }$ . However, the generator is free to map a noisy latent vector to any point on the manifold of valid shapes in $\mathbb { X } _ { c }$ , including shapes that are far from the original partial scan $s$ . As shown in Figure 3, the result is a complete and clean point cloud that can be dissimilar in shape to the partial scanned input. To prevent this, we add a reconstruction loss term $\scriptstyle { \mathcal { L } } _ { \mathrm { r e c o n } }$ to the generator loss:
+
+$$
+\mathcal { L } _ { G } ( \theta ) = \alpha \mathbb { E } _ { y \sim p _ { \mathrm { n o s y \mathrm { s t i a } } } } \big [ F _ { \chi } \big ( G _ { \theta } ( E _ { \gamma } ^ { r } ( y ) ) \big ) - 1 \big ] ^ { 2 } + \beta \mathcal { L } _ { \mathrm { r e c o n } } ^ { \mathrm { H L } } ( \mathcal { S } , D _ { \psi } ^ { c } ( G _ { \theta } ( E _ { \gamma } ^ { r } ( \mathcal { S } ) ) ) ) ,
+$$
+
+where $\mathcal { L } _ { \mathrm { r e c o n } } ^ { \mathrm { H L } }$ denotes the Hausdorff distance loss 1 (HL) from the partial input point set to the completion point set, which encourages the predicted completion point set to match the input only partially. Note that, it is crucial to use $\mathrm { H L }$ as $\scriptstyle { \mathcal { L } } _ { \mathrm { r e c o n } }$ , since the partial input can only provide partial supervision when no ground truth complete point set is available. In contrast, using EMD as $\scriptstyle { \mathcal { L } } _ { \mathrm { r e c o n } }$ forces the network to reconstruct the overall partial input leading to worse completion results. The comparison of these design choices is presented in Section 4. Unless specified, we set the trade-off parameters as $\alpha = 0 . 2 5$ and $\beta = 0 . 7 5$ in all our experiments.
+
+# 4 EXPERIMENTAL EVALUATION
+
+We present quantitative and qualitative experimental results on several noisy and partial datasets. First, we present results on real-world datasets, demonstrating the effectiveness of our method on unpaired raw scans. Second, we thoroughly compare our method to various baseline methods on 3D-EPN dataset, which contains simulated partial scans and corresponding ground truth for full evaluation. Finally, we derive a synthetic noisy-partial scan dataset based on ShapeNet, on which we can evaluate the performance degradation of applying supervised methods to test data of different distribution and the performance of our method under varying levels of incompleteness. A set of ablation studies is also included to evaluate our design choices.
+
+Datasets. (A) Real-world dataset comes from three sources. First, a dataset of ${ \sim } 5 5 0 $ chairs and ${ \sim } 5 5 0 $ tables extracted from the ScanNet dataset split into $90 \%$ - $10 \%$ train-test sets. Second, a dataset of 20 chairs and 20 tables extracted from the Matterport3D dataset. Note that we train our method only on the ScanNet training split, and use the trained model to test on the Matterport3D data to evaluate generalization to new data sources. Third, a dataset containing cars from the KITTI Velodyne point clouds. (B) 3D-EPN dataset provides simulated partial scans with corresponding ground truth. Scans are represented as Signed Distance Field (SDF). We only use the provided point cloud representations of the training data, instead of using the SDF data which holds richer information. $( C )$ Clean and complete point set dataset contains virtually scanned point sets of ShapeNet models covering 8 categories, namely boat, car, chair, dresser, lamp, plane, sofa, and table. We use this dataset for learning the clean-complete point set manifold in all our experiments. $( D )$ Synthetic dataset provides different incomplete scan distribution and at different levels of incompleteness. Ground truth complete scan counterparts are available for evaluation.
+
+Evaluation measures. We assess completion quality using the following measures. (A) Accuracy measures the fraction of points in $P _ { c o m p }$ that are matched by $P _ { g t }$ , where and $P _ { c o m p }$ denote the completion point set and $P _ { g t }$ denote the ground truth point set. Specifically, for each point $v \in P _ { c o m p }$ , we compute $D ( v , P _ { g t } { \ ' } ) { ' } = m i n \{ \| \ \bar { v } - q \ \| , q \in \operatorname { \bar { P } } _ { g t } \}$ . If $\bar { D } ( v , P _ { g t } )$ is within distance threshold $\epsilon = 0 . 0 3$ , we count it as a correct match. The fraction of matched points is reported as the accuracy in percentage. $( B )$ Completeness reports the fraction of points in $P _ { g t }$ that are within distance threshold $\epsilon$ of any point in $P _ { c o m p }$ . $( C ) F I$ score is defined as the harmonic average of the accuracy and the completeness, where F1 reaches its best value at 1 (perfect accuracy and completeness) and worst at 0. $( D )$ Plausibility of the completion is evaluated as the classification accuracy in percentage produced by PointNet++, a SOA point-based classification network. To avoid bias on ShapeNet point clouds, we trained the classification network on the ModelNet40 dataset. We mainly used plausibility score for real-world data completions, where no ground truth data is available for calculating accuracy, completeness, or F1 scores.
+
+In the following, we show all experimental and evaluation results. We trained separate networks for each category. More details are in the appendix.
+
+# 4.1 EXPERIMENTAL RESULTS ON REAL-WORLD DATA
+
+Our method works directly on real-world data where no paired data is available. We train and test our network on noisy-partial chairs and tables extracted from the ScanNet dataset. We further test the network trained on ScanNet dataset on chairs and tables extracted from the Matterport3D dataset, to show how well our network can generalize to definitely unseen data. We present qualitative results of our method in Fig 4. Our method consistently produces plausible completions for the ScanNet and Matterport3D data.
+
+![](images/3b46984f15810a2c412bf127b9da09e242357693a3ee480279e9baab4f8a79c4.jpg)  
+Figure 4: Qualitative comparisons on real-world data, which includes partial scans of ScanNet chairs and tables, Matterport3D chairs and tables, and KITTI cars. We show the partial input in grey and the corresponding completion in gold on the right.
+
+In the absence of ground truth completions on real data, we compare our method quantitatively against others based on the plausibility of the results. The left sub-table of Table 1 shows that our method is superior to those supervised methods, namely 3D-EPN and PCN. Directly applying PCN trained on simulated partial data to real-world data leads to completions that have low plausibility, while our method consistently produces results with high plausibility. 3D-EPN trained on simulated partial data failed to complete the real-world partial scans. In Section 4.2 and Section 4.3, we present more in-depth comparisons on 3D-EPN and our synthetic dataset, where the ground truth is available for computing accuracy, completeness, and F1 of the completions.
+
+Table 1: Completion plausibility on synthetic scans and real-world scans and effects of data distribution discrepancy. (Left) Plausibility comparison on synthetic scans and real-world scans. Synthetic scans includes test data from 3D-EPN, real-world scans includes ScanNet and Matterport3D test data. 3D-EPN failed to produce good completions on real-world data. (Right) On our synthetic data, supervised methods trained on other simulated partial scans produce worse results on partial scans with different data distribution.
+
+<table><tr><td></td><td></td><td>Raw input</td><td>3D-EPN</td><td>PCN</td><td>Ours</td></tr><tr><td rowspan="2">Synthetic</td><td>chair</td><td>73.1</td><td>77.3</td><td>85.0</td><td>91.5</td></tr><tr><td>table</td><td>52.5</td><td>71.2</td><td>72.0</td><td>80.6</td></tr><tr><td rowspan="2">Real-world</td><td>chair</td><td>71.4</td><td>7.1</td><td>78.6</td><td>94.3</td></tr><tr><td>table</td><td>47.8</td><td>4.4</td><td>69.6</td><td>81.2</td></tr></table>
+
+<table><tr><td></td><td colspan="3">3D-EPN</td><td colspan="3">PCN</td><td colspan="3">Ours</td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>chair</td><td>39.6</td><td>61.8</td><td>48.2</td><td>49.3</td><td>76.0</td><td>59.8</td><td>80.7</td><td>80.8</td><td>80.8</td></tr><tr><td>car</td><td>43.8</td><td>62.3</td><td>51.4</td><td>63.2</td><td>81.4</td><td>71.2</td><td>82.6</td><td>80.7</td><td>81.7</td></tr><tr><td>table</td><td>36.6</td><td>61.0</td><td>45.8</td><td>62.3</td><td>80.6</td><td>70.3</td><td>83.1</td><td>84.5</td><td>83.8</td></tr><tr><td>plane</td><td>17.1</td><td>57.6</td><td>26.3</td><td>67.1</td><td>85.4</td><td>75.1</td><td>94.4</td><td>92.7</td><td>93.6</td></tr></table>
+
+Completing the car observations from KITTI is extremely challenging, as each car instance only receives few data points from the Lidar scanner. Fig 4 shows the qualitative results of our method on completing sparse point sets of KITTI cars, we can see that our network can still generate highly plausible cars with such sparse inputs.
+
+We also use a point-based object part segmentation network (Qi et al., 2017b) to indirectly evaluate our completions of real-world data. Due to the absence of ground truth segmentation, we calculate the approximate segmentation accuracy for each completion. Specifically, for the completion of a chair, we count the predicted segmentation label of each point to be correct as long as the predicted label falls into the set of 4 parts (i.e., seat, back, leg, and armrest) of chair class. Our completion results have much higher approximate segmentation accuracy compared to the real-world raw input (chair: $7 7 . 2 \%$ vs. $2 4 . 8 \%$ ; table: $9 6 . 4 \%$ vs. $8 3 . 5 \%$ ; and car: $9 8 . 0 \%$ vs. $5 . 2 \%$ , as segmentation accuracy on our completions versus on original partial input), indicating high completion quality.
+
+# 4.2 COMPARISON WITH BASELINES ON 3D-EPN DATA
+
+We compare our method to several baseline methods and present both quantitative and qualitative comparisons on the 3D-EPN test set:
+
+• Autoencoder (AE), which is trained only with clean and complete point sets. • 3D-EPN (Dai et al., 2017b), a supervised method that requires SDF input and is trained with paired data. We convert its Distance Field representation results into surface meshes, from which we can uniformly sample $N$ points for calculating our point-based measures.
+
+Table 2: Comparison with baselines on the 3D-EPN dataset. Note that 3D-EPN and PCN require paired supervision data, while ours does not. Ours outperforms 3D-EPN and achieves comparable results to PCN. Furthermore, after adapted to leverage the ground truth data as well, our method achieves similar performance to PCN.   
+
+<table><tr><td>一</td><td></td><td>AE</td><td></td><td></td><td>EPN (fully supervised)</td><td></td><td>PCN (fully supervised)</td><td></td><td></td><td></td><td>Ours (unsupervised)</td><td></td><td></td><td>Ours+ (supervised)</td><td></td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>boat</td><td>89.6</td><td>81.4</td><td>85.3</td><td>82.4</td><td>81.4</td><td>81.9</td><td>92.6</td><td>93.4</td><td>93.0</td><td>86.6</td><td>84.7</td><td>85.6</td><td>89.8</td><td>92.0</td><td>90.9</td></tr><tr><td>car</td><td>81.3</td><td>71.1</td><td>75.9</td><td>69.8</td><td>81.7</td><td>75.3</td><td>97.3</td><td>96.1</td><td>96.7</td><td>88.9</td><td>87.6</td><td>88.2</td><td>93.5</td><td>92.8</td><td>93.1</td></tr><tr><td>chair</td><td>79.9</td><td>68.5</td><td>73.8</td><td>61.7</td><td>76.9</td><td>68.5</td><td>91.1</td><td>90.6</td><td>90.9</td><td>78.7</td><td>77.4</td><td>78.0</td><td>82.3</td><td>83.3</td><td>82.8</td></tr><tr><td>dresser</td><td>68.9</td><td>64.2</td><td>66.5</td><td>58.4</td><td>72.7</td><td>64.8</td><td>93.5</td><td>91.5</td><td>92.5</td><td>75.8</td><td>76.5</td><td>76.2</td><td>87.4</td><td>91.5</td><td>89.4</td></tr><tr><td>lamp</td><td>75.9</td><td>79.6</td><td>77.7</td><td>60.8</td><td>67.8</td><td>64.1</td><td>82.9</td><td>88.3</td><td>85.5</td><td>71.3</td><td>80.2</td><td>75.5</td><td>76.6</td><td>86.3</td><td>81.2</td></tr><tr><td>plane</td><td>97.6</td><td>95.1</td><td>96.3</td><td>78.1</td><td>93.5</td><td>85.1</td><td>98.3</td><td>98.2</td><td>98.2</td><td>97.2</td><td>95.9</td><td>96.5</td><td>95.6</td><td>94.8</td><td>95.2</td></tr><tr><td>sofa</td><td>80.3</td><td>64.0</td><td>71.2</td><td>65.0</td><td>72.6</td><td>68.6</td><td>91.5</td><td>90.8</td><td>91.1</td><td>68.2</td><td>72.3</td><td>70.2</td><td>81.0</td><td>87.0</td><td>83.9</td></tr><tr><td>table</td><td>82.8</td><td>72.5</td><td>77.3</td><td>56.8</td><td>75.1</td><td>64.7</td><td>93.4</td><td>89.2</td><td>91.2</td><td>82.2</td><td>77.8</td><td>80.0</td><td>81.2</td><td>81.4</td><td>81.3</td></tr></table>
+
+• PCN (Yuan et al., 2018), which completes partial inputs in a hierarchical manner, receiving supervision from both sparse and dense ground truth point clouds.
+
+• ${ \mathrm { O u r s } } +$ , which is an adaption of our method for training with paired data, to show that our method can be easily adapted to work with ground truth data, improving the completion. Specifically, we set $\alpha = 0$ and use EMD loss as $L _ { r e c o n }$ . More details and discussion about adapting our method to train with paired data can be found in the appendix.
+
+Table 2 shows quantitative results on 3D-EPN test split and summarizes the comparisons: although our network is only trained with unpaired data, our method outperforms 3D-EPN method and achieves comparable results to PCN. Note that both 3D-EPN and PCN require paired data. Furthermore, after adapting our method to be supervised by the ground truth, the performance of our method $( \mathrm { O u r s } { + } )$ improves, achieving similar performance to PCN. Note that a simple autoencoder network trained with only clean-complete data can produce quantitatively good results, especially when the input is rather complete. Thus, we also evaluate the performance of AE on our synthetic data with incompleteness control in Section 4.3, to show that AE performance declines dramatically as the incompleteness of the input increases. Additional comparisons are included in the appendix.
+
+# 4.3 EFFECT OF DATA DISTRIBUTION DISCREPANCY AND VARYING INCOMPLETENESS
+
+Supervised methods assume that simulated partial scans share the same data distribution as the test data. We conduct quantitative experiments to show that applying 3D-EPN and PCN to our synthetic data, which is of different data distribution to its training data and in which the ground truth complete scans are not available for training, lead to performance degradation. The right sub-table of Table 1 shows that our method continues to produce good completions on our synthetic data, as we do not require paired data for training. The visual comparison is presented in the appendix.
+
+To evaluate our method under different levels of input incompleteness, we conduct experiments on our synthetic data, in which we can control the fraction of missing points. Specifically, we train our network with varying levels of incompleteness by randomizing the amount of missing points during training, and afterwards fix the amount of missing points for testing. Table 3 shows the performance of our method on different classes under increasing amount of incompleteness and the comparison to AE. We can see that AE performance declines dramatically as the incompleteness of the input increases, while our method can still produce completions with high plausibility and F1 score.
+
+Table 3: Effect of varying incompleteness. Performance of AE and ours with increasing incompleteness $\%$ of the missing points). Our completions remain robust even with increasing incompleteness as our method restricts the completion via the learned latent shape manifolds.   
+
+<table><tr><td></td><td></td><td colspan="2">Plausibility</td><td colspan="2"></td><td colspan="2"></td><td colspan="2">Plausibility</td><td colspan="2">F1</td><td colspan="2">Plausibility</td><td colspan="2">F1</td><td colspan="2"></td><td colspan="2">Plausibility</td><td colspan="2">F1</td></tr><tr><td>incomp.</td><td>model</td><td>AE</td><td>Ours</td><td>AE</td><td>Ours</td><td>model</td><td></td><td>AE</td><td>Ours</td><td>AE Ours</td><td>model</td><td></td><td>AE</td><td>Ours</td><td>AE</td><td>Ours</td><td>model</td><td>AE</td><td>Ours AE</td><td>Ours</td></tr><tr><td>10</td><td></td><td>96.3</td><td>99.4</td><td>94.9</td><td>85.8</td><td></td><td>88.0</td><td>91.0</td><td>88.4</td><td>87.7</td><td></td><td>69.3</td><td>74.0</td><td>90.0</td><td>90.2</td><td></td><td>88.9</td><td>91.0</td><td>96.6</td><td>96.5</td></tr><tr><td>20</td><td></td><td>96.7</td><td>99.7</td><td>89.5</td><td>84.5</td><td></td><td>81.0</td><td>91.0</td><td>87.2</td><td>85.1</td><td></td><td>65.0</td><td>75.5</td><td>85.0</td><td>87.3</td><td></td><td>89.7</td><td>90.7</td><td>94.0</td><td>95.5</td></tr><tr><td>30</td><td></td><td>95.0</td><td>98.2</td><td>81.8</td><td>83.3</td><td></td><td>67.0</td><td>90.9</td><td>70.8</td><td>80.7</td><td>table</td><td>55.2</td><td>73.4</td><td>77.3</td><td>84.0</td><td></td><td>88.7</td><td>90.7</td><td>89.5</td><td>94.1</td></tr><tr><td>40</td><td>car</td><td>85.4</td><td>96.1</td><td>71.8</td><td>79.7</td><td>chair</td><td>44.0</td><td>89.4</td><td>52.5</td><td>76.9</td><td></td><td>45.1</td><td>71.8</td><td>69.6</td><td>80.1</td><td>plane</td><td>85.0</td><td>89.0</td><td>84.9</td><td>92.8</td></tr><tr><td>50</td><td></td><td>58.6</td><td>96.4</td><td>63.4</td><td>72.5</td><td></td><td>38.0</td><td>83.5</td><td>33.5</td><td>71.8</td><td></td><td>32.5</td><td>73.3</td><td>62.1</td><td>74.5</td><td></td><td>80.0</td><td>90.7</td><td>80.6</td><td>91.0</td></tr></table>
+
+# 4.4 DIVERSITY OF THE COMPLETION RESULTS
+
+Our network is encouraged to partially match the input, alleviating the mode-collapse issue, which often occurs in GAN. Unlike traditional generative model problem, where high diversity in generated results is always better, the diversity in our completion results should match that of the ground truth. Although this can be qualitatively accessed, see Fig. 5 in Appendix, in order to quantitatively quantify the divergence, we compute the Jensen-Shannon Divergence (JSD) between the marginal distribution of ground truth point sets and that of our completions as proposed in Achlioptas et al. (2018). As a reference, we simulate extremely mode-collapsed point cloud sets by repeating a randomly selected point cloud, then report the JSD between ground truth point sets and the simulated extremely mode-collapsed point sets. The JSD scores – lower is better – highlight the diversity of our 3D-EPN completions and the divergence between our diversity and that of the ground truth using the extreme mode-collapse results as reference (the former is ours): 0.06 vs. 0.46 on cars, $0 . 0 5 ~ \nu s$ . 0.61 on chairs, 0.04 vs. 0.53 on planes and 0.04 vs. 0.59 on tables.
+
+# 4.5 ABLATION STUDY
+
+• Ours with partial AE, uses encoder $E _ { \gamma } ^ { r }$ and decoder $D _ { \psi } ^ { r }$ that are trained to reconstruct partial point sets for the latent space of partial input.   
+• Ours with EMD loss, uses EMD as the reconstruction loss.   
+• Ours without GAN, “switch off” the GAN module by simply setting $\alpha = 0$ and $\beta = 1$ , to verify the effectiveness of using adversarial training in our network.   
+• Ours with reconstruction loss, removes the reconstruction loss term by simply setting $\alpha = 1$ and $\beta = 0$ , to verify the effectiveness of the reconstruction loss term in generator loss.
+
+Table 4 presents quantitative results for the ablation experiments, where we demonstrate the importance of various design choices and modules in our proposed network. We can see that our method has the best performance over all other variations.
+
+Table 4: Ablation study showing the importance of various design choices in our proposed network.   
+
+<table><tr><td></td><td colspan="3">Ours w/ partial AE</td><td colspan="3">Ours w/EMD</td><td colspan="3">Ours w/o GAN</td><td colspan="3">Ours w/o Recon.</td><td colspan="3">Ours</td></tr><tr><td></td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>boat</td><td>75.1</td><td>75.4</td><td>75.2</td><td>82.0</td><td>84.8</td><td>83.4</td><td>47.4</td><td>93.1</td><td>62.8</td><td>44.4</td><td>38.1</td><td>41.0</td><td>86.6</td><td>84.7</td><td>85.6</td></tr><tr><td>car</td><td>88.9</td><td>87.6</td><td>88.2</td><td>76.0</td><td>76.8</td><td>76.4</td><td>46.2</td><td>88.3</td><td>60.7</td><td>72.2</td><td>72.7</td><td>72.5</td><td>88.9</td><td>87.7</td><td>88.3</td></tr><tr><td>chair</td><td>64.1</td><td>66.7</td><td>65.4</td><td>78.6</td><td>76.4</td><td>77.5</td><td>41.3</td><td>79.8</td><td>54.4</td><td>75.6</td><td>75.1</td><td>75.3</td><td>78.7</td><td>77.4</td><td>78.0</td></tr><tr><td>dresser</td><td>67.4</td><td>68.6</td><td>68.0</td><td>71.4</td><td>72.3</td><td>71.9</td><td>44.2</td><td>74.4</td><td>55.4</td><td>20.9</td><td>21.9</td><td>21.4</td><td>75.8</td><td>76.5</td><td>76.2</td></tr><tr><td>lamp</td><td>64.0</td><td>74.8</td><td>69.0</td><td>69.9</td><td>79.0</td><td>74.2</td><td>28.6</td><td>84.7</td><td>42.8</td><td>15.6</td><td>22.2</td><td>18.3</td><td>71.3</td><td>80.2</td><td>75.5</td></tr><tr><td>plane</td><td>94.3</td><td>94.9</td><td>94.6</td><td>96.8</td><td>95.4</td><td>96.1</td><td>41.2</td><td>98.3</td><td>58.1</td><td>87.1</td><td>84.7</td><td>85.9</td><td>97.2</td><td>95.9</td><td>96.5</td></tr><tr><td>sofa</td><td>64.8</td><td>67.3</td><td>66.0</td><td>68.6</td><td>69.8</td><td>69.2</td><td>38.6</td><td>75.6</td><td>51.1</td><td>55.1</td><td>58.0</td><td>56.5</td><td>68.2</td><td>72.3</td><td>70.2</td></tr><tr><td>table</td><td>76.0</td><td>77.6</td><td>76.8</td><td>81.5</td><td>75.1</td><td>78.2</td><td>23.0</td><td>59.3</td><td>33.1</td><td>27.4</td><td>23.4</td><td>25.2</td><td>82.2</td><td>77.8</td><td>80.0</td></tr></table>
+
+# 5 CONCLUSION
+
+We presented a point-based unpaired shape completion framework that can be applied directly on raw partial scans to obtain clean and complete point clouds. At the core of the algorithm is an adaptation network acting as a generator that transforms latent code encodings of the raw point scans, and maps them to latent code encodings of clean and complete object scans. The two latent spaces regularize the problem by restricting the transfer problem to respective data manifolds. We extensively evaluated our method on real scans and virtual scans, demonstrating that our approach consistently leads to plausible completions and perform superior to other methods. The work opens up the possibility of generalizing our approach to scene-level scan completions, rather than object-specific completions. Our method shares the same limitations as many of the supervised counterparts: does not produce fine-scale details and assumes input to be canonically oriented. Another interesting future direction will be to combine point- and image-features to apply the completion setup to both geometry and texture details.
+
+# 6 ACKNOWLEDGEMENTS
+
+We thank all the anonymous reviewers for their insightful comments and feedback. This work is supported in part by grants from National Key R&D Program of China (2019YFF0302900), China Scholarship Council, National Natural Science Foundation of China (No.61602273), ERC Starting Grant, ERC PoC Grant, Google Faculty Award, Royal Society Advanced Newton Fellowship, and gifts from Adobe.
+
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+
+# A DETAILS OF DATASETS
+
+Clean and Complete Point Sets are obtained by virtually scanning the models from ShapeNet. We use a subset of 8 categories, namely boat, car, chair, dresser, lamp, plane, sofa and table, in our experiments. To generate clean and complete point set of a model, we virtually scan the models by performing ray-intersection test from cameras placed around the model to obtain the dense point set, followed by a down-sampling procedure to obtain a relatively sparser point set of $N$ points. Note that we use the models without any pose and scale augmentation.
+
+This dataset is used for training to learn the clean-complete point set manifold in all our experiments.   
+The following datasets of different data distributions serve as different noisy-partial input data.
+
+Real-world Data comes from three sources. The first one is derived from ScanNet dataset which provides many mesh objects that have been pre-segmented from its surrounding environment. For the purpose of training and testing our network, we extract ${ \sim } 5 5 0 $ chair objects and ${ \sim } 5 5 0 $ table objects from ScanNet dataset, and manually align them to be consistently orientated with models in ShapeNet dataset. We also split these objects into $90 \% / 1 0 \%$ train/test sets.
+
+The second one consists of 20 chairs and 20 tables from the Matterport3D dataset, to which the same extraction and alignment as is done in ScanNet dataset is also applied. Note that we train our method only on ScanNet training split, and use the trained model to test on Matterport3D data, to show how our method can generalize to absolutely unseen data. For both ScanNet and Matterport3D datasets, we uniformly sample $N$ points on the surface mesh of each object to obtain the input point sets.
+
+Last, we extract car observations from the KITTI dataset using the provided ground truth bounding boxes for training and testing our method. We use KITTI Velodyne point clouds from the 3D object detection benchmark and the split of Qi et al. (2018). We filter the observations such that each car observation contains at least 100 points to avoid overly sparse observations.
+
+3D-EPN Dataset provides partial reconstructions of ShapeNet objects (8 categories) by using volumetric fusion method Curless & Levoy (1996) to integrate depth maps scanned along a virtual scanning trajectory around the model. For each model, a set of trajectories is generated with different levels of incompleteness, reflect the real-world scanning with a hand-held commodity RGB-D sensor. The entire dataset covers 8 categories and a total of 25590 object instances (the test set is composed of 5384 models). Note that, in the original 3D-EPN dataset, the data is represented in Signed Distance Field (SDF) for training data and Distance Field (DF) for test data. As our method works on pure point sets, we only use the point cloud representations of the training data provided by the authors, instead of using the SDF data which holds richer information and is claimed in Dai et al. (2017b) to be crucial for completing partial data.
+
+Synthetic Data serves the purpose of having another dataset of different incomplete scan distribution and controlling the incompleteness of the input. We use ShapeNet to generate a synthetic dataset, in which we can control the incompleteness of the synthetic partial point sets. For the models in each one of the 4 categories (car, chair, plane, and table), we split them into $90 \% / 1 0 \%$ train/test sets. For each model, from which a clean and complete point set has been scanned (as described earlier in this subsection), we can randomly pick a point and remove its $N \times r$ $( r \in [ 0 , 1 )$ ) nearest neighbor points. The parameter $r$ controls the incompleteness of the synthetically-generated input. Furthermore, we add Gaussian noise ${ \mathcal { N } } ( \mu , \sigma ^ { 2 } )$ to each point ( $\scriptstyle \mu = 0$ and $\sigma { = } 0 . 0 1$ for all our experiments). Last, we duplicate the points in the resulting point sets to generate point sets with an equal number of $N$ points.
+
+# B NETWORK ARCHITECTURE DETAILS
+
+In this section, we describe the details of the encoder, decoder, generator and discriminator in our network implementation.
+
+# B.1 AE ARCHITECTURE DETAILS
+
+Encoder consists of 5 1-D convolutional layers which are implemented as 1-D convolutions with ReLU and batch normalization, with kernel size of 1 and stride of 1, to lift the feature of each point to high dimensional feature space independently. In all experiments, we use an encoder with 64,
+
+128, 128, 256 and $k = 1 2 8$ filters in each of its layers, with $k$ being the latent code size. The output of the last convolutional layer is passed to a feature-wise maximum to produce a $k$ -dimensional latent code.
+
+Decoder transforms the latent vector using 3 fully connected layers with 256, 256, and $N \textbf { x } 3$ neurons each, the first two having ReLUs, to reconstruct $N \times 3$ output.
+
+# B.2 GAN ARCHITECTURE DETAILS
+
+Since the generator and discriminator of GAN directly operate on the latent space, the architecture for them is significantly simpler. Specifically, the generator is comprised of two fully connected layers with 128 and 128 neurons each, to map the latent code of noisy and incomplete point sets to that of clean and complete point sets. The discriminator consists of 3 fully connected layers with 256, 512 and 1 neurons each, to produce a single scalar for each latent code.
+
+# C TRAINING DETAILS
+
+To make the training of the entire network trackable, we pre-train the AEs used for obtaining the latent spaces. After that we retain the weights of AEs, only the weights of the generator and discriminator are updated through the back-propagation during the GAN training. The following training hyper-parameters are used in all our experiments.
+
+For training the AE, we use Adam optimizer with an initial learning rate of 0.0005, $\beta _ { 1 } = 0 . 9$ and a batch size of 200 and train for a maximum of 2000 epochs.
+
+For training the generator and discriminator on the latent spaces, we use Adam optimizer with an initial learning rate of 0.0001, $\beta _ { 1 } ~ = ~ 0 . 5$ and a batch size of 24 and train the generator and discriminator alternately for a maximum of 1000 epochs.
+
+# D QUALITATIVE RESULTS ON 3D-EPN DATASET
+
+We present qualitatively comparisons in Fig 5, where we show the partial input, AE, 3D-EPN, PCN, Ours, Our $^ +$ result and the ground truth point set. We can see that, although our method is not quantitatively the best, our results are very qualitatively plausible, as the generator is restricted to generate point sets from learned clean and complete shape manifolds.
+
+# E VISUAL COMPARISON ON TEST DATA WITH DISTRIBUTION DIFFERENT TO TRAINING DATA
+
+We present the visual comparison of 3D-EPN, PCN and our method on our synthetic data, which differs from 3D-EPN and PCN training data. In this experiment, the ground truth of our synthetic data is only available for evaluation. In Fig 6, we can see that our method keeps producing high-quality completions, as our method does not require paired data for training hence can still be trained when no ground truth is available. 3D-EPN and PCN produce much worse results as the data distribution of its training data and our synthetic data differ.
+
+# F VARIATIONS OF LEVERAGING GROUND TRUTH SUPERVISION
+
+To adapt our network for training with ground truth point sets, we first change the reconstruction loss term in the generator loss from HD (Hausdorff Distance) to EMD (Earth Mover’s Distance), as the ground truth point set is complete and thus contains full information for supervising the completion. Note that HD is superior when the ground truth is unavailable for training, as shown in Table 4 of Section 4. Moreover, we present the comparison of different decisions on whether to adopt the adversarial training in our network for training with the ground truth.
+
+![](images/95d46cdd65c548a3c44cec8ef8dab1802645ac2d6129979ede0e38a2d48714b8.jpg)  
+Figure 5: Qualitative comparison on 3D-EPN dataset.
+
+![](images/9ae8268e41cfad97163e9cdcd5c222639f406a629f4d3b95e5e735640fd4754c.jpg)  
+Figure 6: Effect of data distribution discrepancy and qualitative comparison on our synthetic dataset.
+
+• Ours $\mathrm { G T + E M D } $ ), which is also denoted as ${ \mathrm { O u r s } } +$ in the paper, removes the adversarial training in the network by simply setting $\alpha = 0$ and not updating the discriminator weights, hence there is only EMD reconstruction loss for the generator.
+
+• Ours ( $\mathbf { G } \mathbf { T } { \mathrm { + E } } \mathbf { M } \mathbf { D } { \mathrm { + G } } \mathbf { A } \mathbf { N } )$ , in contrast, retains the adversarial training.
+
+Table 5 shows the quantitative comparison results, we can see that, when the ground truth point sets are available, Ours $\mathbf { \bar { G } T + E M D } ,$ produces better results than Ours $\mathrm { ( G T + E M D + G A N ) }$ . Our explanation for why adopting adversarial training here leads to worse results is that: when the ground truth is available, which is complete and contains all information for supervising the network, adding adversarial training will make the network much harder to train, as the network always gets punished by failing to fool the discriminator when it is actually transforming current output closer to the ground truth.
+
+Table 5: Removal of adversarial training when training with ground truth leads to significant improvement.   
+
+<table><tr><td></td><td colspan="3">Ours (GT+EMD)</td><td colspan="3">Ours (GT+EMD+GAN)</td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>car</td><td>93.5</td><td>92.8</td><td>93.1</td><td>80.5</td><td>77.9</td><td>79.2</td></tr><tr><td>chair</td><td>82.3</td><td>83.3</td><td>82.8</td><td>51.5</td><td>58.1</td><td>54.6</td></tr><tr><td> plane</td><td>95.6</td><td>94.8</td><td>95.2</td><td>91.4</td><td>86.3</td><td>88.8</td></tr><tr><td>table</td><td>81.2</td><td>81.4</td><td>81.3</td><td>37.9</td><td>39.3</td><td>38.6</td></tr></table>
+
+# G MORE STATISTICS FRO THE BASELINE COMPARISON
+
+For the baseline methods comparison on 3D-EPN dataset, we also report the Chamfer distance (CD), Earth Mover’s Distance (EMD) and Hausdorff Distance (HD, maximum of the two directional distances) between the ground truth and the completion in Table 6:
+
+Table 6   
+
+<table><tr><td></td><td></td><td>AE</td><td></td><td></td><td>EPN</td><td></td><td></td><td>PCN</td><td></td><td></td><td></td><td>Ours</td><td></td><td>Ours+</td><td></td><td></td></tr><tr><td>model</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td></td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td></tr><tr><td>boat</td><td>0.0012</td><td>0.0530</td><td>0.0864</td><td>0.0009</td><td>0.0500</td><td>0.0562</td><td>0.0006</td><td></td><td>0.0437</td><td>0.0635</td><td>0.0011</td><td>0.0532</td><td>0.0857</td><td>0.0008</td><td>0.0455</td><td>0.0799</td></tr><tr><td>car</td><td>0.0019</td><td>0.0668</td><td>0.1093</td><td>0.0024</td><td>0.0744</td><td>0.0989</td><td>0.0005</td><td></td><td>0.0418</td><td>0.0648</td><td>0.0010</td><td>0.0434</td><td>0.0763</td><td>0.0007</td><td>0.0393</td><td>0.0677</td></tr><tr><td>chair</td><td>0.0031</td><td>0.1003</td><td>0.1374</td><td>0.0016</td><td>0.0704</td><td>0.0877</td><td>0.0009</td><td>0.0586</td><td></td><td>0.0832</td><td>0.0020</td><td>0.0773</td><td>0.1010</td><td>0.0015</td><td>0.0619</td><td>0.0915</td></tr><tr><td>dresser</td><td>0.0037</td><td>0.0985</td><td>0.1295</td><td>0.0027</td><td>0.0783</td><td>0.0963</td><td>0.0008</td><td>0.0545</td><td></td><td>0.0771</td><td>0.0019</td><td>0.0588</td><td>0.0833</td><td>0.0011</td><td>0.0482</td><td>0.0734</td></tr><tr><td>lamp</td><td>0.0026</td><td>0.0857</td><td>0.1092</td><td>0.0038</td><td>0.0966</td><td>0.1154</td><td>0.0013</td><td>0.0692</td><td></td><td>0.0890</td><td>0.0023</td><td>0.0848</td><td>0.1073</td><td>0.0018</td><td>0.0729</td><td>0.1002</td></tr><tr><td>plane</td><td>0.0004</td><td>0.0346</td><td>0.0591</td><td>0.0060</td><td>0.0943</td><td>0.1255</td><td>0.0002</td><td>0.0308</td><td></td><td>0.0394</td><td>0.0004</td><td>0.0338</td><td>0.0545</td><td>0.0005</td><td>0.0405</td><td>0.0685</td></tr><tr><td>sofa</td><td>0.0030</td><td>0.0792</td><td>0.1232</td><td>0.0045</td><td>0.0880</td><td>0.1093</td><td>0.0008</td><td>0.0494</td><td></td><td>0.0651</td><td>0.0026</td><td>0.0655</td><td>0.0928</td><td>0.0012</td><td>0.0536</td><td>0.0958</td></tr><tr><td>table</td><td>0.0044</td><td>0.0886</td><td>0.1518</td><td>0.0014</td><td>0.0681</td><td>0.0975</td><td>0.0010</td><td>0.0603</td><td>0.0968</td><td></td><td>0.0026</td><td>0.068445</td><td>0.1071</td><td>0.0021</td><td>0.0681</td><td>0.1224</td></tr></table>
+
+# H USER STUDY ON REAL-WORLD DATA COMPLETION
+
+We also conducted a user study on the completion results of the real-world scans, where given a partial input users are required to pick the most preferable completion among EPN, PCN and our results. In total, we received 1,000 valid user selections and report the preference (in percentage of the total selections) of each method in the user study. From Fig. 7 we can see that in over half $( 5 2 \% )$ of the selections, our completion results are selected as the best completion, while PCN completion results are better in $45 \%$ of the selections.
+
+Interestingly, although our method outperforms other methods in the user study, our method clearly does not hold a dominant position in this user study. After a more in-depth analysis of the user selections, we found that users intend to pick the completion in which the partial input is embedded, which can be formulated as the Hausdorff distance from the partial input to the completion, and the supervised method PCN preserves the input point cloud in its completion output as this always minimizes the distance loss. The plausibility of the completion result is usually neglected by users, while the plausibility and the Hausdorff distance from the partial input to the completion are both considered as two trade-off terms in the objective function of our completion generator. Fig. 8 gives a typical example, where the PCN completion without clear chair structure is often picked as better completion while our completion tries to trade-off between the HL and the plausibility.
+
+![](images/524355932026585ae173aa1bd72f99ec46ae57a45e89057f15b615323798983b.jpg)  
+Figure 7
+
+![](images/248324f777447e8e23f535fcb822ddbd1d31fe28055f1002364109f55440b06a.jpg)  
+Figure 8
+
+# I GENERALIZATION TO UNSEEN CLASSES
+
+![](images/9c74083cc7a15645561f17e907b18b10deb7c829cb549d4d03ae523646a55ad1.jpg)  
+Figure 9
+
+Our method does generalize to unseen objects from the same category in the test set, which is demonstrated in the experimental results section. However, our method intuitively should not generalize to classes that are not seen during the training, as the autoencoder, which is a fundamental component in our network, does not generalize to unseen classes. We present the qualitative results of applying our table completion network on chair and airplane class. We can see that from Fig. 9, on the unseen chair class, which shares similar structure with table, our table completion network can produce some reasonable structures, but is unable to complete with a seat back as the autoencoder does not have such capability; on the unseen airplane class, which is rather dissimilar to table class, our table completion network failed to complete the partial airplanes.

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+    {
+        "type": "text",
+        "text": "UNPAIRED POINT CLOUD COMPLETION ON REALSCANS USING ADVERSARIAL TRAINING",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Baoquan Chen Peking University ",
+        "bbox": [
+            408,
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+            526,
+            199
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Xuelin Chen Shandong University University College London ",
+        "bbox": [
+            184,
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+            364,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Niloy J. Mitra University College London Adobe Research London ",
+        "bbox": [
+            570,
+            170,
+            751,
+            212
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            452,
+            250,
+            544,
+            263
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "As 3D scanning solutions become increasingly popular, several deep learning setups have been developed for the task of scan completion, i.e., plausibly filling in regions that were missed in the raw scans. These methods, however, largely rely on supervision in the form of paired training data, i.e., partial scans with corresponding desired completed scans. While these methods have been successfully demonstrated on synthetic data, the approaches cannot be directly used on real scans in the absence of suitable paired training data. We develop a first approach that works directly on input point clouds, does not require paired training data, and hence can directly be applied to real scans for scan completion. We evaluate the approach qualitatively on several real-world datasets (ScanNet, Matterport3D, KITTI), quantitatively on 3D-EPN shape completion dataset, and demonstrate realistic completions under varying levels of incompleteness. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            479,
+            336,
+            496
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Robust, efficient, and scalable solutions now exist for easily scanning large environments and workspaces (Dai et al., 2017a; Chang et al., 2017). The resultant scans, however, are often partial and have to be completed (i.e., missing parts have to be hallucinated and filled in) before they can be used in downstream applications, e.g., virtual walk-through, path planning. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The most popular data-driven scan completion methods rely on paired supervision data, i.e., for each incomplete training scan, a corresponding complete data (e.g., voxels, point sets, signed distance fields) is required. One way to establish such a shape completion network is then to train a suitably designed encoder-decoder architecture (Dai et al., 2017b; 2018). The required paired training data is obtained by virtually scanning 3D objects (e.g., SunCG Song et al. (2017), ShapeNet Chang et al. (2015) datasets) to simulate occlusion effects. Such approaches, however, are unsuited for real scans where large volumes of paired supervision data remain difficult to collect. Additionally, when data distributions from virtual scans do not match those from real scans, completion networks trained on synthetic-partial and synthetic-complete data do not sufficiently generalize to real (partial) scans. To the best of our knowledge, no point-based unpaired method exists that learns to translate noisy and incomplete point cloud from raw scans to clean and complete point sets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We propose an unpaired point-based scan completion method that can be trained without requiring explicit correspondence between partial point sets (e.g., raw scans) and example complete shape models (e.g., synthetic models). Note that the network does not require explicit examples of real complete scans and hence existing (unpaired) large-scale real 3D scan (e.g., Dai et al. (2017a); Chang et al. (2017)) and virtual 3D object repositories (e.g., Song et al. (2017); Chang et al. (2015)) can directly be leveraged as training data. Figure 1 shows example scan completions. As we show in Table 1, unlike methods requiring paired supervision, our method continues to perform well even if the data distributions of synthetic complete scans and real partial scans differ. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We achieve this by designing a generative adversarial network (GAN) wherein a generator, i.e., an adaptation network, transforms the input into a suitable latent representation such that a discriminator cannot differentiate between the transformed latent variables and the latent variables obtained from training data (i.e., complete shape models). Intuitively, the generator is responsible for the key task of mapping raw partial point sets into clean and complete point sets, and the process is regularized by working in two different latent spaces that have separately learned manifolds of scanned and synthetic object data. ",
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+    {
+        "type": "image",
+        "img_path": "images/b798dfe863c4b31af9919bc8ab17c25ed320f44084e0af8ef061c3bf2deb9eb6.jpg",
+        "image_caption": [
+            "Figure 1: We present a point-based shape completion network that can be directly used on raw scans without requiring paired training data. Here we show a sampling of results from the ScanNet, Matterport3D, 3D-EPN, and KITTI datasets. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "We demonstrate our method on several publicly available real-world scan datasets namely (i) ScanNet (Dai et al., 2017a) chairs and tables; (ii) Matterport3D (Chang et al., 2017) chairs and tables; and (iii) KITTI (Geiger et al., 2012) cars. In absence of completion ground truth, we cannot directly compute accuracy for the completed scans, and instead compare using plausibility scores. Further, in order to quantitatively evaluate the performance of the network, we report numbers on a synthetic dataset (Dai et al., 2017b) where completed versions are available. Finally, we compare our method against baseline methods to demonstrate the advantages of the proposed unpaired scan completion framework. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            409,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Shape Completion. Many deep neural networks have been proposed to address the shape completion challenge. Inspired by CNN-based 2D image completion networks, 3D convolutional neural networks applied on voxelized inputs have been widely adopted for 3D shape completion task (Dai et al., 2018; 2017b; Sharma et al., 2016; Han et al., 2017; Thanh Nguyen et al., 2016; Yang et al., 2018; Wang et al., 2017). As quantizing shapes to voxel grids lead to geometric information loss, recent approaches (Yuan et al., 2018; Yu et al., 2018b; Achlioptas et al., 2018) operate directly on point sets to fill in missing parts. These works, however, require supervision in the form of partialcomplete paired data for training deep neural networks to directly regress partial input to their ground truth counterparts. Since paired ground truth of real-world data is rarely available such training data is generated using virtual scanning. While the methods work well on synthetic test data, they do not generalize easily to real scans arising from hard-to-model acquisition processes. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Realizing the gap between synthetically-generated data and real-world data, Stutz & Geiger (2018) proposed to directly work on voxelized real-world data. They also work in a latent space created for clean and complete data but measure reconstruction loss using a maximum likelihood estimator. Instead, we propose a GAN setup to learn a mapping between latent spaces respectively arising from partial real and synthetic complete data. Further, by measuring loss using Hausdorff distance on point clouds, we directly work with point sets instead of voxelized input. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Generative Adversarial Network. Since its introduction, GAN (Goodfellow et al., 2014) has been used for a variety of generative tasks. In 2D image domain, researchers have utilized adversarial training to recover richer information from low-resolution images or corrupted images (Ledig et al., 2017; Wang et al., 2018; Mao et al., 2017; Park et al., 2018; Bulat et al., 2018; Yeh et al., 2017; Iizuka et al., 2017). In 3D context, Yang et al. (2018); Wang et al. (2017) combine 3D-CNN and generative adversarial training to complete shapes under the supervision of ground truth data. Gurumurthy & Agrawal (2019) treats the point cloud completion task as denoising AE problem, utilizing adversarial training to optimize on the AE latent space. We also leverage the power of GAN for reasoning the missing part of partial point cloud scanning. However, our method is designed to work with unpaired data, and thus can directly be applied to real-world scans even when real-world and synthetic data distributions differ. Intuitively, our GAN-based approach directly learns a translation mapping between these two different distributions. ",
+        "bbox": [
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+            699,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Deep Learning on Point clouds. Our method is built upon recent advances in deep neural networks for point clouds. PointNet Qi et al. (2017a), the pioneering work on this topic, takes an input point set through point-wise MLP layers followed by a symmetric and permutation-invariant function to produce a compact global feature, which can then be used for a diverse set of tasks (e.g., classification, segmentation). Although many improvements to PointNet have been proposed (Su et al., 2018; Li et al., 2018b; Qi et al., 2017b; Li et al., 2018a; Zaheer et al., 2017), the simplicity and effectiveness of PointNet and its extension PointNet++ make them popular for many other analysis tasks (Yu et al., 2018a; Yin et al., 2018; Yu et al., 2018b; Guerrero et al., 2018). ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/b06c0dd4315e9a53fd65c76c3f940ba8478a2e039703561a061a1c19565099b5.jpg",
+        "image_caption": [
+            "Figure 2: Unpaired Scan Completion Network. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the context of synthesis, Achlioptas et al. (2018) proposed an autoencoder network, using a PointNet-based backbone, to learn compact representations of point clouds. By working in a reduced latent space produced by the autoencoder, they report significant advantages in training GANs, instead of having a generator producing raw point clouds. Inspired by this work, we design a GAN to translate between two different latent spaces to perform unpaired shape completion on real scans. ",
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+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Given a noisy and partial point set ${ \\cal { S } } = \\{ { \\bf { s } } _ { i } \\}$ as input, our goal is to produce a clean and complete point set $\\mathcal { R } = \\left\\{ \\mathbf { r } _ { i } \\right\\}$ as output. Note that although the two sets have the same number of points, there is no explicit correspondence between the sets $s$ and $\\mathcal { R }$ . Further, we assume access to clean and complete point sets for shapes for the object classes. We achieve unpaired completion by learning two class-specific point set manifolds, $\\mathbb { X } _ { r }$ for the scanned inputs, and $\\mathbb { X } _ { c }$ for clean and complete shapes. Solving the shape completion problem then amounts to learning a mapping $\\mathbb { X } _ { r } \\ \\to \\ \\mathbb { X } _ { c }$ between the respective latent spaces. We train a generator $G _ { \\theta } : \\mathbb { X } _ { r }  \\mathbb { X } _ { c }$ to perform the mapping. Note that we do not require the noise characteristics in the two data distributions, i.e., real and synthetic, to be the same. In absence of paired training data, we score the generated output by setting up a min-max game where the generator is trained to fool a discriminator $F _ { \\chi }$ , whose goal is to differentiate between encoded clean and complete shapes, and mapped encodings of the raw and partial inputs. Figure 2 shows the setup of the proposed scan completion network. The latent space encoder-decoders, the mapping generator, and the discriminator are all trained as detailed next. ",
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+    {
+        "type": "text",
+        "text": "3.1 LEARNING LATENT SPACES FOR POINT SETS ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The latent space of a given set of point sets is obtained by training an autoencoder, which encodes the given input to a low-dimension latent feature and then decodes to reconstruct the original input. We work directly on the point sets via these learned latent spaces instead of quantizing them to voxel grids or signed distance fields. ",
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+        "type": "text",
+        "text": "For point sets coming from the clean and complete point sets $\\mathcal { P }$ , we learn an encoder network $E _ { \\eta } ^ { c }$ that maps $\\mathcal { P }$ from the original parameter space $ { \\mathbb { R } } ^ { 3 N }$ , defined by concatenating the coordinates of the $N$ (2048 in all our experiments) points, to a lower-dimensional latent space $\\mathbb { X } _ { c }$ . A decoder network $D _ { \\phi } ^ { c }$ performs the inverse transformation back to $\\mathbb { R } ^ { 3 N }$ giving us a reconstructed point set $\\tilde { \\mathcal P }$ with also $N$ points. The encoder-decoders are trained with reconstruction loss, ",
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+        "type": "equation",
+        "img_path": "images/2d62ff66bc1155c28b965be28be1d1cf740d22f5317f582a531693d1b7acc5ce.jpg",
+        "text": "$$\n\\mathcal { L } ^ { \\mathrm { E M D } } ( \\eta , \\phi ) = \\mathbb { E } _ { \\mathcal { P } \\sim p _ { \\mathrm { c o m p l e t e } } } d ( \\mathcal { P } , D _ { \\phi } ^ { c } ( E _ { \\eta } ^ { c } ( \\mathcal { P } ) ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { P } \\sim p _ { \\mathrm { c o m p l e t e } }$ denotes point set samples drawn from the set of clean and complete point sets, $d ( X _ { 1 } , X _ { 2 } )$ is the Earth Mover’s Distance (EMD) between point sets $X _ { 1 } , X _ { 2 }$ , and $( \\eta , \\phi )$ are the learnable parameters of the encoder and decoder networks, respectively. Once trained, the weights of both networks are held fixed and the latent code $z = E _ { \\eta } ^ { c } ( X )$ , $z \\in \\mathbb { X } _ { c }$ for a clean and complete point set $X$ provides a compact representation for subsequent training and implicitly captures the manifold of clean and complete data. The architecture of the encoder and decoder is similar to Achlioptas et al. (2018); Qi et al. (2017a): using a 5-layer MLP to lift individual points to a deeper feature space, followed by a symmetric function to maintain permutation invariance. This results in a $k$ - dimensional latent code that describes the entire point cloud $k { = } 1 2 8$ in all our experiments). More details of the network architecture can be found in the appendix. ",
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+            "Figure 3: Effect of unpaired scan completion without (Equation 5) and with HL term (Equation 6). Without the HL term, the network produces a clean point set for a complete chair, that is different in shape from the input. With the HL term, the network produces a clean point set that matches the input. "
+        ],
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "As for the point set coming from the noisy-partial point sets $s$ , one can also train another encoder $E _ { \\gamma } ^ { r } : \\mathcal { S }  \\mathbb { X } _ { r }$ and decoder $D _ { \\psi } ^ { r } : \\mathbb { X } _ { r }  \\tilde { \\mathcal { S } }$ pair that provides a latent parameterization $\\mathbb { X } _ { r }$ for the noisy-partial point sets, with the definition of the reconstruction loss as, ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/a83af74c87abcc971f4a48ca4b748ac45de52088b046904545d6d6ee9e5a9d46.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } ^ { \\mathrm { E M D } } ( \\gamma , \\psi ) = \\mathbb { E } _ { S \\sim p _ { \\mathrm { r a w } } } d ( S , D _ { \\psi } ^ { r } ( E _ { \\gamma } ^ { r } ( S ) ) ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathcal { S } } \\sim p _ { \\mathrm { r a w } }$ denotes point set samples drawn from the set of noisy and partial point sets. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Although, in experiments, the latent space of this autoencoder trained on noisy-partial point sets works considerably well as the noisy-partial point set manifold, we found that using the latent space produced by feeding noisy-partial point sets to the autoencoder trained on clean and complete point sets yields slightly better results. Hence, unless specified, we set $\\gamma = \\eta$ and $\\psi = \\phi$ in our experiments. The comparison of different choices to obtain the latent space for noisy-partial point sets is also presented in Section 4. Next, we will describe the GAN setup to learn a mapping between the latent spaces of raw noisy-partial and synthetic clean-complete point sets, i.e., $\\mathbb { X } _ { r } \\to \\mathbb { X } _ { c }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.2 LEARNING A MAPPING BETWEEN LATENT SPACES ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We set up a min-max game between a generator and a discriminator to perform the mapping between the latent spaces. The generator $G _ { \\theta }$ is trained to perform the mapping $\\mathbb { X } _ { r } \\ \\to \\ \\mathbb { X } _ { c }$ such that the discriminator fails to reliably tell if the latent variable comes from original $\\mathbb { X } _ { c }$ or the remapped $\\mathbb { X } _ { r }$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The latent representation of a noisy and partial scan $z _ { r } = E _ { \\gamma } ^ { r } ( S )$ is mapped by the generator to $\\tilde { z } _ { c } = G _ { \\theta } ( z _ { r } )$ . Then, the task of the discriminator $F _ { \\chi }$ is to distinguish between latent representations $\\tilde { z } _ { c }$ and $z _ { c } = E _ { \\eta } ^ { c } ( \\mathcal { P } )$ . We train the mapping function using a GAN. Given training examples of clean latent variables $z _ { c }$ and remapped-noisy latent variables $\\tilde { z } _ { c }$ , we seek to optimize the following adversarial loss over the mapping generator $G _ { \\theta }$ and a discriminator $F _ { \\chi }$ , ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/1866b1c7251014fedd01ee8fdcf96253aa5c8842fc17ed35e7183cf65b0b2611.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { \\theta } \\operatorname* { m a x } _ { \\chi } \\mathbb { E } _ { \\boldsymbol { x } \\sim p _ { \\mathrm { c l e a n - c o n p l e t } } } \\left[ \\log \\left( F _ { \\chi } \\big ( E _ { \\eta } ^ { c } ( x ) \\big ) \\right) \\right] + \\mathbb { E } _ { \\boldsymbol { y } \\sim p _ { \\mathrm { m i s p - r a t i a } } } \\left[ \\log \\left( 1 - F _ { \\chi } \\big ( G _ { \\theta } \\big ( E _ { \\gamma } ^ { r } ( y ) \\big ) \\right) \\right] .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our experiments, we found the least square GAN Mao et al. (2016) to be easier to train and hence minimize both the discriminator and generator losses defined as, ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/3167c9162c3be501b73f1d26535a66523c3ff00a73eb9f3bf4ddeac8ceb24c79.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { F } ( \\chi ) \\ : = \\ : \\mathbb { E } _ { x \\sim p _ { \\mathrm { c l e a n - o m p l e t } } } \\left[ F _ { \\chi } \\big ( E _ { \\eta } ^ { c } ( x ) \\big ) - 1 \\right] ^ { 2 } + \\mathbb { E } _ { y \\sim p _ { \\mathrm { n o i s y p a r i a } } } \\big [ F _ { \\chi } \\big ( G _ { \\theta } ( E _ { \\gamma } ^ { r } ( y ) ) \\big ) \\big ] ^ { 2 } } \\\\ & { \\mathcal { L } _ { G } ( \\theta ) \\ : = \\mathbb { E } _ { y \\sim p _ { \\mathrm { n o i s y p a r i a } } } \\big [ F _ { \\chi } \\big ( G _ { \\theta } ( E _ { \\gamma } ^ { r } ( y ) ) \\big ) - 1 \\big ] ^ { 2 } . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The above setup encourages the generator to perform the mapping $\\mathbb { X } _ { r } \\to \\mathbb { X } _ { c }$ resulting in $D _ { \\psi } ^ { c } ( \\tilde { z _ { c } } )$ to be a clean and complete point cloud $\\mathcal { R }$ . However, the generator is free to map a noisy latent vector to any point on the manifold of valid shapes in $\\mathbb { X } _ { c }$ , including shapes that are far from the original partial scan $s$ . As shown in Figure 3, the result is a complete and clean point cloud that can be dissimilar in shape to the partial scanned input. To prevent this, we add a reconstruction loss term $\\scriptstyle { \\mathcal { L } } _ { \\mathrm { r e c o n } }$ to the generator loss: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/384ec3ee5697aa076b207d93ee4fa64869706ab03b28eb4b29c577054bc2f30e.jpg",
+        "text": "$$\n\\mathcal { L } _ { G } ( \\theta ) = \\alpha \\mathbb { E } _ { y \\sim p _ { \\mathrm { n o s y \\mathrm { s t i a } } } } \\big [ F _ { \\chi } \\big ( G _ { \\theta } ( E _ { \\gamma } ^ { r } ( y ) ) \\big ) - 1 \\big ] ^ { 2 } + \\beta \\mathcal { L } _ { \\mathrm { r e c o n } } ^ { \\mathrm { H L } } ( \\mathcal { S } , D _ { \\psi } ^ { c } ( G _ { \\theta } ( E _ { \\gamma } ^ { r } ( \\mathcal { S } ) ) ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { L } _ { \\mathrm { r e c o n } } ^ { \\mathrm { H L } }$ denotes the Hausdorff distance loss 1 (HL) from the partial input point set to the completion point set, which encourages the predicted completion point set to match the input only partially. Note that, it is crucial to use $\\mathrm { H L }$ as $\\scriptstyle { \\mathcal { L } } _ { \\mathrm { r e c o n } }$ , since the partial input can only provide partial supervision when no ground truth complete point set is available. In contrast, using EMD as $\\scriptstyle { \\mathcal { L } } _ { \\mathrm { r e c o n } }$ forces the network to reconstruct the overall partial input leading to worse completion results. The comparison of these design choices is presented in Section 4. Unless specified, we set the trade-off parameters as $\\alpha = 0 . 2 5$ and $\\beta = 0 . 7 5$ in all our experiments. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTAL EVALUATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We present quantitative and qualitative experimental results on several noisy and partial datasets. First, we present results on real-world datasets, demonstrating the effectiveness of our method on unpaired raw scans. Second, we thoroughly compare our method to various baseline methods on 3D-EPN dataset, which contains simulated partial scans and corresponding ground truth for full evaluation. Finally, we derive a synthetic noisy-partial scan dataset based on ShapeNet, on which we can evaluate the performance degradation of applying supervised methods to test data of different distribution and the performance of our method under varying levels of incompleteness. A set of ablation studies is also included to evaluate our design choices. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Datasets. (A) Real-world dataset comes from three sources. First, a dataset of ${ \\sim } 5 5 0 $ chairs and ${ \\sim } 5 5 0 $ tables extracted from the ScanNet dataset split into $90 \\%$ - $10 \\%$ train-test sets. Second, a dataset of 20 chairs and 20 tables extracted from the Matterport3D dataset. Note that we train our method only on the ScanNet training split, and use the trained model to test on the Matterport3D data to evaluate generalization to new data sources. Third, a dataset containing cars from the KITTI Velodyne point clouds. (B) 3D-EPN dataset provides simulated partial scans with corresponding ground truth. Scans are represented as Signed Distance Field (SDF). We only use the provided point cloud representations of the training data, instead of using the SDF data which holds richer information. $( C )$ Clean and complete point set dataset contains virtually scanned point sets of ShapeNet models covering 8 categories, namely boat, car, chair, dresser, lamp, plane, sofa, and table. We use this dataset for learning the clean-complete point set manifold in all our experiments. $( D )$ Synthetic dataset provides different incomplete scan distribution and at different levels of incompleteness. Ground truth complete scan counterparts are available for evaluation. ",
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+    {
+        "type": "text",
+        "text": "Evaluation measures. We assess completion quality using the following measures. (A) Accuracy measures the fraction of points in $P _ { c o m p }$ that are matched by $P _ { g t }$ , where and $P _ { c o m p }$ denote the completion point set and $P _ { g t }$ denote the ground truth point set. Specifically, for each point $v \\in P _ { c o m p }$ , we compute $D ( v , P _ { g t } { \\ ' } ) { ' } = m i n \\{ \\| \\ \\bar { v } - q \\ \\| , q \\in \\operatorname { \\bar { P } } _ { g t } \\}$ . If $\\bar { D } ( v , P _ { g t } )$ is within distance threshold $\\epsilon = 0 . 0 3$ , we count it as a correct match. The fraction of matched points is reported as the accuracy in percentage. $( B )$ Completeness reports the fraction of points in $P _ { g t }$ that are within distance threshold $\\epsilon$ of any point in $P _ { c o m p }$ . $( C ) F I$ score is defined as the harmonic average of the accuracy and the completeness, where F1 reaches its best value at 1 (perfect accuracy and completeness) and worst at 0. $( D )$ Plausibility of the completion is evaluated as the classification accuracy in percentage produced by PointNet++, a SOA point-based classification network. To avoid bias on ShapeNet point clouds, we trained the classification network on the ModelNet40 dataset. We mainly used plausibility score for real-world data completions, where no ground truth data is available for calculating accuracy, completeness, or F1 scores. ",
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+    {
+        "type": "text",
+        "text": "In the following, we show all experimental and evaluation results. We trained separate networks for each category. More details are in the appendix. ",
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+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL RESULTS ON REAL-WORLD DATA ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our method works directly on real-world data where no paired data is available. We train and test our network on noisy-partial chairs and tables extracted from the ScanNet dataset. We further test the network trained on ScanNet dataset on chairs and tables extracted from the Matterport3D dataset, to show how well our network can generalize to definitely unseen data. We present qualitative results of our method in Fig 4. Our method consistently produces plausible completions for the ScanNet and Matterport3D data. ",
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+    {
+        "type": "image",
+        "img_path": "images/3b46984f15810a2c412bf127b9da09e242357693a3ee480279e9baab4f8a79c4.jpg",
+        "image_caption": [
+            "Figure 4: Qualitative comparisons on real-world data, which includes partial scans of ScanNet chairs and tables, Matterport3D chairs and tables, and KITTI cars. We show the partial input in grey and the corresponding completion in gold on the right. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "In the absence of ground truth completions on real data, we compare our method quantitatively against others based on the plausibility of the results. The left sub-table of Table 1 shows that our method is superior to those supervised methods, namely 3D-EPN and PCN. Directly applying PCN trained on simulated partial data to real-world data leads to completions that have low plausibility, while our method consistently produces results with high plausibility. 3D-EPN trained on simulated partial data failed to complete the real-world partial scans. In Section 4.2 and Section 4.3, we present more in-depth comparisons on 3D-EPN and our synthetic dataset, where the ground truth is available for computing accuracy, completeness, and F1 of the completions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 1: Completion plausibility on synthetic scans and real-world scans and effects of data distribution discrepancy. (Left) Plausibility comparison on synthetic scans and real-world scans. Synthetic scans includes test data from 3D-EPN, real-world scans includes ScanNet and Matterport3D test data. 3D-EPN failed to produce good completions on real-world data. (Right) On our synthetic data, supervised methods trained on other simulated partial scans produce worse results on partial scans with different data distribution. ",
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+    {
+        "type": "table",
+        "img_path": "images/5e509effe447cd900a8fa9c125b5692c614b08150b4aebbda1721273f56e4a15.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>Raw input</td><td>3D-EPN</td><td>PCN</td><td>Ours</td></tr><tr><td rowspan=\"2\">Synthetic</td><td>chair</td><td>73.1</td><td>77.3</td><td>85.0</td><td>91.5</td></tr><tr><td>table</td><td>52.5</td><td>71.2</td><td>72.0</td><td>80.6</td></tr><tr><td rowspan=\"2\">Real-world</td><td>chair</td><td>71.4</td><td>7.1</td><td>78.6</td><td>94.3</td></tr><tr><td>table</td><td>47.8</td><td>4.4</td><td>69.6</td><td>81.2</td></tr></table>",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">3D-EPN</td><td colspan=\"3\">PCN</td><td colspan=\"3\">Ours</td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>chair</td><td>39.6</td><td>61.8</td><td>48.2</td><td>49.3</td><td>76.0</td><td>59.8</td><td>80.7</td><td>80.8</td><td>80.8</td></tr><tr><td>car</td><td>43.8</td><td>62.3</td><td>51.4</td><td>63.2</td><td>81.4</td><td>71.2</td><td>82.6</td><td>80.7</td><td>81.7</td></tr><tr><td>table</td><td>36.6</td><td>61.0</td><td>45.8</td><td>62.3</td><td>80.6</td><td>70.3</td><td>83.1</td><td>84.5</td><td>83.8</td></tr><tr><td>plane</td><td>17.1</td><td>57.6</td><td>26.3</td><td>67.1</td><td>85.4</td><td>75.1</td><td>94.4</td><td>92.7</td><td>93.6</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Completing the car observations from KITTI is extremely challenging, as each car instance only receives few data points from the Lidar scanner. Fig 4 shows the qualitative results of our method on completing sparse point sets of KITTI cars, we can see that our network can still generate highly plausible cars with such sparse inputs. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We also use a point-based object part segmentation network (Qi et al., 2017b) to indirectly evaluate our completions of real-world data. Due to the absence of ground truth segmentation, we calculate the approximate segmentation accuracy for each completion. Specifically, for the completion of a chair, we count the predicted segmentation label of each point to be correct as long as the predicted label falls into the set of 4 parts (i.e., seat, back, leg, and armrest) of chair class. Our completion results have much higher approximate segmentation accuracy compared to the real-world raw input (chair: $7 7 . 2 \\%$ vs. $2 4 . 8 \\%$ ; table: $9 6 . 4 \\%$ vs. $8 3 . 5 \\%$ ; and car: $9 8 . 0 \\%$ vs. $5 . 2 \\%$ , as segmentation accuracy on our completions versus on original partial input), indicating high completion quality. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 COMPARISON WITH BASELINES ON 3D-EPN DATA",
+        "text_level": 1,
+        "bbox": [
+            174,
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+    },
+    {
+        "type": "text",
+        "text": "We compare our method to several baseline methods and present both quantitative and qualitative comparisons on the 3D-EPN test set: ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "• Autoencoder (AE), which is trained only with clean and complete point sets. • 3D-EPN (Dai et al., 2017b), a supervised method that requires SDF input and is trained with paired data. We convert its Distance Field representation results into surface meshes, from which we can uniformly sample $N$ points for calculating our point-based measures. ",
+        "bbox": [
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+            862,
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/af64d38bf83ffd894b2c426ccef8a4fd8662e9e430dd98fd40a099e4ba993f29.jpg",
+        "table_caption": [
+            "Table 2: Comparison with baselines on the 3D-EPN dataset. Note that 3D-EPN and PCN require paired supervision data, while ours does not. Ours outperforms 3D-EPN and achieves comparable results to PCN. Furthermore, after adapted to leverage the ground truth data as well, our method achieves similar performance to PCN. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>一</td><td></td><td>AE</td><td></td><td></td><td>EPN (fully supervised)</td><td></td><td>PCN (fully supervised)</td><td></td><td></td><td></td><td>Ours (unsupervised)</td><td></td><td></td><td>Ours+ (supervised)</td><td></td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>boat</td><td>89.6</td><td>81.4</td><td>85.3</td><td>82.4</td><td>81.4</td><td>81.9</td><td>92.6</td><td>93.4</td><td>93.0</td><td>86.6</td><td>84.7</td><td>85.6</td><td>89.8</td><td>92.0</td><td>90.9</td></tr><tr><td>car</td><td>81.3</td><td>71.1</td><td>75.9</td><td>69.8</td><td>81.7</td><td>75.3</td><td>97.3</td><td>96.1</td><td>96.7</td><td>88.9</td><td>87.6</td><td>88.2</td><td>93.5</td><td>92.8</td><td>93.1</td></tr><tr><td>chair</td><td>79.9</td><td>68.5</td><td>73.8</td><td>61.7</td><td>76.9</td><td>68.5</td><td>91.1</td><td>90.6</td><td>90.9</td><td>78.7</td><td>77.4</td><td>78.0</td><td>82.3</td><td>83.3</td><td>82.8</td></tr><tr><td>dresser</td><td>68.9</td><td>64.2</td><td>66.5</td><td>58.4</td><td>72.7</td><td>64.8</td><td>93.5</td><td>91.5</td><td>92.5</td><td>75.8</td><td>76.5</td><td>76.2</td><td>87.4</td><td>91.5</td><td>89.4</td></tr><tr><td>lamp</td><td>75.9</td><td>79.6</td><td>77.7</td><td>60.8</td><td>67.8</td><td>64.1</td><td>82.9</td><td>88.3</td><td>85.5</td><td>71.3</td><td>80.2</td><td>75.5</td><td>76.6</td><td>86.3</td><td>81.2</td></tr><tr><td>plane</td><td>97.6</td><td>95.1</td><td>96.3</td><td>78.1</td><td>93.5</td><td>85.1</td><td>98.3</td><td>98.2</td><td>98.2</td><td>97.2</td><td>95.9</td><td>96.5</td><td>95.6</td><td>94.8</td><td>95.2</td></tr><tr><td>sofa</td><td>80.3</td><td>64.0</td><td>71.2</td><td>65.0</td><td>72.6</td><td>68.6</td><td>91.5</td><td>90.8</td><td>91.1</td><td>68.2</td><td>72.3</td><td>70.2</td><td>81.0</td><td>87.0</td><td>83.9</td></tr><tr><td>table</td><td>82.8</td><td>72.5</td><td>77.3</td><td>56.8</td><td>75.1</td><td>64.7</td><td>93.4</td><td>89.2</td><td>91.2</td><td>82.2</td><td>77.8</td><td>80.0</td><td>81.2</td><td>81.4</td><td>81.3</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "• PCN (Yuan et al., 2018), which completes partial inputs in a hierarchical manner, receiving supervision from both sparse and dense ground truth point clouds. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "• ${ \\mathrm { O u r s } } +$ , which is an adaption of our method for training with paired data, to show that our method can be easily adapted to work with ground truth data, improving the completion. Specifically, we set $\\alpha = 0$ and use EMD loss as $L _ { r e c o n }$ . More details and discussion about adapting our method to train with paired data can be found in the appendix. ",
+        "bbox": [
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+            337,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2 shows quantitative results on 3D-EPN test split and summarizes the comparisons: although our network is only trained with unpaired data, our method outperforms 3D-EPN method and achieves comparable results to PCN. Note that both 3D-EPN and PCN require paired data. Furthermore, after adapting our method to be supervised by the ground truth, the performance of our method $( \\mathrm { O u r s } { + } )$ improves, achieving similar performance to PCN. Note that a simple autoencoder network trained with only clean-complete data can produce quantitatively good results, especially when the input is rather complete. Thus, we also evaluate the performance of AE on our synthetic data with incompleteness control in Section 4.3, to show that AE performance declines dramatically as the incompleteness of the input increases. Additional comparisons are included in the appendix. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 EFFECT OF DATA DISTRIBUTION DISCREPANCY AND VARYING INCOMPLETENESS ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Supervised methods assume that simulated partial scans share the same data distribution as the test data. We conduct quantitative experiments to show that applying 3D-EPN and PCN to our synthetic data, which is of different data distribution to its training data and in which the ground truth complete scans are not available for training, lead to performance degradation. The right sub-table of Table 1 shows that our method continues to produce good completions on our synthetic data, as we do not require paired data for training. The visual comparison is presented in the appendix. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate our method under different levels of input incompleteness, we conduct experiments on our synthetic data, in which we can control the fraction of missing points. Specifically, we train our network with varying levels of incompleteness by randomizing the amount of missing points during training, and afterwards fix the amount of missing points for testing. Table 3 shows the performance of our method on different classes under increasing amount of incompleteness and the comparison to AE. We can see that AE performance declines dramatically as the incompleteness of the input increases, while our method can still produce completions with high plausibility and F1 score. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5453c098c2184b5336d0b8edcb61e7d85368c65efbfbfacf407e14221efd0946.jpg",
+        "table_caption": [
+            "Table 3: Effect of varying incompleteness. Performance of AE and ours with increasing incompleteness $\\%$ of the missing points). Our completions remain robust even with increasing incompleteness as our method restricts the completion via the learned latent shape manifolds. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td colspan=\"2\">Plausibility</td><td colspan=\"2\"></td><td colspan=\"2\"></td><td colspan=\"2\">Plausibility</td><td colspan=\"2\">F1</td><td colspan=\"2\">Plausibility</td><td colspan=\"2\">F1</td><td colspan=\"2\"></td><td colspan=\"2\">Plausibility</td><td colspan=\"2\">F1</td></tr><tr><td>incomp.</td><td>model</td><td>AE</td><td>Ours</td><td>AE</td><td>Ours</td><td>model</td><td></td><td>AE</td><td>Ours</td><td>AE Ours</td><td>model</td><td></td><td>AE</td><td>Ours</td><td>AE</td><td>Ours</td><td>model</td><td>AE</td><td>Ours AE</td><td>Ours</td></tr><tr><td>10</td><td></td><td>96.3</td><td>99.4</td><td>94.9</td><td>85.8</td><td></td><td>88.0</td><td>91.0</td><td>88.4</td><td>87.7</td><td></td><td>69.3</td><td>74.0</td><td>90.0</td><td>90.2</td><td></td><td>88.9</td><td>91.0</td><td>96.6</td><td>96.5</td></tr><tr><td>20</td><td></td><td>96.7</td><td>99.7</td><td>89.5</td><td>84.5</td><td></td><td>81.0</td><td>91.0</td><td>87.2</td><td>85.1</td><td></td><td>65.0</td><td>75.5</td><td>85.0</td><td>87.3</td><td></td><td>89.7</td><td>90.7</td><td>94.0</td><td>95.5</td></tr><tr><td>30</td><td></td><td>95.0</td><td>98.2</td><td>81.8</td><td>83.3</td><td></td><td>67.0</td><td>90.9</td><td>70.8</td><td>80.7</td><td>table</td><td>55.2</td><td>73.4</td><td>77.3</td><td>84.0</td><td></td><td>88.7</td><td>90.7</td><td>89.5</td><td>94.1</td></tr><tr><td>40</td><td>car</td><td>85.4</td><td>96.1</td><td>71.8</td><td>79.7</td><td>chair</td><td>44.0</td><td>89.4</td><td>52.5</td><td>76.9</td><td></td><td>45.1</td><td>71.8</td><td>69.6</td><td>80.1</td><td>plane</td><td>85.0</td><td>89.0</td><td>84.9</td><td>92.8</td></tr><tr><td>50</td><td></td><td>58.6</td><td>96.4</td><td>63.4</td><td>72.5</td><td></td><td>38.0</td><td>83.5</td><td>33.5</td><td>71.8</td><td></td><td>32.5</td><td>73.3</td><td>62.1</td><td>74.5</td><td></td><td>80.0</td><td>90.7</td><td>80.6</td><td>91.0</td></tr></table>",
+        "bbox": [
+            184,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 DIVERSITY OF THE COMPLETION RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            104,
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+            117
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our network is encouraged to partially match the input, alleviating the mode-collapse issue, which often occurs in GAN. Unlike traditional generative model problem, where high diversity in generated results is always better, the diversity in our completion results should match that of the ground truth. Although this can be qualitatively accessed, see Fig. 5 in Appendix, in order to quantitatively quantify the divergence, we compute the Jensen-Shannon Divergence (JSD) between the marginal distribution of ground truth point sets and that of our completions as proposed in Achlioptas et al. (2018). As a reference, we simulate extremely mode-collapsed point cloud sets by repeating a randomly selected point cloud, then report the JSD between ground truth point sets and the simulated extremely mode-collapsed point sets. The JSD scores – lower is better – highlight the diversity of our 3D-EPN completions and the divergence between our diversity and that of the ground truth using the extreme mode-collapse results as reference (the former is ours): 0.06 vs. 0.46 on cars, $0 . 0 5 ~ \\nu s$ . 0.61 on chairs, 0.04 vs. 0.53 on planes and 0.04 vs. 0.59 on tables. ",
+        "bbox": [
+            173,
+            132,
+            825,
+            299
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            320,
+            341,
+            335
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "• Ours with partial AE, uses encoder $E _ { \\gamma } ^ { r }$ and decoder $D _ { \\psi } ^ { r }$ that are trained to reconstruct partial point sets for the latent space of partial input.   \n• Ours with EMD loss, uses EMD as the reconstruction loss.   \n• Ours without GAN, “switch off” the GAN module by simply setting $\\alpha = 0$ and $\\beta = 1$ , to verify the effectiveness of using adversarial training in our network.   \n• Ours with reconstruction loss, removes the reconstruction loss term by simply setting $\\alpha = 1$ and $\\beta = 0$ , to verify the effectiveness of the reconstruction loss term in generator loss. ",
+        "bbox": [
+            215,
+            342,
+            825,
+            472
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4 presents quantitative results for the ablation experiments, where we demonstrate the importance of various design choices and modules in our proposed network. We can see that our method has the best performance over all other variations. ",
+        "bbox": [
+            176,
+            488,
+            825,
+            529
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/d4db478112d973ca0ea1d8c97e953f36e31c7a69736e31b447dbe1f4b849ac9b.jpg",
+        "table_caption": [
+            "Table 4: Ablation study showing the importance of various design choices in our proposed network. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">Ours w/ partial AE</td><td colspan=\"3\">Ours w/EMD</td><td colspan=\"3\">Ours w/o GAN</td><td colspan=\"3\">Ours w/o Recon.</td><td colspan=\"3\">Ours</td></tr><tr><td></td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>boat</td><td>75.1</td><td>75.4</td><td>75.2</td><td>82.0</td><td>84.8</td><td>83.4</td><td>47.4</td><td>93.1</td><td>62.8</td><td>44.4</td><td>38.1</td><td>41.0</td><td>86.6</td><td>84.7</td><td>85.6</td></tr><tr><td>car</td><td>88.9</td><td>87.6</td><td>88.2</td><td>76.0</td><td>76.8</td><td>76.4</td><td>46.2</td><td>88.3</td><td>60.7</td><td>72.2</td><td>72.7</td><td>72.5</td><td>88.9</td><td>87.7</td><td>88.3</td></tr><tr><td>chair</td><td>64.1</td><td>66.7</td><td>65.4</td><td>78.6</td><td>76.4</td><td>77.5</td><td>41.3</td><td>79.8</td><td>54.4</td><td>75.6</td><td>75.1</td><td>75.3</td><td>78.7</td><td>77.4</td><td>78.0</td></tr><tr><td>dresser</td><td>67.4</td><td>68.6</td><td>68.0</td><td>71.4</td><td>72.3</td><td>71.9</td><td>44.2</td><td>74.4</td><td>55.4</td><td>20.9</td><td>21.9</td><td>21.4</td><td>75.8</td><td>76.5</td><td>76.2</td></tr><tr><td>lamp</td><td>64.0</td><td>74.8</td><td>69.0</td><td>69.9</td><td>79.0</td><td>74.2</td><td>28.6</td><td>84.7</td><td>42.8</td><td>15.6</td><td>22.2</td><td>18.3</td><td>71.3</td><td>80.2</td><td>75.5</td></tr><tr><td>plane</td><td>94.3</td><td>94.9</td><td>94.6</td><td>96.8</td><td>95.4</td><td>96.1</td><td>41.2</td><td>98.3</td><td>58.1</td><td>87.1</td><td>84.7</td><td>85.9</td><td>97.2</td><td>95.9</td><td>96.5</td></tr><tr><td>sofa</td><td>64.8</td><td>67.3</td><td>66.0</td><td>68.6</td><td>69.8</td><td>69.2</td><td>38.6</td><td>75.6</td><td>51.1</td><td>55.1</td><td>58.0</td><td>56.5</td><td>68.2</td><td>72.3</td><td>70.2</td></tr><tr><td>table</td><td>76.0</td><td>77.6</td><td>76.8</td><td>81.5</td><td>75.1</td><td>78.2</td><td>23.0</td><td>59.3</td><td>33.1</td><td>27.4</td><td>23.4</td><td>25.2</td><td>82.2</td><td>77.8</td><td>80.0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            722,
+            318,
+            738
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We presented a point-based unpaired shape completion framework that can be applied directly on raw partial scans to obtain clean and complete point clouds. At the core of the algorithm is an adaptation network acting as a generator that transforms latent code encodings of the raw point scans, and maps them to latent code encodings of clean and complete object scans. The two latent spaces regularize the problem by restricting the transfer problem to respective data manifolds. We extensively evaluated our method on real scans and virtual scans, demonstrating that our approach consistently leads to plausible completions and perform superior to other methods. The work opens up the possibility of generalizing our approach to scene-level scan completions, rather than object-specific completions. Our method shares the same limitations as many of the supervised counterparts: does not produce fine-scale details and assumes input to be canonically oriented. Another interesting future direction will be to combine point- and image-features to apply the completion setup to both geometry and texture details. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 ACKNOWLEDGEMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            398,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We thank all the anonymous reviewers for their insightful comments and feedback. This work is supported in part by grants from National Key R&D Program of China (2019YFF0302900), China Scholarship Council, National Natural Science Foundation of China (No.61602273), ERC Starting Grant, ERC PoC Grant, Google Faculty Award, Royal Society Advanced Newton Fellowship, and gifts from Adobe. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            224,
+            285,
+            239
+        ],
+        "page_idx": 8
+    },
+    {
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+    {
+        "type": "text",
+        "text": "A DETAILS OF DATASETS ",
+        "text_level": 1,
+        "bbox": [
+            178,
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+        "page_idx": 11
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+    {
+        "type": "text",
+        "text": "Clean and Complete Point Sets are obtained by virtually scanning the models from ShapeNet. We use a subset of 8 categories, namely boat, car, chair, dresser, lamp, plane, sofa and table, in our experiments. To generate clean and complete point set of a model, we virtually scan the models by performing ray-intersection test from cameras placed around the model to obtain the dense point set, followed by a down-sampling procedure to obtain a relatively sparser point set of $N$ points. Note that we use the models without any pose and scale augmentation. ",
+        "bbox": [
+            174,
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "This dataset is used for training to learn the clean-complete point set manifold in all our experiments.   \nThe following datasets of different data distributions serve as different noisy-partial input data. ",
+        "bbox": [
+            176,
+            223,
+            821,
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Real-world Data comes from three sources. The first one is derived from ScanNet dataset which provides many mesh objects that have been pre-segmented from its surrounding environment. For the purpose of training and testing our network, we extract ${ \\sim } 5 5 0 $ chair objects and ${ \\sim } 5 5 0 $ table objects from ScanNet dataset, and manually align them to be consistently orientated with models in ShapeNet dataset. We also split these objects into $90 \\% / 1 0 \\%$ train/test sets. ",
+        "bbox": [
+            174,
+            258,
+            825,
+            328
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The second one consists of 20 chairs and 20 tables from the Matterport3D dataset, to which the same extraction and alignment as is done in ScanNet dataset is also applied. Note that we train our method only on ScanNet training split, and use the trained model to test on Matterport3D data, to show how our method can generalize to absolutely unseen data. For both ScanNet and Matterport3D datasets, we uniformly sample $N$ points on the surface mesh of each object to obtain the input point sets. ",
+        "bbox": [
+            174,
+            335,
+            825,
+            405
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Last, we extract car observations from the KITTI dataset using the provided ground truth bounding boxes for training and testing our method. We use KITTI Velodyne point clouds from the 3D object detection benchmark and the split of Qi et al. (2018). We filter the observations such that each car observation contains at least 100 points to avoid overly sparse observations. ",
+        "bbox": [
+            174,
+            412,
+            825,
+            468
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "3D-EPN Dataset provides partial reconstructions of ShapeNet objects (8 categories) by using volumetric fusion method Curless & Levoy (1996) to integrate depth maps scanned along a virtual scanning trajectory around the model. For each model, a set of trajectories is generated with different levels of incompleteness, reflect the real-world scanning with a hand-held commodity RGB-D sensor. The entire dataset covers 8 categories and a total of 25590 object instances (the test set is composed of 5384 models). Note that, in the original 3D-EPN dataset, the data is represented in Signed Distance Field (SDF) for training data and Distance Field (DF) for test data. As our method works on pure point sets, we only use the point cloud representations of the training data provided by the authors, instead of using the SDF data which holds richer information and is claimed in Dai et al. (2017b) to be crucial for completing partial data. ",
+        "bbox": [
+            173,
+            474,
+            825,
+            614
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Synthetic Data serves the purpose of having another dataset of different incomplete scan distribution and controlling the incompleteness of the input. We use ShapeNet to generate a synthetic dataset, in which we can control the incompleteness of the synthetic partial point sets. For the models in each one of the 4 categories (car, chair, plane, and table), we split them into $90 \\% / 1 0 \\%$ train/test sets. For each model, from which a clean and complete point set has been scanned (as described earlier in this subsection), we can randomly pick a point and remove its $N \\times r$ $( r \\in [ 0 , 1 )$ ) nearest neighbor points. The parameter $r$ controls the incompleteness of the synthetically-generated input. Furthermore, we add Gaussian noise ${ \\mathcal { N } } ( \\mu , \\sigma ^ { 2 } )$ to each point ( $\\scriptstyle \\mu = 0$ and $\\sigma { = } 0 . 0 1$ for all our experiments). Last, we duplicate the points in the resulting point sets to generate point sets with an equal number of $N$ points. ",
+        "bbox": [
+            173,
+            621,
+            825,
+            760
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B NETWORK ARCHITECTURE DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            780,
+            514,
+            796
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In this section, we describe the details of the encoder, decoder, generator and discriminator in our network implementation. ",
+        "bbox": [
+            174,
+            810,
+            823,
+            839
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B.1 AE ARCHITECTURE DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            856,
+            421,
+            869
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Encoder consists of 5 1-D convolutional layers which are implemented as 1-D convolutions with ReLU and batch normalization, with kernel size of 1 and stride of 1, to lift the feature of each point to high dimensional feature space independently. In all experiments, we use an encoder with 64, ",
+        "bbox": [
+            176,
+            882,
+            823,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "128, 128, 256 and $k = 1 2 8$ filters in each of its layers, with $k$ being the latent code size. The output of the last convolutional layer is passed to a feature-wise maximum to produce a $k$ -dimensional latent code. ",
+        "bbox": [
+            174,
+            103,
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+            146
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Decoder transforms the latent vector using 3 fully connected layers with 256, 256, and $N \\textbf { x } 3$ neurons each, the first two having ReLUs, to reconstruct $N \\times 3$ output. ",
+        "bbox": [
+            173,
+            165,
+            823,
+            193
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B.2 GAN ARCHITECTURE DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            213,
+            434,
+            228
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Since the generator and discriminator of GAN directly operate on the latent space, the architecture for them is significantly simpler. Specifically, the generator is comprised of two fully connected layers with 128 and 128 neurons each, to map the latent code of noisy and incomplete point sets to that of clean and complete point sets. The discriminator consists of 3 fully connected layers with 256, 512 and 1 neurons each, to produce a single scalar for each latent code. ",
+        "bbox": [
+            174,
+            241,
+            825,
+            311
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "C TRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            334,
+            372,
+            352
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "To make the training of the entire network trackable, we pre-train the AEs used for obtaining the latent spaces. After that we retain the weights of AEs, only the weights of the generator and discriminator are updated through the back-propagation during the GAN training. The following training hyper-parameters are used in all our experiments. ",
+        "bbox": [
+            174,
+            369,
+            825,
+            424
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For training the AE, we use Adam optimizer with an initial learning rate of 0.0005, $\\beta _ { 1 } = 0 . 9$ and a batch size of 200 and train for a maximum of 2000 epochs. ",
+        "bbox": [
+            174,
+            431,
+            821,
+            460
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For training the generator and discriminator on the latent spaces, we use Adam optimizer with an initial learning rate of 0.0001, $\\beta _ { 1 } ~ = ~ 0 . 5$ and a batch size of 24 and train the generator and discriminator alternately for a maximum of 1000 epochs. ",
+        "bbox": [
+            174,
+            467,
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+            510
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "D QUALITATIVE RESULTS ON 3D-EPN DATASET ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            532,
+            589,
+            549
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We present qualitatively comparisons in Fig 5, where we show the partial input, AE, 3D-EPN, PCN, Ours, Our $^ +$ result and the ground truth point set. We can see that, although our method is not quantitatively the best, our results are very qualitatively plausible, as the generator is restricted to generate point sets from learned clean and complete shape manifolds. ",
+        "bbox": [
+            174,
+            568,
+            825,
+            622
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "E VISUAL COMPARISON ON TEST DATA WITH DISTRIBUTION DIFFERENT TO TRAINING DATA ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            648,
+            812,
+            680
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We present the visual comparison of 3D-EPN, PCN and our method on our synthetic data, which differs from 3D-EPN and PCN training data. In this experiment, the ground truth of our synthetic data is only available for evaluation. In Fig 6, we can see that our method keeps producing high-quality completions, as our method does not require paired data for training hence can still be trained when no ground truth is available. 3D-EPN and PCN produce much worse results as the data distribution of its training data and our synthetic data differ. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "F VARIATIONS OF LEVERAGING GROUND TRUTH SUPERVISION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            805,
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+            823
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "To adapt our network for training with ground truth point sets, we first change the reconstruction loss term in the generator loss from HD (Hausdorff Distance) to EMD (Earth Mover’s Distance), as the ground truth point set is complete and thus contains full information for supervising the completion. Note that HD is superior when the ground truth is unavailable for training, as shown in Table 4 of Section 4. Moreover, we present the comparison of different decisions on whether to adopt the adversarial training in our network for training with the ground truth. ",
+        "bbox": [
+            174,
+            840,
+            825,
+            924
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/95d46cdd65c548a3c44cec8ef8dab1802645ac2d6129979ede0e38a2d48714b8.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative comparison on 3D-EPN dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            156,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/9ae8268e41cfad97163e9cdcd5c222639f406a629f4d3b95e5e735640fd4754c.jpg",
+        "image_caption": [
+            "Figure 6: Effect of data distribution discrepancy and qualitative comparison on our synthetic dataset. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "• Ours $\\mathrm { G T + E M D } $ ), which is also denoted as ${ \\mathrm { O u r s } } +$ in the paper, removes the adversarial training in the network by simply setting $\\alpha = 0$ and not updating the discriminator weights, hence there is only EMD reconstruction loss for the generator. ",
+        "bbox": [
+            215,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "• Ours ( $\\mathbf { G } \\mathbf { T } { \\mathrm { + E } } \\mathbf { M } \\mathbf { D } { \\mathrm { + G } } \\mathbf { A } \\mathbf { N } )$ , in contrast, retains the adversarial training. ",
+        "bbox": [
+            217,
+            151,
+            679,
+            165
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Table 5 shows the quantitative comparison results, we can see that, when the ground truth point sets are available, Ours $\\mathbf { \\bar { G } T + E M D } ,$ produces better results than Ours $\\mathrm { ( G T + E M D + G A N ) }$ . Our explanation for why adopting adversarial training here leads to worse results is that: when the ground truth is available, which is complete and contains all information for supervising the network, adding adversarial training will make the network much harder to train, as the network always gets punished by failing to fool the discriminator when it is actually transforming current output closer to the ground truth. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/b9fda1160aa707259b49533825777d91dcd64a77dd00ce8b8e0dd283c9cd956e.jpg",
+        "table_caption": [
+            "Table 5: Removal of adversarial training when training with ground truth leads to significant improvement. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">Ours (GT+EMD)</td><td colspan=\"3\">Ours (GT+EMD+GAN)</td></tr><tr><td>model</td><td>acc.</td><td>comp.</td><td>F1</td><td>acc.</td><td>comp.</td><td>F1</td></tr><tr><td>car</td><td>93.5</td><td>92.8</td><td>93.1</td><td>80.5</td><td>77.9</td><td>79.2</td></tr><tr><td>chair</td><td>82.3</td><td>83.3</td><td>82.8</td><td>51.5</td><td>58.1</td><td>54.6</td></tr><tr><td> plane</td><td>95.6</td><td>94.8</td><td>95.2</td><td>91.4</td><td>86.3</td><td>88.8</td></tr><tr><td>table</td><td>81.2</td><td>81.4</td><td>81.3</td><td>37.9</td><td>39.3</td><td>38.6</td></tr></table>",
+        "bbox": [
+            313,
+            327,
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+            424
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "G MORE STATISTICS FRO THE BASELINE COMPARISON",
+        "text_level": 1,
+        "bbox": [
+            174,
+            457,
+            640,
+            473
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "For the baseline methods comparison on 3D-EPN dataset, we also report the Chamfer distance (CD), Earth Mover’s Distance (EMD) and Hausdorff Distance (HD, maximum of the two directional distances) between the ground truth and the completion in Table 6: ",
+        "bbox": [
+            174,
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+        "page_idx": 14
+    },
+    {
+        "type": "table",
+        "img_path": "images/0163560e532f13c7d5bca274185b62d7f44dd755029856e1e13632a1a55caee9.jpg",
+        "table_caption": [
+            "Table 6 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>AE</td><td></td><td></td><td>EPN</td><td></td><td></td><td>PCN</td><td></td><td></td><td></td><td>Ours</td><td></td><td>Ours+</td><td></td><td></td></tr><tr><td>model</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td></td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td><td>CD</td><td>EMD</td><td>HD</td></tr><tr><td>boat</td><td>0.0012</td><td>0.0530</td><td>0.0864</td><td>0.0009</td><td>0.0500</td><td>0.0562</td><td>0.0006</td><td></td><td>0.0437</td><td>0.0635</td><td>0.0011</td><td>0.0532</td><td>0.0857</td><td>0.0008</td><td>0.0455</td><td>0.0799</td></tr><tr><td>car</td><td>0.0019</td><td>0.0668</td><td>0.1093</td><td>0.0024</td><td>0.0744</td><td>0.0989</td><td>0.0005</td><td></td><td>0.0418</td><td>0.0648</td><td>0.0010</td><td>0.0434</td><td>0.0763</td><td>0.0007</td><td>0.0393</td><td>0.0677</td></tr><tr><td>chair</td><td>0.0031</td><td>0.1003</td><td>0.1374</td><td>0.0016</td><td>0.0704</td><td>0.0877</td><td>0.0009</td><td>0.0586</td><td></td><td>0.0832</td><td>0.0020</td><td>0.0773</td><td>0.1010</td><td>0.0015</td><td>0.0619</td><td>0.0915</td></tr><tr><td>dresser</td><td>0.0037</td><td>0.0985</td><td>0.1295</td><td>0.0027</td><td>0.0783</td><td>0.0963</td><td>0.0008</td><td>0.0545</td><td></td><td>0.0771</td><td>0.0019</td><td>0.0588</td><td>0.0833</td><td>0.0011</td><td>0.0482</td><td>0.0734</td></tr><tr><td>lamp</td><td>0.0026</td><td>0.0857</td><td>0.1092</td><td>0.0038</td><td>0.0966</td><td>0.1154</td><td>0.0013</td><td>0.0692</td><td></td><td>0.0890</td><td>0.0023</td><td>0.0848</td><td>0.1073</td><td>0.0018</td><td>0.0729</td><td>0.1002</td></tr><tr><td>plane</td><td>0.0004</td><td>0.0346</td><td>0.0591</td><td>0.0060</td><td>0.0943</td><td>0.1255</td><td>0.0002</td><td>0.0308</td><td></td><td>0.0394</td><td>0.0004</td><td>0.0338</td><td>0.0545</td><td>0.0005</td><td>0.0405</td><td>0.0685</td></tr><tr><td>sofa</td><td>0.0030</td><td>0.0792</td><td>0.1232</td><td>0.0045</td><td>0.0880</td><td>0.1093</td><td>0.0008</td><td>0.0494</td><td></td><td>0.0651</td><td>0.0026</td><td>0.0655</td><td>0.0928</td><td>0.0012</td><td>0.0536</td><td>0.0958</td></tr><tr><td>table</td><td>0.0044</td><td>0.0886</td><td>0.1518</td><td>0.0014</td><td>0.0681</td><td>0.0975</td><td>0.0010</td><td>0.0603</td><td>0.0968</td><td></td><td>0.0026</td><td>0.068445</td><td>0.1071</td><td>0.0021</td><td>0.0681</td><td>0.1224</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "H USER STUDY ON REAL-WORLD DATA COMPLETION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            718,
+            629,
+            733
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "We also conducted a user study on the completion results of the real-world scans, where given a partial input users are required to pick the most preferable completion among EPN, PCN and our results. In total, we received 1,000 valid user selections and report the preference (in percentage of the total selections) of each method in the user study. From Fig. 7 we can see that in over half $( 5 2 \\% )$ of the selections, our completion results are selected as the best completion, while PCN completion results are better in $45 \\%$ of the selections. ",
+        "bbox": [
+            173,
+            750,
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+            833
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Interestingly, although our method outperforms other methods in the user study, our method clearly does not hold a dominant position in this user study. After a more in-depth analysis of the user selections, we found that users intend to pick the completion in which the partial input is embedded, which can be formulated as the Hausdorff distance from the partial input to the completion, and the supervised method PCN preserves the input point cloud in its completion output as this always minimizes the distance loss. The plausibility of the completion result is usually neglected by users, while the plausibility and the Hausdorff distance from the partial input to the completion are both considered as two trade-off terms in the objective function of our completion generator. Fig. 8 gives a typical example, where the PCN completion without clear chair structure is often picked as better completion while our completion tries to trade-off between the HL and the plausibility. ",
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/524355932026585ae173aa1bd72f99ec46ae57a45e89057f15b615323798983b.jpg",
+        "image_caption": [
+            "Figure 7 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            302,
+            99,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/248324f777447e8e23f535fcb822ddbd1d31fe28055f1002364109f55440b06a.jpg",
+        "image_caption": [
+            "Figure 8 "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            305,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "I GENERALIZATION TO UNSEEN CLASSES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            575,
+            532,
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+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/9c74083cc7a15645561f17e907b18b10deb7c829cb549d4d03ae523646a55ad1.jpg",
+        "image_caption": [
+            "Figure 9 "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            838
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Our method does generalize to unseen objects from the same category in the test set, which is demonstrated in the experimental results section. However, our method intuitively should not generalize to classes that are not seen during the training, as the autoencoder, which is a fundamental component in our network, does not generalize to unseen classes. We present the qualitative results of applying our table completion network on chair and airplane class. We can see that from Fig. 9, on the unseen chair class, which shares similar structure with table, our table completion network can produce some reasonable structures, but is unable to complete with a seat back as the autoencoder does not have such capability; on the unseen airplane class, which is rather dissimilar to table class, our table completion network failed to complete the partial airplanes. ",
+        "bbox": [
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+        "page_idx": 15
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+    {
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+]

parse/train/Ysuv-WOFeKR/Ysuv-WOFeKR_content_list.json

@@ -0,0 +1,1941 @@
+[
+    {
+        "type": "text",
+        "text": "PARROT: DATA-DRIVEN BEHAVIORAL PRIORS FOR REINFORCEMENT LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            98,
+            821,
+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Avi Singh∗, Huihan $\\mathbf { L i u } ^ { * }$ , Gaoyue Zhou, Albert Yu, Nicholas Rhinehart, Sergey Levine University of California, Berkeley ",
+        "bbox": [
+            186,
+            169,
+            784,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            250
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Reinforcement learning provides a general framework for flexible decision making and control, but requires extensive data collection for each new task that an agent needs to learn. In other machine learning fields, such as natural language processing or computer vision, pre-training on large, previously collected datasets to bootstrap learning for new tasks has emerged as a powerful paradigm to reduce data requirements when learning a new task. In this paper, we ask the following question: how can we enable similarly useful pre-training for RL agents? We propose a method for pre-training behavioral priors that can capture complex input-output relationships observed in successful trials from a wide range of previously seen tasks, and we show how this learned prior can be used for rapidly learning new tasks without impeding the RL agent’s ability to try out novel behaviors. We demonstrate the effectiveness of our approach in challenging robotic manipulation domains involving image observations and sparse reward functions, where our method outperforms prior works by a substantial margin. Additional materials can be found on our project website: https://sites.google.com/view/parrot-rl ",
+        "bbox": [
+            232,
+            267,
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+            489
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            518,
+            334,
+            534
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Reinforcement Learning (RL) is an attractive paradigm for robotic learning because of its flexibility in being able to learn a diverse range of skills and its capacity to continuously improve. However, RL algorithms typically require a large amount of data to solve each individual task, including simple ones. Since an RL agent is generally initialized without any prior knowledge, it must try many largely unproductive behaviors before it discovers a high-reward outcome. In contrast, humans rarely attempt to solve new tasks in this way: they draw on their prior experience of what is useful when they attempt a new task, which substantially shrinks the task search space. For example, faced with a new task involving objects on a table, a person might grasp an object, stack multiple objects, or explore other object rearrangements, rather than re-learning how to move their arms and fingers. ",
+        "bbox": [
+            174,
+            551,
+            825,
+            676
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Can we endow RL agents with a similar sort of behavioral prior from past experience? In other fields of machine learning, the use of large prior datasets to bootstrap acquisition of new capabilities has been studied extensively to good effect. For example, language models trained on large, diverse datasets offer representations that drastically improve the efficiency of learning downstream tasks (Devlin et al., 2019). What would be the analogue of this kind of pre-training in robotics and RL? One way we can approach this problem is to leverage successful trials from a wide range of previously seen tasks to improve learning for new tasks. The data could come from previously learned policies, from human demonstrations, or even unstructured teleoperation of robots (Lynch et al., 2019). In this paper, we show that behavioral priors can be obtained through representation learning, and the representation in question must not only be a representation of inputs, but actually a representation of input-output relationships – a space of possible and likely mappings from states to actions among which the learning process can interpolate when confronted with a new task. ",
+        "bbox": [
+            174,
+            683,
+            825,
+            849
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "What makes for a good representation for RL? Given a new task, a good representation must (a) provide an effective exploration strategy, (b) simplify the policy learning problem for the RL algorithm, and (c) allow the RL agent to retain full control over the environment. In this paper, we address ",
+        "bbox": [
+            176,
+            856,
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+            898
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/3cf924a289e0fcdc95a90d419c43c1d5e5e637b657ba0f9ca4072d113a28f90e.jpg",
+        "image_caption": [
+            "Figure 1: Our problem setting. Our training dataset consists of near-optimal state-action trajectories (without reward labels) from a wide range of tasks. Each task might involve interacting with a different set of objects. Even for the same set of objects, the task can be different depending on our objective. For example, in the upper right corner, the objective could be picking up a cup, or it could be to place the bottle on the yellow cube. We learn a behavioral prior from this multi-task dataset capable of trying many different useful behaviors when placed in a new environment, and can aid an RL agent to quickly learn a specific task in this new environment. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            101,
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+            270
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Transfer Behavioral all of these challenges through learning an invertible function that maps noise vectors to complex, Prior Learning New Taskshigh-dimensional environment actions. Building on prior work in normalizing flows (Dinh et al., 2017), we train this mapping to maximize the (conditional) log-likelihood of actions observed in Trial 2successful trials from past tasks. When dropped into a new MDP, the RL agent can now sample from a unit Gaussian, and use the learned mapping (which we refer to as the behavioral prior) to generate likely environment actions, conditional on the current observation. This learned mapping essentially transforms the original MDP into a simpler one for the RL agent, as long as the original Trial n-1 MDP shares (partial) structure with previously seen MDPs (see Section 3). Furthermore, since this mapping is invertible, the RL agent still retains full control over the original MDP: for every possible Trial n environment action, there exists a point within the support of the Gaussian distribution that maps to that action. This allows the RL agent to still try out new behaviors that are distinct from what was previously observed. ",
+        "bbox": [
+            174,
+            378,
+            825,
+            545
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our main contribution is a framework for pre-training in RL from a diverse multi-task dataset, which produces a behavioral prior that accelerates acquisition of new skills. We present an instantiation of this framework in robotic manipulation, where we utilize manipulation data from a diverse range of prior tasks to train our behavioral prior, and then use it to bootstrap exploration for new tasks. By making it possible to pre-train action representations on large prior datasets for robotics and RL, we hope that our method provides a path toward leveraging large datasets in the RL and robotics settings, much like language models can leverage large text corpora in NLP and unsupervised pretraining can leverage large image datasets in computer vision. Our method, which we call Prior AcceleRated ReinfOrcemenT (PARROT), is able to quickly learn tasks that involve manipulating previously unseen objects, from image observations and sparse rewards, in settings where RL from scratch fails to learn a policy at all. We also compare against prior works that incorporate prior data for RL, and show that PARROT substantially outperforms these prior works. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            747,
+            343,
+            763
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Combining RL with demonstrations. Our work is related to methods for learning from demonstrations (Pomerleau, 1989; Schaal et al., 2003; Ratliff et al., 2007; Pastor et al., 2009; Ho & Ermon, 2016; Finn et al., 2017b; Giusti et al., 2016; Sun et al., 2017; Zhang et al., 2017; Lynch et al., 2019). While demonstrations can also be used to speed up RL (Schaal, 1996; Peters & Schaal, 2006; Kormushev et al., 2010; Hester et al., 2017; Vecer´ık et al., 2017; Nair et al., 2018; Rajeswaran et al., 2018; Silver et al., 2018; Peng et al., 2018; Johannink et al., 2019; Gupta et al., 2019), this usually requires collecting demonstrations for the specific task that is being learned. In contrast, we use data from a wide range of other prior tasks to speed up RL for a new task. As we show in our experiments, PARROT is better suited to this problem setting when compared to prior methods that combine imitation and RL for the same task. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Generative modeling and RL. Several prior works model multi-modal action distributions using expert trajectories from different tasks. IntentionGAN (Hausman et al.) and InfoGAIL (Li et al., 2017) learn multi-modal policies via interaction with an environment using an adversarial imitation approach (Ho & Ermon, 2016), but we learn these distributions only from data. Other works learn these distributions from data (Xie et al., 2019; Rhinehart et al., 2020) and utilize them for planning at test time to optimize a user-provided cost function. In contrast, we use the behavioral prior to augment model-free RL of a new task. This allows us to learn policies for new tasks that may be substantially different from prior tasks, since we can collect data specific to the new task at hand, and we do not explicitly need to model the environment, which can be complicated for high-dimensional state and action spaces, such as when performing continuous control from images observations. Another line of work (Ghadirzadeh et al., 2017; Ham¨ al¨ ainen et al. ¨ , 2019; Ghadirzadeh et al., 2020) explores using generative models for RL, using a variational autoencoder (Kingma & Welling, 2014) to model entire trajectories in an observation-independent manner, and then learning an open-loop, single-step policy using RL to solve the downstream task. Our approach differs in several key aspects: (1) our model is observation-conditioned, allowing it to prioritize actions that are relevant to the current scene or environment, (2) our model allows for closed-loop feedback control, and (3) our model is invertible, allowing the high-level policy to retain full control over the action space. Our experiments demonstrate these aspects are crucial for solving harder tasks. ",
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+        "type": "text",
+        "text": "Hierarchical learning. Our method can be interpreted as training a hierarchical model: the lowlevel policy is the behavioral prior trained on prior data, while the high-level policy is trained using RL and controls the low-level policy. This structure is similar to prior work in hierarchical RL (Dayan & Hinton, 1992; Parr & Russell, 1997; Dietterich, 1998; Sutton et al., 1999; Kulkarni et al., 2016). We divide prior work in hierarchical learning into two categories: methods that seek to learn both the low-level and high-level policies through active interaction with an environment (Kupcsik et al., 2013; Heess et al., 2016; Bacon et al., 2017; Florensa et al., 2017; Haarnoja et al., 2018a; Nachum et al., 2018; Chandak et al., 2019; Peng et al., 2019), and methods that learn temporally extended actions, also known as options, from demonstrations, and then recompose them to perform long-horizon tasks through RL or planning (Fox et al., 2017; Krishnan et al., 2017; Kipf et al., 2019; Shankar et al., 2020; Shankar & Gupta, 2020). Our work shares similarities with the data-driven approach of the latter methods, but work on options focuses on modeling the temporal structure in demonstrations for a small number of long-horizon tasks, while our behavioral prior is not concerned with temporally-extended abstractions, but rather with transforming the original MDP into one where potentially useful behaviors are more likely, and useless behaviors are less likely. ",
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+        "text": "Meta-learning. Our goal in this paper is to utilize data from previously seen tasks to speed up RL for new tasks. Meta-RL (Duan et al., 2016; Wang et al., 2016; Finn et al., 2017a; Mishra et al., 2017; Rakelly et al., 2019; Mendonca et al., 2019; Zintgraf et al., 2020; Fakoor et al., 2020) and meta-imitation methods (Duan et al., 2017; Finn et al., 2017c; Huang et al., 2018; James et al., 2018; Paine et al., 2018; Yu et al., 2018; Huang et al., 2019; Zhou et al., 2020) also seek to speed up learning for new tasks by leveraging experience from previously seen tasks. While meta-learning provides an appealing and principled framework to accelerate acquisition of future tasks, we focus on a more lightweight approach with relaxed assumptions that make our method more practically applicable, and we discuss these assumptions in detail in the next section. ",
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+        "type": "text",
+        "text": "3 PROBLEM SETUP ",
+        "text_level": 1,
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+        "text": "Our goal is to improve an agent’s ability to learn new tasks by incorporating a behavioral prior, which it can acquire from previously seen tasks. Each task can be considered a Markov decision process (MDP), which is defined by a tuple $( S , \\mathcal { A } , \\mathrm { T } , r , \\gamma )$ , where $s$ and $\\mathcal { A }$ represent state and action spaces, $\\mathrm { T } ( s ^ { \\prime } | s , a )$ and $r ( s , a )$ represent the dynamics and reward functions, and $\\gamma \\in ( 0 , 1 )$ represents the discount factor. Let $p ( M )$ denote a distribution over such MDPs, with the constraint that the state and action spaces are fixed. In our experiments, we treat high-dimensional images as $s$ , which means that this constraint is not very restrictive in practice. In order for the behavioral prior to be able to accelerate the acquisition of new skills, we assume the behavioral prior is trained on data that structurally resembles potential optimal policies for all or part of the new task. For example, if the new task requires placing a bottle in a tray, the prior data might include some behaviors that involve picking up objects. There are many ways to formalize this assumption. One way to state this formally is to assume that prior data consists of executions of near-optimal policies for MDPs drawn according to $M \\sim p ( M )$ , and the new task $M ^ { \\star }$ is likewise drawn from $p ( M )$ . In this case, the generative process for the prior data can be expressed as: ",
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+            "Figure 2: PARROT. Using successful trials from a large variety of tasks, we learn an invertible mapping $f _ { \\phi }$ s that maps noise $z$ to useful actions $a$ Z0 Z1 Z2 Z3=a . This mapping is conditioned on the current observation, which in our case is an RGB image. The image is passed through a stack of convolutional layers and flattened to obtain an image encoding $\\psi ( s )$ , and this image encoding is then used to condition each individual transformation $f _ { i }$ pi(z|s)of our overall mapping function $f _ { \\phi }$ . The parameters of the mapping (including the convolutional encoder) are a learned through maximizing the conditional log-likelihood of state-action pairs observed in the dataset. When learning a new task, this mapping can simplify the MDP for an RL agent by mapping actions sampled from a randomly initialized policy to actions that are likely to lead to useful behavior in the current scene. Since the mapping is invertible, the RL agent still retains full control over the action space of the original MDP, simply the likelihood of executing a useful action is increased through use of the pre-trained mapping. "
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+        "img_path": "images/3121320ba6fa2b75684b9b640763bbb9d12dd9ca960ab6a92cbb1c43985c846a.jpg",
+        "text": "$$\nM \\sim p ( M ) , \\quad \\pi _ { M } ( \\tau ) = \\arg \\operatorname* { m a x } _ { \\pi } \\mathbb { E } _ { \\pi , M } [ R _ { M } ] , \\quad \\tau _ { M } \\sim \\pi _ { M } ( \\tau ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\tau _ { M } = ( s _ { 1 } , a _ { 1 } , s _ { 2 } , a _ { 2 } , . . . , s _ { T } , a _ { T } )$ is a sequence of state and actions, $\\pi _ { M } ( \\tau )$ denotes a nearoptimal policy (Kearns & Singh, 2002) for MDP $M$ and $\\textstyle R _ { M } = \\sum _ { t = 0 } ^ { \\infty } \\gamma ^ { t } r _ { t }$ . When incorporating the behavioral prior for learning a new task $M ^ { \\star }$ , our goal is the same as standard RL: to find a policy $\\pi$ that maximizes the expected return ar $\\operatorname { \\mu } _ { 5 } \\operatorname* { m a x } _ { \\pi } \\mathbb { E } _ { \\pi , M ^ { \\star } } [ R _ { M ^ { \\star } } ]$ . Our assumption on tasks being drawn from a distribution $p ( M )$ shares similarities with the meta-RL problem (Wang et al., 2016; Duan et al., 2016), but our setup is different: it does not require accessing any task in $p ( M )$ except the new task we are learning, $M ^ { \\star }$ . Meta-RL methods need to interact with the tasks in $p ( M )$ during meta-training, with access to rewards and additional samples, whereas we learn our behavioral prior simply from data, without even requiring this data to be labeled with rewards. This is of particular importance for real-world problem settings such as robotics: it is much easier to store data from prior tasks (e.g., different environments) than to have a robot physically revisit those prior settings and retry those tasks, and not requiring known rewards makes it possible to use data from a variety of sources, including human-provided demonstrations. In our setting, RL is performed in only one environment, while the prior data can come from many environments. ",
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+        "text": "Our setting is related to meta-imitation learning (Duan et al., 2017; Finn et al., 2017c), as we speed up learning new tasks using data collected from past tasks. However, meta-imitation learning methods require at least one demonstration for each new task, whereas our method can learn new tasks without any demonstrations. Further, our data requirements are less stringent: meta-imitation learning methods require all demonstrations to be optimal, require all trajectories in the dataset to have a task label, and requires “paired demonstrations”, i.e. at least two demonstrations for each task (since meta-imitation methods maximize the likelihood of actions from one demonstration after conditioning the policy on another demonstration from the same task). Relaxing these requirements increases the scalability of our method: we can incorporate data from a wider range of sources, and we do not need to explicitly organize it into specific tasks. ",
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+        "type": "text",
+        "text": "4 BEHAVIORAL PRIORS FOR REINFORCEMENT LEARNING ",
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+        "text": "Our method learns a behavioral prior for downstream RL by utilizing a dataset $\\mathcal { D }$ of (near-optimal) state-action pairs from previously seen tasks. We do so by learning a state-conditioned mapping $f _ { \\phi } \\colon { \\mathcal { Z } } \\times { \\mathcal { S } } \\to { \\mathcal { A } }$ (where $\\phi$ denotes learnable parameters) that transforms a noise vector $z$ into an action $a$ that is likely to be useful in the current state $s$ . This removes the need for exploring via “meaningless” random behavior, and instead enables an exploration process where the agent attempts behaviors that have been shown to be useful in previously seen domains. For example, if a robotic arm is placed in front of several objects, randomly sampling $z$ (from a simple distribution, such as the unit Gaussian) and applying the mapping $a = f _ { \\phi } ( z ; s )$ should result in actions that, when executed, result in meaningful interactions with the objects. This learned mapping essentially transforms the MDP experienced by the RL agent into a simpler one, where every random action executed in this transformed MDP is much more likely to lead to a useful behavior. ",
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+        "text": "How can we learn such a mapping? In this paper, we propose to learn this mapping through stateconditioned generative modeling of the actions observed in the original dataset $\\mathcal { D }$ , and we refer to this state-conditioned distribution over actions as the behavioral prior $p _ { \\mathrm { p r i o r } } ( a | s )$ . A deep generative model takes noise as input, and outputs a plausible sample from the target distribution, i.e. it can represent $p _ { \\mathrm { p r i o r } } ( a | s )$ as a distribution over noise $z$ using a deterministic mapping $f _ { \\phi } : \\mathcal { Z } \\times \\mathcal { S } \\mapsto A$ When learning a new task, we can use this mapping to reparametrize the action space of the RL agent: if the action chosen by the randomly initialized neural network policy is $z$ , then we execute the action $a = f _ { \\phi } ( z ; s )$ in the original MDP, and learn a policy $\\pi ( \\boldsymbol { z } | \\boldsymbol { s } )$ that maximizes the task reward through learning to control the inputs to the mapping $f _ { \\phi }$ . The training of the behavioral prior and the task-specific policy is decoupled, allowing us to mix and match RL algorithms and generative models to best suit the application of interest. An overview of our overall architecture is depicted in Figure 2. In the next subsection, we discuss what properties we would like the behavioral prior to satisfy, and present one particular choice for learning a prior that satisfies all of these properties. ",
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+        "type": "text",
+        "text": "4.1 LEARNING A BEHAVIORAL PRIOR WITH NORMALIZING FLOWS ",
+        "text_level": 1,
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+        "text": "For the behavioral prior to be effective, it needs to satisfy certain properties. Since we learn the prior from a multi-task dataset, containing several different behaviors even for the same initial state, the learned prior should be capable of representing complex, multi-modal distributions. Second, it should provide a mapping for generating “useful” actions from noise samples when learning a new task. Third, the prior should be state-conditioned, so that only actions that are relevant to the current state are sampled. And finally, the learned mapping should allow easier learning in the reparameterized action space without hindering the RL agent’s ability to attempt novel behaviors, including actions that might not have been observed in the dataset $\\mathcal { D }$ . Generative models based on normalizing flows (Dinh et al., 2017) satisfy all of these properties well: they allow maximizing the model’s exact log-likelihood of observed examples, and learn a deterministic, invertible mapping that transforms samples from a simple distribution $p _ { z }$ to examples observed in the training dataset. In particular, the real-valued non-volume preserving (real NVP) architecture introduced by Dinh et al. (2017) allows using deep neural networks to parameterize this mapping (making it expressive) While the original real NVP work modelled unconditional distributions, follow-up work has found that it can be easily extended to incorporate conditioning information (Ardizzone et al., 2019). We refer the reader to prior work (Dinh et al., 2017) for a complete description of real NVPs, and summarize its key features here. Given an invertible mapping $a = f _ { \\phi } ( z ; s )$ , the change of variable formula allows expressing the likelihood of the observed actions using samples from $\\mathcal { D }$ in the following way: ",
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+        "img_path": "images/3e994494eba57fd08f15f3299fe9ce0123822cc54c9bccd6ca4dd506e614f05a.jpg",
+        "text": "$$\np _ { \\mathrm { p r i o r } } ( a | s ) = p _ { z } \\left( f _ { \\phi } ^ { - 1 } ( a ; s ) \\right) \\left| \\operatorname* { d e t } \\left( \\partial f _ { \\phi } ^ { - 1 } ( a ; s ) / \\partial a \\right) \\right|\n$$",
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+        "text": "Dinh et al. (2017) propose a particular (unconditioned) form of the invertible mapping $f _ { \\phi }$ , called an affine coupling layer, that maintains tractability of the likelihood term above, while still allowing the mapping $f _ { \\phi }$ to be expressive. Several coupling layers can be composed together to transform simple noise vectors into samples from complex distributions, and each layer can be conditioned on other variables, as shown in Figure 2. ",
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+        "type": "text",
+        "text": "4.2 ACCELERATED REINFORCEMENT LEARNING VIA BEHAVIORAL PRIORS ",
+        "text_level": 1,
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+        "text": "After we obtain the mapping $f _ { \\phi } ( z ; s )$ from the behavioral prior learned by maximizing the likelihood term in Equation 2, we would like to use it to accelerate RL when solving a new task. Instead of learning a policy $\\pi _ { \\boldsymbol { \\theta } } ( a | s )$ that directly executes its actions in the original MDP, we learn a policy $\\pi _ { \\boldsymbol { \\theta } } { \\left( z | \\boldsymbol { s } \\right) }$ , and execute an action in the environment according to $a = f _ { \\phi } ( z ; s )$ . As shown in Figure 2, this essentially transforms the MDP experienced for the RL agent into one where random actions $z \\sim p _ { z }$ (where $p _ { z }$ is the base distribution used for training the mapping $f _ { \\phi }$ ) are much more likely to result in useful behaviors. To enable effective exploration at the start of the learning period, we initialize the RL policy to the base distribution used for training the prior, so that at the beginning of training, $\\pi _ { \\theta } ( z | s ) \\mathbf { \\bar { \\theta } } { : = } \\bar { p _ { z } } ( z )$ . Since the mapping $f _ { \\phi }$ is invertible, the RL agent still retains full control over the action space: for any given $a$ , it can always find a $z$ that generates $z = f _ { \\phi } ^ { - 1 } ( a ; s )$ in the original MDP. The learned mapping increases the likelihood of useful actions without crippling the RL agent, making it ideal for fine-tuning from task-specific data. Our complete method is described in Algorithm 1 in Appendix A. Note that we need to learn the mapping $f _ { \\phi }$ only once, and it can be used for accelerated learning of any new task. ",
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+        "text": "4.3 IMPLEMENTATION DETAILS ",
+        "text_level": 1,
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+        "text": "We use real NVP to learn $f _ { \\phi }$ , and as shown in Figure 2, each coupling layer in the real NVP takes as input the the output of the previous coupling layer, and the conditioning information. The conditioning information in our case corresponds to RGB image observations, which allows us to train a single behavioral prior across a wide variety of tasks, even when the tasks might have different underlying states (for example, different objects). We train a real NVP model with four coupling layers; the exact architecture, and other hyperparameters, are detailed in Appendix B. The behavioral prior can be combined with any RL algorithm that is suitable for continuous action spaces, and we chose to use the soft actor-critic (Haarnoja et al., 2018b) due to its stability and ease of use. ",
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+        "text": "5 EXPERIMENTS ",
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+        "text": "Our experiments seek to answer: (1) Can the behavioral prior accelerate learning of new tasks? (2) How does PARROT compare to prior works that accelerate RL with demonstrations? (3) How does PARROT compare to prior methods that combine hierarchical imitation with RL? ",
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+        "text": "Domains. We evaluate our method on a suite of challenging robotic manipulation tasks, a subset of which are depicted in Figure 3. Each task involves controlling a 6-DoF robotic arm and its gripper, with a 7D action space. The observation is a $4 8 \\times 4 8$ RGB image, which allows us to use the same observation representation across tasks, even though each underlying task might have a different underlying state (e.g., different objects). No other observations (such as joint angles or end-effector positions) are provided. In each task, the robot needs to interact with one or two objects in the scene to achieve its objective, and there are three objects in each scene. Note that all of the objects in the test scenes are novel – the dataset $\\mathcal { D }$ contains no interactions with these objects. The object positions at the start of each trial are randomized, and the policy must infer these positions from image observations in order to successfully solve the task. A reward of $+ 1$ is provided when the objective for the task is achieved, and the reward is zero otherwise. Detailed information on the objective for each task and example rollouts are provided in Appendix C.1, and on our anonymous project website1. ",
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+        "type": "text",
+        "text": "Data collection. Our behavioral prior is trained on a diverse dataset of trajectories from a wide range of tasks, and then utilized to accelerate reinforcement learning of new tasks. As discussed in Section 3, for the prior to be effective, it needs to be trained on a dataset that structurally resembles the behaviors that might be optimal for the new tasks. In our case, all of the behaviors involve repositioning objects (i.e., picking up objects and moving them to new locations), which represents a very general class of tasks that might be performed by a robotic arm. While the dataset can be collected in many ways, such as from human demonstrations or prior tasks solved by the robot, we collect it using a set of randomized scripted policies, see Appendix C.2 for details. Since the policies are randomized, not every execution of such a policy results in a useful behavior, and we decide to keep or discard a collected trajectory based on a simple predefined rule: if the trajectory collected ends with a successful grasp or rearrangement of any one of the objects in the scene, we add this trajectory to our dataset. We collect a dataset of 50K trajectories, where each trajectory is of length 25 timesteps ${ \\approx } 5 – 6$ seconds), for a total of $1 . 2 5 \\mathrm { m }$ observation-action pairs. The observation is a $4 8 \\times 4 8$ RGB image, while the actions are continuous 7D vectors. Data collection involves interactions with over 50 everyday objects (see Appendix C.3); the diversity of this dataset enables learning priors that can produce useful behavior when interacting with a new object. ",
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+        "img_path": "images/b36fce4e54479f5d06fd57353f9add4588c8c16905918bb6288c534601591ccb.jpg",
+        "image_caption": [
+            "Figure 3: Tasks. A subset of our evaluation tasks, with one task shown in each row. In the first task (first row), the objective is to pick up a can and place it in the pan. In the second task, the robot must pick up the vase and put it in the basket. In the third task, the goal is to place the chair on top of the checkerboard. In the fourth task, the robot must pick up the mug and hold it above a certain height. Initial positions of all objects are randomized, and must be inferred from visual observations. Not all objects in the scene are relevant to the current task. "
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+        "text": "5.1 RESULTS, COMPARISONS AND ANALYSIS ",
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+        "text": "To answer the questions posed at the start of this section, we compare PARROT against a number of prior works, as well as ablations of our method. Additional implementation details and hyperparameters can be found in Appendix B. ",
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+        "type": "text",
+        "text": "Soft-Actor Critic (SAC). For a basic RL comparison, we compare against the vanilla soft-actor critic algorithm (Haarnoja et al., 2018b), which does not incorporate any previously collected data. ",
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+        "text": "SAC with demonstrations (BC-SAC). We compare against a method that incorporates demonstrations to speed up learning of new tasks. In particular, we initialize the SAC policy by performing behavioral cloning on the entire dataset $\\mathcal { D }$ , and then fine-tune it using SAC. This approach is similar to what has been used in prior work (Rajeswaran et al., 2018), except we use SAC as our RL algorithm. While we did test other methods that are designed to use demonstration data with RL such as DDPGfD (Vecer´ık et al., 2017) and AWAC (Nair et al., 2020), we found that our simple $\\mathrm { B C } + \\mathrm { S A C }$ variant performed better. This somewhat contradicts the results reported in prior work (Nair et al., 2020), but we believe that this is because the prior data is not labeled with rewards (all transitions are assigned a reward of 0), and more powerful demonstration $+ \\mathrm { R L }$ methods require access to these rewards, and subsequently struggle due to the reward misspecification. ",
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+        "text": "Transfer Learning via Feature Learning (VAE-features). We compare against prior methods for transfer learning (in RL) that involve learning a robust representation of the input observation. Similar to Higgins et al. (2017b), we train a $\\beta$ -VAE using the observations in our training set, and train a policy on top of the features learned by this VAE when learning downstream tasks. ",
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+    {
+        "type": "text",
+        "text": "Trajectory modeling and RL (TrajRL). Ghadirzadeh et al. (2020) model entire trajectories using a VAE, and learn a one-step policy on top of the VAE to solve tasks using RL. Our implementation of this method uses a VAE architecture identical to the original paper’s, and we then train a policy using SAC to solve new tasks with the action space induced by the VAE. We performed additional hyperparameter tuning for this comparison, the details of which can be found in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "Hierarchical imitation and RL (HIRL). Prior works in hierarchical imitation learning (Fox et al., 2017; Shankar & Gupta, 2020) train latent variable models over expert demonstrations to discover options, and later utilize these options to learn longhorizon tasks using RL. While PARROT can also be extended to model the temporal structure in trajectories through conditioning on past states and actions, by modeling $p _ { \\mathrm { p r i o r } } ( a _ { t } , \\vert s _ { t } , s _ { t - 1 } , . . . , a _ { t - 1 } , . . . , a _ { 0 } )$ instead of $p _ { \\mathrm { p r i o r } } ( a _ { t } | s _ { t } )$ , we focus on a simpler version of the model in this paper that does not condition on the past. In order to provide a fair comparison, we modify the model proposed by Shankar & Gupta (2020) to remove the past conditioning, which then reduces to training a conditional VAE, and performing RL on the action space induced by the latent space of this VAE. This comparison is similar to our proposed approach, but with one crucial difference: the mapping we learn is invertible, and allows the ",
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+        "image_caption": [
+            "Figure 4: We plot trajectories from executing a random policy, with and without the behavioral prior. We see that the behavioral prior substantially increases the likelihood of executing an action that is likely to lead to a meaningful interaction with an object, while still exploring a diverse set of actions. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "RL agent to retain full control over the final actions in the environment (since for every $a \\in { \\mathcal { A } }$ , there exist some $z = f _ { \\phi } ^ { - 1 } ( a ; s )$ , while a latent space learned by a VAE provides no such guarantee). ",
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+            "Figure 5: Results. The lines represent average performance across multiple random seeds, and the shaded areas represent the standard deviation. PARROT is able to learn much faster than prior methods on a majority of the tasks, and shows little variance across runs (all experiments were run with three random seeds, computational constraints of image-based RL make it difficult to run more seeds). Note that some methods that failed to make any progress on certain tasks (such as “Place Sculpture in Basket”) overlap each other with a success rate of zero. SAC and VAE-features fail to make progress on any of the tasks. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "Exploration via behavioral prior (Prior-explore). We also run experiments with an ablation of our method: instead of using a behavioral prior to transform the MDP being experienced by the RL agent, we use it to simply aid the exploration process. While collecting data, an action is executed from the prior with probability $\\epsilon$ , else an action is executed from the learned policy. We experimented with $\\epsilon = 0 . 1 , 0 . 3 , 0 . 7 , 0 . 9$ , and found 0.9 to perform best. ",
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+    },
+    {
+        "type": "text",
+        "text": "Main results. Our results are summarised in Figure 5. We see that PARROT is able to solve all of the tasks substantially faster and achieve substantially higher final returns than other methods. The SAC baseline (which does not use any prior data) fails to make progress on any of the tasks, which we suspect is due to the challenge of exploring in sparse reward settings with a randomly initialized policy. Figure 4 illustrates a comparison between using a behavioral prior and a random policy for exploration. The VAE-features baseline similarly fails to make any progress, and due to the same reason: the difficulty of exploration in a sparse reward setting. Initializing the SAC policy with behavior cloning allows it to make progress on only two of the tasks, which is not surprising: a Gaussian policy learned through a behavior cloning loss is not expressive enough to represent the complex, multi-modal action distributions observed in dataset $\\mathcal { D }$ . Both TrajRL and HIRL perform much better than any of the other baselines, but their performance plateaus a lot earlier than PARROT. While the initial exploration performance of our learned behavioral prior is not substantially better from these methods (denoted by the initial success rate in the learning curves), the flexibility of the representation it offers (through learning an invertible mapping) allows the RL agent to improve far beyond its initial performance. Prior-explore, an ablation of our method, is able to make progress on most tasks, but is unable to learn as fast as our method, and also demonstrates unstable learning on some of the tasks. We suspect this is due to the following reason: while off-policy RL methods like SAC aim to learn from data collected by any policy, they are in practice quite sensitive to the data distribution, and can run into issues if the data collection policy differs substantially from the policy being learned (Kumar et al., 2019). ",
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+    {
+        "type": "text",
+        "text": "Impact of dataset size on performance. We conducted additional experiments on a subset of our tasks to evaluate how final performance is impacted as a result of dataset size, results from which are shown in Figure 6. As one might expect, the size of the dataset positively correlates with performance, but about 10K trajectories are sufficient for obtaining good performance, and collecting additional data yields diminishing returns. Note that initializing with even a smaller dataset size (like 5K trajectories) yields much better performance than learning from scratch. ",
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+    {
+        "type": "image",
+        "img_path": "images/87515611fe55cabe6c38f511cdcd9334dd7d7d4eba6406b801d418d6ab1d9432.jpg",
+        "image_caption": [
+            "Figure 6: Impact of dataset size on performance. We observe that training on 10K, 25K or 50K trajectories yields similar performance. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mismatch between train and test tasks. We ran experiments in which we deliberately bias the training dataset so that the training tasks and test tasks are functionally different (i.e. involve substantially different actions), the results from which are shown in Figure 7. We observe that if the prior is trained on pick and place tasks alone, it can still solve downstream grasping tasks well. However, if the prior is trained only on grasping, it is unable to perform well when solving pick and place tasks. We suspect this is due to the fact that pick and place tasks involve a completely new action (that of opening the gripper), which is never observed by the prior if it is trained only on grasping, making it difficult to learn this behavior from scratch for downstream tasks. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/1c702e4fba9af88ce0efc764e1ece6595eae7d6955825e3481ac3f1004538d6b.jpg",
+        "image_caption": [
+            "Figure 7: Impact of train/test mismatch on performance. Each plot shows results for four tasks. Note that for the pick and place tasks, the performance is close to zero, and the curves mostly overlap each other on the $\\mathbf { X }$ -axis. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We presented PARROT, a method for learning behavioral priors using successful trials from a wide range of tasks. Learning from priors accelerates RL on new tasks–including manipulating previously unseen objects from high-dimensional image observations–which RL from scratch often fails to learn. Our method also compares favorably to other prior works that use prior data to bootstrap learning for new tasks. While our method learns faster and performs better than prior work in learning novel tasks, it still requires thousands of trials to attain high success rates. Improving this efficiency even further, perhaps inspired by ideas in meta-learning, could be a promising direction for future work. Our work opens the possibility for several exciting future directions. PARROT provides a mapping for executing actions in new environments structurally similar to those of prior tasks. While we primarily utilized this mapping to accelerate learning of new tasks, future work could investigate how it can also enable safe exploration of new environments (Hunt et al., 2020; Rhinehart et al., 2020). While the invertibility of our learned mapping ensures that it is theoretically possible for the RL policy to execute any action in the original MDP, the probability of executing an action can become very low if this action was never seen in the training set. This can be an issue if there is a significant mismatch between the training dataset and the downstream task (as shown in our experiments), and tackling this issue would make for an interesting problem. Since our method speeds up learning using a problem setup that takes into account real world considerations (no rewards for prior data, no need to revisit prior tasks, etc.), we are also excited about its future application to domains like real world robotics. ",
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+    {
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+        "text": "Appendices ",
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+        "text": "A ALGORITHM ",
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+        "text": "Algorithm 1 RL with Behavioral Priors ",
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+        "type": "text",
+        "text": "1: Input: Dataset $\\mathcal { D }$ of state-action pairs $( s , a )$ from previous tasks, new task $M ^ { \\star }$   \n2: Learn $f _ { \\phi }$ by maximizing the likelihood term in Equation 2   \n3: for step $k$ in $\\{ 1 , . . . , \\Nu \\}$ do   \n4: $s $ current observation   \n5: Sample $z \\sim \\pi _ { \\theta } ( z | s )$   \n6: $a \\gets f _ { \\phi } ( z ; s )$   \n7: $s ^ { \\prime } , r \\gets$ Execute $a$ in $M ^ { \\star }$   \n8: Update $\\pi _ { \\boldsymbol { \\theta } } { \\left( z | \\boldsymbol { s } \\right) }$ with $( s , z , s ^ { \\prime } , r )$   \n9: end for   \n10: Return: Policy $\\pi _ { \\boldsymbol { \\theta } } { \\left( z | \\boldsymbol { s } \\right) }$ for task $M ^ { \\star }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "B IMPLEMENTATION DETAILS AND HYPERPARAMETER TUNING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We now provide details of the neural network architectures and other hyperparameters used in our experiments. ",
+        "bbox": [
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+        "page_idx": 14
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+    {
+        "type": "text",
+        "text": "Behavioral prior. We use a conditional real NVP with four affine coupling layers as our behavioral prior. The architecture for a single coupling layer is shown in Figure 8. We use a learning rate of $1 e { - 4 }$ and the Adam (Kingma & Ba, 2015) optimizer to train the behavioral prior for 500K steps. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/d8259f7032d0a26269de84982caf5fb5ae835fd2fcb2703cc2856a97cfa68b01.jpg",
+        "image_caption": [
+            "Figure 8: Coupling layer architecture. A computation graph for a single affine coupling layer is shown in (a). Given an input noise $z$ , the coupling layers transform it into $z ^ { \\prime }$ through the following operations: $z _ { 1 : d } ^ { \\prime } = z _ { 1 : d }$ and $z _ { d + 1 : D } ^ { \\prime } = z _ { d + 1 : D } \\odot \\exp ( v ( z _ { 1 : d } ; \\phi ( s ) ) ) + t ( z _ { 1 : d } ; \\phi ( s ) )$ , where the $v$ , $t$ and $\\psi$ are functions implemented using neural networks whose architectures are shown in (b) and (c). Since $v$ and $t$ have the same input, they are implemented using a single fully connected neural network (shown in (b)), and the output of this network is split into two. The image encoder, $\\psi ( s )$ is implemented using a convolutional neural network with parameters shown in (c). "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            207,
+            469,
+            792,
+            708
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "TrajVAE. For this comparison, we use the same architecture as Ghadirzadeh et al. (2020). The decoder consists of three fully connected layers with 128, 256, and 512 units respectively. BatchNorm (Ioffe & Szegedy, 2015) and ReLU nonlinearity are applied after each layer. The encoder is symmetric: 512, 256, and 128 layers, respectively. The size of the latent space is 8 (same as the behavioral prior). We sweep the following values for the $\\beta$ parameter (Higgins et al., 2017a): 0.1, 0.01, 0.005, 0.001, 0.0005, and find 0.001 to be optimal. We initialize $\\beta$ to zero at the start of training, and anneal it to the target $\\beta$ value using a logistic function, achieving half of the target value in ",
+        "bbox": [
+            173,
+            825,
+            825,
+            924
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "25K steps. We use a learning rate of $1 e { - 4 }$ and the Adam (Kingma & Ba, 2015) optimizer to train this model for 500K steps. ",
+        "bbox": [
+            173,
+            103,
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+            132
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "HIRL. This comparison is implemented using a conditional variational autoencoder, and uses an architecture that is similar to the one used by the TrajVAE, but with two differences: since this comparison uses image conditioning, we use the same convolutional network $\\psi$ as the behavioral prior to encode the image (shown in Figure 8), and pass it as conditioning information to both the encoder and decoder networks. Second, instead of modeling the entire trajectory in a single forward pass, it instead models individual actions, allowing the high-level policy to perform closed-loop control, similar to the behavioral prior model. We sweep the following values for the $\\beta$ parameter: 0.1, 0.01, 0.005, 0.001, 0.0005, and find 0.001 to be optimal. We found the annealing process to be essential for obtaining good RL performance using this method. We use a learning rate of $1 e { - 4 }$ and the Adam (Kingma & Ba, 2015) optimizer to train this model for 500K steps. ",
+        "bbox": [
+            173,
+            138,
+            825,
+            279
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Behavior cloning (BC). We implement behavior cloning via maximum likelihood with a Gaussian policy (and entropy regularization (Haarnoja et al., 2017)). For both behavior cloning and RL with SAC, we used the same policy network architecture as shown in Figure 9. We train this model for 2M steps, using Adam with a learning rate of $3 e ^ { - 4 }$ . ",
+        "bbox": [
+            174,
+            285,
+            825,
+            340
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "VAE-features. For this comparison, we use the standard VAE architecture used for CIFAR-10 experiments (van den Oord et al., 2017). The encoder consists of two strided convolutional layers (stride 2, window size $4 \\times 4$ ), which is followed by two residual $3 \\times 3$ blocks, all of which have 256 hidden units. Each residual block is implemented as ReLU, 3x3 conv, ReLU, 1x1 conv. The decoder is symmetric to the encoder. We train this model for $1 . 5 \\mathbf { M }$ steps, using Adam with a learning rate of $1 e ^ { - 3 }$ and a batch size of 128. ",
+        "bbox": [
+            174,
+            347,
+            825,
+            431
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "Soft Actor Critic (SAC). We use the soft actor critic method (Haarnoja et al., 2018b) as our RL algorithm, with the hyperparameters shown in Table 1. We use the same hyperparameters for all of our RL experiments (our method, HIRL, TrajRL, $\\mathrm { B C + S A C }$ , SAC). ",
+        "bbox": [
+            174,
+            438,
+            825,
+            481
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "table",
+        "img_path": "images/c67fb408378010ec6bed2d65a75aa25dc839dff737959d9641b10c774446514e.jpg",
+        "table_caption": [
+            "Table 1: Hyperparameters for soft-actor critic (SAC) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>value used</td></tr><tr><td>Target network update period</td><td>1000 steps</td></tr><tr><td>discount factor y</td><td>0.99</td></tr><tr><td>policy learning rate</td><td>3e-4</td></tr><tr><td>Q-function learning rate</td><td>3e-4</td></tr><tr><td>reward scale</td><td>1.0</td></tr><tr><td>automatic entropy tuning number of update steps per env step</td><td>enabled 1</td></tr></table>",
+        "bbox": [
+            338,
+            518,
+            655,
+            638
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "image",
+        "img_path": "images/a212ba77eae356406c1ef304168eef8040fcaeb7683fbbcf7e6973fa18cb81fb.jpg",
+        "image_caption": [
+            "Figure 9: Policy and Q-function network architectures. We use a convolutional neural network to represent the Q-function for SAC, shown in this figure. The policy network is identical, except it does not take in an action as an input and outputs a 7D action instead of a scalar Q-value. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            664,
+            818,
+            768
+        ],
+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "C EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            400,
+            118
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "C.1 TASKS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            133,
+            264,
+            148
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "We provided a visual depiction of 4 of our 8 evaluations tasks in Figure 3, and the remaining tasks are shown here in Figure 10. ",
+        "bbox": [
+            173,
+            159,
+            823,
+            188
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "image",
+        "img_path": "images/997596562173eeaa1e0aa5481037930eb5a85fac3177b215921df467e5ec1da1.jpg",
+        "image_caption": [
+            "Figure 10: In the first row, the objective is to grasp a can and lift it above a certain height. Rows two and three are similar, except the objective is to grasp a vase and a baseball cap, respectively. The final row depicts a task where the goal is to pick the baseball cap and place it on the marble cube. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            334,
+            204,
+            661,
+            401
+        ],
+        "page_idx": 16
+    },
+    {
+        "type": "text",
+        "text": "C.2 DATA COLLECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            349,
+            117
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "We collected our dataset using scripted policies detailed in Algorithms 2 and 3. ",
+        "bbox": [
+            174,
+            130,
+            691,
+            143
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "table",
+        "img_path": "images/48300a74e52bdae75dc4b211c9eac5f7575316aff063c5788509e35cfce690e2.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm 2 Scripted Grasping</td><td></td><td>Algorithm3 Scripted Pick and Place</td></tr><tr><td>1:threshold ←0.02</td><td></td><td>1:threshold ← 0.02</td></tr><tr><td>2:1 numTimesteps ←25</td><td></td><td>2:numTimesteps ←25</td></tr><tr><td>3:targetPoint ← object position</td><td></td><td>3:placeAttempted ←False</td></tr><tr><td>4: for tin(O,numTimesteps) do</td><td></td><td>4: dropPos ←point above container</td></tr><tr><td>5:</td><td>eePos ← end effector position</td><td>5: for t in (O, numTimesteps) do</td></tr><tr><td>6:</td><td>targetEEDist ← distance(targetPoint,eePos)</td><td>6: eePos ← end effector position</td></tr><tr><td>7:</td><td>if targetEEDist &gt; threshold then</td><td>7: objectDropDist ← distance(eePos,dropPos)</td></tr><tr><td>8:</td><td>action ← targetPoint-eePos</td><td>if placeAttempted then</td></tr><tr><td>9:</td><td>else if gripperOpened then</td><td>8: 9: action ←0</td></tr><tr><td>10:</td><td>action ← close gripper</td><td>10: else if object not grasped AND objectDropDist</td></tr><tr><td>11:</td><td>else if object not raised high enough then</td><td>&gt; threshold then Execute grasp using Algorithm 2</td></tr><tr><td>12:</td><td>action ← lift upward</td><td>11:</td></tr><tr><td>13:</td><td>else</td><td>12: else if objectDropDist &gt;threshold then</td></tr><tr><td>14:</td><td>action←0</td><td>13: action ← dropPos－eePos</td></tr><tr><td>15:</td><td>end if</td><td>14: else</td></tr><tr><td>16:</td><td>noise ~ N(0,0.1)</td><td>15: action ← open gripper</td></tr><tr><td>17:</td><td>action ←action+noise</td><td>16: placeAttempted ←True 17:</td></tr><tr><td>18:</td><td>s&#x27;←env.step(action)</td><td>else</td></tr><tr><td>19: end for</td><td></td><td>action←0</td></tr><tr><td>20:</td><td>19:</td><td>end if</td></tr><tr><td></td><td>20:</td><td>noise ~ N(0,0.1)</td></tr><tr><td></td><td>21:</td><td>action ← action+noise</td></tr><tr><td></td><td>22:</td><td>s&#x27;← env.step(action)</td></tr><tr><td></td><td>23: end for</td><td></td></tr></table>",
+        "bbox": [
+            173,
+            176,
+            830,
+            502
+        ],
+        "page_idx": 17
+    },
+    {
+        "type": "text",
+        "text": "C.3 SIMULATION OBJECTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            375,
+            118
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "text",
+        "text": "To collect data in diverse environments, we used 3D object models from the ShapeNet dataset (Chang et al., 2015) and the PyBullet (Coumans & Bai, 2016) object libraries. ",
+        "bbox": [
+            173,
+            130,
+            825,
+            159
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "image",
+        "img_path": "images/70a13307ae9387287d751006ca299f8b6ba9fd3ca9f1601621f68eb785c66bdd.jpg",
+        "image_caption": [
+            "Figure 11: Train objects. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            172,
+            823,
+            523
+        ],
+        "page_idx": 18
+    },
+    {
+        "type": "image",
+        "img_path": "images/009106603d4e59ab9c688d634d9b6ddb184158e1951ddad365613029261b79d7.jpg",
+        "image_caption": [
+            "Figure 12: Test objects "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            174,
+            569,
+            825,
+            821
+        ],
+        "page_idx": 18
+    }
+]

parse/train/ZsGg52s-cQZ/ZsGg52s-cQZ.md

@@ -0,0 +1,273 @@
+# Topology-Imbalance Learning for Semi-Supervised Node Classification
+
+Deli Chen1,2, Yankai $\mathbf { L i n } ^ { 1 }$ , Guangxiang Zhao2, Xuancheng Ren2, Peng $\mathbf { L i } ^ { 1 }$ , Jie $\mathbf { Z } \mathbf { h o u } ^ { 1 }$ , $\mathbf { X } \mathbf { u } \mathbf { S } \mathbf { u } \mathbf { n } ^ { 2 }$ 1Pattern Recognition Center, WeChat AI, Tencent Inc., China 2MOE Key Lab of Computational Linguistics, School of EECS, Peking University {delichen, yankailin, patrickpli,withtomzhou}@tencent.com {zhaoguangxiang,renxc,xusun}@pku.edu.cn
+
+# Abstract
+
+The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semisupervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection–based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.1
+
+# 1 Introduction
+
+Graph is a widely-used data structure [51], where the nodes are connected to each other through natural or handcrafted edges. Similar to other data structures, the representation learning for node classification faces the challenge of quantity-imbalance issue, where the labeling size varies among classes and the decision boundaries of trained classifiers are mainly decided by the majority classes [46]. There have been a series of studies [35, 11, 49] handling the Quantity-Imbalance Node Representation Learning (short as QINL). However, different with other data structures, graph-structured data suffers from another aspect of the imbalance problem: the imbalance caused by the asymmetric and uneven topology of labeled nodes, where the decision boundaries are driven by the labeled nodes close to the topological class boundaries (left of Figure 1) thus interfering with the model learning.
+
+Present Work. For the first time, we recognize the Topology-Imbalance Node Representation Learning (short as TINL) as a graph-specific imbalance learning topic, which mainly focus on the decision boundaries shift phenomena driven by the topology imbalance in graph and is an essential component for node imbalance learning. Comparing with the well-explored QINL that studies the imbalance caused by the numbers of labeled nodes, TINL explores the imbalance caused by the positions of labeled nodes and owns the following characteristics:
+
+![](images/3c5d5345b792342769fcf85d480df7dfaf12f9fa1c75f46eec6382748a5fb423.jpg)  
+Figure 1: Schematic diagram of the topology-imbalance issue in node representation learning. The color and the hue denote the type and the intensity of each node’s received influence from the labeled nodes, respectively. The left shows that nodes close to the boundary have the risk of information conflict and nodes far away from labeled nodes have the risk of information insufficient. The right shows that our method can decrease the training weights of labeled nodes (R1) close to the class boundary and increase the weights of labeled nodes (B and R2) close to the class centers, thus relieving the topology-imbalance issue.
+
+• Ubiquity: Due to the complex connections of the graph nodes, the topology structure of nodes in different categories is naturally asymmetric, which makes TINL an essential characteristic in node representation learning. Hence, it is difficult to construct a completely symmetric labeling set even with an abundant annotation budget. • Perniciousness: The influence from labeled nodes decays with the topology distance [3]. The asymmetric topology of labeled nodes in different classes and the uneven distribution of labeled nodes in the same class will cause the influence conflict and influence insufficient problems (left of Figure 1) respectively, resulting in a shift of decision boundaries. • Orthogonality: Quantity-imbalance studies [49, 8, 5] usually treat the labeled nodes of the same class as a whole and devise solutions based on the total numbers of each class, while TINL explores the influence of the unique position of each labeled node on decision boundaries. Thus, TINL is independent of QINL in terms of the object of study.
+
+Exploring TINL is of great importance for node representation learning due to its ubiquity and perniciousness. However, the methods [17, 22] for quantity imbalance can be hardly applied to TINL because of the orthogonality. To remedy the topology-imbalance issue, thus promoting the node classification, we propose a model-agnostic training framework ReNode to re-weight the labeled nodes according to their positions. We devise the conflict detection-based Topology Relative Location (Totoro) metric to leverage the interaction among labeled nodes across the whole graph to locate their structural positions. Based on the Totoro metric, we further increase the training weights of nodes with small conflict that are highly likely to be close to topological class centers to make them play a more pivotal role during training, and vice versa (right of Figure 1). Empirical results of various imbalance scenarios (TINL, QINL, large-scale graph) and multiple graph neural networks (GNNs) demonstrate the effectiveness and generalizability of our method. Besides, we provide the sensitivity to topology imbalance as a new evaluation perspective for different GNN architectures.
+
+# 2 Topology-Imbalance Node Representation Learning
+
+# 2.1 Notations and Preliminary
+
+In this work, we follow the well-established semi-supervised node classification setting [47, 18] to conduct analyses and experiments. Given an undirected and unweighted graph $\mathcal { G } = ( \boldsymbol { \nu } , \pmb { \varepsilon } , \pmb { c } )$ , where $\nu$ is the node set represented by the feature matrix $\boldsymbol { X } \in \mathbb { R } ^ { n * d }$ $\dot { \boldsymbol { n } } = | \boldsymbol { \nu } |$ is the node size and $d$ is the node embedding dimension), $\varepsilon$ is the edge set which is represented by an adjacency matrix $A \in \mathbb { R } ^ { n * n }$ , $\pmb { \mathcal { L } } \subset \nu$ is the labeled node set and usually we have $| \bar { \boldsymbol { L } } | \ll | \boldsymbol { \nu } |$ , the node classification task is to train a classifier $\mathcal { F }$ (usually a GNN) to predict the class label y for the unlabeled node set $u = \nu - c$ . The training sets for different classes are represented by $( \pmb { \mathscr { C } } _ { 1 } , \pmb { \mathscr { C } } _ { 2 } , \cdots , \pmb { \mathscr { C } } _ { k } )$ and $k$ is the number of classes. The labeling ratio $\delta = \angle \mathcal { x } / \nu$ is the proportion of labeled nodes in all nodes. In this work, we focus on TINL in homogeneously-connected graphs and hope to inspire future studies on the critical topology-imbalance issue.
+
+![](images/25999ec10387c1b8ccfbc868ce85fd4adb3997f394bbe9fe5415c3fa41a2bab0.jpg)  
+Figure 2: Node influence and boundary shift caused by quantity- and topology-imbalance. (a): The prediction results of GCN and LP are highly consistent (t-SNE [39] visualization of the $C O R A$ dataset). (b): The node influence boundary (the yellow dotted line) is shifted towards the small class from the true class boundary (the black dotted line) under the quantity- and topology-imbalance scene. (c): The node influence boundary is shifted towards the large class under the quantity-balanced, topology-imbalanced scene. We regard the large class as positive class to indicate the results.
+
+# 2.2 Understanding Topology Imbalance via Label Propagation
+
+From Figure 1, we can intuitively perceive the imbalance brought by the positions of labeled nodes; in this part, we further explore the nature of topology imbalance with the well-known Label Propagation [50] algorithm (short as LP) and provide a uniform analysis framework for the comprehensive node imbalance issue. In LP, labels are propagated from the labeled nodes and aggregated along edges, which can also be viewed as a random walk process from labeled nodes. The convergence result $\mathbf { Y }$ after repeated propagation is regarded as the nodes soft-labels:
+
+$$
+\pmb { Y } = \alpha ( \pmb { I } - ( 1 - \alpha ) \pmb { A } ^ { \prime } ) ^ { - 1 } \pmb { Y } ^ { 0 } ,
+$$
+
+where $\pmb { I }$ is the identity matrix, $\alpha \in ( 0 , 1 ]$ is the random walk restart probability, $A ^ { \prime } = D ^ { - { \frac { 1 } { 2 } } } A D ^ { - { \frac { 1 } { 2 } } }$ is the adjacency matrix normalized by the diagonal degree matrix $_ { D }$ , $\mathbf { \dot { Y } } ^ { 0 }$ is the initial label distribution where labeled nodes are represented by the one-hot vectors. The prediction label for the $i$ -th node is $q _ { i } = \arg \operatorname* { m a x } _ { j } Y _ { i j }$ . LP is a simple yet successful model [37] and can be unified with GNN models owning the message-passing mechanism [41]. From Figure 2(a), we can empirically find that there is a significant correlation between the results of LP and GCN (T/F indicates prediction is True/False).
+
+The LP prediction $\pmb q$ can be viewed as the distribution of the (labeled) node influence [41] (i.e. each node is mostly influenced by which class’s information); hence the boundaries of the node influence can act as an effective reflection for the GNN model decision boundaries considering the high consistency between LP and GNN. Moreover, node influence offers a unified view of TINL and QINL: ideally, the node influence boundaries should be consistent with the true class boundaries, but both the labeled nodes’ numbers (QINL) and positions (TINL) can cause a shift of the node influence boundaries from the true one, resulting in deviation of the model decision boundaries.
+
+Node imbalance issue is composed of topology- and quantity-imbalance. Figure 2 illustrates two examples of node influence boundary shift. In Figure 2(b), when the uniform selection is adopted to generate training set, both the quantity and the topology are imbalanced for model training; then the large class with more total nodes (denotes by blue color) will own stronger influence than the small class with fewer total nodes (denotes by red color) due to the quantity advantage and the node influence boundary is shifted towards the small class. In Figure 2(c), when the quantity-balanced strategy is adopted for sampling training nodes, it will be easier for the small class to has more labeled nodes close to the class boundary and the boundary of the node influence is shifted into the large class. We can find that even when the training set is quantity-balanced, the topology-imbalance issue still exists and hinders the node classification learning. Hence, we can conclude that node imbalance learning is caused by the joint effect of TINL and QINL. Separately considering TINL or QINL will lead to a one-sided solution to node imbalance learning.
+
+![](images/f912716e23c177a4938148c7a1170b81fdfe86390b15dbfd19bd85e1becda3fb.jpg)  
+Figure 3: Effectiveness of Totoro at (a) Node Level: labeled nodes (t-SNE visualization of the CORA dataset) with less influence conflict (lighter color) are farther-away from class boundaries than those with high conflict (darker color), and (b) Dataset Level: There is a significant negative correlation between the GNN (GCN) performance and overall conflict of the training set (the Pearson correlation coefficient is $- 0 . 6 1 8$ over 50 randomly selected training sets with the $p$ value smaller than 0.01).
+
+# 2.3 Measuring Topology Imbalance by Influence Conflict
+
+Although we have realized that the imbalance of node topology interferes with model learning, how to measure the labeled node’s relative topological position to its class (being far away from or close to the class center) remains the key challenge in handling the topology-imbalance issue due to the complex graph connections and the unknown class labels for most nodes in the graph. As the nodes are homogeneously connected when constructing the graph, even nodes close to the class boundaries own similar characteristics to their neighbors. Thus it is unreliable to leverage the difference between the characteristics of one labeled node and its surrounding subgraphs to locate its topological position. Instead, we propose to utilize the node topology information by considering the node influence conflict across the whole graph and devise the Conflict Detection-based Topology Relative Location metric (Totoro).
+
+Similar to Eq (1), we calculate the Personalized PageRank [27] matrix $_ { r }$ to measure node influence distribution from each labeled node:
+
+$$
+P = \alpha ( { \cal I } - ( 1 - \alpha ) A ^ { \prime } ) ^ { - 1 } .
+$$
+
+Node influence conflict denotes topological position. According to related studies [41, 19, 2], $_ { r }$ can be viewed as the distribution of influence exerted outward from each node. We assume that if a labeled node $v \in \nu$ encounters strong heterogeneous influence from the other classes’ labeled nodes in the subgraph around node $v$ where node $v$ itself owns great influence, we have the conclusion that node $v$ meets large influence conflict in message passing and it is close to topological class boundaries, and vice versa. Based on this hypothesis, we take the expectation of the influence conflict between the node $v$ and the labeled nodes from other classes when node $v$ randomly walks across the entire graph as a measurement of how topologically close node $v$ is to the center of the class it belongs to. The Totoro value of node $v$ is computed as:
+
+$$
+\pmb { T } _ { v } = \mathbb { E } _ { \boldsymbol { x } \sim \pmb { P } _ { v , : } } [ \sum _ { \substack { j \in [ 1 , k ] , j \neq y _ { v } } } \frac { 1 } { | \pmb { \mathcal { C } } _ { j } | } \sum _ { i \in \pmb { \mathcal { C } } _ { j } } \pmb { P } _ { i , x } ] ,
+$$
+
+where $\mathbf { \nabla } _ { \mathbf { y } _ { v } }$ is the ground-truth label of node $v$ , $P _ { v }$ indicates the personalized PageRank probability vector for the node $v$ . A larger Totoro value $\mathbf { \delta } _ { \mathbf { \mathcal { T } } _ { v } }$ indicates that node $v$ is topologically closer to class boundaries, and vice versa. The normalization item $1 / | c _ { j } |$ is added to make the influence from the different classes comparable when computing conflict.
+
+We visualize the node labels and the Totoro values (scaled to $[ 0 , 1 ] $ ) of labeled nodes in Figure 3(a). We can find that the labeled nodes with smaller Totoro values are farther away from the class boundaries, demonstrating the effectiveness of Totoro in locating the positions of labeled nodes. Besides, we sum the conflict of all the labeled nodes $\textstyle \sum _ { b \in { \mathcal { L } } } T _ { v }$ to measure the overall conflict of the dataset, which can be viewed as the metric for the overall topology imbalance given the graph $\mathfrak { g }$ and the training set $\mathcal { L }$ . Figure 3(b) shows that there is a significant negative correlation between the overall conflict and the model performance, which further demonstrates the effectiveness of Totoro in measuring the intensity of topology imbalance at the dataset level.
+
+# 2.4 Alleviate Topology Imbalance by Instance-wise Node Re-weighting
+
+In this section, we introduce ReNode, a model-agnostic training weight schedule mechanism to address TINL for general GNN encoder in a plug-and-play manner. Inspired by the analysis in Section 2.2, the ReNode method is devised to promote the training weights of the labeled nodes that are close to the topological class centers, so as to make these nodes play a more active role in model learning, and vice versa. Specifically, we devise a cosine annealing mechanise 2 for the training node weights based on their Totoro values:
+
+$$
+{ \pmb w } _ { v } = w _ { \mathrm { m i n } } + \frac { 1 } { 2 } ( w _ { \mathrm { m a x } } - w _ { \mathrm { m i n } } ) ( 1 + \cos ( \frac { \mathrm { R a n k } ( { \pmb T } _ { v } ) } { | { \pmb L } | } \pi ) ) , \quad v \in { \pmb C }
+$$
+
+where $\pmb { w } _ { v }$ is the modified training weight for the labeled node $v , w _ { \mathrm { m i n } } , w _ { \mathrm { m a x } }$ are the hyper-parameters indicating the lower bound and upper bound of the weight correction factor, $\mathrm { R a n k } ( \pmb { T } _ { v } )$ is the ranking order of $\mathbf { \delta } _ { \mathbf { \mathcal { T } } _ { v } }$ from the smallest to the largest. The training loss $L _ { T }$ for the quantity-balanced, topologyimbalanced node classification task is computed by the following equations:
+
+$$
+L _ { T } = - \frac { 1 } { | { \cal { L } } | } \sum _ { v \in { \cal { L } } } w _ { v } \sum _ { c = 1 } ^ { k } y _ { v } ^ { * c } \log \ g _ { v } ^ { c } , \quad g = \mathrm { s o f t m a x } ( { \mathcal { F } } ( X , A , \theta ) ) ,
+$$
+
+where $\mathcal { F }$ denotes any GNN encoder, $\pmb \theta$ is the parameter of ${ \mathcal { F } } , g _ { i }$ is the GNN output for node $i$ , $\mathbf { \nabla } _ { \mathbf { \boldsymbol { y } } _ { i } ^ { * } }$ is the gold label for node $i$ in one-hot embedding. By encouraging the positive effects of the labeled nodes near the class topological centers, and reducing the negative effects of those near the topological class boundaries, our ReNode method is expected to minimize the deviation between the node influence boundaries and the true class boundaries, so as to correct the class imbalance caused by the positions of labeled nodes.
+
+ReNode to Jointly Handle TINL and QINL In this part, we introduce the application of the ReNode method in a more general graph imbalance scenario where both the topology- and quantityimbalance issues exist. As analyzed in previous sections, the TINL and QINL are orthogonal problems. Therefore, we propose that our ReNode method based on (labeled) node topology can be seamlessly combined with the existing methods designed for the quantity-imbalance learning. Without loss of generality, we present how our ReNode method can be combined with the vanilla class frequency-based re-weight method [17]. The training loss $L _ { Q }$ for the quantity-imbalanced, topology-imbalanced node classification task is formalized in the following equation:
+
+$$
+L _ { Q } = - \frac { 1 } { | \mathcal { L } | } \sum _ { v \in \mathcal { L } } w _ { v } \frac { | \bar { \mathcal { C } } | } { | \mathcal { C } _ { j } | } \sum _ { c = 1 } ^ { k } { y } _ { v } ^ { * c } \log \textbf { \em g } _ { v } ^ { c } ,
+$$
+
+where $| \bar { c } |$ is the average number of the class training sizes. With this method, the final weight of the labeled node is affected by two perspectives: training examples of the minority classes will have higher weights than that of the majority classes; training examples close to the topological class centers will have higher weights than those are close to the topological class boundaries.
+
+ReNode for Large-scale Graph There are mainly two challenges when applying ReNode to largescale graphs: (1) how to calculate the PageRank matrix, and (2) how to train the GNN model in an inductive setting [13]. In this work, we follow the PPRGo method [2] to implement our method on the large-scale graph, which can decouple the feature learning process from the information transmission process to resolve the dependence on the global graph topology structure and can be carried out much efficiently. Following PPRGo, the Personalized PageRank matrix $\hat { P }$ and the corresponding training ReNode factor $\hat { \pmb { w } }$ are generated by the estimation method from Andersen et al. [1] and then $\hat { P }$ is directly employed as the aggregation weights from all the other nodes regardless of their topology distance from the current node:
+
+Table 1: ReNode (short as RN) for the pure topology-imbalance issue. We report Weighted-F1 (W-F, $\%$ ), Macro-F1 (M-F, $\%$ ) and the corresponding standard deviation for each group of experiments. $^ *$ and $^ { \ast \ast }$ represent the result is significant in student t-test with $p < 0 . 0 5$ and $p < 0 . 0 1$ , respectively.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Training</td><td colspan="2">CORA</td><td colspan="2">CiteSeer</td><td colspan="2">PubMed</td><td colspan="2">Photo</td><td colspan="2">Computers</td></tr><tr><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td></tr><tr><td rowspan="2">GCN</td><td>w/oRN</td><td>79.1±1.1</td><td>77.8±1.5</td><td>66.2±1.0</td><td>62.0±1.3</td><td>74.6±2.1</td><td>74.7±1.9</td><td>86.8±2.0</td><td>84.7±1.7</td><td>74.2±2.6</td><td>73.6±2.9</td></tr><tr><td>w/RN</td><td>79.8**±0.9</td><td>78.6**±1.2</td><td>66.9* ±1.1</td><td>62.8* ±1.4</td><td>76.1** ±1.5</td><td>76.1**±1.8</td><td>87.7**±2.2</td><td>85.4**±1.9</td><td>74.7* ±2.2</td><td>74.5**±2.3</td></tr><tr><td rowspan="2">GAT</td><td>w/o RN</td><td>76.0±1.7</td><td>74.9±1.9</td><td>66.3±2.8</td><td>62.4±2.6</td><td>73.9±2.2</td><td>73.9±2.1</td><td>88.3±2.0</td><td>86.2±2.2</td><td>79.0±2.1</td><td>78.8±2.3</td></tr><tr><td>W/RN</td><td>77.7**±*2.0</td><td>76.2**±1.8</td><td>67.1*±1.9</td><td>63.2*±1.6</td><td>75.2**±2.0</td><td>75.1**±2.5</td><td>89.1**±2.0</td><td>87.1**±2.0</td><td>78.8±1.9</td><td>78.7±2.0</td></tr><tr><td rowspan="2">PPNP</td><td>w/oRN</td><td>80.5±1.6</td><td>79.1±1.4</td><td>67.5±1.8</td><td>63.2±1.6</td><td>74.6±1.9</td><td>74.7±1.7</td><td>89.3±1.3</td><td>86.8±1.4</td><td>78.7±1.5</td><td>77.7±1.7</td></tr><tr><td>w/RN</td><td>81.9**±0.6</td><td>80.5**±0.8</td><td>68.1* ±1.4</td><td>63.7* ±2.0</td><td>76.0**±2.0</td><td>76.1**±2.2</td><td>89.7*±1.0</td><td>87.2* ±1.3</td><td>79.0* ±1.1</td><td>78.3* ±11</td></tr><tr><td rowspan="2">SAGE</td><td>w/o RN</td><td>75.1±1.7</td><td>74.6±1.4</td><td>67.0±1.4</td><td>63.0±1.4</td><td>74.2±2.2</td><td>74.2±2.1</td><td>86.2±2.6</td><td>83.9±2.4</td><td>73.5±3.4</td><td>71.6±2.5</td></tr><tr><td>w/RN</td><td>75.7**±1.7</td><td>75.1**±1.4</td><td>67.3±1.4</td><td>63.5* ±1.2</td><td>74.9**±1.9</td><td>78.2**±2.3</td><td>86.5±1.7</td><td>84.1±1.7</td><td>74.9**±3.0</td><td>72.3**±2.5</td></tr><tr><td rowspan="2">CHEB</td><td>w/oRN</td><td>74.5±1.1</td><td>73.4±1.1</td><td>66.8±1.8</td><td>63.2±1.6</td><td>75.1±1.8</td><td>75.2±1.1</td><td>82.1±2.2</td><td>79.4±3.5</td><td>70.3±4.0</td><td>68.4±3.4</td></tr><tr><td>w/RN</td><td>75.3**±1.1</td><td>74.0**±1.1</td><td>67.5**±1.6</td><td>63.8**±1.5</td><td>76.2**±1.4</td><td>76.3**±1.2</td><td>84.8**±2.4</td><td>82.1**±2.8</td><td>70.5±4.0</td><td>68.6±3.4</td></tr><tr><td rowspan="2">SGC</td><td>w/oRN</td><td>74.9±2.1</td><td>73.8±2.1</td><td>65.7±1.6</td><td>61.8±1.6</td><td>72.9±2.3</td><td>73.1±2.6</td><td>87.1±1.3</td><td>84.9±11</td><td>77.4±1.7</td><td>76.8±1.8</td></tr><tr><td>w/RN</td><td>77.0**±1.1</td><td>76.0**±1.1</td><td>67.2**±1.3</td><td>62.9**±1.8</td><td>73.7**±2.8</td><td>73.8**±2.1</td><td>87.4±1.5</td><td>85.2±1.5</td><td>78.2**±1.8</td><td>77.8**±1.2</td></tr></table>
+
+Table 2: Result of different dataset conflict levels (High/Middle/Low). Our ReNode method improve the GNN (GCN) performance most when the conflict level of graph is high.   
+
+<table><tr><td>W-F(%)</td><td>CORA-H</td><td>CORA-M</td><td>CORA-L</td><td>CiteSeer-H</td><td>CiteSeer-M</td><td>CiteSeer-L</td><td>PubMed-H</td><td>PubMed-M</td><td>|PubMed-L</td></tr><tr><td>w/o RN w/RN</td><td>76.5±1.3 78.7**±0.8</td><td>78.4±0.7 79.3**±0.6</td><td>79.7±0.8 80.4**±0.6</td><td>62.6±1.5 63.8**±1.3</td><td>65.3±0.6 66.0**±0.8</td><td>67.3±1.1 67.5±1.4</td><td>72.1±2.4 74.3**±2.1</td><td>74.7±1.8 75.6**±1.9</td><td>78.3±1.8 78.8* ±1.5</td></tr></table>
+
+$$
+\pmb { g } ^ { \prime } = \mathrm { s o f t m a x } ( \hat { P } \mathcal { F } ^ { \prime } ( \pmb { X } , \pmb { \theta } ^ { \prime } ) ) ,
+$$
+
+where ${ \mathcal { F } } ^ { \prime }$ can be a linear layer or a multi-layer perceptron with parameter $\theta ^ { \prime }$ . The final training loss for large-scale graph $L _ { L }$ follows Eq (5) and (6), and replaces $\pmb { w }$ and $\textbf {  { g } }$ with $\hat { \pmb { w } }$ and $\pmb { g } ^ { \prime }$ .
+
+# 3 Experiments
+
+In this section, we will first introduce the experimental datasets for both transductive and inductive semi-supervised node classification. Then we introduce the experiments to verify the effectiveness of the proposed ReNode method in three different imbalance situations: (1) TINL only, (2) TINL and QINL, (3) Large-scale Graph.
+
+# 3.1 Datasets
+
+We adopt two sets of graph datasets to conduct experiments. For the transductive setting [13], we take the widely-used Plantoid paper citation graphs [33] (CORA,CiteSeer, Pubmed) and the Amazon copurchase graphs [24] (Photo,Computers) to verify the effectiveness of our method. For the inductive setting, we conduct experiments on the popular Reddit dataset [13] and the enormous MAG-Scholar dataset (coarse-grain version) [2] which owns millions of nodes and features. For each of these datasets, we repeat experiments on 5 different datasets splittings [34] and we run 3 times for each splitting to reduce the random variance. More details about the datasets and experiment settings are presented in Appendix A.
+
+# 3.2 ReNode for the Pure Topology-imbalance Issue
+
+Settings When considering topology-imbalance only, the labeling set takes a balanced setting and the annotation size for each class is all equal to $| \dot { \mathcal { L } } | / k$ . Following the most widely-used semisupervised setting in node classification studies [47, 18], we randomly select 20 nodes in each class for training and 30 nodes per class for validation; all the remaining nodes form the test set. We display the experiment results for the 5 transductive datasets on 6 widely-used GNN models: GCN [18], GAT [40], PPNP [19], GraphSAGE [13] (short as SAGE), ChebGCN [9] (short as CHEB) and SGC [43]. We strictly align the hyperparameters in each group of experiments to show the pure improvement brought by our ReNode method (similarly hereinafter). The training loss $L _ { T }$ from section 2.4 is adopted.
+
+Table 3: ReNode method for the compound scene of TINL and QINL. The imbalance ratio $\rho$ is set to different levels ([5, 10]) to test the effect of our method under different imbalance intensities.   
+
+<table><tr><td rowspan=1 colspan=1>Macro-F1(%)</td><td rowspan=1 colspan=2>CORA</td><td rowspan=1 colspan=2>CiteSeer</td><td rowspan=1 colspan=2>PubMed</td><td rowspan=1 colspan=2>Photo</td><td rowspan=1 colspan=2>Computers</td></tr><tr><td rowspan=1 colspan=1>Imbalance Ratio</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td></tr><tr><td rowspan=1 colspan=1>CE</td><td rowspan=1 colspan=1>60.9±1.5</td><td rowspan=1 colspan=1>41.0±3.5</td><td rowspan=1 colspan=1>53.6±2.1</td><td rowspan=1 colspan=1>47.6±2.8</td><td rowspan=1 colspan=1>61.0±1.9</td><td rowspan=1 colspan=1>49.7±2.6</td><td rowspan=1 colspan=1>62.0±2.7</td><td rowspan=1 colspan=1>40.7±3.4</td><td rowspan=1 colspan=1>50.4±2.6</td><td rowspan=1 colspan=1>35.5±3.2</td></tr><tr><td rowspan=1 colspan=1>DR-GCN</td><td rowspan=1 colspan=1>67.7±1.1</td><td rowspan=1 colspan=1>51.3±1.4</td><td rowspan=1 colspan=1>54.7±1.7</td><td rowspan=1 colspan=1>52.5±2.6</td><td rowspan=1 colspan=1>79.4±1.2</td><td rowspan=1 colspan=1>78.0±1.6</td><td rowspan=1 colspan=1>80.8±2.3</td><td rowspan=1 colspan=1>79.5±2.8</td><td rowspan=1 colspan=1>66.9±3.5</td><td rowspan=1 colspan=1>67.4±3.6</td></tr><tr><td rowspan=2 colspan=1>RA-GCNG-SMOTE</td><td rowspan=1 colspan=1>69.0±1.5</td><td rowspan=2 colspan=1>51.7±1.749.6±1.1</td><td rowspan=2 colspan=1>55.6±1.354.0±1.6</td><td rowspan=1 colspan=1>52.7±2.1</td><td rowspan=2 colspan=1>80.6±1.879.7±1.2</td><td rowspan=2 colspan=1>78.1±2.176.4±1.5</td><td rowspan=2 colspan=1>81.4±2.682.2±1.8</td><td rowspan=2 colspan=1>79.4±3.277.5±2.1</td><td rowspan=2 colspan=1>71.2±2.871.9±2.5</td><td rowspan=1 colspan=1>68.7±3.0</td></tr><tr><td rowspan=1 colspan=1>68.1±0.9</td><td rowspan=1 colspan=1>51.8±1.3</td><td rowspan=1 colspan=1>61.3±3.2</td></tr><tr><td rowspan=1 colspan=1>RW (w/o RN)</td><td rowspan=1 colspan=1>69.1±1.4</td><td rowspan=1 colspan=1>49.7±1.6</td><td rowspan=1 colspan=1>53.6±2.3</td><td rowspan=1 colspan=1>52.9±2.6</td><td rowspan=1 colspan=1>80.5±1.5</td><td rowspan=1 colspan=1>78.0±2.0</td><td rowspan=1 colspan=1>80.5±2.7</td><td rowspan=1 colspan=1>80.4±3.3</td><td rowspan=1 colspan=1>70.5±3.2</td><td rowspan=1 colspan=1>67.8±4.2</td></tr><tr><td rowspan=1 colspan=1>RW (w/ RN)</td><td rowspan=1 colspan=1>70.0*±1.3</td><td rowspan=1 colspan=1>50.1±1.7</td><td rowspan=1 colspan=1>55.2**±1.8</td><td rowspan=1 colspan=1>54.0**±2.5</td><td rowspan=1 colspan=1>81.2* ±1.0</td><td rowspan=1 colspan=1>78.5*±2.2</td><td rowspan=1 colspan=1>83.9**±2.1</td><td rowspan=1 colspan=1>81.3**±3.2</td><td rowspan=1 colspan=1>72.4**±2.6</td><td rowspan=1 colspan=1>70.2**±2.4</td></tr><tr><td rowspan=2 colspan=1>FOCAL (w/o RN)FOCAL (w/RN)</td><td rowspan=1 colspan=1>66.4±1.6</td><td rowspan=1 colspan=1>51.9±1.8</td><td rowspan=1 colspan=1>54.3±1.3</td><td rowspan=1 colspan=1>54.0±1.9</td><td rowspan=1 colspan=1>80.5±0.7</td><td rowspan=1 colspan=1>78.0±1.6</td><td rowspan=1 colspan=1>79.3±1.9</td><td rowspan=1 colspan=1>79.2±2.2</td><td rowspan=1 colspan=1>65.8±2.7</td><td rowspan=1 colspan=1>63.9±2.6</td></tr><tr><td rowspan=1 colspan=1>68.7**±0.7</td><td rowspan=1 colspan=1>52.6**±1.9</td><td rowspan=1 colspan=1>54.6±1.2</td><td rowspan=1 colspan=1>54.7*±1.5</td><td rowspan=1 colspan=1>80.9*±0.8</td><td rowspan=1 colspan=1>78.7**±1.4</td><td rowspan=1 colspan=1>80.0**±*2.3</td><td rowspan=1 colspan=1>80.7**±2.9</td><td rowspan=1 colspan=1>68.6**±3.1</td><td rowspan=1 colspan=1>65.5**±3.5</td></tr><tr><td rowspan=2 colspan=1>CB (w/o RN)CB (w/RN)</td><td rowspan=1 colspan=1>69.8±1.5</td><td rowspan=2 colspan=1>51.5±1.551.9*±1.2</td><td rowspan=2 colspan=1>54.1±1.354.7*±1.6</td><td rowspan=2 colspan=1>53.5±0.854.3**±2.3</td><td rowspan=2 colspan=1>80.6±0.881.2*±1.8</td><td rowspan=2 colspan=1>77.6±1.678.3**±2.6</td><td rowspan=2 colspan=1>77.9±2.679.6** ±2.7</td><td rowspan=2 colspan=1>78.8±3.180.4**±3.3</td><td rowspan=2 colspan=1>69.6±2.273.1**±3.1</td><td rowspan=2 colspan=1>64.8±2.966.5**±3.6</td></tr><tr><td rowspan=1 colspan=1>71.1**±0.6</td></tr></table>
+
+Results From Table 1, we can find that our ReNode method can effectively improve the overall performance (Weighted-F1) and the class-balance performance (Macro-F1) for all the 6 experiment GNNs in most cases, which proves the effectiveness and generalizability of our method. Our method considers the graph-specific topology imbalance issue which has been usually neglected in existing methods and conducts a fine-grained and self-adaptive adjustment to the training node weights based on their topological positions. We notice that the improvement for the CiteSeer dataset is less than the other datasets. We analyze the reason lies in that the connectivity of CiteSeer is poor, which makes the conflict detection–based method fail to reflect the node topological position well. To verify the motivation of relieving topology-imbalance, we set training sets with different levels of topologyimbalance to test our method3. Table 2 displays that our ReNode method improves the performance of GNN (GCN) most when the dataset is highly topologically imbalanced, which demonstrates that our method can effectively alleviate topology-imbalance and improve GNN performance.
+
+# 3.3 ReNode for the Compound Scene of TINL and QINL
+
+Settings When jointly considering both topology- and quantity-imbalance issues, following existing studies [5, 4], we take the step imbalance setting, in which all the minority classes have the same labeling size $n _ { i }$ and all the majority classes have the same labeling size $n _ { a } = \rho * n _ { i }$ . The imbalance ratio $\rho$ denotes the intensity of quantity imbalance which is equal to the ratio of the node size of the most frequent to least frequent class. In this work, the imbalance ratio $\rho$ is set to [5, 10] for each dataset. The fraction of the majority classes is $\mu$ , and for all experiments, we set $\mu = 0 . 5$ and round down the result $\mu * k$ . The training loss $L _ { Q }$ from section 2.4 is adopted. We implement two groups of baselines for comparison: (1) Popular quantity-imbalance methods for general scenarios: Re-weight [17] (RW), Focal Loss [22] (Focal) and Class Balanced Loss [8] (CB); (2) Graph-specific quantity-imbalance methods: DR-GCN [35], RA-GCN [11] and GraphSMOTE [49]. To jointly handle the topology- and quantity-imbalance issues and demonstrate the orthogonality of them, we combine our ReNode method with these three general quantity-imbalance methods (RW, Focal, CB)4. The backbone model is GCN [18], and the labeling ratio $\delta$ is set to $5 \%$ .
+
+Results From Table 3 (Macro-F1 is reported here for a fair comparison with these methods designed for class-balance performance), we can find that our ReNode method significantly outperforms both the general and the graph-specific quantity-imbalance methods in most situations by simultaneously alleviating the topology- and quantity-imbalance issues. Even when the training set is severely quantity-imbalanced $\scriptstyle ( \rho = 1 0 )$ , our method still effectively alleviates the imbalance issue and promotes model performance well. The performance of the quantity-imbalance methods from the general field (RW, Focal, CB) is on par with or less effective than the graph-specific quantity-imbalance methods (DR-GCN, RA-GCN, G-SMOTE), while the combination of our ReNode method and these general quantity-imbalance methods can surpass the graph-specific quantity-imbalance methods, which demonstrates that the node imbalance learning can be further solved by jointly handling the topology- and quantity-imbalance issues instead of considering the quantity-imbalance issue only.
+
+![](images/6d160bd3b091be39bb9f07d48335845a9ed9ec4d5bd61d729b2de3828a23d52b.jpg)  
+Figure 4: Experimental results (Weighted-F1, $\%$ ) on the large-scale Reddit and MAG-Scholar graphs. Our ReNode method can effectively improve the model performance under different labeling sizes.
+
+![](images/f5bc5a21a4d8e008c5065041fd9c8ee0bd160c6729bf1cb6c89a70ee0cd10f49.jpg)  
+Figure 5: Evaluating GNNs from the aspect of topology-imbalance sensitivity (Metric: Weighted-F1 $( \% ) ,$ ). We can summarize the ranking of topology-imbalance sensitivity: $\mathrm { G C N } > \mathrm { P P N P } > \mathrm { G A T }$ .
+
+# 3.4 ReNode for Large-scale Graphs
+
+Settings We conduct experiments on the two large-scale datasets: Reddit and MAG-Scholar, to verify the effectiveness of our ReNode method in the inductive setting. We conduct experiments with different labeling sizes (20/50/100 training nodes per class) and imbalance settings (TINL-only, TINL and QINL). The backbone GNN model is PPRGo [2] 5. For QINL, we take the uniform selection to sample training nodes to be consistent with PPRGo. The training loss $L _ { L }$ from section 2.4 is adopted. Both baseline and our methods are not combined with any quantity-imbalance method.
+
+Results In Figure 4, we present the experiment results with different labeling sizes and imbalance settings, we can find that our method can effectively promote the performance on the large-scale graphs comparing to the popular PPRGo model across different settings, which demonstrates the applicability of our method for extremely-large graphs. We also notice that our method can bring greater improvement when the labeling size is large. We explain the reason lies in that when the labeling size is large, the positions located by the conflicts among nodes will be more accurate, thus bringing more reasonable weight adjustments. On the other hand, when the labeling ratio is extremely small (especially for the enormous MAG-Scholar graph) and the influence conflict between the labeled nodes is negligible, our method exhibits the cold start problem.
+
+# 4 Discussions
+
+# 4.1 Evaluating GNNs from the Aspect of Topology-Imbalance Sensitivity
+
+In Figure 5, we evaluate the GNN’s capability for handling topology-imbalance and find that different GNNs present significant difference in the topology-imbalance sensitivity across multiple datasets. The GCN model is susceptible to the topology-imbalance level of the graph and its performance decays greatly when the topology-imbalance increases. On the opposite, the GAT model is less sensitive to the topology-imbalance level and can achieve the best results when the topology-imbalance level is high. The PPNP model can achieve ideal performance when the topology-imbalance level is low, and its performance does not drop as sharply as GCN when the topology-imbalance level is high. We analyze the reason lies in that: (1) the aggregation operation of GCN is equivalent to directly averaging neighbor features [45] that lacks the noise filtering mechanism, so it is more sensitive to the topology-imbalance level of the graph; (2) the GAT model can dynamically adjust the aggregation weight from different neighbors, which increases its robustness to the high topology-imbalance situation but hinders the model performance when the graph topology-imbalance level is low and there is less need to filter neighbor information; (3) the infinite convolution mechanism of the PPNP model makes it possible to aggregate the information from distant nodes to enhance its robustness to the graph topology imbalance.
+
+Shchur et al. [34] notice that the performance ranking of GNNs varies with the training set selection. Hence, existing node classification studies [32, 14] usually repeat experiments multiple times with different training sets to reduce this randomness. The results from Figure 5 inspire us that the topology imbalance can partly explain the randomness of GNN performance caused by the training set selection and we can adopt the topology-imbalance sensitivity as a new aspect in evaluating the performance of different GNN architectures.
+
+# 4.2 Limitations of Method
+
+Although our ReNode method has proven effective in multiple scenarios, we also notice some limitations of it because of the complexity of node imbalance learning. First, the ReNode method is devised for homogeneously-connected graphs (linked nodes are expected to be similar, such as the various datasets in experiments), and it needs a further update for heterogeneously-connected graphs (such as protein networks). Besides, the ReNode method improves less when the graph connectivity is poor (Section 3.2) or the labeling ratio is extremely low (Section 3.3) because in these cases, the conflict level among nodes is low thus the nodes topological positions are insufficiently reflected.
+
+# 5 Related Work
+
+Imbalanced classification problems are widespread in real scenarios and have attracted extensive attention from both academia and industry. Most existing studies on this topic focus on the classimbalanced quantity distribution [15], where the model’s inference ability for the majority classes will be significantly better than that of minority classes [12]. The existing methods for solving the quantity-imbalance issue can be roughly divided into methods for the data selection phase and the model training phase. Active learning [31, 10, 42] and Re-sampling [6, 16, 25] are two classical examples designed to construct a quantity-balanced training set . On the other hand, Re-weighting is a simple but effective solution for the model training phase, which adjusts the weights of training samples in different classes based on the labeling sizes [17, 30, 8, 5]. However, directly applying these methods into the graph scene lacks the consideration for the graph-specific topology-imbalance issue. Unlike the re-weight methods which conduct class-lever re-weighting, our ReNode method is a more fine-grained one and assign weights to each node individually.
+
+There have been quantity-imbalance studies (Tomek links [38], NearMiss [23], One-Sided Selection [20]) trying to exclude the negative influence of labeling samples close to class boundaries by measuring the similarity of sample features. However, in the graph scene, the prior knowledge contained in node connections is more reliable than directly calculating the feature similarity. Besides, the number of labeled nodes is quite small in the semi-supervised setting. Thus it is not robust to locate their positions by computing similarity among a small number of nodes and we propose to leverage the influence conflict across the whole graph to locate node position to boundaries.
+
+Graph data structure owns a wide range of applications, such as social media [13], stock exchange [21], shopping [34], medicine [44], transportation [28] and so on. Similar to other data structures, graph node representation learning also suffer from the quantity-imbalance issue [35]. Apart from the universal quantity-balance approaches introduced in Section 5 which can be transferred to the graph scene, there are some graph-specific quantity-imbalance methods recently proposed. DR-GCN [35] propose two types of regularization to tackle quantity imbalance: class-conditioned adversarial training and unlabeled nodes latent distribution constraint. RA-GCN [11] propose to automatically learn to weight the training samples in different classes in an adversarial training manner. AdaGCN Shi et al. [36] propose to leverage the boosting algorithm to handle the quantity-imbalance issue for the node classification task. GraphSMOTE [49] combines the synthetic node generation and the edge generation to up-sample nodes for the minority classes. However, these studies only pay attention to the quantity imbalance and overlook the topology imbalance.
+
+Different from these studies [48, 29, 26] that try to locate the absolute positions for all the nodes by measuring their distance from the selected anchor nodes, our Totoro metric is devised to locate the relative positions to the class boundary for the labeling nodes by considering the influence conflict and can get rid of the dependence on the anchor nodes. Besides, our relative positions can more accurately reflect node class information because we distinguish the information from different classes while existing studies [48, 29] treat all the anchor nodes the same and ignore the class difference.
+
+# 6 Conclusion and Future Work
+
+In this work, we recognize the topology-imbalance node representation learning (TINL) as a graphspecific imbalance learning problem that has not been studied so far. We find that the topologyimbalance issue widely exists in graphs and severely hinders the learning of node classification. We unify TINL with the quantity-imbalance node representation learning (QINL) by considering the shift of the node influence boundaries from true class boundaries. To measure the degree of topology imbalance, we devise a conflict detection–based metric Totoro to locate node position, and further propose the ReNode method to adaptively adjust the training weights of labeled nodes based on their topological positions. Extensive empirical results have verified the effectiveness of our method in various settings: TINL-only, both TINL and QINL, and large-scale graph. Besides, we also propose the topology-imbalance sensitivity as a new metric to evaluate GNNs.
+
+Considering the importance of the topology-imbalance issue and the limitations of our approach, advanced methods with stronger theoretical or experimental support are expected in future work. Moreover, since topology imbalance is widespread in graph-related tasks other than node classification, how to measure and solve the topology-imbalance issues in broader graph scopes remains a meaningful challenge for future study.
+
+# 7 Acknowledgement
+
+We appreciate all the thoughtful and insightful suggestions from reviews. This work was supported in part by a Tencent Research Grant and National Natural Science Foundation of China (No. 61673028). Xu Sun is the corresponding author of this paper.
+
+# References
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+        "text": "Topology-Imbalance Learning for Semi-Supervised Node Classification ",
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+        "text": "Deli Chen1,2, Yankai $\\mathbf { L i n } ^ { 1 }$ , Guangxiang Zhao2, Xuancheng Ren2, Peng $\\mathbf { L i } ^ { 1 }$ , Jie $\\mathbf { Z } \\mathbf { h o u } ^ { 1 }$ , $\\mathbf { X } \\mathbf { u } \\mathbf { S } \\mathbf { u } \\mathbf { n } ^ { 2 }$ 1Pattern Recognition Center, WeChat AI, Tencent Inc., China 2MOE Key Lab of Computational Linguistics, School of EECS, Peking University {delichen, yankailin, patrickpli,withtomzhou}@tencent.com {zhaoguangxiang,renxc,xusun}@pku.edu.cn ",
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+        "text": "Abstract ",
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+        "text": "The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semisupervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection–based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.1 ",
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+        "text": "1 Introduction ",
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+        "text": "Graph is a widely-used data structure [51], where the nodes are connected to each other through natural or handcrafted edges. Similar to other data structures, the representation learning for node classification faces the challenge of quantity-imbalance issue, where the labeling size varies among classes and the decision boundaries of trained classifiers are mainly decided by the majority classes [46]. There have been a series of studies [35, 11, 49] handling the Quantity-Imbalance Node Representation Learning (short as QINL). However, different with other data structures, graph-structured data suffers from another aspect of the imbalance problem: the imbalance caused by the asymmetric and uneven topology of labeled nodes, where the decision boundaries are driven by the labeled nodes close to the topological class boundaries (left of Figure 1) thus interfering with the model learning. ",
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+        "text": "Present Work. For the first time, we recognize the Topology-Imbalance Node Representation Learning (short as TINL) as a graph-specific imbalance learning topic, which mainly focus on the decision boundaries shift phenomena driven by the topology imbalance in graph and is an essential component for node imbalance learning. Comparing with the well-explored QINL that studies the imbalance caused by the numbers of labeled nodes, TINL explores the imbalance caused by the positions of labeled nodes and owns the following characteristics: ",
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+        "img_path": "images/3c5d5345b792342769fcf85d480df7dfaf12f9fa1c75f46eec6382748a5fb423.jpg",
+        "image_caption": [
+            "Figure 1: Schematic diagram of the topology-imbalance issue in node representation learning. The color and the hue denote the type and the intensity of each node’s received influence from the labeled nodes, respectively. The left shows that nodes close to the boundary have the risk of information conflict and nodes far away from labeled nodes have the risk of information insufficient. The right shows that our method can decrease the training weights of labeled nodes (R1) close to the class boundary and increase the weights of labeled nodes (B and R2) close to the class centers, thus relieving the topology-imbalance issue. "
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+        "text": "• Ubiquity: Due to the complex connections of the graph nodes, the topology structure of nodes in different categories is naturally asymmetric, which makes TINL an essential characteristic in node representation learning. Hence, it is difficult to construct a completely symmetric labeling set even with an abundant annotation budget. • Perniciousness: The influence from labeled nodes decays with the topology distance [3]. The asymmetric topology of labeled nodes in different classes and the uneven distribution of labeled nodes in the same class will cause the influence conflict and influence insufficient problems (left of Figure 1) respectively, resulting in a shift of decision boundaries. • Orthogonality: Quantity-imbalance studies [49, 8, 5] usually treat the labeled nodes of the same class as a whole and devise solutions based on the total numbers of each class, while TINL explores the influence of the unique position of each labeled node on decision boundaries. Thus, TINL is independent of QINL in terms of the object of study. ",
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+        "type": "text",
+        "text": "Exploring TINL is of great importance for node representation learning due to its ubiquity and perniciousness. However, the methods [17, 22] for quantity imbalance can be hardly applied to TINL because of the orthogonality. To remedy the topology-imbalance issue, thus promoting the node classification, we propose a model-agnostic training framework ReNode to re-weight the labeled nodes according to their positions. We devise the conflict detection-based Topology Relative Location (Totoro) metric to leverage the interaction among labeled nodes across the whole graph to locate their structural positions. Based on the Totoro metric, we further increase the training weights of nodes with small conflict that are highly likely to be close to topological class centers to make them play a more pivotal role during training, and vice versa (right of Figure 1). Empirical results of various imbalance scenarios (TINL, QINL, large-scale graph) and multiple graph neural networks (GNNs) demonstrate the effectiveness and generalizability of our method. Besides, we provide the sensitivity to topology imbalance as a new evaluation perspective for different GNN architectures. ",
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+        "text": "2 Topology-Imbalance Node Representation Learning ",
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+        "text": "2.1 Notations and Preliminary ",
+        "text_level": 1,
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+        "text": "In this work, we follow the well-established semi-supervised node classification setting [47, 18] to conduct analyses and experiments. Given an undirected and unweighted graph $\\mathcal { G } = ( \\boldsymbol { \\nu } , \\pmb { \\varepsilon } , \\pmb { c } )$ , where $\\nu$ is the node set represented by the feature matrix $\\boldsymbol { X } \\in \\mathbb { R } ^ { n * d }$ $\\dot { \\boldsymbol { n } } = | \\boldsymbol { \\nu } |$ is the node size and $d$ is the node embedding dimension), $\\varepsilon$ is the edge set which is represented by an adjacency matrix $A \\in \\mathbb { R } ^ { n * n }$ , $\\pmb { \\mathcal { L } } \\subset \\nu$ is the labeled node set and usually we have $| \\bar { \\boldsymbol { L } } | \\ll | \\boldsymbol { \\nu } |$ , the node classification task is to train a classifier $\\mathcal { F }$ (usually a GNN) to predict the class label y for the unlabeled node set $u = \\nu - c$ . The training sets for different classes are represented by $( \\pmb { \\mathscr { C } } _ { 1 } , \\pmb { \\mathscr { C } } _ { 2 } , \\cdots , \\pmb { \\mathscr { C } } _ { k } )$ and $k$ is the number of classes. The labeling ratio $\\delta = \\angle \\mathcal { x } / \\nu$ is the proportion of labeled nodes in all nodes. In this work, we focus on TINL in homogeneously-connected graphs and hope to inspire future studies on the critical topology-imbalance issue. ",
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+        "image_caption": [
+            "Figure 2: Node influence and boundary shift caused by quantity- and topology-imbalance. (a): The prediction results of GCN and LP are highly consistent (t-SNE [39] visualization of the $C O R A$ dataset). (b): The node influence boundary (the yellow dotted line) is shifted towards the small class from the true class boundary (the black dotted line) under the quantity- and topology-imbalance scene. (c): The node influence boundary is shifted towards the large class under the quantity-balanced, topology-imbalanced scene. We regard the large class as positive class to indicate the results. "
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+        "text": "2.2 Understanding Topology Imbalance via Label Propagation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "From Figure 1, we can intuitively perceive the imbalance brought by the positions of labeled nodes; in this part, we further explore the nature of topology imbalance with the well-known Label Propagation [50] algorithm (short as LP) and provide a uniform analysis framework for the comprehensive node imbalance issue. In LP, labels are propagated from the labeled nodes and aggregated along edges, which can also be viewed as a random walk process from labeled nodes. The convergence result $\\mathbf { Y }$ after repeated propagation is regarded as the nodes soft-labels: ",
+        "bbox": [
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+        "img_path": "images/42bcb685bc540a9eee6075578f556e2471c48f1ff915ac1c346657af459f487b.jpg",
+        "text": "$$\n\\pmb { Y } = \\alpha ( \\pmb { I } - ( 1 - \\alpha ) \\pmb { A } ^ { \\prime } ) ^ { - 1 } \\pmb { Y } ^ { 0 } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\pmb { I }$ is the identity matrix, $\\alpha \\in ( 0 , 1 ]$ is the random walk restart probability, $A ^ { \\prime } = D ^ { - { \\frac { 1 } { 2 } } } A D ^ { - { \\frac { 1 } { 2 } } }$ is the adjacency matrix normalized by the diagonal degree matrix $_ { D }$ , $\\mathbf { \\dot { Y } } ^ { 0 }$ is the initial label distribution where labeled nodes are represented by the one-hot vectors. The prediction label for the $i$ -th node is $q _ { i } = \\arg \\operatorname* { m a x } _ { j } Y _ { i j }$ . LP is a simple yet successful model [37] and can be unified with GNN models owning the message-passing mechanism [41]. From Figure 2(a), we can empirically find that there is a significant correlation between the results of LP and GCN (T/F indicates prediction is True/False). ",
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+    {
+        "type": "text",
+        "text": "The LP prediction $\\pmb q$ can be viewed as the distribution of the (labeled) node influence [41] (i.e. each node is mostly influenced by which class’s information); hence the boundaries of the node influence can act as an effective reflection for the GNN model decision boundaries considering the high consistency between LP and GNN. Moreover, node influence offers a unified view of TINL and QINL: ideally, the node influence boundaries should be consistent with the true class boundaries, but both the labeled nodes’ numbers (QINL) and positions (TINL) can cause a shift of the node influence boundaries from the true one, resulting in deviation of the model decision boundaries. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Node imbalance issue is composed of topology- and quantity-imbalance. Figure 2 illustrates two examples of node influence boundary shift. In Figure 2(b), when the uniform selection is adopted to generate training set, both the quantity and the topology are imbalanced for model training; then the large class with more total nodes (denotes by blue color) will own stronger influence than the small class with fewer total nodes (denotes by red color) due to the quantity advantage and the node influence boundary is shifted towards the small class. In Figure 2(c), when the quantity-balanced strategy is adopted for sampling training nodes, it will be easier for the small class to has more labeled nodes close to the class boundary and the boundary of the node influence is shifted into the large class. We can find that even when the training set is quantity-balanced, the topology-imbalance issue still exists and hinders the node classification learning. Hence, we can conclude that node imbalance learning is caused by the joint effect of TINL and QINL. Separately considering TINL or QINL will lead to a one-sided solution to node imbalance learning. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f912716e23c177a4938148c7a1170b81fdfe86390b15dbfd19bd85e1becda3fb.jpg",
+        "image_caption": [
+            "Figure 3: Effectiveness of Totoro at (a) Node Level: labeled nodes (t-SNE visualization of the CORA dataset) with less influence conflict (lighter color) are farther-away from class boundaries than those with high conflict (darker color), and (b) Dataset Level: There is a significant negative correlation between the GNN (GCN) performance and overall conflict of the training set (the Pearson correlation coefficient is $- 0 . 6 1 8$ over 50 randomly selected training sets with the $p$ value smaller than 0.01). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.3 Measuring Topology Imbalance by Influence Conflict ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Although we have realized that the imbalance of node topology interferes with model learning, how to measure the labeled node’s relative topological position to its class (being far away from or close to the class center) remains the key challenge in handling the topology-imbalance issue due to the complex graph connections and the unknown class labels for most nodes in the graph. As the nodes are homogeneously connected when constructing the graph, even nodes close to the class boundaries own similar characteristics to their neighbors. Thus it is unreliable to leverage the difference between the characteristics of one labeled node and its surrounding subgraphs to locate its topological position. Instead, we propose to utilize the node topology information by considering the node influence conflict across the whole graph and devise the Conflict Detection-based Topology Relative Location metric (Totoro). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Similar to Eq (1), we calculate the Personalized PageRank [27] matrix $_ { r }$ to measure node influence distribution from each labeled node: ",
+        "bbox": [
+            174,
+            568,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e827f488f2cb6f4bae1776661058118e29eb4a6a3cf0b0275ff28b885f7fb059.jpg",
+        "text": "$$\nP = \\alpha ( { \\cal I } - ( 1 - \\alpha ) A ^ { \\prime } ) ^ { - 1 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Node influence conflict denotes topological position. According to related studies [41, 19, 2], $_ { r }$ can be viewed as the distribution of influence exerted outward from each node. We assume that if a labeled node $v \\in \\nu$ encounters strong heterogeneous influence from the other classes’ labeled nodes in the subgraph around node $v$ where node $v$ itself owns great influence, we have the conclusion that node $v$ meets large influence conflict in message passing and it is close to topological class boundaries, and vice versa. Based on this hypothesis, we take the expectation of the influence conflict between the node $v$ and the labeled nodes from other classes when node $v$ randomly walks across the entire graph as a measurement of how topologically close node $v$ is to the center of the class it belongs to. The Totoro value of node $v$ is computed as: ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/ced03fa0654fa8e24cf5155f24288804077529fb029dcce36ba9dafdf7019461.jpg",
+        "text": "$$\n\\pmb { T } _ { v } = \\mathbb { E } _ { \\boldsymbol { x } \\sim \\pmb { P } _ { v , : } } [ \\sum _ { \\substack { j \\in [ 1 , k ] , j \\neq y _ { v } } } \\frac { 1 } { | \\pmb { \\mathcal { C } } _ { j } | } \\sum _ { i \\in \\pmb { \\mathcal { C } } _ { j } } \\pmb { P } _ { i , x } ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { \\nabla } _ { \\mathbf { y } _ { v } }$ is the ground-truth label of node $v$ , $P _ { v }$ indicates the personalized PageRank probability vector for the node $v$ . A larger Totoro value $\\mathbf { \\delta } _ { \\mathbf { \\mathcal { T } } _ { v } }$ indicates that node $v$ is topologically closer to class boundaries, and vice versa. The normalization item $1 / | c _ { j } |$ is added to make the influence from the different classes comparable when computing conflict. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We visualize the node labels and the Totoro values (scaled to $[ 0 , 1 ] $ ) of labeled nodes in Figure 3(a). We can find that the labeled nodes with smaller Totoro values are farther away from the class boundaries, demonstrating the effectiveness of Totoro in locating the positions of labeled nodes. Besides, we sum the conflict of all the labeled nodes $\\textstyle \\sum _ { b \\in { \\mathcal { L } } } T _ { v }$ to measure the overall conflict of the dataset, which can be viewed as the metric for the overall topology imbalance given the graph $\\mathfrak { g }$ and the training set $\\mathcal { L }$ . Figure 3(b) shows that there is a significant negative correlation between the overall conflict and the model performance, which further demonstrates the effectiveness of Totoro in measuring the intensity of topology imbalance at the dataset level. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.4 Alleviate Topology Imbalance by Instance-wise Node Re-weighting ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce ReNode, a model-agnostic training weight schedule mechanism to address TINL for general GNN encoder in a plug-and-play manner. Inspired by the analysis in Section 2.2, the ReNode method is devised to promote the training weights of the labeled nodes that are close to the topological class centers, so as to make these nodes play a more active role in model learning, and vice versa. Specifically, we devise a cosine annealing mechanise 2 for the training node weights based on their Totoro values: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/97fa692803647ece0e15e8dc9163cbf376d0f9667dfe1963ea76ebb6f2d2a15e.jpg",
+        "text": "$$\n{ \\pmb w } _ { v } = w _ { \\mathrm { m i n } } + \\frac { 1 } { 2 } ( w _ { \\mathrm { m a x } } - w _ { \\mathrm { m i n } } ) ( 1 + \\cos ( \\frac { \\mathrm { R a n k } ( { \\pmb T } _ { v } ) } { | { \\pmb L } | } \\pi ) ) , \\quad v \\in { \\pmb C }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            285,
+            292,
+            714,
+            327
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\pmb { w } _ { v }$ is the modified training weight for the labeled node $v , w _ { \\mathrm { m i n } } , w _ { \\mathrm { m a x } }$ are the hyper-parameters indicating the lower bound and upper bound of the weight correction factor, $\\mathrm { R a n k } ( \\pmb { T } _ { v } )$ is the ranking order of $\\mathbf { \\delta } _ { \\mathbf { \\mathcal { T } } _ { v } }$ from the smallest to the largest. The training loss $L _ { T }$ for the quantity-balanced, topologyimbalanced node classification task is computed by the following equations: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/40cd7196ef8bd4df78cc3f6c94cf3f60db3b71d839a0cc42b944755b0b8fc868.jpg",
+        "text": "$$\nL _ { T } = - \\frac { 1 } { | { \\cal { L } } | } \\sum _ { v \\in { \\cal { L } } } w _ { v } \\sum _ { c = 1 } ^ { k } y _ { v } ^ { * c } \\log \\ g _ { v } ^ { c } , \\quad g = \\mathrm { s o f t m a x } ( { \\mathcal { F } } ( X , A , \\theta ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+            395,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { F }$ denotes any GNN encoder, $\\pmb \\theta$ is the parameter of ${ \\mathcal { F } } , g _ { i }$ is the GNN output for node $i$ , $\\mathbf { \\nabla } _ { \\mathbf { \\boldsymbol { y } } _ { i } ^ { * } }$ is the gold label for node $i$ in one-hot embedding. By encouraging the positive effects of the labeled nodes near the class topological centers, and reducing the negative effects of those near the topological class boundaries, our ReNode method is expected to minimize the deviation between the node influence boundaries and the true class boundaries, so as to correct the class imbalance caused by the positions of labeled nodes. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ReNode to Jointly Handle TINL and QINL In this part, we introduce the application of the ReNode method in a more general graph imbalance scenario where both the topology- and quantityimbalance issues exist. As analyzed in previous sections, the TINL and QINL are orthogonal problems. Therefore, we propose that our ReNode method based on (labeled) node topology can be seamlessly combined with the existing methods designed for the quantity-imbalance learning. Without loss of generality, we present how our ReNode method can be combined with the vanilla class frequency-based re-weight method [17]. The training loss $L _ { Q }$ for the quantity-imbalanced, topology-imbalanced node classification task is formalized in the following equation: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/550bbdc0f33c4f67fad7538f929d6d585fa604bbd528576f360259da3d083c28.jpg",
+        "text": "$$\nL _ { Q } = - \\frac { 1 } { | \\mathcal { L } | } \\sum _ { v \\in \\mathcal { L } } w _ { v } \\frac { | \\bar { \\mathcal { C } } | } { | \\mathcal { C } _ { j } | } \\sum _ { c = 1 } ^ { k } { y } _ { v } ^ { * c } \\log \\textbf { \\em g } _ { v } ^ { c } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            359,
+            661,
+            637,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $| \\bar { c } |$ is the average number of the class training sizes. With this method, the final weight of the labeled node is affected by two perspectives: training examples of the minority classes will have higher weights than that of the majority classes; training examples close to the topological class centers will have higher weights than those are close to the topological class boundaries. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ReNode for Large-scale Graph There are mainly two challenges when applying ReNode to largescale graphs: (1) how to calculate the PageRank matrix, and (2) how to train the GNN model in an inductive setting [13]. In this work, we follow the PPRGo method [2] to implement our method on the large-scale graph, which can decouple the feature learning process from the information transmission process to resolve the dependence on the global graph topology structure and can be carried out much efficiently. Following PPRGo, the Personalized PageRank matrix $\\hat { P }$ and the corresponding training ReNode factor $\\hat { \\pmb { w } }$ are generated by the estimation method from Andersen et al. [1] and then $\\hat { P }$ is directly employed as the aggregation weights from all the other nodes regardless of their topology distance from the current node: ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/00496b03416eee86d41061c56867037edfd20150971023a1fb06382e90a276e9.jpg",
+        "table_caption": [
+            "Table 1: ReNode (short as RN) for the pure topology-imbalance issue. We report Weighted-F1 (W-F, $\\%$ ), Macro-F1 (M-F, $\\%$ ) and the corresponding standard deviation for each group of experiments. $^ *$ and $^ { \\ast \\ast }$ represent the result is significant in student t-test with $p < 0 . 0 5$ and $p < 0 . 0 1$ , respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Training</td><td colspan=\"2\">CORA</td><td colspan=\"2\">CiteSeer</td><td colspan=\"2\">PubMed</td><td colspan=\"2\">Photo</td><td colspan=\"2\">Computers</td></tr><tr><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td><td>W-F</td><td>M-F</td></tr><tr><td rowspan=\"2\">GCN</td><td>w/oRN</td><td>79.1±1.1</td><td>77.8±1.5</td><td>66.2±1.0</td><td>62.0±1.3</td><td>74.6±2.1</td><td>74.7±1.9</td><td>86.8±2.0</td><td>84.7±1.7</td><td>74.2±2.6</td><td>73.6±2.9</td></tr><tr><td>w/RN</td><td>79.8**±0.9</td><td>78.6**±1.2</td><td>66.9* ±1.1</td><td>62.8* ±1.4</td><td>76.1** ±1.5</td><td>76.1**±1.8</td><td>87.7**±2.2</td><td>85.4**±1.9</td><td>74.7* ±2.2</td><td>74.5**±2.3</td></tr><tr><td rowspan=\"2\">GAT</td><td>w/o RN</td><td>76.0±1.7</td><td>74.9±1.9</td><td>66.3±2.8</td><td>62.4±2.6</td><td>73.9±2.2</td><td>73.9±2.1</td><td>88.3±2.0</td><td>86.2±2.2</td><td>79.0±2.1</td><td>78.8±2.3</td></tr><tr><td>W/RN</td><td>77.7**±*2.0</td><td>76.2**±1.8</td><td>67.1*±1.9</td><td>63.2*±1.6</td><td>75.2**±2.0</td><td>75.1**±2.5</td><td>89.1**±2.0</td><td>87.1**±2.0</td><td>78.8±1.9</td><td>78.7±2.0</td></tr><tr><td rowspan=\"2\">PPNP</td><td>w/oRN</td><td>80.5±1.6</td><td>79.1±1.4</td><td>67.5±1.8</td><td>63.2±1.6</td><td>74.6±1.9</td><td>74.7±1.7</td><td>89.3±1.3</td><td>86.8±1.4</td><td>78.7±1.5</td><td>77.7±1.7</td></tr><tr><td>w/RN</td><td>81.9**±0.6</td><td>80.5**±0.8</td><td>68.1* ±1.4</td><td>63.7* ±2.0</td><td>76.0**±2.0</td><td>76.1**±2.2</td><td>89.7*±1.0</td><td>87.2* ±1.3</td><td>79.0* ±1.1</td><td>78.3* ±11</td></tr><tr><td rowspan=\"2\">SAGE</td><td>w/o RN</td><td>75.1±1.7</td><td>74.6±1.4</td><td>67.0±1.4</td><td>63.0±1.4</td><td>74.2±2.2</td><td>74.2±2.1</td><td>86.2±2.6</td><td>83.9±2.4</td><td>73.5±3.4</td><td>71.6±2.5</td></tr><tr><td>w/RN</td><td>75.7**±1.7</td><td>75.1**±1.4</td><td>67.3±1.4</td><td>63.5* ±1.2</td><td>74.9**±1.9</td><td>78.2**±2.3</td><td>86.5±1.7</td><td>84.1±1.7</td><td>74.9**±3.0</td><td>72.3**±2.5</td></tr><tr><td rowspan=\"2\">CHEB</td><td>w/oRN</td><td>74.5±1.1</td><td>73.4±1.1</td><td>66.8±1.8</td><td>63.2±1.6</td><td>75.1±1.8</td><td>75.2±1.1</td><td>82.1±2.2</td><td>79.4±3.5</td><td>70.3±4.0</td><td>68.4±3.4</td></tr><tr><td>w/RN</td><td>75.3**±1.1</td><td>74.0**±1.1</td><td>67.5**±1.6</td><td>63.8**±1.5</td><td>76.2**±1.4</td><td>76.3**±1.2</td><td>84.8**±2.4</td><td>82.1**±2.8</td><td>70.5±4.0</td><td>68.6±3.4</td></tr><tr><td rowspan=\"2\">SGC</td><td>w/oRN</td><td>74.9±2.1</td><td>73.8±2.1</td><td>65.7±1.6</td><td>61.8±1.6</td><td>72.9±2.3</td><td>73.1±2.6</td><td>87.1±1.3</td><td>84.9±11</td><td>77.4±1.7</td><td>76.8±1.8</td></tr><tr><td>w/RN</td><td>77.0**±1.1</td><td>76.0**±1.1</td><td>67.2**±1.3</td><td>62.9**±1.8</td><td>73.7**±2.8</td><td>73.8**±2.1</td><td>87.4±1.5</td><td>85.2±1.5</td><td>78.2**±1.8</td><td>77.8**±1.2</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/13e36310934705c5781a87916fbfdcec3ac3224954790f2a39226e1b68937f5b.jpg",
+        "table_caption": [
+            "Table 2: Result of different dataset conflict levels (High/Middle/Low). Our ReNode method improve the GNN (GCN) performance most when the conflict level of graph is high. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>W-F(%)</td><td>CORA-H</td><td>CORA-M</td><td>CORA-L</td><td>CiteSeer-H</td><td>CiteSeer-M</td><td>CiteSeer-L</td><td>PubMed-H</td><td>PubMed-M</td><td>|PubMed-L</td></tr><tr><td>w/o RN w/RN</td><td>76.5±1.3 78.7**±0.8</td><td>78.4±0.7 79.3**±0.6</td><td>79.7±0.8 80.4**±0.6</td><td>62.6±1.5 63.8**±1.3</td><td>65.3±0.6 66.0**±0.8</td><td>67.3±1.1 67.5±1.4</td><td>72.1±2.4 74.3**±2.1</td><td>74.7±1.8 75.6**±1.9</td><td>78.3±1.8 78.8* ±1.5</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/c1d448c4035fcc19ece2457264f5788047bdd7c12f8b0da0ea4e63a6a5003357.jpg",
+        "text": "$$\n\\pmb { g } ^ { \\prime } = \\mathrm { s o f t m a x } ( \\hat { P } \\mathcal { F } ^ { \\prime } ( \\pmb { X } , \\pmb { \\theta } ^ { \\prime } ) ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            400,
+            426,
+            594,
+            446
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathcal { F } } ^ { \\prime }$ can be a linear layer or a multi-layer perceptron with parameter $\\theta ^ { \\prime }$ . The final training loss for large-scale graph $L _ { L }$ follows Eq (5) and (6), and replaces $\\pmb { w }$ and $\\textbf {  { g } }$ with $\\hat { \\pmb { w } }$ and $\\pmb { g } ^ { \\prime }$ . ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will first introduce the experimental datasets for both transductive and inductive semi-supervised node classification. Then we introduce the experiments to verify the effectiveness of the proposed ReNode method in three different imbalance situations: (1) TINL only, (2) TINL and QINL, (3) Large-scale Graph. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.1 Datasets ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We adopt two sets of graph datasets to conduct experiments. For the transductive setting [13], we take the widely-used Plantoid paper citation graphs [33] (CORA,CiteSeer, Pubmed) and the Amazon copurchase graphs [24] (Photo,Computers) to verify the effectiveness of our method. For the inductive setting, we conduct experiments on the popular Reddit dataset [13] and the enormous MAG-Scholar dataset (coarse-grain version) [2] which owns millions of nodes and features. For each of these datasets, we repeat experiments on 5 different datasets splittings [34] and we run 3 times for each splitting to reduce the random variance. More details about the datasets and experiment settings are presented in Appendix A. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 ReNode for the Pure Topology-imbalance Issue ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            761,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Settings When considering topology-imbalance only, the labeling set takes a balanced setting and the annotation size for each class is all equal to $| \\dot { \\mathcal { L } } | / k$ . Following the most widely-used semisupervised setting in node classification studies [47, 18], we randomly select 20 nodes in each class for training and 30 nodes per class for validation; all the remaining nodes form the test set. We display the experiment results for the 5 transductive datasets on 6 widely-used GNN models: GCN [18], GAT [40], PPNP [19], GraphSAGE [13] (short as SAGE), ChebGCN [9] (short as CHEB) and SGC [43]. We strictly align the hyperparameters in each group of experiments to show the pure improvement brought by our ReNode method (similarly hereinafter). The training loss $L _ { T }$ from section 2.4 is adopted. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/d1bb9abdc48efa57ccfd11940d646394dc2aae52d1d770844156057bc45f9349.jpg",
+        "table_caption": [
+            "Table 3: ReNode method for the compound scene of TINL and QINL. The imbalance ratio $\\rho$ is set to different levels ([5, 10]) to test the effect of our method under different imbalance intensities. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Macro-F1(%)</td><td rowspan=1 colspan=2>CORA</td><td rowspan=1 colspan=2>CiteSeer</td><td rowspan=1 colspan=2>PubMed</td><td rowspan=1 colspan=2>Photo</td><td rowspan=1 colspan=2>Computers</td></tr><tr><td rowspan=1 colspan=1>Imbalance Ratio</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td><td rowspan=1 colspan=1>5</td><td rowspan=1 colspan=1>10</td></tr><tr><td rowspan=1 colspan=1>CE</td><td rowspan=1 colspan=1>60.9±1.5</td><td rowspan=1 colspan=1>41.0±3.5</td><td rowspan=1 colspan=1>53.6±2.1</td><td rowspan=1 colspan=1>47.6±2.8</td><td rowspan=1 colspan=1>61.0±1.9</td><td rowspan=1 colspan=1>49.7±2.6</td><td rowspan=1 colspan=1>62.0±2.7</td><td rowspan=1 colspan=1>40.7±3.4</td><td rowspan=1 colspan=1>50.4±2.6</td><td rowspan=1 colspan=1>35.5±3.2</td></tr><tr><td rowspan=1 colspan=1>DR-GCN</td><td rowspan=1 colspan=1>67.7±1.1</td><td rowspan=1 colspan=1>51.3±1.4</td><td rowspan=1 colspan=1>54.7±1.7</td><td rowspan=1 colspan=1>52.5±2.6</td><td rowspan=1 colspan=1>79.4±1.2</td><td rowspan=1 colspan=1>78.0±1.6</td><td rowspan=1 colspan=1>80.8±2.3</td><td rowspan=1 colspan=1>79.5±2.8</td><td rowspan=1 colspan=1>66.9±3.5</td><td rowspan=1 colspan=1>67.4±3.6</td></tr><tr><td rowspan=2 colspan=1>RA-GCNG-SMOTE</td><td rowspan=1 colspan=1>69.0±1.5</td><td rowspan=2 colspan=1>51.7±1.749.6±1.1</td><td rowspan=2 colspan=1>55.6±1.354.0±1.6</td><td rowspan=1 colspan=1>52.7±2.1</td><td rowspan=2 colspan=1>80.6±1.879.7±1.2</td><td rowspan=2 colspan=1>78.1±2.176.4±1.5</td><td rowspan=2 colspan=1>81.4±2.682.2±1.8</td><td rowspan=2 colspan=1>79.4±3.277.5±2.1</td><td rowspan=2 colspan=1>71.2±2.871.9±2.5</td><td rowspan=1 colspan=1>68.7±3.0</td></tr><tr><td rowspan=1 colspan=1>68.1±0.9</td><td rowspan=1 colspan=1>51.8±1.3</td><td rowspan=1 colspan=1>61.3±3.2</td></tr><tr><td rowspan=1 colspan=1>RW (w/o RN)</td><td rowspan=1 colspan=1>69.1±1.4</td><td rowspan=1 colspan=1>49.7±1.6</td><td rowspan=1 colspan=1>53.6±2.3</td><td rowspan=1 colspan=1>52.9±2.6</td><td rowspan=1 colspan=1>80.5±1.5</td><td rowspan=1 colspan=1>78.0±2.0</td><td rowspan=1 colspan=1>80.5±2.7</td><td rowspan=1 colspan=1>80.4±3.3</td><td rowspan=1 colspan=1>70.5±3.2</td><td rowspan=1 colspan=1>67.8±4.2</td></tr><tr><td rowspan=1 colspan=1>RW (w/ RN)</td><td rowspan=1 colspan=1>70.0*±1.3</td><td rowspan=1 colspan=1>50.1±1.7</td><td rowspan=1 colspan=1>55.2**±1.8</td><td rowspan=1 colspan=1>54.0**±2.5</td><td rowspan=1 colspan=1>81.2* ±1.0</td><td rowspan=1 colspan=1>78.5*±2.2</td><td rowspan=1 colspan=1>83.9**±2.1</td><td rowspan=1 colspan=1>81.3**±3.2</td><td rowspan=1 colspan=1>72.4**±2.6</td><td rowspan=1 colspan=1>70.2**±2.4</td></tr><tr><td rowspan=2 colspan=1>FOCAL (w/o RN)FOCAL (w/RN)</td><td rowspan=1 colspan=1>66.4±1.6</td><td rowspan=1 colspan=1>51.9±1.8</td><td rowspan=1 colspan=1>54.3±1.3</td><td rowspan=1 colspan=1>54.0±1.9</td><td rowspan=1 colspan=1>80.5±0.7</td><td rowspan=1 colspan=1>78.0±1.6</td><td rowspan=1 colspan=1>79.3±1.9</td><td rowspan=1 colspan=1>79.2±2.2</td><td rowspan=1 colspan=1>65.8±2.7</td><td rowspan=1 colspan=1>63.9±2.6</td></tr><tr><td rowspan=1 colspan=1>68.7**±0.7</td><td rowspan=1 colspan=1>52.6**±1.9</td><td rowspan=1 colspan=1>54.6±1.2</td><td rowspan=1 colspan=1>54.7*±1.5</td><td rowspan=1 colspan=1>80.9*±0.8</td><td rowspan=1 colspan=1>78.7**±1.4</td><td rowspan=1 colspan=1>80.0**±*2.3</td><td rowspan=1 colspan=1>80.7**±2.9</td><td rowspan=1 colspan=1>68.6**±3.1</td><td rowspan=1 colspan=1>65.5**±3.5</td></tr><tr><td rowspan=2 colspan=1>CB (w/o RN)CB (w/RN)</td><td rowspan=1 colspan=1>69.8±1.5</td><td rowspan=2 colspan=1>51.5±1.551.9*±1.2</td><td rowspan=2 colspan=1>54.1±1.354.7*±1.6</td><td rowspan=2 colspan=1>53.5±0.854.3**±2.3</td><td rowspan=2 colspan=1>80.6±0.881.2*±1.8</td><td rowspan=2 colspan=1>77.6±1.678.3**±2.6</td><td rowspan=2 colspan=1>77.9±2.679.6** ±2.7</td><td rowspan=2 colspan=1>78.8±3.180.4**±3.3</td><td rowspan=2 colspan=1>69.6±2.273.1**±3.1</td><td rowspan=2 colspan=1>64.8±2.966.5**±3.6</td></tr><tr><td rowspan=1 colspan=1>71.1**±0.6</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Results From Table 1, we can find that our ReNode method can effectively improve the overall performance (Weighted-F1) and the class-balance performance (Macro-F1) for all the 6 experiment GNNs in most cases, which proves the effectiveness and generalizability of our method. Our method considers the graph-specific topology imbalance issue which has been usually neglected in existing methods and conducts a fine-grained and self-adaptive adjustment to the training node weights based on their topological positions. We notice that the improvement for the CiteSeer dataset is less than the other datasets. We analyze the reason lies in that the connectivity of CiteSeer is poor, which makes the conflict detection–based method fail to reflect the node topological position well. To verify the motivation of relieving topology-imbalance, we set training sets with different levels of topologyimbalance to test our method3. Table 2 displays that our ReNode method improves the performance of GNN (GCN) most when the dataset is highly topologically imbalanced, which demonstrates that our method can effectively alleviate topology-imbalance and improve GNN performance. ",
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+    {
+        "type": "text",
+        "text": "3.3 ReNode for the Compound Scene of TINL and QINL ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Settings When jointly considering both topology- and quantity-imbalance issues, following existing studies [5, 4], we take the step imbalance setting, in which all the minority classes have the same labeling size $n _ { i }$ and all the majority classes have the same labeling size $n _ { a } = \\rho * n _ { i }$ . The imbalance ratio $\\rho$ denotes the intensity of quantity imbalance which is equal to the ratio of the node size of the most frequent to least frequent class. In this work, the imbalance ratio $\\rho$ is set to [5, 10] for each dataset. The fraction of the majority classes is $\\mu$ , and for all experiments, we set $\\mu = 0 . 5$ and round down the result $\\mu * k$ . The training loss $L _ { Q }$ from section 2.4 is adopted. We implement two groups of baselines for comparison: (1) Popular quantity-imbalance methods for general scenarios: Re-weight [17] (RW), Focal Loss [22] (Focal) and Class Balanced Loss [8] (CB); (2) Graph-specific quantity-imbalance methods: DR-GCN [35], RA-GCN [11] and GraphSMOTE [49]. To jointly handle the topology- and quantity-imbalance issues and demonstrate the orthogonality of them, we combine our ReNode method with these three general quantity-imbalance methods (RW, Focal, CB)4. The backbone model is GCN [18], and the labeling ratio $\\delta$ is set to $5 \\%$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Results From Table 3 (Macro-F1 is reported here for a fair comparison with these methods designed for class-balance performance), we can find that our ReNode method significantly outperforms both the general and the graph-specific quantity-imbalance methods in most situations by simultaneously alleviating the topology- and quantity-imbalance issues. Even when the training set is severely quantity-imbalanced $\\scriptstyle ( \\rho = 1 0 )$ , our method still effectively alleviates the imbalance issue and promotes model performance well. The performance of the quantity-imbalance methods from the general field (RW, Focal, CB) is on par with or less effective than the graph-specific quantity-imbalance methods (DR-GCN, RA-GCN, G-SMOTE), while the combination of our ReNode method and these general quantity-imbalance methods can surpass the graph-specific quantity-imbalance methods, which demonstrates that the node imbalance learning can be further solved by jointly handling the topology- and quantity-imbalance issues instead of considering the quantity-imbalance issue only. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d160bd3b091be39bb9f07d48335845a9ed9ec4d5bd61d729b2de3828a23d52b.jpg",
+        "image_caption": [
+            "Figure 4: Experimental results (Weighted-F1, $\\%$ ) on the large-scale Reddit and MAG-Scholar graphs. Our ReNode method can effectively improve the model performance under different labeling sizes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f5bc5a21a4d8e008c5065041fd9c8ee0bd160c6729bf1cb6c89a70ee0cd10f49.jpg",
+        "image_caption": [
+            "Figure 5: Evaluating GNNs from the aspect of topology-imbalance sensitivity (Metric: Weighted-F1 $( \\% ) ,$ ). We can summarize the ranking of topology-imbalance sensitivity: $\\mathrm { G C N } > \\mathrm { P P N P } > \\mathrm { G A T }$ . "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "3.4 ReNode for Large-scale Graphs ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Settings We conduct experiments on the two large-scale datasets: Reddit and MAG-Scholar, to verify the effectiveness of our ReNode method in the inductive setting. We conduct experiments with different labeling sizes (20/50/100 training nodes per class) and imbalance settings (TINL-only, TINL and QINL). The backbone GNN model is PPRGo [2] 5. For QINL, we take the uniform selection to sample training nodes to be consistent with PPRGo. The training loss $L _ { L }$ from section 2.4 is adopted. Both baseline and our methods are not combined with any quantity-imbalance method. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Results In Figure 4, we present the experiment results with different labeling sizes and imbalance settings, we can find that our method can effectively promote the performance on the large-scale graphs comparing to the popular PPRGo model across different settings, which demonstrates the applicability of our method for extremely-large graphs. We also notice that our method can bring greater improvement when the labeling size is large. We explain the reason lies in that when the labeling size is large, the positions located by the conflicts among nodes will be more accurate, thus bringing more reasonable weight adjustments. On the other hand, when the labeling ratio is extremely small (especially for the enormous MAG-Scholar graph) and the influence conflict between the labeled nodes is negligible, our method exhibits the cold start problem. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4 Discussions ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Evaluating GNNs from the Aspect of Topology-Imbalance Sensitivity ",
+        "text_level": 1,
+        "bbox": [
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+            737,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Figure 5, we evaluate the GNN’s capability for handling topology-imbalance and find that different GNNs present significant difference in the topology-imbalance sensitivity across multiple datasets. The GCN model is susceptible to the topology-imbalance level of the graph and its performance decays greatly when the topology-imbalance increases. On the opposite, the GAT model is less sensitive to the topology-imbalance level and can achieve the best results when the topology-imbalance level is high. The PPNP model can achieve ideal performance when the topology-imbalance level is low, and its performance does not drop as sharply as GCN when the topology-imbalance level is high. We analyze the reason lies in that: (1) the aggregation operation of GCN is equivalent to directly averaging neighbor features [45] that lacks the noise filtering mechanism, so it is more sensitive to the topology-imbalance level of the graph; (2) the GAT model can dynamically adjust the aggregation weight from different neighbors, which increases its robustness to the high topology-imbalance situation but hinders the model performance when the graph topology-imbalance level is low and there is less need to filter neighbor information; (3) the infinite convolution mechanism of the PPNP model makes it possible to aggregate the information from distant nodes to enhance its robustness to the graph topology imbalance. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Shchur et al. [34] notice that the performance ranking of GNNs varies with the training set selection. Hence, existing node classification studies [32, 14] usually repeat experiments multiple times with different training sets to reduce this randomness. The results from Figure 5 inspire us that the topology imbalance can partly explain the randomness of GNN performance caused by the training set selection and we can adopt the topology-imbalance sensitivity as a new aspect in evaluating the performance of different GNN architectures. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.2 Limitations of Method ",
+        "text_level": 1,
+        "bbox": [
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+            295,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Although our ReNode method has proven effective in multiple scenarios, we also notice some limitations of it because of the complexity of node imbalance learning. First, the ReNode method is devised for homogeneously-connected graphs (linked nodes are expected to be similar, such as the various datasets in experiments), and it needs a further update for heterogeneously-connected graphs (such as protein networks). Besides, the ReNode method improves less when the graph connectivity is poor (Section 3.2) or the labeling ratio is extremely low (Section 3.3) because in these cases, the conflict level among nodes is low thus the nodes topological positions are insufficiently reflected. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 Related Work ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Imbalanced classification problems are widespread in real scenarios and have attracted extensive attention from both academia and industry. Most existing studies on this topic focus on the classimbalanced quantity distribution [15], where the model’s inference ability for the majority classes will be significantly better than that of minority classes [12]. The existing methods for solving the quantity-imbalance issue can be roughly divided into methods for the data selection phase and the model training phase. Active learning [31, 10, 42] and Re-sampling [6, 16, 25] are two classical examples designed to construct a quantity-balanced training set . On the other hand, Re-weighting is a simple but effective solution for the model training phase, which adjusts the weights of training samples in different classes based on the labeling sizes [17, 30, 8, 5]. However, directly applying these methods into the graph scene lacks the consideration for the graph-specific topology-imbalance issue. Unlike the re-weight methods which conduct class-lever re-weighting, our ReNode method is a more fine-grained one and assign weights to each node individually. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "There have been quantity-imbalance studies (Tomek links [38], NearMiss [23], One-Sided Selection [20]) trying to exclude the negative influence of labeling samples close to class boundaries by measuring the similarity of sample features. However, in the graph scene, the prior knowledge contained in node connections is more reliable than directly calculating the feature similarity. Besides, the number of labeled nodes is quite small in the semi-supervised setting. Thus it is not robust to locate their positions by computing similarity among a small number of nodes and we propose to leverage the influence conflict across the whole graph to locate node position to boundaries. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Graph data structure owns a wide range of applications, such as social media [13], stock exchange [21], shopping [34], medicine [44], transportation [28] and so on. Similar to other data structures, graph node representation learning also suffer from the quantity-imbalance issue [35]. Apart from the universal quantity-balance approaches introduced in Section 5 which can be transferred to the graph scene, there are some graph-specific quantity-imbalance methods recently proposed. DR-GCN [35] propose two types of regularization to tackle quantity imbalance: class-conditioned adversarial training and unlabeled nodes latent distribution constraint. RA-GCN [11] propose to automatically learn to weight the training samples in different classes in an adversarial training manner. AdaGCN Shi et al. [36] propose to leverage the boosting algorithm to handle the quantity-imbalance issue for the node classification task. GraphSMOTE [49] combines the synthetic node generation and the edge generation to up-sample nodes for the minority classes. However, these studies only pay attention to the quantity imbalance and overlook the topology imbalance. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Different from these studies [48, 29, 26] that try to locate the absolute positions for all the nodes by measuring their distance from the selected anchor nodes, our Totoro metric is devised to locate the relative positions to the class boundary for the labeling nodes by considering the influence conflict and can get rid of the dependence on the anchor nodes. Besides, our relative positions can more accurately reflect node class information because we distinguish the information from different classes while existing studies [48, 29] treat all the anchor nodes the same and ignore the class difference. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 Conclusion and Future Work ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "In this work, we recognize the topology-imbalance node representation learning (TINL) as a graphspecific imbalance learning problem that has not been studied so far. We find that the topologyimbalance issue widely exists in graphs and severely hinders the learning of node classification. We unify TINL with the quantity-imbalance node representation learning (QINL) by considering the shift of the node influence boundaries from true class boundaries. To measure the degree of topology imbalance, we devise a conflict detection–based metric Totoro to locate node position, and further propose the ReNode method to adaptively adjust the training weights of labeled nodes based on their topological positions. Extensive empirical results have verified the effectiveness of our method in various settings: TINL-only, both TINL and QINL, and large-scale graph. Besides, we also propose the topology-imbalance sensitivity as a new metric to evaluate GNNs. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Considering the importance of the topology-imbalance issue and the limitations of our approach, advanced methods with stronger theoretical or experimental support are expected in future work. Moreover, since topology imbalance is widespread in graph-related tasks other than node classification, how to measure and solve the topology-imbalance issues in broader graph scopes remains a meaningful challenge for future study. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "7 Acknowledgement ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We appreciate all the thoughtful and insightful suggestions from reviews. This work was supported in part by a Tencent Research Grant and National Natural Science Foundation of China (No. 61673028). Xu Sun is the corresponding author of this paper. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            564,
+            266,
+            580
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
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parse/train/nYz2_BbZnYk/nYz2_BbZnYk.md

@@ -0,0 +1,268 @@
+# Representing Long-Range Context for Graph Neural Networks with Global Attention
+
+Zhanghao $\mathbf { W _ { u } } ^ { * _ { 1 } }$ , Paras $\mathbf { J a i n } ^ { * _ { 1 } }$ , Matthew A. Wright1 Azalia Mirhoseini2, Joseph E. Gonzalez1, Ion Stoica1 1UC Berkeley, 2Google Brain Correspondence to: {zhwu, paras_jain}@berkeley.edu \*equal contribution, determined via a random coin flip.
+
+# Abstract
+
+Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs encounter optimization instabilities such as vanishing gradients and representation oversmoothing, while pooling-based approaches have yet to become as universally useful as in computer vision. In this work, we propose the use of Transformer-based self-attention to learn long-range pairwise relationships, with a novel “readout” mechanism to obtain a global graph embedding. Inspired by recent computer vision results that find position-invariant attention performant in learning long-range relationships, our method, which we call GraphTrans, applies a permutation-invariant Transformer module after a standard GNN module. This simple architecture leads to state-of-the-art results on several graph classification tasks, outperforming methods that explicitly encode graph structure. Our results suggest that purely-learning-based approaches without graph structure may be suitable for learning high-level, long-range relationships on graphs. Code for GraphTrans is available at https://github.com/ucbrise/graphtrans.
+
+# 1 Introduction
+
+Graph neural networks (GNNs) enable deep networks to process structured inputs such as molecules or social networks. GNNs learn mappings that compute representations at graph nodes and/or edges from the structure of and features in their neighborhoods. This neighborhood-local aggregation leverages the relational inductive bias encoded by the graph’s connectivity [3]. Similar to convolutional neural networks (CNNs), GNNs can aggregate information from beyond local neighborhoods by stacking layers, effectively broadening the GNN receptive field.
+
+However, GNN performance drops dramatically when its depth increases [21]. This limitation has hurt the performance of GNNs on whole-graph classification and regression tasks, where we want to predict a target value describing the whole graph that may rely on long-range dependencies that may not be captured by a GNN with a limited receptive field [35]. Consider for example a large graph where node $A$ must attend to a distant node $B$ which is $K$ -hops away. If our GNN layer aggregates only over a node’s one-hop neighborhood, then a $K$ -layer GNN is required. However, the width of the receptive field of this GNN will grow exponentially, diluting the signal from node $B$ . That is, simply expanding the receptive field to a $K$ -hop neighborhood may not capture these long-range dependencies either [40]. Often, “too deep” GNNs lead to node representations that collapse to be equivalent over the entire graph, a phenomenon sometimes called oversmoothing or oversquashing [21, 5, 2]. Therefore, the maximum context size for common GNN architectures is effectively limited.
+
+![](images/683affe83e723a01a8b9435dc1317df9e71facb008c6dc50de4e1d558ea4d436.jpg)  
+Figure 1: Architecture of GraphTrans. A standard GNN submodule learns local, short-range structure, then a global Transformer submodule learns global, long-range relationships.
+
+Several proposed methods combat the oversmoothing problem via intermediate pooling operations similar to those found in today’s CNNs. Graph pooling operations gradually coarsen the graph in progressive GNN layers, usually by collapsing neighborhoods into single nodes [9, 37, 20, etc.]. In theory, hierarchical coarsening should allow better long-range learning, both by reducing the distance information has to travel and by filtering out unimportant nodes. However, no graph pooling operation has been found that is as universally applicable as CNN pooling. State-of-the-art results are often obtained with models using no intermediate graph coarsening [27], and some results suggest neighborhood-local coarsening may be unnecessary or counterproductive [23].
+
+In this work, we take a different approach at graph pooling and learning long-range dependencies in GNNs. Like hierarchical pooling, our method is also inspired by methods for computer vision: we replace some of the atomic operations that explicitly encode relevant relational inductive biases (i.e., convolutions or spatial pooling in CNNs, neighborhood coarsening in GNNs) with purely learned operations like attention [11, 4, 7].
+
+Our method, which we call Graph Transformer (GraphTrans, see Fig. 1), adds a Transformer subnetwork on top of a standard GNN layer stack. This Transformer subnetwork explicitly computes all pairwise node interactions in a position-agnostic fashion. This approach is intuitive as it retains the GNN as a specialized architecture to learn local representations of the structure of a node’s immediate neighborhood while leveraging the Transformer as a powerful global reasoning module. This parallels recent computer vision architectures, where authors have found hard relational inductive biases important for learning short-range patterns but less useful or even counterproductive in modeling long-range dependencies [25]. As the Transformer without a positional encoding is permutationinvariant, we find it is a natural fit for graphs. Moreover, GraphTrans does not require any specialized modules or architectures and can be implemented in any framework atop any existing GNN backbone.
+
+We evaluate GraphTrans on a variety of popular graph classification datasets. We find significant improvements in accuracy on OpenGraphBenchmark [15] where we achieve state-of-the-art results on two graph classification tasks. Moreover, we find substantial improvements on the molecular dataset NCI1. Surprisingly, we find our simple model outperforms complex baselines for long-range modeling in graphs via hierarchical clustering such as self-attention pooling [20].
+
+Our contributions are as follows:
+
+• We show that long-range reasoning via Transformers improve graph neural network (GNN) accuracy. Our results suggest that modelling all pairwise node-node interactions in the graph is particularly important for large graph classification tasks.   
+• We introduce a novel GNN “readout module.” Inspired by text-classification applications of Transformers, we use a special $^ { 6 6 } < \mathrm { C L S } > ^ { , , }$ token whose output embedding aggregates all pairwise interactions into a single classification vector. We find that this approach outperforms both non-learned readout methods like global pooling as well as learned aggregation methods like graph-specific pooling methods [37, 20] and “virtual node” approaches.   
+• Using our novel architecture GraphTrans, we obtain state-of-the-art results on several OpenGraphBenchmark [15] datasets and the NCI biomolecular datasets [30].
+
+# 2 Related Work
+
+Graph Classification. Graph classification is an important task in real-world applications. Though GNNs encode the structured data into the node representations, aggregation of the representations to a single graph embedding for graph classification is still a problem. Similar to CNNs, pooling in GNNs can be either global, reducing a set of node and/or edge encodings to a single graph encoding, or local, collapsing subsets of nodes and/or edges to create a coarser graph. Paralleling the use of intermediate pooling within CNNs, several authors have proposed local pooling operations meant to be used within the GNN layer stack, progressively coarsening the graph. Methods proposed include both learned pooling schemes [37, 20, 14, 16, 1, etc.] and non-learned pooling methods based on classic graph coarsening schemes [10, 9, etc.]. However, the effectiveness or necessity of hierarchical, coarsening-based pooling in GNNs is unclear [23]. On the other hand, the most common global, whole-graph pooling methods, are i) non-learned mean or max-pooling over nodes and ii) the “virtual node” approach, where a final GNN layer outputs an embedding for a single virtual node that is connected to every “real” node in the graph.
+
+A notable work related to graph pooling is the DAGNN (Directed Acyclic Graph Neural Network) of Thost and Chen [27], which had obtained the previous state-of-the-art accuracy on OGBG-Code2. The DAGNN layer aggregates over the entire graph within each layer via an RNN that traverses the DAG, unlike most GNN layers that only aggregate over a node’s neighborhood. While they did not characterize this method as a pooling operation, it is similar to GraphTrans in that it acts as a learned global pooling (in that it aggregates the embeddings of every node in a DAG into the sink nodes) that can model long-range dependencies. Note that GraphTrans is also complementary to DAGNN because their final graph-level pooling operation is a global max-pooling over the sink nodes rather than a learned operation.
+
+Transformers on Graphs. Several authors have investigated applications of Transformer architectures to graphs. Recent works such as Zhang et al. [38], Rong et al. [24], and Dwivedi and Bresson [12] propose GNN layers that let nodes attend to other nodes in some surrounding neighborhood via Transformer-style attention, whereas we use self attention for a permutation-invariant, graph-level pooling or “readout” operation that collapses node encodings to a single graph encoding. Of these, Zhang et al. [38] and Rong et al. [24] tackle the problem of learning long-range dependencies without over smoothing by allowing nodes to attend to more than just the one-hop neighborhood: Zhang et al. [38] take the attended neighborhood radius as a tuning parameter and Rong et al. [24] attend to neighborhoods of random size during training and inference. In contrast, we use whole-graph self-attention to allow for learning of long-range dependencies.
+
+While Zhang et al. [38] do not consider whole-graph prediction problems, in the case of Dwivedi and Bresson [12], when a graph-wide embedding was needed for graph classification or regression, they used global average pooling over the nodes, while Rong et al. [24] take a weighted sum over nodes with the weights computed bypassing the $h _ { v } ^ { L }$ ’s to a two-layer MLP. Note also that prior works consider graph-specific versions of a Transformer’s positional encoding, while we omit positional encodings to ensure permutation invariance.
+
+Efficient Transformers. Transformer [28] has been widely used in sequence modeling. Recently, modifications of the transformer architecture emerge to further improve the efficiency [34, 19, 6]. The LiteTransformer [34] with less FLOPs, Reformer [19] with complexity, and Performer [6] with both less computation and memory complexity. Neural architecture search (NAS) was also applied to Transformer to fulfill the resource constraints for the edge devices [32]. These off-the-shelf architectures are orthogonal to our GraphTrans and can be adopted to improve the scalability.
+
+# 3 Motivation: Modeling Long-Range Pairwise Interactions
+
+To summarize, attempting long-range learning on graphs via stacking GNN layers or hierarchical pooling have not yet led to performance increases, and while some works have shown some success in expanding the receptive field of a single GNN layer beyond a one-hop neighborhood [38, 24, 40], it remains to be seen how this approach will scale to very large graphs with thousands of nodes.
+
+An inspiration for an alternative approach can be found in the recent computer vision literature. In the last few years, researchers have found that attention mechanisms can act as drop-in replacements for traditional CNN convolutions [4, 7]: attention layers can learn to reproduce the strong relational inductive biases induced by local convolutions. More recently, state-of-the-art approaches to several computer vision tasks use an attention-style submodule on top of a traditional CNN backbone [2, 33, etc.]. These results suggest that while strong relational inductive biases are helpful for learning local, short-range correlations, for long-range correlations less structured modules may be preferred [2].
+
+![](images/e6c2cd05688cb8a40bd29608cb3f973374e76213f083b8deddef57403f7562de.jpg)  
+Figure 2: Example graph and attention map in our GraphTrans. The graph is randomly sampled from the Code2 validation set. The attention map is retrieved from the first layer of the transformer module in our GraphTrans. The horizontal axis corresponds to targets and the horizontal axis corresponds to sources (so, attention weights will sum to one over the horizontal axis). Note that in (b), index 18 corresponds to the special ${ \mathrm { \overline { { \mathbf { \Lambda } } } } } { \mathrm { C L S } } { \mathrm { \overline { { \mathbf { \Lambda } } } } }$ token described in section 4.
+
+We leverage this insight to the graph learning domain with our GraphTrans model, which uses a traditional GNN subnetwork as a backbone, but leaves learning long-range dependencies to a Transformer subnetwork with no graph spatial priors. As mentioned, our Transformer application lets every node attend to every other node (unlike other approaches of applying Transformers to graphs that only allow attention to neighborhoods), which incentivizes the Transformer to learn the most important node-node relationships, instead of favoring nearby nodes (the latter task having been offloaded to the preceding GNN module).
+
+Qualitatively, this scheme provides evidence that long-range relationships are indeed important. An example application of GraphTrans on the OGB Code2 dataset is depicted in Figure 2. In this task, we take in the Abstract Sentence Tree obtained by parsing a Python method and need to predict the tokens that form the method name. The attention map exhibits similar patterns to those found in NLP applications of Transformers: some nodes receive significant weighting from many other nodes, regardless of the distance between them. Note that node 17 assigns significant importance to node 8, despite these two nodes being five hops away. Also, in Figure 2’s attention map, index 18 refers to the embedding corresponding to the special ${ \tt C L S } >$ token we use as a readout mechanism, described in more detail below. We allow this embedding to be learnable, so the many nodes attending to it (represented by the many dark cells in column 18) may suggest these nodes are obtaining some graphgeneral memory from the learned embedding. This qualitative visualization, along with our new state-of-the-art results, suggest that removing spatial priors when learning long-range dependencies may be necessary for effective graph summarization.
+
+# 4 Learning Global Information with GraphTrans
+
+Referring back to Figure 1, GraphTrans consists of two primary modules: a GNN subnetwork followed by a Transformer subnetwork. We discuss these in detail next.
+
+GNN module. We consider graph property prediction, i.e., for each graph $\mathcal { G } = ( \nu , \mathcal { E } )$ we have a graph-specific prediction target $y _ { \mathcal { G } }$ . We suppose that each node $v \in \nu$ has an initial feature vector $\bar { h } _ { v } ^ { 0 } \in \mathbb { R } ^ { \hat { d } _ { 0 } }$ . As GraphTrans is a generally-applicable framework that can be used in concert with a
+
+variety of GNNs, we make very few assumptions on the GNN layers that feed into the Transformer subnetwork. A generic GNN layer stack can be expressed as
+
+$$
+\begin{array} { r } { \pmb { h } _ { v } ^ { \ell } = f _ { \ell } \left( \pmb { h } _ { v } ^ { \ell - 1 } , \{ \pmb { h } _ { u } ^ { \ell - 1 } | u \in \mathcal { N } ( v ) \} \right) , \quad \ell = 1 , \dots , L _ { \mathrm { G N N } } } \end{array}
+$$
+
+where $L _ { \mathrm { G N N } }$ is the total number of GNN layers, ${ \mathcal { N } } ( v ) \subseteq \gamma$ is some neighborhood of $v$ , and $f _ { \ell } ( \cdot )$ is some function parameterized by a neural network. Note that many GNN layers admit edge features, but to avoid notational clutter we omit discussion of them here.
+
+Transformer module. Once we have the final per-node GNN encodings $h _ { v } ^ { L _ { \mathrm { G N N } } }$ , we pass these to GraphTrans’s Transformer subnetwork. The Transformer subnetwork operates as follows. We first perform a linear projection of the $h _ { v } ^ { L _ { \mathrm { G N N } } }$ ’s to the Transformer dimension and a Layer Normalization to normalize the embedding:
+
+$$
+\bar { h } _ { v } ^ { 0 } = \mathrm { L a y e r N o r m } ( W ^ { \mathrm { P r o j } } h _ { v } ^ { L _ { \mathrm { G N N } } } )
+$$
+
+where $W ^ { \mathrm { P r o j } } \in \mathbb { R } ^ { d _ { \mathrm { T F } } \times d _ { L _ { \mathrm { G N N } } } }$ is a learnable weight matrix, and $d _ { \mathrm { T F } }$ and $d _ { L _ { \mathrm { G N N } } }$ are the Transformer dimension and the dimension of the final GNN embedding, respectively. The projected node embeddings $\bar { h } _ { v } ^ { 0 }$ are then fed into a standard Transformer layer stack, with no additive positional embeddings, as we expect the GNN to have already encoded the structural information into the node embeddings:
+
+$$
+\begin{array} { c } { { a _ { v , u } ^ { \ell } = ( W _ { \ell } ^ { Q } \bar { h } _ { v } ^ { \ell - 1 } ) ^ { \top } ( W _ { \ell } ^ { K } \bar { h } _ { u } ^ { \ell - 1 } ) / \sqrt { d _ { \mathrm { T F } } } \qquad \alpha _ { v , u } ^ { \ell } = \displaystyle { \operatorname { s o f t m a x } _ { w \in \mathcal { V } } ( a _ { v , w } ^ { \ell } ) } } } \\ { { \bar { h } _ { v } ^ { \prime \ell } = \displaystyle { \sum _ { w \in \mathcal { V } } \alpha _ { v , w } ^ { \ell } W _ { \ell } ^ { V } \bar { h } _ { w } ^ { \ell - 1 } } } } \end{array}
+$$
+
+where $W _ { \ell } ^ { Q } , W _ { \ell } ^ { K } , W _ { \ell } ^ { V } \in \mathbb { R } ^ { d _ { \mathrm { T F } } / n _ { \mathrm { h e a d } } \times d _ { \mathrm { T F } } / n _ { \mathrm { h e a d } } }$ are the learned query, key, and value matrices, respectively, for a single attention head in layer $\ell$ . As is standard, we run $n _ { \mathrm { h e a d } }$ parallel attention heads and concatenate the resulting per-head encodings $\bar { h } _ { v } ^ { \prime \ell }$ . Concatenated encodings are then passed to a Transformer fully-connected subnetwork, consisting of the standard Dropout $ \mathrm { L a y e r N o r m }  \mathrm { F C }$ nonlinearity Dropout $ \mathrm { F C }  \mathrm { D r o p o u t }  \mathrm { I }$ ayer Norm sequence, with residual connections from $\bar { h } _ { v } ^ { \ell - 1 }$ to after the first dropout, and from before the first fully-connected sublayer to after the dropout immediately following the second fully-connected sublayer.
+
+${ \tt C L S } >$ embedding as a GNN “readout” method. As mentioned, for whole-graph classification we require a single embedding vector that describes the whole graph. In the GNN literature, this module that collapses embeddings for every node and/or edge to a single embedding is called the “readout” module, and the most common readout modules are simple mean or max pooling, or a single “virtual node” that is connected to every other node in the network.
+
+In this work, we propose a special-token readout module similar to those used in other applications of Transformers. In text classification tasks with Transformers, a common practice is to append a special ${ \tt C L S } >$ token to the input sequence before passing it into the network, then to take the output embedding corresponding to this token’s position as the representation of the whole sentence. In that way, the Transformer will be trained to aggregate information of the sentence to that embedding, by calculating the one-to-one relationships between the ${ \tt C L S } >$ token and each other tokens in the sentence with the attention module.
+
+Our application of special-token readout is similar to this. Concretely, when feeding the transformed per-node embeddings $\bar { h } _ { v } ^ { 0 }$ , we append an additional learnable embedding $h _ { < \mathrm { C L S } > }$ to the sequence, and take the first embedding $\bar { h } _ { < \mathrm { C L S } > } \in \mathbb { R } ^ { d _ { \mathrm { T F } } }$ from the transformer output as the representation of the whole graph (note that since we do not include positional encodings, placing the special token at the “beginning” of the sentence has no special computational meaning; the location is chosen by convention). Finally, we apply a linear projection followed by a softmax to generate the prediction:
+
+$$
+y = \mathrm { s o f t m a x } ( W ^ { \mathrm { o u t } } \bar { h } _ { < \mathrm { C L S } > } ^ { L _ { \mathrm { T F } } } ) .
+$$
+
+where $L _ { \mathrm { T F } }$ is the number of Transformer layers.
+
+This special-token readout mechanism may be viewed as a generalization or a “deep” version of a virtual node readout. While a virtual node method requires every node in the graph to send its information to the virtual node and does not allow for learning pairwise relationships between graph nodes except within the virtual node’s embedding (possibly creating an information bottleneck), a Transformer-style special-token readout method lets the network learn long-range node-to-node relationships in earlier layers before needing to distill them in the later layers.
+
+# 5 Experiments
+
+We evaluate GraphTrans on graph classification tasks from three modalities: biology, computer programming, and chemistry. Our GraphTrans achieves consistent improvement over all of these benchmarks, indicating the generality and effectiveness of the framework. All of our models are trained with the Adam optimizer [17] with a learning rate of 0.0001, a weight decay of 0.0001, and the default Adam $\beta$ parameters. All Transformer modules used in our experiments have an embedding dimension $d _ { \mathrm { T F } }$ of 128 and a hidden dimension of 512 in the feedforward subnetwork. The Transformer baselines described below are trained with only the sequence of node embeddings, discarding the graph structure.
+
+# 5.1 Biological benchmarks
+
+Datasets. We choose two commonly used graph classification benchmarks, NCI1 and NCI109 [31]. Each of them contains about 4000 graphs with around 30 nodes on average, representing biochemical compounds. The task is to predict whether a compound contains anti-lung-cancer activity. We follow the settings in [20, 2] for the NCI1 and NCI109, randomly splitting the dataset into training, validation, and test set by a ratio of 8:1:1.
+
+Training Setup. We trained GraphTrans on both the NCI1 and NCI109 datasets for 100 epochs with a batch size of 256. We run each experiment 20 times with different random seeds and calculate the average and standard deviation of the test accuracies. All the model follows the architecture in Figure 1, with 4 transformer layers and a dropout ratio of 0.1 for both the GNN and Transformer modules. We use two different settings adopted from prior literature for the width and depth of the GNN submodule in GraphTrans. The GNN module width and depth in the small GraphTrans model are copied from the simple baseline, i.e. the settings in [20], which has a hidden dimension of 128 and 3 GNN layers. The settings of the GNN module in the large GraphTrans model are adopted from the default GCN/GIN model provided by OGB, which has a hidden dimension of 300 and 4 GNN layers. We also adopt a cosine annealing schedule [22] for learning rate decay.
+
+Results. We report the results on both NCI1 and NCI109 in Table 1. The simple baselines, including GCN Set2Set, SortPool, and SAGPool, are taken from [20], while the strong baselines [13], as well as the FA layer [2]. In Table 1, Our Graph Transformer (small) has the same architecture as the simple baseline but improves the average accuracy by $7 . 1 \%$ for NCI1 and $5 . 1 \%$ for NCI109. We also tested the framework with GIN as the encoder (GraphTrans (large)) to align with the settings in the strong baseline, which also significantly improves the accuracy of the strong baseline by $1 . 1 \%$ for NCI1 and the $8 . 2 \%$ for NCI109, even without the deep GNN, using 4 layers instead of 8.
+
+# 5.2 Chemical benchmarks
+
+Datasets. For chemical benchmarks, we evaluate our GraphTrans on a dataset larger than NCI dataset, molpcba from the Open Graph Benchmark (OGB) [15]. It contains 437929 graphs with 28 nodes on average. Each graph in the dataset represents a molecule, where nodes and edges are atoms and chemical bonds, respectively. The task is to predict the multiple properties of a molecule. We use the standard splitting from the benchmark. The performance on the GIN and GIN-Virtual baselines are as reported on the OGB leaderboard [15].
+
+Training Setups. All the GNN modules in the experiments follow the settings of the default GIN model provided in OGB, with 4 layers and 300 hidden dimension. We train all the models for 100 epochs with a batch size of 256 and report the test result with the best validation ROC-AUC. For both GNN and Transformer modules, we apply a dropout of 0.3. We use GIN as the baseline and the GNN module, since it performs better than GCN models on the Molpcba dataset.
+
+Table 1: NCI biological datasets GraphTrans outperforms past baselines on both NCI1 and NCI109 test accuracy while using fewer GNN layers than prior SOTA baselines.   
+
+<table><tr><td>Model</td><td>GNN Type</td><td>GNN layer count</td><td>NCI1 (%)</td><td>NCI109 (%)</td></tr><tr><td>Set2Set [29,20]</td><td>GCN</td><td>3</td><td>68.6± 1.9</td><td>69.8±1.2</td></tr><tr><td>SortPool [39,20]</td><td>GCN</td><td>3</td><td>73.8±1.0</td><td>74.0±1.2</td></tr><tr><td>SAGPoolh [20]</td><td>GCN</td><td>3</td><td>67.5±1.1</td><td>67.9±1.4</td></tr><tr><td>SAGPoolg [20]</td><td>GCN</td><td>3</td><td>74.2±1.2</td><td>74.1±0.8</td></tr><tr><td>Errica et al. [13]</td><td>GIN</td><td>8</td><td>80.0±1.4</td><td></td></tr><tr><td>Alon and Yahav [2]</td><td>GIN</td><td>8</td><td>81.5±1.2</td><td>1</td></tr><tr><td>Transformer [28]</td><td>1</td><td>二</td><td>68.5±2.6</td><td>70.1± 2.3</td></tr><tr><td>GraphTrans (small)</td><td>GCN</td><td>3</td><td>81.3±1.9</td><td>79.2±2.2</td></tr><tr><td>GraphTrans (large)</td><td>GIN</td><td>4</td><td>82.6±1.2</td><td>82.3±2.6</td></tr></table>
+
+Table 2: OpenGraphBenchmark Molpcba dataset Overall, GraphTrans outperforms competitive baselines with two backbone GNN architectures.   
+
+<table><tr><td>Model</td><td>Valid ROC-AUC</td><td>Test ROC-AUC</td></tr><tr><td>GCN [18]</td><td>0.2059±0.0033</td><td>0.2020±0.0024</td></tr><tr><td>GIN [36]</td><td>0.2305±0.0027</td><td>0.2266±0.0028</td></tr><tr><td>GCN-Virtual [18]</td><td>0.2495±0.0042</td><td>0.2424±0.0034</td></tr><tr><td>GIN-Virtual [36]</td><td>0.2798±0.0025</td><td>0.2703±0.0023</td></tr><tr><td>Transformer [28]</td><td>0.1316±0.0012</td><td>0.1281±0.0039</td></tr><tr><td>GraphTrans (GIN)</td><td>0.2893±0.0050</td><td>0.2756±0.0039</td></tr><tr><td>GraphTrans (GIN-Virtual)</td><td>0.2867±0.0022</td><td>0.2761±0.0029</td></tr></table>
+
+Results. In Table 2, we report the ROC-AUC on validation and test set of Molpcba. Though Transformer alone works very badly on this dataset, our GraphTrans still improves the ROC-AUC of the GIN and GIN-Virtual baseline. It indicates that our design could take benefit from both the local graph structure learned by the GNN and the long-range concept retrieved by the Transformer module based on the GNN embeddings.
+
+# 5.3 Computer programming benchmark
+
+Datasets. For the computer programming benchmark, we also adopt a large dataset, code2 from OGB, which has 45741 graphs each with 125 nodes on average. The dataset is a collection of Abstract Syntax Trees (ASTs) from about $4 5 0 \mathrm { k }$ Python method definitions. The task is to predict the sub-tokens forming the method name, given the method body represented by the AST. We also adopt the standard dataset splitting from the benchmark. All baseline performances are as reported on the OGB leaderboard.
+
+Training Setups. We also apply the default settings of GCN for Code2 from OGB, with 4 GNN layers, 300 hidden dimension, and a dropout ratio of 0.0. We apply a dropout ratio of 0.3 to the Transformer module to avoid overfitting. We train all the models for 30 epochs with a batch size of 16, due to the large scale of the dataset. For the GraphTrans (PNA) model, we follow the settings in [26], with a hidden embedding of 272 for the GNN module and a weight decay of 3e-6. The only difference is that we still use the learning rate of 0.0001, instead of the heavily tuned 0.00063096 [26]. We run each experiment 5 times and take the average and standard deviation of the F1 score.
+
+Results. In Table 3, we compare our GraphTrans with top tier architectures on the leaderboard on Code2 dataset. As the average number of nodes in each graph increases, the global information becomes more important as it becomes more difficult for the GNN to gather information from nodes far away. Even without heavy tuning, GraphTrans significantly outperforms the state-ofthe-art (DAGNN) [27] on the leaderboard. We also include the results for the PNA model and our GraphTrans with the PNA model as the GNN encoder. Our GraphTrans also significantly improves the result, which indicates that our architecture is orthogonal to the variants of the GNN encoder module.
+
+Table 3: OpenGraphBenchmark Code2 dataset All the baselines are collected from the OGB leaderboard. GraphTrans outperforms the state-of-the-art DAGNN. The improvement based on PNA model indicates that our method is orthogonal to the type of GNN module.   
+
+<table><tr><td>Model</td><td>Valid F1 score</td><td>Test F1 score</td></tr><tr><td>GIN [36]</td><td>0.1376±0.0016</td><td>0.1495±0.0023</td></tr><tr><td>GCN [18]</td><td>0.1399±0.0017</td><td>0.1507±0.0018</td></tr><tr><td>GIN-Virtual [36]</td><td>0.1439±0.0026</td><td>0.1581±0.0020</td></tr><tr><td>GCN-Virtual [18]</td><td>0.1461±0.0013</td><td>0.1595±0.0018</td></tr><tr><td>PNA [8]</td><td>0.1453±0.0025</td><td>0.1570±0.0032</td></tr><tr><td>DAGNN (SOTA) [27]</td><td>0.1607±0.0040</td><td>0.1751±0.0049</td></tr><tr><td>Transformer [28]</td><td>0.1546±0.0018</td><td>0.1670±0.0015</td></tr><tr><td>GraphTrans (GCN)</td><td>0.1599±0.0009</td><td>0.1751±0.0015</td></tr><tr><td>GraphTrans (PNA)</td><td>0.1622±0.0025</td><td>0.1765±0.0033</td></tr><tr><td>GraphTrans (GCN-Virtual)</td><td>0.1661±0.0012</td><td>0.1830±0.0024</td></tr></table>
+
+Table 4: Ablation of Transformer module On the Code2 dataset, only training the Transformer module in GraphTrans with a frozen pre-trained GNN module also improves the F1-score. It indicates that training the Transformer on GNN embeddings can learn information that is not captured by the GNN.   
+
+<table><tr><td>Model</td><td>Valid F1 score</td><td>Test F1 score</td></tr><tr><td>Pre-trained GCN-Virtual</td><td>0.1457</td><td>0.1574</td></tr><tr><td>GraphTrans, pre-trained GCN-Virtual, frozen GNN</td><td>0.1479</td><td>0.1616</td></tr><tr><td>GraphTrans, pre-trained GCN-Virtual, fine-tuned GNN</td><td>0.1564</td><td>0.1733</td></tr></table>
+
+# 5.4 Transformers can capture long-range relationships
+
+As we previously observed in Figure 2 and discussed in Section 3, the attention inside the transformer module can capture long-range information that is hard to be learned by the GNN module.
+
+To further verify the hypothesis, we designed an experiment to show that the Transformer module can learn additional information to the GNN module. In Table 4, we first pretrain a GNN (GCN-Virtual) until converge on the Code2 dataset, and then freeze the GNN model and plug our Transformer module after it. By training the model on the training set with a fixed GNN module, we can still observe a 0.0022 F1-score improvement on validation set and 0.0042 on test set. It indicates that the Transformer can learn additional information that is hard to be learned by the GNN module along.
+
+With pretrained and unfrozen GNN module, our GraphTrans can achieve an even higher F1-score. That may because the GNN module can now focus on learning the local structure information, by leaving the long-range information learning to the Transformer layer after it. The model benefits from the specialization as mentioned in [34]. Note that for all the experiments in Table 4, we do not concatenate the embeddings from the input graph to the input of Transformer for simplicity.
+
+# 5.5 Effectiveness of ${ \tt C L S } >$ embedding
+
+In Figure 2b, we can observe that row 18 (the last row is for ${ \mathrm { \tt C L S } } ^ { }$ ) has dark red on multiple columns, which indicates that the ${ \tt C L S } >$ learns to attend to important nodes in the graph to learn the representation for the whole graph.
+
+Table 5: Ablation of ${ \tt C L S } >$ token The mean and last are two commonly used embedding aggregation method for sequence classification.   
+
+<table><tr><td>Model</td><td>Valid</td><td>Test</td></tr><tr><td>GraphTrans, mean</td><td>0.1398</td><td>0.1509</td></tr><tr><td>GraphTrans,last</td><td>0.1566</td><td>0.1716</td></tr><tr><td>GraphTrans,&lt;CLS&gt;</td><td>0.1593</td><td>0.1784</td></tr><tr><td>GraphTrans,&lt;CLS&gt;,cat</td><td>0.1670</td><td>0.1810</td></tr></table>
+
+Table 6: Scalability of Transformer to large graphs We profile our Code2 model on random graphs and list runtime in milliseconds. GraphTrans scales comparably to the GCN model due to the high cost neighbor sampling in GNN training. With graphs over 1000 nodes, GraphTrans is no less scalable than the GCN baseline.   
+
+<table><tr><td colspan="2"></td><td colspan="4">Edge Density</td></tr><tr><td>Node count</td><td>Model</td><td>20%</td><td>40%</td><td>60%</td><td>80%</td></tr><tr><td rowspan="2">500</td><td>GCN-Virtual [18]</td><td>44.3</td><td>58.5</td><td>79.3</td><td>99.0</td></tr><tr><td>GraphTrans (GCN)</td><td>48.4</td><td>57.5</td><td>76.4</td><td>93.7</td></tr><tr><td rowspan="2">1000</td><td>GCN-Virtual [18]</td><td>99.1</td><td>171.8</td><td>249.5</td><td>0OM</td></tr><tr><td>GraphTrans (GCN)</td><td>96.9</td><td>168.4</td><td>244.3</td><td>00M</td></tr><tr><td rowspan="2">1200</td><td>GCN-Virtual [18]</td><td>131.8</td><td>237.7</td><td>0OM</td><td>0OM</td></tr><tr><td>GraphTrans (GCN)</td><td>127.9</td><td>236.6</td><td>00M</td><td>0OM</td></tr></table>
+
+We also examined the effectiveness of our ${ \tt C L S } >$ embedding quantitatively. In Table 5, we tested several common methods to for sequence classification. The mean operation averages the output embeddings of the transformer to a single graph embedding; the last operation takes the last embedding in the output sequence as the graph embedding. The quantitative results indicate that the ${ \tt C L S } >$ embedding is most effective with 0.0275 improvements on the test set, as the model can learn to retrieve information from different nodes and aggregate them into one embedding. The concatenation of the embeddings in the input graph and the input embeddings of the transformer can further improve the validation and test F1-score to 0.1670 and 0.1733.
+
+# 5.6 Scalability
+
+To quantitatively benchmark how GraphTrans scales with large graphs over 100 nodes, we ran a microbenchmark of iteration time for training with varying graph size and edge density. We train baselines on randomly generated Erdos-Renyi graphs with a varying number of nodes and edge density. As shown in the Table 6, our GraphTrans model scales at least as well as the GCN model when the number of nodes and edge density increases. Both GCN and GraphTrans see out of memory errors (OOM) with large dense graphs, but we note that GraphTrans had similar memory consumption to the GCN baseline.
+
+# 5.7 Computational efficiency
+
+To evaluate the overhead that our GraphTrans adds over a specific GNN backbone, we evaluate the forward pass runtime and backward pass runtime per iteration. We normalize models to have roughly similar parameter counts. The results are shown in Table 7. For the NCI1 dataset, GraphTrans is actually faster to train than a comparable GCN model. For the OGB-molpcba and OGB-Code2 datasets, GraphTrans is $7 . 1 1 \%$ slower than the baseline GNN architectures.
+
+# 5.8 Number of parameters
+
+We compare the number of parameters of the GNN baseline and the GraphTrans on different dataset in Table 8. Overall, GraphTrans only increases total parameters marginally for Molpcba and NCI.
+
+Table 7: Speedup of Transformer module For GraphTrans models trained over the NCI1, OGBGMolpcba and OGBG-Code2 datasets, we find that the Transformer module adds minimal overhead. Speedup is the training iteration speed compared to GNN based model; larger number indicates a faster running speed.   
+
+<table><tr><td>Dataset</td><td>Method</td><td>Forward time (ms)</td><td>Backward time (ms)</td><td> Speedup</td></tr><tr><td rowspan="3">NCI1</td><td>GCN-Virtual [18]</td><td>22.27 ± 2.04</td><td>14.35 ± 2.46</td><td>1.00×</td></tr><tr><td>Transformer</td><td>12.31 ± 1.68</td><td>9.32 ± 1.68</td><td>1.69×</td></tr><tr><td>GraphTrans</td><td>15.01 ± 1.63</td><td>12.04 ± 2.25</td><td>1.35×</td></tr><tr><td rowspan="3">Molpcba</td><td>GCN-Virtual [18]</td><td>14.79 ± 2.54</td><td>12.75 ± 3.00</td><td>1.00×</td></tr><tr><td>Transformer</td><td>12.34 ± 1.43</td><td>10.52 ± 1.60</td><td>1.20×</td></tr><tr><td>GraphTrans</td><td>16.55 ± 2.93</td><td>14.3 ± 3.15</td><td>0.89×</td></tr><tr><td rowspan="3">Code2</td><td>GCN-Virtual [18]</td><td>22.97 ± 6.13</td><td>38.53 ± 6.92</td><td>1.00×</td></tr><tr><td>Transformer</td><td>31.01 ± 9.00</td><td>33.30 ± 16.09</td><td>0.96×</td></tr><tr><td>GraphTrans</td><td>34.93 ± 6.85</td><td>31.14 ± 12.90</td><td>0.93×</td></tr></table>
+
+Table 8: Parameter count Overall, GraphTrans achieves improved accuracy with a minor increase in parameters.   
+
+<table><tr><td>Dataset</td><td>GNN</td><td>GraphTrans</td><td>Delta</td></tr><tr><td>Molpcba</td><td>3.4M</td><td>4.2M</td><td>0.8M</td></tr><tr><td>NCI</td><td>0.4M</td><td>0.5M</td><td>0.1M</td></tr><tr><td>Code2</td><td>12.5M</td><td>9.1M</td><td>-3.4M</td></tr></table>
+
+For Code2, GraphTrans is substantially more parameter-efficient than the GNN while improving test F1 score from 0.1629 to 0.1810. One reason for improved parameter efficiency is that the Transformer reduces feature dimension before the expensive final prediction layer.
+
+# 6 Conclusion
+
+We proposed GraphTrans, a simple yet powerful framework for learning long-range relationships with GNNs. Leveraging recent results that suggest structural priors may be unnecessary or even counterproductive for high-level, long-range relationships, we augment standard GNN layer stacks with a subsequent permutation-invariant Transformer module. The Transformer module acts as a novel GNN “readout” module, simultaneously allowing the learning of pairwise interactions between graph nodes and summarizing them into a special token’s embedding as is done in common NLP applications of Transformers. This simple framework leads to surprising improvements upon the state of the art in several graph classification tasks across program analysis, molecules and protein association networks. In some cases, GraphTrans outperforms methods that attempt to encode domain-specific structural information. Overall, GraphTrans presents a simple yet general approach to improve long-range graph classification; next directions include applications to node and edge classification tasks as well as further scalability improvements of the Transformer to large graphs.
+
+# 7 Acknowledgements
+
+We thank Ethan Mehta, Azade Nazi, Daniel Rothschild, Adnan Sherif and Justin Wong for thoughtful discussions and feedback. In addition to NSF CISE Expeditions Award CCF-1730628, this research is supported by gifts from Amazon Web Services, Ant Group, Ericsson, Facebook, Futurewei, Google, Intel, Microsoft, Scotiabank, and VMware.
+
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+        "text": "Representing Long-Range Context for Graph Neural Networks with Global Attention ",
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+        "text": "Zhanghao $\\mathbf { W _ { u } } ^ { * _ { 1 } }$ , Paras $\\mathbf { J a i n } ^ { * _ { 1 } }$ , Matthew A. Wright1 Azalia Mirhoseini2, Joseph E. Gonzalez1, Ion Stoica1 1UC Berkeley, 2Google Brain Correspondence to: {zhwu, paras_jain}@berkeley.edu \\*equal contribution, determined via a random coin flip. ",
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+        "text": "Abstract ",
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+        "text": "Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs encounter optimization instabilities such as vanishing gradients and representation oversmoothing, while pooling-based approaches have yet to become as universally useful as in computer vision. In this work, we propose the use of Transformer-based self-attention to learn long-range pairwise relationships, with a novel “readout” mechanism to obtain a global graph embedding. Inspired by recent computer vision results that find position-invariant attention performant in learning long-range relationships, our method, which we call GraphTrans, applies a permutation-invariant Transformer module after a standard GNN module. This simple architecture leads to state-of-the-art results on several graph classification tasks, outperforming methods that explicitly encode graph structure. Our results suggest that purely-learning-based approaches without graph structure may be suitable for learning high-level, long-range relationships on graphs. Code for GraphTrans is available at https://github.com/ucbrise/graphtrans. ",
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+        "text": "1 Introduction ",
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+        "text": "Graph neural networks (GNNs) enable deep networks to process structured inputs such as molecules or social networks. GNNs learn mappings that compute representations at graph nodes and/or edges from the structure of and features in their neighborhoods. This neighborhood-local aggregation leverages the relational inductive bias encoded by the graph’s connectivity [3]. Similar to convolutional neural networks (CNNs), GNNs can aggregate information from beyond local neighborhoods by stacking layers, effectively broadening the GNN receptive field. ",
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+        "text": "However, GNN performance drops dramatically when its depth increases [21]. This limitation has hurt the performance of GNNs on whole-graph classification and regression tasks, where we want to predict a target value describing the whole graph that may rely on long-range dependencies that may not be captured by a GNN with a limited receptive field [35]. Consider for example a large graph where node $A$ must attend to a distant node $B$ which is $K$ -hops away. If our GNN layer aggregates only over a node’s one-hop neighborhood, then a $K$ -layer GNN is required. However, the width of the receptive field of this GNN will grow exponentially, diluting the signal from node $B$ . That is, simply expanding the receptive field to a $K$ -hop neighborhood may not capture these long-range dependencies either [40]. Often, “too deep” GNNs lead to node representations that collapse to be equivalent over the entire graph, a phenomenon sometimes called oversmoothing or oversquashing [21, 5, 2]. Therefore, the maximum context size for common GNN architectures is effectively limited. ",
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+        "image_caption": [
+            "Figure 1: Architecture of GraphTrans. A standard GNN submodule learns local, short-range structure, then a global Transformer submodule learns global, long-range relationships. "
+        ],
+        "image_footnote": [],
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+        "text": "Several proposed methods combat the oversmoothing problem via intermediate pooling operations similar to those found in today’s CNNs. Graph pooling operations gradually coarsen the graph in progressive GNN layers, usually by collapsing neighborhoods into single nodes [9, 37, 20, etc.]. In theory, hierarchical coarsening should allow better long-range learning, both by reducing the distance information has to travel and by filtering out unimportant nodes. However, no graph pooling operation has been found that is as universally applicable as CNN pooling. State-of-the-art results are often obtained with models using no intermediate graph coarsening [27], and some results suggest neighborhood-local coarsening may be unnecessary or counterproductive [23]. ",
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+        "text": "In this work, we take a different approach at graph pooling and learning long-range dependencies in GNNs. Like hierarchical pooling, our method is also inspired by methods for computer vision: we replace some of the atomic operations that explicitly encode relevant relational inductive biases (i.e., convolutions or spatial pooling in CNNs, neighborhood coarsening in GNNs) with purely learned operations like attention [11, 4, 7]. ",
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+        "text": "Our method, which we call Graph Transformer (GraphTrans, see Fig. 1), adds a Transformer subnetwork on top of a standard GNN layer stack. This Transformer subnetwork explicitly computes all pairwise node interactions in a position-agnostic fashion. This approach is intuitive as it retains the GNN as a specialized architecture to learn local representations of the structure of a node’s immediate neighborhood while leveraging the Transformer as a powerful global reasoning module. This parallels recent computer vision architectures, where authors have found hard relational inductive biases important for learning short-range patterns but less useful or even counterproductive in modeling long-range dependencies [25]. As the Transformer without a positional encoding is permutationinvariant, we find it is a natural fit for graphs. Moreover, GraphTrans does not require any specialized modules or architectures and can be implemented in any framework atop any existing GNN backbone. ",
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+        "text": "We evaluate GraphTrans on a variety of popular graph classification datasets. We find significant improvements in accuracy on OpenGraphBenchmark [15] where we achieve state-of-the-art results on two graph classification tasks. Moreover, we find substantial improvements on the molecular dataset NCI1. Surprisingly, we find our simple model outperforms complex baselines for long-range modeling in graphs via hierarchical clustering such as self-attention pooling [20]. ",
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+        "text": "Our contributions are as follows: ",
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+        "text": "• We show that long-range reasoning via Transformers improve graph neural network (GNN) accuracy. Our results suggest that modelling all pairwise node-node interactions in the graph is particularly important for large graph classification tasks.   \n• We introduce a novel GNN “readout module.” Inspired by text-classification applications of Transformers, we use a special $^ { 6 6 } < \\mathrm { C L S } > ^ { , , }$ token whose output embedding aggregates all pairwise interactions into a single classification vector. We find that this approach outperforms both non-learned readout methods like global pooling as well as learned aggregation methods like graph-specific pooling methods [37, 20] and “virtual node” approaches.   \n• Using our novel architecture GraphTrans, we obtain state-of-the-art results on several OpenGraphBenchmark [15] datasets and the NCI biomolecular datasets [30]. ",
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+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+        "text": "Graph Classification. Graph classification is an important task in real-world applications. Though GNNs encode the structured data into the node representations, aggregation of the representations to a single graph embedding for graph classification is still a problem. Similar to CNNs, pooling in GNNs can be either global, reducing a set of node and/or edge encodings to a single graph encoding, or local, collapsing subsets of nodes and/or edges to create a coarser graph. Paralleling the use of intermediate pooling within CNNs, several authors have proposed local pooling operations meant to be used within the GNN layer stack, progressively coarsening the graph. Methods proposed include both learned pooling schemes [37, 20, 14, 16, 1, etc.] and non-learned pooling methods based on classic graph coarsening schemes [10, 9, etc.]. However, the effectiveness or necessity of hierarchical, coarsening-based pooling in GNNs is unclear [23]. On the other hand, the most common global, whole-graph pooling methods, are i) non-learned mean or max-pooling over nodes and ii) the “virtual node” approach, where a final GNN layer outputs an embedding for a single virtual node that is connected to every “real” node in the graph. ",
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+        "type": "text",
+        "text": "A notable work related to graph pooling is the DAGNN (Directed Acyclic Graph Neural Network) of Thost and Chen [27], which had obtained the previous state-of-the-art accuracy on OGBG-Code2. The DAGNN layer aggregates over the entire graph within each layer via an RNN that traverses the DAG, unlike most GNN layers that only aggregate over a node’s neighborhood. While they did not characterize this method as a pooling operation, it is similar to GraphTrans in that it acts as a learned global pooling (in that it aggregates the embeddings of every node in a DAG into the sink nodes) that can model long-range dependencies. Note that GraphTrans is also complementary to DAGNN because their final graph-level pooling operation is a global max-pooling over the sink nodes rather than a learned operation. ",
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+        "type": "text",
+        "text": "Transformers on Graphs. Several authors have investigated applications of Transformer architectures to graphs. Recent works such as Zhang et al. [38], Rong et al. [24], and Dwivedi and Bresson [12] propose GNN layers that let nodes attend to other nodes in some surrounding neighborhood via Transformer-style attention, whereas we use self attention for a permutation-invariant, graph-level pooling or “readout” operation that collapses node encodings to a single graph encoding. Of these, Zhang et al. [38] and Rong et al. [24] tackle the problem of learning long-range dependencies without over smoothing by allowing nodes to attend to more than just the one-hop neighborhood: Zhang et al. [38] take the attended neighborhood radius as a tuning parameter and Rong et al. [24] attend to neighborhoods of random size during training and inference. In contrast, we use whole-graph self-attention to allow for learning of long-range dependencies. ",
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+        "type": "text",
+        "text": "While Zhang et al. [38] do not consider whole-graph prediction problems, in the case of Dwivedi and Bresson [12], when a graph-wide embedding was needed for graph classification or regression, they used global average pooling over the nodes, while Rong et al. [24] take a weighted sum over nodes with the weights computed bypassing the $h _ { v } ^ { L }$ ’s to a two-layer MLP. Note also that prior works consider graph-specific versions of a Transformer’s positional encoding, while we omit positional encodings to ensure permutation invariance. ",
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+        "type": "text",
+        "text": "Efficient Transformers. Transformer [28] has been widely used in sequence modeling. Recently, modifications of the transformer architecture emerge to further improve the efficiency [34, 19, 6]. The LiteTransformer [34] with less FLOPs, Reformer [19] with complexity, and Performer [6] with both less computation and memory complexity. Neural architecture search (NAS) was also applied to Transformer to fulfill the resource constraints for the edge devices [32]. These off-the-shelf architectures are orthogonal to our GraphTrans and can be adopted to improve the scalability. ",
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+        "type": "text",
+        "text": "3 Motivation: Modeling Long-Range Pairwise Interactions ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To summarize, attempting long-range learning on graphs via stacking GNN layers or hierarchical pooling have not yet led to performance increases, and while some works have shown some success in expanding the receptive field of a single GNN layer beyond a one-hop neighborhood [38, 24, 40], it remains to be seen how this approach will scale to very large graphs with thousands of nodes. ",
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+        "type": "text",
+        "text": "An inspiration for an alternative approach can be found in the recent computer vision literature. In the last few years, researchers have found that attention mechanisms can act as drop-in replacements for traditional CNN convolutions [4, 7]: attention layers can learn to reproduce the strong relational inductive biases induced by local convolutions. More recently, state-of-the-art approaches to several computer vision tasks use an attention-style submodule on top of a traditional CNN backbone [2, 33, etc.]. These results suggest that while strong relational inductive biases are helpful for learning local, short-range correlations, for long-range correlations less structured modules may be preferred [2]. ",
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+        "img_path": "images/e6c2cd05688cb8a40bd29608cb3f973374e76213f083b8deddef57403f7562de.jpg",
+        "image_caption": [
+            "Figure 2: Example graph and attention map in our GraphTrans. The graph is randomly sampled from the Code2 validation set. The attention map is retrieved from the first layer of the transformer module in our GraphTrans. The horizontal axis corresponds to targets and the horizontal axis corresponds to sources (so, attention weights will sum to one over the horizontal axis). Note that in (b), index 18 corresponds to the special ${ \\mathrm { \\overline { { \\mathbf { \\Lambda } } } } } { \\mathrm { C L S } } { \\mathrm { \\overline { { \\mathbf { \\Lambda } } } } }$ token described in section 4. "
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "We leverage this insight to the graph learning domain with our GraphTrans model, which uses a traditional GNN subnetwork as a backbone, but leaves learning long-range dependencies to a Transformer subnetwork with no graph spatial priors. As mentioned, our Transformer application lets every node attend to every other node (unlike other approaches of applying Transformers to graphs that only allow attention to neighborhoods), which incentivizes the Transformer to learn the most important node-node relationships, instead of favoring nearby nodes (the latter task having been offloaded to the preceding GNN module). ",
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+    {
+        "type": "text",
+        "text": "Qualitatively, this scheme provides evidence that long-range relationships are indeed important. An example application of GraphTrans on the OGB Code2 dataset is depicted in Figure 2. In this task, we take in the Abstract Sentence Tree obtained by parsing a Python method and need to predict the tokens that form the method name. The attention map exhibits similar patterns to those found in NLP applications of Transformers: some nodes receive significant weighting from many other nodes, regardless of the distance between them. Note that node 17 assigns significant importance to node 8, despite these two nodes being five hops away. Also, in Figure 2’s attention map, index 18 refers to the embedding corresponding to the special ${ \\tt C L S } >$ token we use as a readout mechanism, described in more detail below. We allow this embedding to be learnable, so the many nodes attending to it (represented by the many dark cells in column 18) may suggest these nodes are obtaining some graphgeneral memory from the learned embedding. This qualitative visualization, along with our new state-of-the-art results, suggest that removing spatial priors when learning long-range dependencies may be necessary for effective graph summarization. ",
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+    {
+        "type": "text",
+        "text": "4 Learning Global Information with GraphTrans ",
+        "text_level": 1,
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+        "text": "Referring back to Figure 1, GraphTrans consists of two primary modules: a GNN subnetwork followed by a Transformer subnetwork. We discuss these in detail next. ",
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+        "type": "text",
+        "text": "GNN module. We consider graph property prediction, i.e., for each graph $\\mathcal { G } = ( \\nu , \\mathcal { E } )$ we have a graph-specific prediction target $y _ { \\mathcal { G } }$ . We suppose that each node $v \\in \\nu$ has an initial feature vector $\\bar { h } _ { v } ^ { 0 } \\in \\mathbb { R } ^ { \\hat { d } _ { 0 } }$ . As GraphTrans is a generally-applicable framework that can be used in concert with a ",
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+        "type": "text",
+        "text": "variety of GNNs, we make very few assumptions on the GNN layers that feed into the Transformer subnetwork. A generic GNN layer stack can be expressed as ",
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+    {
+        "type": "equation",
+        "img_path": "images/3b0307d878d9d98cc62fa1076377e347ff26ea63bb7d449f43f5d8730ce339ca.jpg",
+        "text": "$$\n\\begin{array} { r } { \\pmb { h } _ { v } ^ { \\ell } = f _ { \\ell } \\left( \\pmb { h } _ { v } ^ { \\ell - 1 } , \\{ \\pmb { h } _ { u } ^ { \\ell - 1 } | u \\in \\mathcal { N } ( v ) \\} \\right) , \\quad \\ell = 1 , \\dots , L _ { \\mathrm { G N N } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $L _ { \\mathrm { G N N } }$ is the total number of GNN layers, ${ \\mathcal { N } } ( v ) \\subseteq \\gamma$ is some neighborhood of $v$ , and $f _ { \\ell } ( \\cdot )$ is some function parameterized by a neural network. Note that many GNN layers admit edge features, but to avoid notational clutter we omit discussion of them here. ",
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+        "type": "text",
+        "text": "Transformer module. Once we have the final per-node GNN encodings $h _ { v } ^ { L _ { \\mathrm { G N N } } }$ , we pass these to GraphTrans’s Transformer subnetwork. The Transformer subnetwork operates as follows. We first perform a linear projection of the $h _ { v } ^ { L _ { \\mathrm { G N N } } }$ ’s to the Transformer dimension and a Layer Normalization to normalize the embedding: ",
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+        "type": "equation",
+        "img_path": "images/bef863520ea045e2aff60730877a3c3f7533029de7aecd185b7d85c565467ef3.jpg",
+        "text": "$$\n\\bar { h } _ { v } ^ { 0 } = \\mathrm { L a y e r N o r m } ( W ^ { \\mathrm { P r o j } } h _ { v } ^ { L _ { \\mathrm { G N N } } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $W ^ { \\mathrm { P r o j } } \\in \\mathbb { R } ^ { d _ { \\mathrm { T F } } \\times d _ { L _ { \\mathrm { G N N } } } }$ is a learnable weight matrix, and $d _ { \\mathrm { T F } }$ and $d _ { L _ { \\mathrm { G N N } } }$ are the Transformer dimension and the dimension of the final GNN embedding, respectively. The projected node embeddings $\\bar { h } _ { v } ^ { 0 }$ are then fed into a standard Transformer layer stack, with no additive positional embeddings, as we expect the GNN to have already encoded the structural information into the node embeddings: ",
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+        "type": "equation",
+        "img_path": "images/c63399eb447756f496191224bef5b12ea60e9f64d0b5859d2a70a4263e8b1d5e.jpg",
+        "text": "$$\n\\begin{array} { c } { { a _ { v , u } ^ { \\ell } = ( W _ { \\ell } ^ { Q } \\bar { h } _ { v } ^ { \\ell - 1 } ) ^ { \\top } ( W _ { \\ell } ^ { K } \\bar { h } _ { u } ^ { \\ell - 1 } ) / \\sqrt { d _ { \\mathrm { T F } } } \\qquad \\alpha _ { v , u } ^ { \\ell } = \\displaystyle { \\operatorname { s o f t m a x } _ { w \\in \\mathcal { V } } ( a _ { v , w } ^ { \\ell } ) } } } \\\\ { { \\bar { h } _ { v } ^ { \\prime \\ell } = \\displaystyle { \\sum _ { w \\in \\mathcal { V } } \\alpha _ { v , w } ^ { \\ell } W _ { \\ell } ^ { V } \\bar { h } _ { w } ^ { \\ell - 1 } } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $W _ { \\ell } ^ { Q } , W _ { \\ell } ^ { K } , W _ { \\ell } ^ { V } \\in \\mathbb { R } ^ { d _ { \\mathrm { T F } } / n _ { \\mathrm { h e a d } } \\times d _ { \\mathrm { T F } } / n _ { \\mathrm { h e a d } } }$ are the learned query, key, and value matrices, respectively, for a single attention head in layer $\\ell$ . As is standard, we run $n _ { \\mathrm { h e a d } }$ parallel attention heads and concatenate the resulting per-head encodings $\\bar { h } _ { v } ^ { \\prime \\ell }$ . Concatenated encodings are then passed to a Transformer fully-connected subnetwork, consisting of the standard Dropout $ \\mathrm { L a y e r N o r m }  \\mathrm { F C }$ nonlinearity Dropout $ \\mathrm { F C }  \\mathrm { D r o p o u t }  \\mathrm { I }$ ayer Norm sequence, with residual connections from $\\bar { h } _ { v } ^ { \\ell - 1 }$ to after the first dropout, and from before the first fully-connected sublayer to after the dropout immediately following the second fully-connected sublayer. ",
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+        "type": "text",
+        "text": "${ \\tt C L S } >$ embedding as a GNN “readout” method. As mentioned, for whole-graph classification we require a single embedding vector that describes the whole graph. In the GNN literature, this module that collapses embeddings for every node and/or edge to a single embedding is called the “readout” module, and the most common readout modules are simple mean or max pooling, or a single “virtual node” that is connected to every other node in the network. ",
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+    {
+        "type": "text",
+        "text": "In this work, we propose a special-token readout module similar to those used in other applications of Transformers. In text classification tasks with Transformers, a common practice is to append a special ${ \\tt C L S } >$ token to the input sequence before passing it into the network, then to take the output embedding corresponding to this token’s position as the representation of the whole sentence. In that way, the Transformer will be trained to aggregate information of the sentence to that embedding, by calculating the one-to-one relationships between the ${ \\tt C L S } >$ token and each other tokens in the sentence with the attention module. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our application of special-token readout is similar to this. Concretely, when feeding the transformed per-node embeddings $\\bar { h } _ { v } ^ { 0 }$ , we append an additional learnable embedding $h _ { < \\mathrm { C L S } > }$ to the sequence, and take the first embedding $\\bar { h } _ { < \\mathrm { C L S } > } \\in \\mathbb { R } ^ { d _ { \\mathrm { T F } } }$ from the transformer output as the representation of the whole graph (note that since we do not include positional encodings, placing the special token at the “beginning” of the sentence has no special computational meaning; the location is chosen by convention). Finally, we apply a linear projection followed by a softmax to generate the prediction: ",
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+        "page_idx": 4
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+    {
+        "type": "equation",
+        "img_path": "images/3c826140008247ab67baf020da250d37f3d1411d37f06ef1ef1b9e2212e5ae0d.jpg",
+        "text": "$$\ny = \\mathrm { s o f t m a x } ( W ^ { \\mathrm { o u t } } \\bar { h } _ { < \\mathrm { C L S } > } ^ { L _ { \\mathrm { T F } } } ) .\n$$",
+        "text_format": "latex",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "where $L _ { \\mathrm { T F } }$ is the number of Transformer layers. ",
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+        "type": "text",
+        "text": "This special-token readout mechanism may be viewed as a generalization or a “deep” version of a virtual node readout. While a virtual node method requires every node in the graph to send its information to the virtual node and does not allow for learning pairwise relationships between graph nodes except within the virtual node’s embedding (possibly creating an information bottleneck), a Transformer-style special-token readout method lets the network learn long-range node-to-node relationships in earlier layers before needing to distill them in the later layers. ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "5 Experiments ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate GraphTrans on graph classification tasks from three modalities: biology, computer programming, and chemistry. Our GraphTrans achieves consistent improvement over all of these benchmarks, indicating the generality and effectiveness of the framework. All of our models are trained with the Adam optimizer [17] with a learning rate of 0.0001, a weight decay of 0.0001, and the default Adam $\\beta$ parameters. All Transformer modules used in our experiments have an embedding dimension $d _ { \\mathrm { T F } }$ of 128 and a hidden dimension of 512 in the feedforward subnetwork. The Transformer baselines described below are trained with only the sequence of node embeddings, discarding the graph structure. ",
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+    {
+        "type": "text",
+        "text": "5.1 Biological benchmarks ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Datasets. We choose two commonly used graph classification benchmarks, NCI1 and NCI109 [31]. Each of them contains about 4000 graphs with around 30 nodes on average, representing biochemical compounds. The task is to predict whether a compound contains anti-lung-cancer activity. We follow the settings in [20, 2] for the NCI1 and NCI109, randomly splitting the dataset into training, validation, and test set by a ratio of 8:1:1. ",
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+    {
+        "type": "text",
+        "text": "Training Setup. We trained GraphTrans on both the NCI1 and NCI109 datasets for 100 epochs with a batch size of 256. We run each experiment 20 times with different random seeds and calculate the average and standard deviation of the test accuracies. All the model follows the architecture in Figure 1, with 4 transformer layers and a dropout ratio of 0.1 for both the GNN and Transformer modules. We use two different settings adopted from prior literature for the width and depth of the GNN submodule in GraphTrans. The GNN module width and depth in the small GraphTrans model are copied from the simple baseline, i.e. the settings in [20], which has a hidden dimension of 128 and 3 GNN layers. The settings of the GNN module in the large GraphTrans model are adopted from the default GCN/GIN model provided by OGB, which has a hidden dimension of 300 and 4 GNN layers. We also adopt a cosine annealing schedule [22] for learning rate decay. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results. We report the results on both NCI1 and NCI109 in Table 1. The simple baselines, including GCN Set2Set, SortPool, and SAGPool, are taken from [20], while the strong baselines [13], as well as the FA layer [2]. In Table 1, Our Graph Transformer (small) has the same architecture as the simple baseline but improves the average accuracy by $7 . 1 \\%$ for NCI1 and $5 . 1 \\%$ for NCI109. We also tested the framework with GIN as the encoder (GraphTrans (large)) to align with the settings in the strong baseline, which also significantly improves the accuracy of the strong baseline by $1 . 1 \\%$ for NCI1 and the $8 . 2 \\%$ for NCI109, even without the deep GNN, using 4 layers instead of 8. ",
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+    },
+    {
+        "type": "text",
+        "text": "5.2 Chemical benchmarks ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            715,
+            369,
+            729
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Datasets. For chemical benchmarks, we evaluate our GraphTrans on a dataset larger than NCI dataset, molpcba from the Open Graph Benchmark (OGB) [15]. It contains 437929 graphs with 28 nodes on average. Each graph in the dataset represents a molecule, where nodes and edges are atoms and chemical bonds, respectively. The task is to predict the multiple properties of a molecule. We use the standard splitting from the benchmark. The performance on the GIN and GIN-Virtual baselines are as reported on the OGB leaderboard [15]. ",
+        "bbox": [
+            174,
+            741,
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+            824
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training Setups. All the GNN modules in the experiments follow the settings of the default GIN model provided in OGB, with 4 layers and 300 hidden dimension. We train all the models for 100 epochs with a batch size of 256 and report the test result with the best validation ROC-AUC. For both GNN and Transformer modules, we apply a dropout of 0.3. We use GIN as the baseline and the GNN module, since it performs better than GCN models on the Molpcba dataset. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ca289683c0093fa7b100f53657cdb1fbe2a33abdc96f176a3be2b2249d211dd0.jpg",
+        "table_caption": [
+            "Table 1: NCI biological datasets GraphTrans outperforms past baselines on both NCI1 and NCI109 test accuracy while using fewer GNN layers than prior SOTA baselines. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>GNN Type</td><td>GNN layer count</td><td>NCI1 (%)</td><td>NCI109 (%)</td></tr><tr><td>Set2Set [29,20]</td><td>GCN</td><td>3</td><td>68.6± 1.9</td><td>69.8±1.2</td></tr><tr><td>SortPool [39,20]</td><td>GCN</td><td>3</td><td>73.8±1.0</td><td>74.0±1.2</td></tr><tr><td>SAGPoolh [20]</td><td>GCN</td><td>3</td><td>67.5±1.1</td><td>67.9±1.4</td></tr><tr><td>SAGPoolg [20]</td><td>GCN</td><td>3</td><td>74.2±1.2</td><td>74.1±0.8</td></tr><tr><td>Errica et al. [13]</td><td>GIN</td><td>8</td><td>80.0±1.4</td><td></td></tr><tr><td>Alon and Yahav [2]</td><td>GIN</td><td>8</td><td>81.5±1.2</td><td>1</td></tr><tr><td>Transformer [28]</td><td>1</td><td>二</td><td>68.5±2.6</td><td>70.1± 2.3</td></tr><tr><td>GraphTrans (small)</td><td>GCN</td><td>3</td><td>81.3±1.9</td><td>79.2±2.2</td></tr><tr><td>GraphTrans (large)</td><td>GIN</td><td>4</td><td>82.6±1.2</td><td>82.3±2.6</td></tr></table>",
+        "bbox": [
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+            136,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/6c796bd390d7522d678846877738a91dd6d9dfa932b31d89b44da0aede3880e2.jpg",
+        "table_caption": [
+            "Table 2: OpenGraphBenchmark Molpcba dataset Overall, GraphTrans outperforms competitive baselines with two backbone GNN architectures. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Valid ROC-AUC</td><td>Test ROC-AUC</td></tr><tr><td>GCN [18]</td><td>0.2059±0.0033</td><td>0.2020±0.0024</td></tr><tr><td>GIN [36]</td><td>0.2305±0.0027</td><td>0.2266±0.0028</td></tr><tr><td>GCN-Virtual [18]</td><td>0.2495±0.0042</td><td>0.2424±0.0034</td></tr><tr><td>GIN-Virtual [36]</td><td>0.2798±0.0025</td><td>0.2703±0.0023</td></tr><tr><td>Transformer [28]</td><td>0.1316±0.0012</td><td>0.1281±0.0039</td></tr><tr><td>GraphTrans (GIN)</td><td>0.2893±0.0050</td><td>0.2756±0.0039</td></tr><tr><td>GraphTrans (GIN-Virtual)</td><td>0.2867±0.0022</td><td>0.2761±0.0029</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results. In Table 2, we report the ROC-AUC on validation and test set of Molpcba. Though Transformer alone works very badly on this dataset, our GraphTrans still improves the ROC-AUC of the GIN and GIN-Virtual baseline. It indicates that our design could take benefit from both the local graph structure learned by the GNN and the long-range concept retrieved by the Transformer module based on the GNN embeddings. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3 Computer programming benchmark ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Datasets. For the computer programming benchmark, we also adopt a large dataset, code2 from OGB, which has 45741 graphs each with 125 nodes on average. The dataset is a collection of Abstract Syntax Trees (ASTs) from about $4 5 0 \\mathrm { k }$ Python method definitions. The task is to predict the sub-tokens forming the method name, given the method body represented by the AST. We also adopt the standard dataset splitting from the benchmark. All baseline performances are as reported on the OGB leaderboard. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Training Setups. We also apply the default settings of GCN for Code2 from OGB, with 4 GNN layers, 300 hidden dimension, and a dropout ratio of 0.0. We apply a dropout ratio of 0.3 to the Transformer module to avoid overfitting. We train all the models for 30 epochs with a batch size of 16, due to the large scale of the dataset. For the GraphTrans (PNA) model, we follow the settings in [26], with a hidden embedding of 272 for the GNN module and a weight decay of 3e-6. The only difference is that we still use the learning rate of 0.0001, instead of the heavily tuned 0.00063096 [26]. We run each experiment 5 times and take the average and standard deviation of the F1 score. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results. In Table 3, we compare our GraphTrans with top tier architectures on the leaderboard on Code2 dataset. As the average number of nodes in each graph increases, the global information becomes more important as it becomes more difficult for the GNN to gather information from nodes far away. Even without heavy tuning, GraphTrans significantly outperforms the state-ofthe-art (DAGNN) [27] on the leaderboard. We also include the results for the PNA model and our GraphTrans with the PNA model as the GNN encoder. Our GraphTrans also significantly improves the result, which indicates that our architecture is orthogonal to the variants of the GNN encoder module. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/11044f427b5dfb13f4dc6e0d5fe67e0a61773218ac32562c3f6a693d529ba180.jpg",
+        "table_caption": [
+            "Table 3: OpenGraphBenchmark Code2 dataset All the baselines are collected from the OGB leaderboard. GraphTrans outperforms the state-of-the-art DAGNN. The improvement based on PNA model indicates that our method is orthogonal to the type of GNN module. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Valid F1 score</td><td>Test F1 score</td></tr><tr><td>GIN [36]</td><td>0.1376±0.0016</td><td>0.1495±0.0023</td></tr><tr><td>GCN [18]</td><td>0.1399±0.0017</td><td>0.1507±0.0018</td></tr><tr><td>GIN-Virtual [36]</td><td>0.1439±0.0026</td><td>0.1581±0.0020</td></tr><tr><td>GCN-Virtual [18]</td><td>0.1461±0.0013</td><td>0.1595±0.0018</td></tr><tr><td>PNA [8]</td><td>0.1453±0.0025</td><td>0.1570±0.0032</td></tr><tr><td>DAGNN (SOTA) [27]</td><td>0.1607±0.0040</td><td>0.1751±0.0049</td></tr><tr><td>Transformer [28]</td><td>0.1546±0.0018</td><td>0.1670±0.0015</td></tr><tr><td>GraphTrans (GCN)</td><td>0.1599±0.0009</td><td>0.1751±0.0015</td></tr><tr><td>GraphTrans (PNA)</td><td>0.1622±0.0025</td><td>0.1765±0.0033</td></tr><tr><td>GraphTrans (GCN-Virtual)</td><td>0.1661±0.0012</td><td>0.1830±0.0024</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/4640c9c5830d583b101b847de4066b09e40c9b02f984fdea2049357636605ec8.jpg",
+        "table_caption": [
+            "Table 4: Ablation of Transformer module On the Code2 dataset, only training the Transformer module in GraphTrans with a frozen pre-trained GNN module also improves the F1-score. It indicates that training the Transformer on GNN embeddings can learn information that is not captured by the GNN. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Valid F1 score</td><td>Test F1 score</td></tr><tr><td>Pre-trained GCN-Virtual</td><td>0.1457</td><td>0.1574</td></tr><tr><td>GraphTrans, pre-trained GCN-Virtual, frozen GNN</td><td>0.1479</td><td>0.1616</td></tr><tr><td>GraphTrans, pre-trained GCN-Virtual, fine-tuned GNN</td><td>0.1564</td><td>0.1733</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4 Transformers can capture long-range relationships ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As we previously observed in Figure 2 and discussed in Section 3, the attention inside the transformer module can capture long-range information that is hard to be learned by the GNN module. ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To further verify the hypothesis, we designed an experiment to show that the Transformer module can learn additional information to the GNN module. In Table 4, we first pretrain a GNN (GCN-Virtual) until converge on the Code2 dataset, and then freeze the GNN model and plug our Transformer module after it. By training the model on the training set with a fixed GNN module, we can still observe a 0.0022 F1-score improvement on validation set and 0.0042 on test set. It indicates that the Transformer can learn additional information that is hard to be learned by the GNN module along. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "With pretrained and unfrozen GNN module, our GraphTrans can achieve an even higher F1-score. That may because the GNN module can now focus on learning the local structure information, by leaving the long-range information learning to the Transformer layer after it. The model benefits from the specialization as mentioned in [34]. Note that for all the experiments in Table 4, we do not concatenate the embeddings from the input graph to the input of Transformer for simplicity. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.5 Effectiveness of ${ \\tt C L S } >$ embedding ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            843,
+            447,
+            858
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In Figure 2b, we can observe that row 18 (the last row is for ${ \\mathrm { \\tt C L S } } ^ { }$ ) has dark red on multiple columns, which indicates that the ${ \\tt C L S } >$ learns to attend to important nodes in the graph to learn the representation for the whole graph. ",
+        "bbox": [
+            176,
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/8eb1ef5da3ae52f04e23c53719b1e26612a06d57903d8b891f49e0f5b5271d0b.jpg",
+        "table_caption": [
+            "Table 5: Ablation of ${ \\tt C L S } >$ token The mean and last are two commonly used embedding aggregation method for sequence classification. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Valid</td><td>Test</td></tr><tr><td>GraphTrans, mean</td><td>0.1398</td><td>0.1509</td></tr><tr><td>GraphTrans,last</td><td>0.1566</td><td>0.1716</td></tr><tr><td>GraphTrans,&lt;CLS&gt;</td><td>0.1593</td><td>0.1784</td></tr><tr><td>GraphTrans,&lt;CLS&gt;,cat</td><td>0.1670</td><td>0.1810</td></tr></table>",
+        "bbox": [
+            336,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/b31019c598f917b7eeb6731b16d89c0d6cfc9622a1767ec718df0bd812fc62c8.jpg",
+        "table_caption": [
+            "Table 6: Scalability of Transformer to large graphs We profile our Code2 model on random graphs and list runtime in milliseconds. GraphTrans scales comparably to the GCN model due to the high cost neighbor sampling in GNN training. With graphs over 1000 nodes, GraphTrans is no less scalable than the GCN baseline. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"4\">Edge Density</td></tr><tr><td>Node count</td><td>Model</td><td>20%</td><td>40%</td><td>60%</td><td>80%</td></tr><tr><td rowspan=\"2\">500</td><td>GCN-Virtual [18]</td><td>44.3</td><td>58.5</td><td>79.3</td><td>99.0</td></tr><tr><td>GraphTrans (GCN)</td><td>48.4</td><td>57.5</td><td>76.4</td><td>93.7</td></tr><tr><td rowspan=\"2\">1000</td><td>GCN-Virtual [18]</td><td>99.1</td><td>171.8</td><td>249.5</td><td>0OM</td></tr><tr><td>GraphTrans (GCN)</td><td>96.9</td><td>168.4</td><td>244.3</td><td>00M</td></tr><tr><td rowspan=\"2\">1200</td><td>GCN-Virtual [18]</td><td>131.8</td><td>237.7</td><td>0OM</td><td>0OM</td></tr><tr><td>GraphTrans (GCN)</td><td>127.9</td><td>236.6</td><td>00M</td><td>0OM</td></tr></table>",
+        "bbox": [
+            253,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We also examined the effectiveness of our ${ \\tt C L S } >$ embedding quantitatively. In Table 5, we tested several common methods to for sequence classification. The mean operation averages the output embeddings of the transformer to a single graph embedding; the last operation takes the last embedding in the output sequence as the graph embedding. The quantitative results indicate that the ${ \\tt C L S } >$ embedding is most effective with 0.0275 improvements on the test set, as the model can learn to retrieve information from different nodes and aggregate them into one embedding. The concatenation of the embeddings in the input graph and the input embeddings of the transformer can further improve the validation and test F1-score to 0.1670 and 0.1733. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.6 Scalability ",
+        "text_level": 1,
+        "bbox": [
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+            606,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To quantitatively benchmark how GraphTrans scales with large graphs over 100 nodes, we ran a microbenchmark of iteration time for training with varying graph size and edge density. We train baselines on randomly generated Erdos-Renyi graphs with a varying number of nodes and edge density. As shown in the Table 6, our GraphTrans model scales at least as well as the GCN model when the number of nodes and edge density increases. Both GCN and GraphTrans see out of memory errors (OOM) with large dense graphs, but we note that GraphTrans had similar memory consumption to the GCN baseline. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.7 Computational efficiency ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            746,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the overhead that our GraphTrans adds over a specific GNN backbone, we evaluate the forward pass runtime and backward pass runtime per iteration. We normalize models to have roughly similar parameter counts. The results are shown in Table 7. For the NCI1 dataset, GraphTrans is actually faster to train than a comparable GCN model. For the OGB-molpcba and OGB-Code2 datasets, GraphTrans is $7 . 1 1 \\%$ slower than the baseline GNN architectures. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5.8 Number of parameters ",
+        "text_level": 1,
+        "bbox": [
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+            858,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We compare the number of parameters of the GNN baseline and the GraphTrans on different dataset in Table 8. Overall, GraphTrans only increases total parameters marginally for Molpcba and NCI. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/47e3f59dff0d3d81e0b89144dd3d4a50b8c009bac38b221733ab67f8b6871bbf.jpg",
+        "table_caption": [
+            "Table 7: Speedup of Transformer module For GraphTrans models trained over the NCI1, OGBGMolpcba and OGBG-Code2 datasets, we find that the Transformer module adds minimal overhead. Speedup is the training iteration speed compared to GNN based model; larger number indicates a faster running speed. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>Forward time (ms)</td><td>Backward time (ms)</td><td> Speedup</td></tr><tr><td rowspan=\"3\">NCI1</td><td>GCN-Virtual [18]</td><td>22.27 ± 2.04</td><td>14.35 ± 2.46</td><td>1.00×</td></tr><tr><td>Transformer</td><td>12.31 ± 1.68</td><td>9.32 ± 1.68</td><td>1.69×</td></tr><tr><td>GraphTrans</td><td>15.01 ± 1.63</td><td>12.04 ± 2.25</td><td>1.35×</td></tr><tr><td rowspan=\"3\">Molpcba</td><td>GCN-Virtual [18]</td><td>14.79 ± 2.54</td><td>12.75 ± 3.00</td><td>1.00×</td></tr><tr><td>Transformer</td><td>12.34 ± 1.43</td><td>10.52 ± 1.60</td><td>1.20×</td></tr><tr><td>GraphTrans</td><td>16.55 ± 2.93</td><td>14.3 ± 3.15</td><td>0.89×</td></tr><tr><td rowspan=\"3\">Code2</td><td>GCN-Virtual [18]</td><td>22.97 ± 6.13</td><td>38.53 ± 6.92</td><td>1.00×</td></tr><tr><td>Transformer</td><td>31.01 ± 9.00</td><td>33.30 ± 16.09</td><td>0.96×</td></tr><tr><td>GraphTrans</td><td>34.93 ± 6.85</td><td>31.14 ± 12.90</td><td>0.93×</td></tr></table>",
+        "bbox": [
+            192,
+            164,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/1f1f608c3f036fecef17258053b1996fa490cbb7c5a8e49d614527b47474b39b.jpg",
+        "table_caption": [
+            "Table 8: Parameter count Overall, GraphTrans achieves improved accuracy with a minor increase in parameters. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>GNN</td><td>GraphTrans</td><td>Delta</td></tr><tr><td>Molpcba</td><td>3.4M</td><td>4.2M</td><td>0.8M</td></tr><tr><td>NCI</td><td>0.4M</td><td>0.5M</td><td>0.1M</td></tr><tr><td>Code2</td><td>12.5M</td><td>9.1M</td><td>-3.4M</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "For Code2, GraphTrans is substantially more parameter-efficient than the GNN while improving test F1 score from 0.1629 to 0.1810. One reason for improved parameter efficiency is that the Transformer reduces feature dimension before the expensive final prediction layer. ",
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+    {
+        "type": "text",
+        "text": "6 Conclusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We proposed GraphTrans, a simple yet powerful framework for learning long-range relationships with GNNs. Leveraging recent results that suggest structural priors may be unnecessary or even counterproductive for high-level, long-range relationships, we augment standard GNN layer stacks with a subsequent permutation-invariant Transformer module. The Transformer module acts as a novel GNN “readout” module, simultaneously allowing the learning of pairwise interactions between graph nodes and summarizing them into a special token’s embedding as is done in common NLP applications of Transformers. This simple framework leads to surprising improvements upon the state of the art in several graph classification tasks across program analysis, molecules and protein association networks. In some cases, GraphTrans outperforms methods that attempt to encode domain-specific structural information. Overall, GraphTrans presents a simple yet general approach to improve long-range graph classification; next directions include applications to node and edge classification tasks as well as further scalability improvements of the Transformer to large graphs. ",
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+    {
+        "type": "text",
+        "text": "7 Acknowledgements ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We thank Ethan Mehta, Azade Nazi, Daniel Rothschild, Adnan Sherif and Justin Wong for thoughtful discussions and feedback. In addition to NSF CISE Expeditions Award CCF-1730628, this research is supported by gifts from Amazon Web Services, Ant Group, Ericsson, Facebook, Futurewei, Google, Intel, Microsoft, Scotiabank, and VMware. ",
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+    {
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parse/train/r1gRTCVFvB/r1gRTCVFvB.md

@@ -0,0 +1,339 @@
+# DECOUPLING REPRESENTATION AND CLASSIFIERFOR LONG-TAILED RECOGNITION
+
+Bingyi $\mathbf { K a n g } ^ { 1 , 2 }$ , Saining $\mathbf { X i e ^ { 1 } }$ , Marcus Rohrbach1, Zhicheng $\mathbf { Y a n ^ { 1 } }$ , Albert Gordo1,   
+Jiashi Feng2, Yannis Kalantidis1   
+1Facebook AI, 2National University of Singapore   
+kang@u.nus.edu,{s9xie,mrf,zyan3,agordo,yannisk}@fb.com,elefjia@nus.edu.sg
+
+# ABSTRACT
+
+The long-tail distribution of the visual world poses great challenges for deep learning based classification models on how to handle the class imbalance problem. Existing solutions usually involve class-balancing strategies, e.g. by loss re-weighting, data re-sampling, or transfer learning from head- to tail-classes, but most of them adhere to the scheme of jointly learning representations and classifiers. In this work, we decouple the learning procedure into representation learning and classification, and systematically explore how different balancing strategies affect them for long-tailed recognition. The findings are surprising: (1) data imbalance might not be an issue in learning high-quality representations; (2) with representations learned with the simplest instance-balanced (natural) sampling, it is also possible to achieve strong long-tailed recognition ability by adjusting only the classifier. We conduct extensive experiments and set new state-of-the-art performance on common long-tailed benchmarks like ImageNet-LT, Places-LT and iNaturalist, showing that it is possible to outperform carefully designed losses, sampling strategies, even complex modules with memory, by using a straightforward approach that decouples representation and classification. Our code is available at https://github.com/facebookresearch/classifier-balancing.
+
+# 1 INTRODUCTION
+
+Visual recognition research has made rapid advances during the past years, driven primarily by the use of deep convolutional neural networks (CNNs) and large image datasets, most importantly the ImageNet Challenge (Russakovsky et al., 2015). Such datasets are usually artificially balanced with respect to the number of instances for each object/class in the training set. Visual phenomena, however, follow a long-tailed distribution that many standard approaches fail to properly model, leading to a significant drop in accuracy. Motivated by this, a number of works have recently emerged that try to study long-tailed recognition, i.e., recognition in a setting where the number of instances in each class highly varies and follows a long-tailed distribution.
+
+When learning with long-tailed data, a common challenge is that instance-rich (or head) classes dominate the training procedure. The learned classification model tends to perform better on these classes, while performance is significantly worse for instance-scarce (or tail) classes. To address this issue and to improve performance across all classes, one can re-sample the data or design specific loss functions that better facilitate learning with imbalanced data (Chawla et al., 2002; Cui et al., 2019; Cao et al., 2019). Another direction is to enhance recognition performance of the tail classes by transferring knowledge from the head classes (Wang et al., 2017; 2018; Zhong et al., 2019; Liu et al., 2019). Nevertheless, the common belief behind existing approaches is that designing proper sampling strategies, losses, or even more complex models, is useful for learning high-quality representations for long-tailed recognition.
+
+Most aforementioned approaches thus learn the classifiers used for recognition jointly with the data representations. However, such a joint learning scheme makes it unclear how the long-tailed recognition ability is achieved—is it from learning a better representation or by handling the data imbalance better via shifting classifier decision boundaries? To answer this question, we take one step back and decouple long-tail recognition into representation learning and classification. For learning representations, the model is exposed to the training instances and trained through different sampling strategies or losses. For classification, upon the learned representations, the model recognizes the long-tailed classes through various classifiers. We evaluate the performance of various sampling and classifier training strategies for long-tailed recognition under both joint and decoupled learning schemes.
+
+Specifically, we first train models to learn representations with different sampling strategies, including the standard instance-based sampling, class-balanced sampling and a mixture of them. Next, we study three different basic approaches to obtain a classifier with balanced decision boundaries, on top of the learned representations. They are 1) re-training the parametric linear classifier in a class-balancing manner (i.e., re-sampling); 2) non-parametric nearest class mean classifier, which classifies the data based on their closest class-specific mean representations from the training set; and 3) normalizing the classifier weights, which adjusts the weight magnitude directly to be more balanced, adding a temperature to modulate the normalization procedure.
+
+We conduct extensive experiments to compare the aforementioned instantiations of the decoupled learning scheme with the conventional scheme that jointly trains the classifier and the representations. We also compare to recent, carefully designed and more complex models, including approaches using memory (e.g., OLTR (Liu et al., 2019)) as well as more sophisticated losses (Cui et al., 2019). From our extensive study across three long-tail datasets, ImageNet-LT, Places-LT and iNaturalist, we make the following intriguing observations:
+
+• We find that decoupling representation learning and classification has surprising results that challenge common beliefs for long-tailed recognition: instance-balanced sampling learns the best and most generalizable representations. • It is advantageous in long-tailed recognition to re-adjust the decision boundaries specified by the jointly learned classifier during representation learning: Our experiments show that this can either be achieved by retraining the classifier with class-balanced sampling or by a simple, yet effective, classifier weight normalization which has only a single hyperparameter controlling the “temperature” and which does not require additional training. • By applying the decoupled learning scheme to standard networks (e.g., ResNeXt), we achieve significantly higher accuracy than well established state-of-the-art methods (different sampling strategies, new loss designs and other complex modules) on multiple longtailed recognition benchmark datasets, including ImageNet-LT, Places-LT, and iNaturalist.
+
+# 2 RELATED WORK
+
+Long-tailed recognition has attracted increasing attention due to the prevalence of imbalanced data in real-world applications (Wang et al., 2017; Zhou et al., 2017; Mahajan et al., 2018; Zhong et al., 2019; Gupta et al., 2019). Recent studies have mainly pursued the following three directions:
+
+Data distribution re-balancing. Along this direction, researchers have proposed to re-sample the dataset to achieve a more balanced data distribution. These methods include over-sampling (Chawla et al., 2002; Han et al., 2005) for the minority classes (by adding copies of data), undersampling (Drummond et al., 2003) for the majority classes (by removing data), and class-balanced sampling (Shen et al., 2016; Mahajan et al., 2018) based on the number of samples for each class.
+
+Class-balanced Losses. Various methods are proposed to assign different losses to different training samples for each class. The loss can vary at class-level for matching a given data distribution and improving the generalization of tail classes (Cui et al., 2019; Khan et al., 2017; Cao et al., 2019; Khan et al., 2019; Huang et al., 2019). A more fine-grained control of the loss can also be achieved at sample level, e.g. with Focal loss (Lin et al., 2017), Meta-Weight-Net (Shu et al., 2019), re-weighted training (Ren et al., 2018), or based on Bayesian uncertainty (Khan et al., 2019). Recently, Hayat et al. (2019) proposed to balance the classification regions of head and tail classes using an affinity measure to enforce cluster centers of classes to be uniformly spaced and equidistant.
+
+Transfer learning from head- to tail classes. Transfer-learning based methods address the issue of imbalanced training data by transferring features learned from head classes with abundant training instances to under-represented tail classes. Recent work includes transferring the intra-class variance (Yin et al., 2019) and transferring semantic deep features (Liu et al., 2019). However it is usually a non-trivial task to design specific modules (e.g. external memory) for feature transfer.
+
+A benchmark for low-shot recognition was proposed by Hariharan & Girshick (2017) and consists of a representation learning phase without access to the low-shot classes and a subsequent low-shot learning phase. In contrast, the setup for long-tail recognition assumes access to both head and tail classes and a more continuous decrease in in class labels. Recently, Liu et al. (2019) and Cao et al. (2019) adopt re-balancing schedules that learn representation and classifier jointly within a two-stage training scheme. OLTR (Liu et al., 2019) uses instance-balanced sampling to first learn representations that are fine-tuned in a second stage with class-balanced sampling together with a memory module. LDAM (Cao et al., 2019) introduces a label-distribution-aware margin loss that expands the decision boundaries of few-shot classes. In Section 5 we exhaustively compare to OLTR and LDAM, since they report state-of-the-art results for the ImageNet-LT, Places-LT and iNaturalist datasets. In our work, we argue for decoupling representation and classification. We demonstrate that in a long-tailed scenario, this separation allows straightforward approaches to achieve high recognition performance, without the need for designing sampling strategies, balance-aware losses or adding memory modules.
+
+# 3 LEARNING REPRESENTATIONS FOR LONG-TAILED RECOGNITION
+
+For long-tailed recognition, the training set follows a long-tailed distribution over the classes. As we have less data about infrequent classes during training, the models trained using imbalanced datasets tend to exhibit under-fitting on the few-shot classes. But in practice we are interested in obtaining the model capable of recognizing all classes well. Various re-sampling strategies (Chawla et al., 2002; Shen et al., 2016; Cao et al., 2019), loss reweighting and margin regularization over few-shot classes are thus proposed. However, it remains unclear how they achieve performance improvement, if any, for long-tailed recognition. Here we systematically investigate their effectiveness by disentangling representation learning from classifier learning, in order to identify what indeed matters for longtailed recognition.
+
+Notation. We define the notation used through the paper. Let $X = \{ x _ { i } , y _ { i } \} , i \in \{ 1 , \dots , n \}$ be a   
+trainiclass we a g set, wh, and let ume that $y _ { i }$ bel for data point be the total num sorted by cardin $x _ { i }$ . Let r of tty in $n _ { j }$ denote the number oning samples. Withoreasing order, i.e., if ing ss of g, then $j$ $\begin{array} { r } { n = \sum _ { j = 1 } ^ { C } n _ { j } } \end{array}$ $i < j$ $n _ { i } \geq n _ { j }$   
+Additionally, since we are in a long-tail setting, $n _ { 1 } \gg n _ { C }$ . Finally, we denote with $f ( x ; \theta ) = z$   
+the representation for $x$ , where $f ( x ; \theta )$ is implemented by a deep CNN model with parameter $\theta$ .   
+The final class prediction $\tilde { y }$ is given by a classifier function $g$ , such that $\tilde { y } = \arg \operatorname* { m a x } g ( z )$ . For the   
+common case, $g$ is a linear classifier, i.e., $g ( z ) = W ^ { \top } z + b$ , where $W$ denotes the classifier weight   
+matrix, and $^ { b }$ is the bias. We present other instantiations of $g$ in Section 4.
+
+Sampling strategies. In this section we present a number of sampling strategies that aim at rebalancing the data distribution for representation and classifier learning. For most sampling strategies presented below, the probability $p _ { j }$ of sampling a data point from class $j$ is given by:
+
+$$
+p _ { j } = \frac { n _ { j } ^ { q } } { \sum _ { i = 1 } ^ { C } n _ { i } ^ { q } } ,
+$$
+
+where $q \in [ 0 , 1 ]$ and $C$ is the number of training classes. Different sampling strategies arise for different values of $q$ and below we present strategies that correspond to $q = 1$ , $q = 0$ , and $q = 1 / 2$ .
+
+Instance-balanced sampling. This is the most common way of sampling data, where each training example has equal probability of being selected. For instance-balanced sampling, the probability $p _ { j } ^ { \mathrm { I B } }$ is given by Equation 1 with $q = 1$ , i.e., a data point from class $j$ will be sampled proportionally to the cardinality $n _ { j }$ of the class in the training set.
+
+Class-balanced sampling. For imbalanced datasets, instance-balanced sampling has been shown to be sub-optimal (Huang et al., 2016; Wang et al., 2017) as the model under-fits for few-shot classes leading to lower accuracy, especially for balanced test sets. Class-balanced sampling has been used to alleviate this discrepancy, as, in this case, each class has an equal probability of being selected. The probability $p _ { j } ^ { \mathrm { C B } }$ is given by Eq. (1) with $q = 0$ , i.e., $p _ { j } ^ { \mathrm { C B } } = 1 / \bar { C }$ . One can see this as a twostage sampling strategy, where first a class is selected uniformly from the set of classes, and then an instance from that class is subsequently uniformly sampled.
+
+Square-root sampling. A number of variants of the previous sampling strategies have been explored. A commonly used variant is square-root sampling (Mikolov et al., 2013; Mahajan et al., 2018), where $q$ is set to $1 / 2$ in Eq. (1) above.
+
+Progressively-balanced sampling. Recent approaches (Cui et al., 2018; Cao et al., 2019) utilized mixed ways of sampling, i.e., combinations of the sampling strategies presented above. In practice this involves first using instance-balanced sampling for a number of epochs, and then class-balanced sampling for the last epochs. These mixed sampling approaches require setting the number of epochs before switching the sampling strategy as an explicit hyper-parameter. Here, we experiment with a softer version, progressively-balanced sampling, that progressively “interpolates” between instancebalanced and class-balanced sampling as learning progresses. Its sampling probability/weight $p _ { j }$ for class $j$ is now a function of the epoch $t$ ,
+
+$$
+p _ { j } ^ { \mathrm { P B } } ( t ) = ( 1 - \frac { t } { T } ) p _ { j } ^ { \mathrm { I B } } + \frac { t } { T } p _ { j } ^ { \mathrm { C B } } ,
+$$
+
+where $T$ is the total number of epochs. Figure 3 in appendix depicts the sampling probabilities.
+
+Loss re-weighting strategies. Loss re-weighting functions for imbalanced data have been extensively studied, and it is beyond the scope of this paper to examine all related approaches. What is more, we found that some of the most recent approaches reporting high performance were hard to train and reproduce and in many cases require extensive, dataset-specific hyper-parameter tuning. In Section A of the Appendix we summarize the latest, best performing methods from this area. In Section 5 we show that, without bells and whistles, baseline methods equipped with a properly balanced classifier can perform equally well, if not better, than the latest loss re-weighting approaches.
+
+# 4 CLASSIFICATION FOR LONG-TAILED RECOGNITION
+
+When learning a classification model on balanced datasets, the classifier weights $W$ and $^ { b }$ are usually trained jointly with the model parameters $\theta$ for extracting the representation $f ( x _ { i } ; \theta )$ by minimizing the cross-entropy loss between the ground truth $y _ { i }$ and prediction $\boldsymbol { W } ^ { \top } f ( x _ { i } ; \dot { \theta } ) + \boldsymbol { b }$ . This is also a typical baseline for long-tailed recognition. Though various approaches of re-sampling, reweighting and transferring representations from head to tail classes have been proposed, the general scheme remains the same: classifiers are either learned jointly with the representations either endto-end, or via a two-stage approach where the classifier and the representation are jointly fine-tuned with variants of class-balanced sampling as a second stage (Cui et al., 2018; Cao et al., 2019).
+
+In this section, we consider decoupling the representation from the classification in long-tailed recognition. We present ways of learning classifiers aiming at rectifying the decision boundaries on head- and tail-classes via fine-tuning with different sampling strategies or other non-parametric ways such as nearest class mean classifiers. We also consider an approach to rebalance the classifier weights that exhibits a high long-tailed recognition accuracy without any additional retraining.
+
+Classifier Re-training (cRT). A straightforward approach is to re-train the classifier with classbalanced sampling. That is, keeping the representations fixed, we randomly re-initialize and optimize the classifier weights $W$ and $^ { b }$ for a small number of epochs using class-balanced sampling. A similar methodology was also recently used in (Zhang et al., 2019) for action recognition on a long-tail video dataset.
+
+Nearest Class Mean classifier (NCM). Another commonly used approach is to first compute the mean feature representation for each class on the training set and then perform nearest neighbor search either using cosine similarity or the Euclidean distance computed on $L _ { 2 }$ normalized mean features (Snell et al., 2017; Guerriero et al., 2018; Rebuffi et al., 2017). Despite its simplicity, this is a strong baseline $\cdot f$ . the experimental evaluation in Section 5); the cosine similarity alleviates the weight imbalance problem via its inherent normalization (see also Figure 4).
+
+$\tau$ -normalized classifier ( $\tau$ -normalized). We investigate an efficient approach to re-balance the decision boundaries of classifiers, inspired by an empirical observation: after joint training with instance-balanced sampling, the norms of the weights $\| w _ { j } \|$ are correlated with the cardinality of the classes $n _ { j }$ , while, after fine-tuning the classifiers using class-balanced sampling, the norms of the classifier weights tend to be more similar ( $_ { c f }$ . Figure 2-left).
+
+Inspired by the above observations, we consider rectifying imbalance of decision boundaries by adjusting the classifier weight norms directly through the following $\tau$ -normalization procedure. Formally, let $W = \{ w _ { j } \} \in \mathbf { \bar { \mathbb { R } } } ^ { d \times C }$ , where $\boldsymbol { w _ { j } } \in \mathbb { R } ^ { d }$ are the classifier weights corresponding to class $j$ . We scale the weights of $W$ to get $\widetilde { W } = \{ \widetilde { w _ { j } } \}$ by:
+
+$$
+\widetilde { w _ { i } } = \frac { w _ { i } } { \vert \vert w _ { i } \vert \vert \tau } ,
+$$
+
+where $\tau$ is a hyper-parameter controlling the “temperature” of the normalization, and $| | \cdot | |$ denotes the $L _ { 2 }$ norm. When $\tau = 1$ , it reduces to standard $L _ { 2 }$ -normalization. When $\tau = 0$ , no scaling is imposed. We empirically choose $\tau \in ( 0 , 1 )$ such that the weights can be rectified smoothly. After $\tau$ -normalization, the classification logits are given by $\widehat { y } = \widetilde { W } ^ { \top } f ( x ; \theta )$ . Note that we discard the bias term $^ { b }$ here due to its negligible effect on the logits and final predictions.
+
+Learnable weight scaling (LWS). Another way of interpreting $\tau$ -normalization would be to think of it as a re-scaling of the magnitude for each classifier $w _ { i }$ keeping the direction unchanged. This could be written as
+
+$$
+{ \widetilde { w _ { i } } } = f _ { i } * w _ { i } , { \mathrm { w h e r e ~ } } f _ { i } = { \frac { 1 } { | | w _ { i } | | ^ { \tau } } } .
+$$
+
+Although for $\tau$ -normalized in general $\tau$ is chosen through cross-validation, we further investigate learning $f _ { i }$ on the training set, using class-balanced sampling (like cRT). In this case, we keep both the representations and classifier weights fixed and only learn the scaling factors $f _ { i }$ . We denote this variant as Learnable Weight Scaling (LWS) in our experiments.
+
+# 5 EXPERIMENTS
+
+# 5.1 EXPERIMENTAL SETUP
+
+Datasets. We perform extensive experiments on three large-scale long-tailed datasets, including Places-LT (Liu et al., 2019), ImageNet-LT (Liu et al., 2019), and iNaturalist 2018 (iNatrualist, 2018). Places-LT and ImageNet-LT are artificially truncated from their balanced versions (Places2 (Zhou et al., 2017) and ImageNet-2012 (Deng et al., 2009)) so that the labels of the training set follow a long-tailed distribution. Places-LT contains images from 365 categories and the number of images per class ranges from 4980 to 5. ImageNet-LT has 1000 classes and the number of images per class ranges from 1280 to 5 images. iNaturalist 2018 is a real-world, naturally long-tailed dataset, consisting of samples from 8,142 species.
+
+Evaluation Protocol. After training on the long-tailed datasets, we evaluate the models on the corresponding balanced test/validation datasets and report the commonly used top-1 accuracy over all classes, denoted as All. To better examine performance variations across classes with different number of examples seen during training, we follow Liu et al. (2019) and further report accuracy on three splits of the set of classes: Many-shot (more than 100 images), Medium-shot ( $2 0 \mathrm { \sim } 1 0 0$ images) and Few-shot (less than 20 images). Accuracy is reported as a percentage.
+
+Implementation. We use the PyTorch (Paszke et al., 2017) framework for all experiments1. For Places-LT, we choose ResNet-152 as the backbone network and pretrain it on the full ImageNet2012 dataset, following Liu et al. (2019). On ImageNet-LT, we report results with ResNet$\{ 1 0 , 5 0 , 1 0 1 , 1 5 2 \}$ (He et al., 2016) and ResNeXt- $\{ 5 0 , 1 0 1 , 1 5 2 \} ( 3 2 \mathrm { x } 4 \mathrm { d } )$ (Xie et al., 2017) but mainly use ResNeXt-50 for analysis. Similarly, ResNet- $\{ 5 0 , 1 0 1 , 1 5 2 \}$ is also used for iNaturalist 2018. For all experiements, if not specified, we use SGD optimizer with momentum 0.9, batch size 512, cosine learning rate schedule (Loshchilov & Hutter, 2016) gradually decaying from 0.2 to 0 and image resolution $2 2 4 \times 2 2 4$ . In the first representation learning stage, the backbone network is usually trained for 90 epochs. In the second stage, i.e., for retraining a classifier (cRT), we restart the learning rate and train it for 10 epochs while keeping the backbone network fixed.
+
+![](images/c7c795cddb1a4756336c3e1334a47c4cd057d9edf32e620d31d71c276908449e.jpg)  
+Figure 1: The performance of different classifiers for each split on ImageNet-LT with ResNeXt-50. Colored markers denote the sampling strategies used to learn the representations.
+
+# 5.2 SAMPLING STRATEGIES AND DECOUPLED LEARNING
+
+In Figure 1, we compare different sampling strategies for the conventional joint training scheme to a number of variations of the decoupled learning scheme on the ImageNet-LT dataset. For the joint training scheme (Joint), the linear classifier and backbone for representation learning are jointly trained for 90 epochs using a standard cross-entropy loss and different sampling strategies, i.e., Instance-balanced, Class-balanced, Square-root, and Progressively-balanced. For the decoupled learning schemes, we present results when learning the classifier in all the ways presented in Section 4, i.e., re-initialize and re-train (cRT), Nearest Class Mean (NCM) as well as $\tau$ -normalized classifier. Below, we discuss a number of key observations.
+
+Sampling matters when training jointly. From the Joint results in Figure 1 across sampling methods and splits, we see consistent gains in performance when using better sampling strategies (see also Table 5). The trends are consistent for the overall performance as well as the medium- and fewshot classes, with progressively-balanced sampling giving the best results. As expected, instancebalanced sampling gives the highest performance for the many-shot classes. This is well expected since the resulted model is highly skewed to the many-shot classes. Our results for different sampling strategies on joint training validate related works that try to design better data sampling methods.
+
+Joint or decoupled learning? For most cases presented in Figure 1, performance using decoupled methods is significantly better in terms of overall performance, as well as all splits apart from the many-shot case. Even the nonparametric NCM approach is highly competitive in most cases, while cRT and $\tau$ -normalized outperform the jointly trained baseline by a large margin (i.e. $5 \%$ higher than the jointly learned classifier), and even achieving $2 \%$ higher overall accuracy than the best jointly trained setup with progressively-balanced sampling. The gains are even higher for mediumand few-shot classes at $5 \%$ and $11 \%$ , respectively.
+
+Table 1: Retraining/finetuning different parts of a ResNeXt-50 model on ImageNet-LT. B: backbone; C: classifier; LB: last block.   
+
+<table><tr><td>Re-train</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>B+C</td><td>55.4</td><td>45.3</td><td>24.5</td><td>46.3</td></tr><tr><td>B+C(0.1×lr)</td><td>61.9</td><td>45.6</td><td>22.8</td><td>48.8</td></tr><tr><td>LB+C</td><td>61.4</td><td>45.8</td><td>24.5</td><td>48.9</td></tr><tr><td>C</td><td>61.5</td><td>46.2</td><td>27.0</td><td>49.5</td></tr></table>
+
+To further justify our claim that it is beneficial to decouple representation and classifier, we experiment with fine-tuning the backbone network (ResNeXt-50) jointly with the linear classifier. In Table 1, we present results when fine-tuning the whole network with standard or smaller $( 0 . 1 \times )$ learning rate, fine-tuning only the last block in the backbone, or only retraining the linear classifier and fixing the representation. Fine-tuning the whole network yields the worst performance $( 4 6 . 3 \%$ and $4 8 . 8 \%$ ), while keeping the representation frozen performs best $( 4 9 . 5 \% )$ . The trend is even more evident for the medium/few-shot classes. This result suggests that decoupling representation and classifier is desirable for long-tailed recognition.
+
+![](images/9a0b168a4ef4c472181bb24d579d1c9d389052eee172b139dccfca870d86a1aa.jpg)  
+Figure 2: Left: Classifier weight norms for ImageNet-LT validation set when classes are sorted by descending values of $n _ { j }$ . Blue line: classifier weights learned with instance-balanced sampling. Green line: weights after fine-tuning with class-balanced sampling. Gold line: after $\tau$ normalization. Brown line: weights by learnable weight scaling. Right: Accuracy with different values of the normalization parameter $\tau$ .
+
+Instance-balanced sampling gives the most generalizable representations. Among all decoupled methods, when it comes to overall performance and all splits apart from the many-shot classes, we see that Instance-balanced sampling gives the best results. This is particularly interesting, as it implies that data imbalance might not be an issue learning high-quality representations.
+
+# 5.3 HOW TO BALANCE YOUR CLASSIFIER?
+
+Among the ways of balancing the classifier explored in Figure 1, the non-parametric NCM seems to perform slightly worse than cRT and $\tau$ -normalization. Those two methods are consistently better in most cases apart from the few-shot case, where NCM performs comparably. The biggest drop for the NCM approach comes from the many-shot case. It is yet still somehow surprising that both the NCM and $\tau$ -normalized cases give competitive performance even though they are free of additional training and involve no additional sampling procedure. As discussed in Section 4, their strong performance may stem from their ability to adaptively adjust the decision boundaries for many-, medium- and few-shot classes (see also Figure 4).
+
+In Figure 2 (left) we empirically show the $L _ { 2 }$ norms of the weight vectors for all classifiers, as well as the training data distribution sorted in a descending manner with respect to the number of instances in the training set. We can observe that the weight norm of the joint classifier (blue line) is positively correlated with the number of training instances of the corresponding class. More-shot classes tend to learn a classifier with larger magnitudes. As illustrated in Figure 4, this yields a wider classification boundary in feature space, allowing the classifier to have much higher accuracy on data-rich classes, but hurting data-scarce classes. $\tau$ -normalized classifiers (gold line) alleviate this issue to some extent by providing more balanced classifier weight magnitudes. For retraining (green line), the weights are almost balanced except that few-shot classes have slightly larger classifier weight norms. Note that the NCM approach would give a horizontal line in the figure as the mean vectors are $L _ { 2 }$ -normalized before nearest neighbor search.
+
+In Figure 2 (right), we further investigate how the performance changes as the temperature parameter $\tau$ for the $\tau$ -normalized classifier varies. The figure shows that as $\tau$ increases from 0, many-shot accuracy decays dramatically while few-shot accuracy increases dramatically.
+
+# 5.4 COMPARISON WITH THE STATE-OF-THE-ART ON LONG-TAILED DATASETS
+
+In this section, we compare the performance of the decoupled schemes to other recent works that report state-of-the-art results on on three common long-tailed benchmarks: ImageNet-LT, iNaturalist and Places-LT. Results are presented in Tables 2, 3 and 4, respectively.
+
+Table 2: Long-tail recognition accuracy on ImageNet-LT for different backbone architectures. $^ \dagger$ denotes results directly copied from Liu et al. (2019). \* denotes results reproduced with the authors’ code. \*\* denotes OLTR with our representation learning stage.   
+
+<table><tr><td>Method</td><td>ResNet-10 ResNeXt-50 ResNeXt-152</td><td></td></tr><tr><td>FSLwFt (Gidaris &amp; Komodakis,2018)</td><td>28.4</td><td></td></tr><tr><td>Focal Losst (Lin et al.,2017)</td><td>30.5</td><td></td></tr><tr><td>Range Losst (Zhang et al., 2017)</td><td>30.7</td><td></td></tr><tr><td>Lifted Losst (Oh Song et al., 2016)</td><td>30.8</td><td>=</td></tr><tr><td>OLTR† (Liu et al., 2019)</td><td>35.6</td><td>=</td></tr><tr><td>OLTR*</td><td>34.1</td><td>24.8</td></tr><tr><td>OLTR**</td><td>37.3</td><td>50.3</td></tr><tr><td>Joint</td><td>34.8</td><td>44.4 47.8</td></tr><tr><td>NCM</td><td>35.5</td><td>51.3</td></tr><tr><td>cRT</td><td>41.8</td><td>52.4</td></tr><tr><td>T-normalized</td><td>40.6</td><td>52.8</td></tr><tr><td>LWS</td><td>41.4</td><td>53.3</td></tr></table>
+
+ImageNet-LT. Table 2 presents results for ImageNet-LT. Although related works present results with ResNet-10 (Liu et al., 2019), we found that using bigger backbone architectures increases performance significantly on this dataset. We therefore present results for three backbones: ResNet-10, ResNeXt-50 and the larger ResNeXt-152. For the state-of-the-art OLTR method of Liu et al. (2019) we adopt results reported in the paper, as well as results we reproduced using the authors’ opensourced codebase2 with two training settings: the one suggested in the codebase and the one using our training setting for the representation learning. From the table we see that the non-parametric decoupled NCM method performs on par with the state-of-the-art for most architectures. We also see that when re-balancing the classifier properly, either by re-training or $\tau$ -normalizing, we get results that, without bells and whistles outperform the current state-of-the-art for all backbone architectures. We further experimented with adding the memory mechanism of Liu et al. (2019) on top of our decoupled cRT setup, but the memory mechanism didn’t seem to further boost performance (see Appendix B.4).
+
+iNaturalist 2018. We further evaluate our decoupled methods on the iNaturalist 2018 dataset. We present results after 90 and 200 epochs, as we found that 90 epochs were not enough for the representation learning stage to converge; this is different from Cao et al. (2019) where they train for 90 epochs. From Table 3 we see that results are consistent with the ImageNet-LT case: re-balancing the classifier gives results that outperform CB-Focal (Cui et al., 2019). Our performance, when training only for 90 epochs, is slightly lower than the very recently proposed LDAM $^ +$ DRW (Cao et al., 2019). However, with 200 training epochs and classifier normalization, we achieve a new state-of-the-art of 69.3 with ResNet-50 that can be further improved to 72.5 for ResNet-152. It is further worth noting that we cannot reproduce the numbers reported in Cao et al. (2019). We find that the $\tau$ -normalized classifier performs best and gives a new state-of-the-art for the dataset, while surprisingly achieving similar accuracy $( 6 9 \% / 7 2 \%$ for ResNet-50/ResNet-152) across all many-, medium- and few-shot class splits, a highly desired result for long-tailed recognition. Complete results, i.e., for all splits and more backbone architectures can be found in Table 8 of the Appendix.
+
+Places-LT. For Places-LT we follow the protocol of Liu et al. (2019) and start from a ResNet-152 backbone pre-trained on the full ImageNet dataset. Similar to Liu et al. (2019), we then fine-tune the backbone with Instance-balanced sampling for representation learning. Classification follows with fixed representations for our decoupled methods. As we see in Table 4, all three decoupled methods outperform the state-of-the-art approaches, including Lifted Loss (Oh Song et al., 2016), Focal Loss (Lin et al., 2017), Range Loss (Zhang et al., 2017), FSLwF (Gidaris & Komodakis, 2018) and OLTR (Liu et al., 2019). Once again, the $\tau$ -normalized classifier give the top performance, with impressive gains for the medium- and few-shot classes.
+
+Table 3: Overall accuracy on iNaturalist 2018. Rows with $^ \dagger$ denote results directly copied from Cao et al. (2019). We present results when training for 90/200 epochs.   
+
+<table><tr><td>Method</td><td>ResNet-50</td><td>ResNet-152</td></tr><tr><td>CB-Focalt</td><td>61.1</td><td></td></tr><tr><td>LDAMt</td><td>64.6</td><td></td></tr><tr><td>LDAM+DRW†</td><td>68.0</td><td>=</td></tr><tr><td>Joint</td><td>61.7/65.8</td><td>65.0/69.0</td></tr><tr><td>NCM</td><td>58.2/63.1</td><td>61.9/67.3</td></tr><tr><td>cRT</td><td>65.2/67.6</td><td>68.5/71.2</td></tr><tr><td>T-normalized</td><td>65.6/69.3</td><td>68.8/72.5</td></tr><tr><td>LWS</td><td>65.9/69.5</td><td>69.1/72.1</td></tr></table>
+
+Table 4: Results on Places-LT, starting from an ImageNet pre-trained ResNet152. $^ \dagger$ denotes results directly copied from Liu et al. (2019).   
+
+<table><tr><td>Method</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>Lifted Losst</td><td>41.1</td><td>35.4</td><td>24.0</td><td>35.2</td></tr><tr><td>Focal Losst</td><td>41.1</td><td>34.8</td><td>22.4</td><td>34.6</td></tr><tr><td>Range Losst</td><td>41.1</td><td>35.4</td><td>23.2</td><td>35.1</td></tr><tr><td>FSLwFt</td><td>43.9</td><td>29.9</td><td>29.5</td><td>34.9</td></tr><tr><td>OLTR†</td><td>44.7</td><td>37.0</td><td>25.3</td><td>35.9</td></tr><tr><td>Joint</td><td>45.7</td><td>27.3</td><td>8.2</td><td>30.2</td></tr><tr><td>NCM</td><td>40.4</td><td>37.1</td><td>27.3</td><td>36.4</td></tr><tr><td>cRT</td><td>42.0</td><td>37.6</td><td>24.9</td><td>36.7</td></tr><tr><td>T-normalized</td><td>37.8</td><td>40.7</td><td>31.8</td><td>37.9</td></tr><tr><td>LWS</td><td>40.6</td><td>39.1</td><td>28.6</td><td>37.6</td></tr></table>
+
+# 6 CONCLUSIONS
+
+In this work, we explore a number of learning schemes for long-tailed recognition and compare jointly learning the representation and classifier to a number of straightforward decoupled methods. Through an extensive study we find that although sampling strategies matter when jointly learning representation and classifiers, instance-balanced sampling gives more generalizable representations that can achieve state-of-the-art performance after properly re-balancing the classifiers and without need of carefully designed losses or memory units. We set new state-of-the-art performance for three long-tailed benchmarks and believe that our findings not only contribute to a deeper understanding of the long-tailed recognition task, but can offer inspiration for future work.
+
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+
+# A LOSS RE-WEIGHTING STRATEGIES
+
+Here, we summarize some of the best performing loss re-weighting methods that we compare against in Section 5. Introduced in the context of object detection where imbalance exists in most common benchmarks, the Focal loss (Lin et al., 2017) aims to balance the sample-wise classification loss for model training by down-weighing easy samples. To this end, given a probability prediction $h _ { i }$ for the sample $x _ { i }$ over its true category $y _ { i }$ , it adds a re-weighting factor $( 1 - h _ { i } ) ^ { \gamma }$ with $\gamma > 0$ into the standard cross-entropy loss $\mathcal { L } _ { C E }$ :
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { f o c a l } } : = ( 1 - h _ { i } ) ^ { \gamma } \mathcal { L } _ { C E } = - ( 1 - h _ { i } ) ^ { \gamma } \log ( h _ { i } ) . } \end{array}
+$$
+
+For easy samples (which may dominate the training samples) with large predicted probability $h _ { i }$ for their true categories, their corresponding cross entropy loss will be down weighted. Recently, Cui et al. (2019) presented a class balanced variant of the focal loss and applied it to long-tailed recognition. They modulated the Focal loss for a sample from class $j$ with a balance-aware coefficient equal to $( 1 - \beta ) / ( 1 - \beta _ { j } ^ { n } )$ . Very recently, Cao et al. (2019) proposed a label-distribution-aware margin (LDAM) loss that encourages few-shot classes to have larger margins, and their final loss is formulated as a cross-entropy loss with enforced margins:
+
+$$
+\mathcal { L } _ { \mathrm { L D A M } } : = - \log \frac { e ^ { \hat { y } _ { j } - \Delta _ { j } } } { e ^ { \hat { y } _ { j } - \Delta _ { j } } + \sum _ { c } \neq j e ^ { \hat { y } _ { c } - \Delta _ { c } } } ,
+$$
+
+$\hat { y }$ are the logits and $\Delta _ { j }$ is a class-aware margin, inversely proportional to $n _ { j } ^ { 1 / 4 }$
+
+# B FURTHER ANALYSIS AND RESULTS
+
+# B.1 SAMPLING STRATEGIES
+
+In Figure 3 we visualize the sampling weights for the four sampling strategies we explore. In Table 5 we present accuracy on ImageNet-LT for “all” classes when training the representation and classifier jointly. It is clear that better sampling strategies help when jointly training the classifier with the representations/backbone architecture.
+
+![](images/2df5e5b8d75d4fc7d7d9861d4e31623d0cfec054cfc9448d1bce13462df50e53.jpg)  
+Figure 3: Sampling weights $p _ { j }$ for ImageNet-LT. Classes are ordered with decreasing $n _ { j }$ on the $\mathbf { X }$ -axis. Left: instance-balanced, class-balanced and square-root sampling. Right: Progressivelybalanced sampling; as epochs progress, sampling goes from instance-balanced to class-balanced sampling.
+
+# B.2 CLASSIFIER DECISION BOUNDARIES FOR $\tau$ -NORMALIZED AND NCM
+
+In Figure 4 we illustrate the classifier decision boundaries before/after normalization with Eq.(3), as well as when using cosine distance. Balancing the norms also leads to more balanced decision boundaries, allowing the classifiers for few-shot classes to occupy more space.
+
+Table 5: Accuracy on ImageNet-LT when jointly learning the representation and classifier using different sampling strategies. Results in this Table are a subset of the results presented in Figure 1.   
+
+<table><tr><td>Sampling</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>Instance-balanced</td><td>65.9</td><td>37.5</td><td>7.7</td><td>44.4</td></tr><tr><td>Class-balanced</td><td>61.8</td><td>40.1</td><td>15.5</td><td>45.1</td></tr><tr><td>Square-root</td><td>64.3</td><td>41.2</td><td>17.0</td><td>46.8</td></tr><tr><td>Progressively-balanced</td><td>61.9</td><td>43.2</td><td>19.4</td><td>47.2</td></tr></table>
+
+![](images/603a6c1584ec7c1e20351777b1e7add16a47d9bb2331054d9d7313fd06cb739b.jpg)  
+Figure 4: Illustrations on different classifiers and their corresponding decision boundaries, where $w _ { i }$ and $w _ { j }$ denote the classification weight for class $i$ and $j$ respectively, $\mathcal { C } _ { i }$ is the classification cone belongs to class $i$ in the feature space, $m _ { i }$ is the feature mean for class $i$ . From left to right: $\tau$ -normalized classifiers with $\tau  0$ : the classifier with larger weights have wider decision boundaries; $\tau$ -normalized classifiers with $\tau  1$ : the decision boundaries are more balanced for different classes; NCM with cosine-similarity whose decision boundary is independent of the classifier weights; NCM with Euclidean-similarity whose decision boundaries partition the feature space into Voronoi cells.
+
+# B.3 CLASSIFIER LEARNING COMPARISON TABLE
+
+Table 6 presents some comparative analysis for the four different ways of learning the classifier that are presented in Section 4.
+
+# B.4 VARYING THE BACKBONE ARCHITECTURE SIZE
+
+ImageNet-LT. In Figure 5 we compare the performance of different backbone architecture sizes (model capacity) under different methods, including of different methods 1) OLTR (Liu et al., 2019) using the authors’ codebase settings (OLTR\*); 2) OLTR using the representation learning stage detailed in Section 5 $( \mathrm { O L T R ^ { * * } } )$ ; 3) cRT with the memory module from Liu et al. (2019) while training the classifier; 4) cRT; and 5) $\tau$ -normalized. we see that a) the authors’ implementation of OLTR over-fits for larger models, b) overfitting can be alleviated with our training setup (different training and LR schedules) c) adding the memory unit when re-training the classifier doesn’t increase performance. Additional results of Table 2 are given in Table 7.
+
+iNaturalist 2018. In Table 8 we present an extended version of the results of Table 3. We show results per split as well as results with a ResNet-101 backbone. As we see from the table and mentioned in Section 5, training only for 90 epochs gives sub-optimal representations, while both large models and longer training result in much higher accuracy on this challenging, large-scale task. What is even more interesting, we see performance across the many-, medium- and few-shot splits being approximately equal after re-balancing the classifier, with only a small advantage for the many-shot classes.
+
+<table><tr><td></td><td>Joint</td><td>NCM</td><td>cRT</td><td>T-normalized</td><td>LWS</td></tr><tr><td>Decoupled from repr.</td><td>×</td><td>√</td><td>√</td><td>√</td><td>√</td></tr><tr><td>No extra training</td><td>√</td><td>√</td><td>×</td><td>√</td><td>X</td></tr><tr><td>No extra hyper-parameters</td><td>√</td><td>√</td><td>√</td><td>X</td><td>√</td></tr><tr><td>Performance</td><td>★</td><td></td><td>***</td><td>***</td><td>★**</td></tr></table>
+
+Table 6: Comparative analysis for different ways of learning the classifier for long-tail recognition.
+
+![](images/9f01aa1136750a64bde842797fac9386ba8a218ed98bc838f625acdb1cd5ec04.jpg)  
+Figure 5: Accuracy on ImageNet-LT for different backbones
+
+Table 7: Comprehensive results on ImageNet-LT with different backbone networks {ResNet, ResNeXt}-{50, 101,152}   
+
+<table><tr><td rowspan="2">Backbone</td><td rowspan="2">Method</td><td colspan="4">ResNet</td><td colspan="4">ResNeXt</td></tr><tr><td>Many</td><td>Medium</td><td>Few</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td rowspan="5">*-50</td><td>Joint</td><td>64.0</td><td>33.8</td><td>5.8</td><td>41.6</td><td>65.9</td><td>37.5</td><td>7.7</td><td>44.4</td></tr><tr><td>NCM</td><td>53.1</td><td>42.3</td><td>26.5</td><td>44.3</td><td>56.6</td><td>45.3</td><td>28.1</td><td>47.3</td></tr><tr><td>cRT</td><td>58.8</td><td>44.0</td><td>26.1</td><td>47.3</td><td>61.8</td><td>46.2</td><td>27.4</td><td>49.6</td></tr><tr><td>T-normalized</td><td>56.6</td><td>44.2</td><td>27.4</td><td>46.7</td><td>59.1</td><td>46.9</td><td>30.7</td><td>49.4</td></tr><tr><td>LWS</td><td>57.1</td><td>45.2</td><td>29.3</td><td>47.7</td><td>60.2</td><td>47.2</td><td>30.3</td><td>49.9</td></tr><tr><td rowspan="5">*-101</td><td>Joint</td><td>66.6</td><td>36.8</td><td>7.1</td><td>44.2</td><td>66.2</td><td>37.8</td><td>8.6</td><td>44.8</td></tr><tr><td>NCM</td><td>56.8</td><td>45.1</td><td>28.8</td><td>47.4</td><td>57.2</td><td>45.5</td><td>29.5</td><td>47.8</td></tr><tr><td>cRT</td><td>61.6</td><td>46.5</td><td>28.0</td><td>49.8</td><td>61.7</td><td>46.0</td><td>27.0</td><td>49.4</td></tr><tr><td>T-normalized</td><td>59.4</td><td>47.0</td><td>30.6</td><td>49.6</td><td>59.1</td><td>47.0</td><td>31.7</td><td>49.6</td></tr><tr><td>LWS</td><td>60.1</td><td>47.6</td><td>31.2</td><td>50.2</td><td>60.5</td><td>47.2</td><td>31.2</td><td>50.1</td></tr><tr><td rowspan="5">*-152</td><td>Joint</td><td>66.9</td><td>27.7</td><td>7.7</td><td>44.9</td><td>69.1</td><td>41.4</td><td>10.4</td><td>47.8</td></tr><tr><td>NCM</td><td>56.9</td><td>45.6</td><td>29.9</td><td>47.8</td><td>60.3</td><td>49.0</td><td>33.6</td><td>51.3</td></tr><tr><td>cRT</td><td>61.8</td><td>46.8</td><td>28.4</td><td>50.1</td><td>64.7</td><td>49.1</td><td>29.4</td><td>52.4</td></tr><tr><td>T-normalized</td><td>59.6</td><td>47.5</td><td>32.2</td><td>50.1</td><td>62.2</td><td>50.1</td><td>35.8</td><td>52.8</td></tr><tr><td>LWS</td><td>60.6</td><td>47.8</td><td>31.4</td><td>50.5</td><td>63.5</td><td>50.4</td><td>34.2</td><td>53.3</td></tr></table>
+
+# B.5 ON THE EXPLORATION OF DETERMINING $\tau$
+
+The current tau-normalization strategy does require a validation set to choose tau, which could be a disadvantage depending on the practical scenario. Can we do better?
+
+Finding $\tau$ value on training set. We also attempted to select $\tau$ directly on the training dataset.   
+Surprisingly, final performance on testing set is very similar, with $\tau$ selected using training set only.
+
+We achieve this goal by simulating a balanced testing distribution from the training set. We first feed the whole training set through the network to get the top-1 accuracy for each of the classes. Then, we average the class-specific accuracies and use the averaged accuracy as the metric to determine the tau value. As shown in Table 9, we compare the $\tau$ found on training set and validation set for all three datasets. We can see that both the vale of $\tau$ and the overall performances are very close to each other, which demonstrates the effectiveness of searching for $\tau$ on training set. This strategy offers a practical way to find $\tau$ even when validation set is not available.
+
+Learning $\tau$ value on training set. We further investigate if we can automatically learn the $\tau$ value instead of grid search. To this end, following cRT, we set $\tau$ as a learnable parameter and learn it on the training set with balanced sampling, while keeping all the other parameters fixed (including both the backbone network and classifier). Also, we compare the learned $\tau$ value and the corresponding results in the Table 9 (denoted by “learn” $= \checkmark$ ). This further reduces the manual effort of searching best $\tau$ values and make the strategy more accessible for practical usage.
+
+Table 8: Comprehensive results on iNaturalist 2018 with different backbone networks (ResNet-50, ResNet-101 & ResNet-152) and different training epochs (90 & 200)   
+
+<table><tr><td rowspan="2">Backbone</td><td rowspan="2">Method</td><td colspan="4">90 Epochs</td><td colspan="4">200 Epochs</td></tr><tr><td>Many</td><td>Medium</td><td>Few</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td rowspan="5">ResNet-50</td><td>Joint</td><td>72.2</td><td>63.0</td><td>57.2</td><td>61.7</td><td>75.7</td><td>66.9</td><td>61.7</td><td>65.8</td></tr><tr><td>NCM</td><td>55.5</td><td>57.9</td><td>59.3</td><td>58.2</td><td>61.0</td><td>63.5</td><td>63.3</td><td>63.1</td></tr><tr><td>cRT</td><td>69.0</td><td>66.0</td><td>63.2</td><td>65.2</td><td>73.2</td><td>68.8</td><td>66.1</td><td>68.2</td></tr><tr><td>T-normalized</td><td>65.6</td><td>65.3</td><td>65.9</td><td>65.6</td><td>71.1</td><td>68.9</td><td>69.3</td><td>69.3</td></tr><tr><td>LWS</td><td>65.0</td><td>66.3</td><td>65.5</td><td>65.9</td><td>71.0</td><td>69.8</td><td>68.8</td><td>69.5</td></tr><tr><td rowspan="5">ResNet-101</td><td>Joint</td><td>75.9</td><td>66.0</td><td>59.9</td><td>64.6</td><td>75.5</td><td>68.9</td><td>63.2</td><td>67.3</td></tr><tr><td>NCM</td><td>58.6</td><td>61.9</td><td>61.8</td><td>61.5</td><td>63.7</td><td>65.7</td><td>65.3</td><td>65.3</td></tr><tr><td>cRT</td><td>73.0</td><td>68.9</td><td>65.7</td><td>68.1</td><td>73.9</td><td>70.4</td><td>67.8</td><td>69.7</td></tr><tr><td>T-normalized</td><td>69.7</td><td>68.3</td><td>68.3</td><td>68.5</td><td>68.6</td><td>70.6</td><td>72.2</td><td>71.0</td></tr><tr><td>LWS</td><td>69.6</td><td>69.1</td><td>67.9</td><td>68.7</td><td>71.5</td><td>71.3</td><td>69.7</td><td>70.7</td></tr><tr><td rowspan="5">ResNet-152</td><td>Joint</td><td>75.2</td><td>66.3</td><td>60.7</td><td>65.0</td><td>78.2</td><td>70.6</td><td>64.7</td><td>69.0</td></tr><tr><td>NCM</td><td>59.3</td><td>61.9</td><td>62.6</td><td>61.9</td><td>66.3</td><td>67.5</td><td>67.2</td><td>67.3</td></tr><tr><td>cRT</td><td>73.6</td><td>69.3</td><td>66.3</td><td>68.5</td><td>75.9</td><td>71.9</td><td>69.1</td><td>71.2</td></tr><tr><td>T-normalized</td><td>69.8</td><td>68.5</td><td>68.9</td><td>68.8</td><td>74.3</td><td>72.3</td><td>72.2</td><td>72.5</td></tr><tr><td>LWS</td><td>69.4</td><td>69.5</td><td>68.6</td><td>69.1</td><td>74.3</td><td>72.4</td><td>71.2</td><td>72.1</td></tr></table>
+
+Table 9: Determining $\tau$ on the training set   
+
+<table><tr><td>Dataset</td><td>split</td><td>learn</td><td>T</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td rowspan="3">ImageNet-LT</td><td>val</td><td>×</td><td>0.7</td><td>59.1</td><td>46.9</td><td>30.7</td><td>49.4</td></tr><tr><td>train</td><td>X</td><td>0.7</td><td>59.1</td><td>46.9</td><td>30.7</td><td>49.4</td></tr><tr><td>train</td><td>√</td><td>0.6968</td><td>59.2</td><td>46.9</td><td>30.6</td><td>49.4</td></tr><tr><td rowspan="3">iNaturalist</td><td>val</td><td>X</td><td>0.3</td><td>65.6</td><td>65.3</td><td>65.9</td><td>65.6</td></tr><tr><td>train</td><td>×</td><td>0.2</td><td>69.0</td><td>65.2</td><td>63.6</td><td>65.0</td></tr><tr><td>train</td><td>√</td><td>0.3146</td><td>65.1</td><td>65.2</td><td>66.1</td><td>65.6</td></tr><tr><td rowspan="3">Places-LT</td><td>val</td><td>X</td><td>0.8</td><td>37.8</td><td>40.7</td><td>31.8</td><td>37.9</td></tr><tr><td>train</td><td>×</td><td>0.6</td><td>41.4</td><td>39.3</td><td>25.3</td><td>37.4</td></tr><tr><td>train</td><td>√</td><td>0.5246</td><td>42.6</td><td>38.3</td><td>22.7</td><td>36.8</td></tr></table>
+
+# B.6 COMPARING MLP CLASSFIIER WITH LINEAR CLASSIFIER
+
+We experimented with MLPs with different layers (2 or 3) and different number of hidden neurons (2048 or 512). We use ReLU as activation function, set the batch size to be 512, and train the MLP using balanced sampling on fixed representation for 10 epochs with a cosine learning rate schedule, which gradually decrease the learning rate to zero. We conducted experiments on two datasets.
+
+On ImageNet-LT, we use ResNeXt50 as the backbone network. The results are summarized in Table 10. We can see that when the MLP going deeper, the performance are getting worse. It probably means the backbone network is enough to learn discriminative representation.
+
+Table 10: MLP classifier on ImageNet-LT   
+
+<table><tr><td rowspan="2">Layers</td><td colspan="4">hid-dim : 2048</td><td colspan="4">hid-dim : 512</td></tr><tr><td>Many</td><td>Medium</td><td>Few</td><td>All</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>1</td><td>61.7</td><td>45.9</td><td>26.8</td><td>49.4</td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td>60.8</td><td>44.4</td><td>24.5</td><td>48.0</td><td>59.9</td><td>44.3</td><td>25.1</td><td>47.7</td></tr><tr><td>3</td><td>60.3</td><td>44.3</td><td>23.7</td><td>47.7</td><td>59.3</td><td>43.7</td><td>23.9</td><td>47.0</td></tr></table>
+
+For iNaturalist, we use the representation from a ResNet50 model trained for 200 epochs. We only consider a hidden dimension of 2048, as this dataset contains much more classes. The results are shown in Table 11, and show that performance drop is even more severe when a deeper classifier is used.
+
+Table 11: MLP classifier on iNaturalst   
+
+<table><tr><td>Layers|</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>1</td><td>73.2</td><td>68.8</td><td>66.1</td><td>68.2</td></tr><tr><td>2</td><td>60.4</td><td>61.8</td><td>60.6</td><td>61.2</td></tr><tr><td>3</td><td>68.5</td><td>63.6</td><td>60.1</td><td>62.8</td></tr></table>
+
+# B.7 COSINE SIMILARITY FOR CLASSIFICATION
+
+We tried to replace the linear classifier with a cosine similarity classifier with (denoted by “cos”) and without (denoted by ”cos(noRelu)”) the last ReLU activation function, following Gidaris & Komodakis (2018). We summarize the results in Table 12, which show that they are comparable to each other.
+
+Table 12: Cosine similarity Classifier   
+
+<table><tr><td>Classifier</td><td>Many</td><td>Medium</td><td>Few</td><td>All</td></tr><tr><td>NCM</td><td>56.6</td><td>45.3</td><td>28.1</td><td>47.3</td></tr><tr><td>cRT</td><td>61.7</td><td>45.9</td><td>26.8</td><td>49.4</td></tr><tr><td>T-normalized</td><td>59.1</td><td>46.9</td><td>30.7</td><td>49.4</td></tr><tr><td>cos</td><td>60.4</td><td>46.8</td><td>29.3</td><td>49.7</td></tr><tr><td>cos(noRelu)</td><td>60.7</td><td>46.9</td><td>28.0</td><td>49.6</td></tr></table>