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+# A NEW METHOD OF REGION EMBEDDING FOR TEXT CLASSIFICATION
+
+Chao $\mathbf { Q } \mathbf { i } \mathbf { a } \mathbf { o } ^ { * \ddagger }$ , Bo Huang†‡, Guocheng $\mathbf { N i u } ^ { \ddag }$ , Daren $\mathbf { L i } ^ { \dagger }$ , Daxiang $\mathbf { D o n g ^ { \ddagger \ S } }$ , Wei $\mathbf { H e } ^ { \ddagger }$ , Dianhai $\mathbf { Y } \mathbf { u } ^ { \ddag \ S }$ , Hua $\mathbf { W _ { u } } ^ { \ddagger \ S }$
+
+‡ Baidu Inc., Beijing, China   
+§ National Engineering Laboratory of Deep Learning Technology and Application, China   
+{qiaochao, huangbo02, niuguocheng, lidaren,   
+daxiangdong, hewei06, yudianhai, wu hua}@baidu.com
+
+# ABSTRACT
+
+To represent a text as a bag of properly identified “phrases” and use the representation for processing the text is proved to be useful. The key question here is how to identify the phrases and represent them. The traditional method of utilizing n-grams can be regarded as an approximation of the approach. Such a method can suffer from data sparsity, however, particularly when the length of n-gram is large. In this paper, we propose a new method of learning and utilizing task-specific distributed representations of n-grams, referred to as “region embeddings”. Without loss of generality we address text classification. We specifically propose two models for region embeddings. In our models, the representation of a word has two parts, the embedding of the word itself, and a weighting matrix to interact with the local context, referred to as local context unit. The region embeddings are learned and used in the classification task, as parameters of the neural network classifier. Experimental results show that our proposed method outperforms existing methods in text classification on several benchmark datasets. The results also indicate that our method can indeed capture the salient phrasal expressions in the texts.
+
+# 1 INTRODUCTION
+
+Text classification is an important task for many applications, including topic categorization, search query classification, and sentiment analysis, which has been studied for years. A simple yet effective approach for text classification is to represent documents as bag-of-words, and train a classifier on the basis of the representations using methods such as logistic regression, support vector machines (Joachims, 1998; Fan et al., 2008), and naive Bayes (McCallum et al., 1998). Although bag-of-words methods are effective and efficient, they also have limitations. The representations do not take into account the word order information which has been proved to be useful at least in some applications such as sentiment analysis (Pang et al., 2002).
+
+To make effective use of word order information for text classification, people have traditionally exploited n-grams, i.e., short sequences of words in the texts. Previous work shows that the use of n-grams is effective in the text classification task (Pang et al., 2002; Wang & Manning, 2012; Joulin et al., 2016). Although n-grams are very useful, they have certain limitations. 1) The number of n-grams increases exponentially when the length of n-gram $n$ increases. This makes it difficult to exploit large n-grams (e.g., $n > 4$ ). 2) Since the number of parameters in an n-gram model is very large, the estimation of the parameters usually suffers from the data sparsity problem.
+
+Recently, the method of FastText has been proposed (Joulin et al., 2016), which can learn and use distributed embeddings of n-grams. More specifically, the embedding of an n-gram is defined as a low-dimensional vector representation of the n-gram. Note that the n-grams in a vocabulary can also be represented as one-hot vectors Wang & Manning (2012).
+
+In this paper, we propose to learn embeddings of n-grams for a specific task (e.g., classification), which are more compact and thus easy to obtain. We call the embeddings region embeddings, following the work in Johnson & Zhang (2015). Our method significantly differs from their method, however, in the sense that the region embeddings in our method are task-dependent and acquired from supervised learning, while those in their method are task-independent and acquired from unsupervised learning. Our method is also largely different from FastText, as it learns richer models for region embeddings.
+
+Intuitively, the meaning of a word is defined by the meaning of itself as well as the meanings of words in the surrounding context. The extended embedding of a word in an n-gram thus consists of two parts, the embedding of the word itself and a matrix to interact with the local context, named “local context unit”. The embedding of a word is a column vector, and the local context unit of a word is a matrix in which the columns are used to interact with words in the local context. The region embedding of an n-gram is then constructed by the extended embeddings of all words in the n-gram. In this paper, we introduce two models for region embeddings.
+
+For the text classification task, a document is viewed as a bag of region embeddings, and the bag of region embeddings is fed into a classifier. The parameters of the local context units and word embeddings are trained together with the parameters of the classifier which is a fully connected neural network. Our models achieve better results than the state-of-the-art methods on several benchmark datasets of text classification. Experiments show that our proposed models can really capture important information for the task.
+
+# 2 RELATED WORK
+
+Text classification has been studied for years, traditional approaches focused on feature engineering and using different types of machine learning algorithms. For feature engineering, bag-of-words features are efficient and popular. In addition, the hand-crafted n-grams or phrases are added to make use of word order in text data, which has been shown effective on Wang & Manning (2012). For machine learning algorithms, linear classifiers are widely used, such as naive bayes (McCallum et al., 1998), logistic regression and support vector machines (Joachims, 1998; Fan et al., 2008). However, these models commonly suffer the data sparsity problem.
+
+Recently, several neural models have been proposed, the pre-trained word embeddings of word2vec (Mikolov et al., 2013) have been widely used as inputs to deep neural models such as recursive tensor networks (Socher et al., 2013). On the other hand, some simple and efficient models which can directly learn task specific word embeddings or fine-tune on pre-trained word embeddings have been proposed recently, such as Deep Averaging Networks (Iyyer et al., 2015), FastText (Joulin et al., 2016). Several neural models have been proposed to make use of word order information, most models are based on convolutional neural network (CNN) (Kim, 2014; Johnson & Zhang, 2014; Zhang et al., 2015) and recurrent neural network (RNN) (Tang et al., 2015; Lai et al., 2015; Yogatama et al., 2017). More recently, the Transformer (Vaswani et al., 2017), a sequence transduction model based solely on attention mechanisms has been proposed. Although Transformer was not designed for the text classification task, it has similarities with our work. In the rest of this section, we will briefly introduce FastText, CNN and Transformer, which are the most relevant to our work.
+
+FastText FastText averages the word embeddings to represent a document, and uses a full connected linear layer as the classifier. The word embeddings are trained for each task specifically. To utilize the local word order information of small regions, FastText uses hand-crafted n-grams as features in addition to single words. With the simple architecture, FastText has been proved to be effective and highly efficient on text classification tasks. Similarly, our models use bag of region embeddings to represent a document, and use the same linear classifier. Differently, our models directly learn the semantics of regions based on word sequence, hand-crafted features are not required.
+
+CNN CNN is a feed-forward network with convolutional layers interleaved with pooling layers, which are originally used for image processing tasks. For natural language processing, words are commonly converted to vectors. CNN directly applies convolutional layer on word vectors, both word vectors and the shared (word independent) kernels are the parameters of CNN, which can be learned to capture the predictive structures of small regions. The essence of CNN is to learn embeddings for small fixed size regions, each kernel of the convolutional layer tries to capture a specific semantic or structural feature. Our purpose is similar with CNN, which tries to learn task specific representations of regions. Unlike CNN, we apply local context units on word vectors, which are word dependent, moreover, the convolution kernels extract the predictive features by applying convolution operation on word sequences, while we use local context units as distinct linear projection functions on context words in corresponding relative positions to get region representations.
+
+Transformer Vaswani et al. (2017) proposed a sequence transduction model, the Transformer, based solely on attention mechanisms. Both Transformer and our method can capture word order information without any CNN or RNN component, and the scalar form of context units (introduced in our ablation experiments) can be regarded as a kind of local attention. There are also some differences here: the motivation we proposed local context units is to address word specific influence between word and its context, while Vaswani et al. (2017) has proposed a parallelable sequence transduction framework based entirely on attention; To utilize position information, in our method, words are interacted with context words at different relative positions by corresponding columns in their context units, while Transformer use fixed sin and cos function based position encoding.
+
+# 3 METHOD
+
+In this paper, we focus on learning the representations of small text regions which preserve the local internal structural information for text classification. The regions in a document can be considered as fixed length contiguous subsequences of the document. More specifically, with $w _ { i }$ standing for the $i$ -th(starting from 0) word of the document, we use region $( i , c )$ to denote the $2 \times c + 1$ length region with middle word $w _ { i }$ . For instance, given a sentence such as The food is not very good in this hotel, region $( 3 , 2 )$ means the subsequence food is not very good.
+
+In this work, we use the interactions between words and their local context based on word embeddings as well as the local context units to produce region embeddings. In the rest of this section, we will introduce the local context units firstly, and two architectures to generate the region embeddings through local context units will be introduced, finally we will introduce how we use the region embeddings on text classification.
+
+![](images/cbb613170613bb105975169510719e7d281fcb6e107e0f198c3343b5e22f32c7.jpg)  
+Figure 1: Architectures of region embedding using local context units in different perspectives
+
+# 3.1 LOCAL CONTEXT UNIT
+
+In natural language processing, words are commonly converted to low dimensional vectors(word embeddings) as the inputs to neural networks. More formally, the embedding ${ \bf e } _ { w }$ of word $w$ is represented by a column in a matrix $\mathbf { E } \in \mathcal { R } ^ { h \times v }$ with a look up layer, where $v$ is the size of the vocabulary, $h$ is the embedding size.
+
+To utilize the information of words’ relative positions and local context, we learn a local context unit for each word in addition to the word embedding, and both the unit and word embedding are learned as model parameters. Formally, we define the local context unit ${ \bf K } _ { w _ { i } } \in \mathcal { R } ^ { h \times ( 2 \times c + \bar { 1 } ) }$ of $w _ { i }$ as a matrix which can be looked up in the tensor $\mathbf { U } \in \mathcal { R } ^ { h \times ( 2 \times c + 1 ) \times v }$ by $w _ { i }$ ’s index in the vocabulary.
+
+Each column in ${ \bf K } _ { w _ { i } }$ can be used to interact with the context word in corresponding relative position of $w _ { i }$ . In fact, the columns of a unit matrix can be regarded as distinctive linear projection functions on the embeddings of words in the local context. The parameters of these projection functions(i.e., columns of each unit matrix) can be learned to capture the semantic and syntactic influence of the word to its context. Word embeddings are used as inputs to the projection functions, and we call the outputs projected word embeddings.
+
+Formally, let $\mathbf { p } _ { w _ { i + t } } ^ { i }$ be the projected word embedding of $w _ { i + t }$ in $i$ -th word’s view, and ${ \bf K } _ { w _ { i } , t }$ be the $( c + t )$ -th column in ${ \bf K } _ { w _ { i } }$ $\scriptstyle - c < = t < = c )$ , given the unit ${ \bf K } _ { w _ { i } }$ of $w _ { i }$ and the embedding $\mathbf { e } _ { w _ { i + t } }$ of $w _ { i + t }$ , we use an element-wise multiplication(denoted by $\odot$ ) to compute $\mathbf { p } _ { w _ { i + t } } ^ { i }$ :
+
+$$
+\mathbf { p } _ { w _ { i + t } } ^ { i } = \mathbf { K } _ { w _ { i } , t } \odot \mathbf { e } _ { w _ { i + t } }
+$$
+
+For a context word in a particular relative position of $w _ { i }$ , there is a corresponding linear projection function(a particular column of ${ \bf K } _ { w _ { i } }$ ), thus our proposed local context units can utilize the local ordered word information in a novel way. Note that the middle column ${ \bf K } _ { w _ { i } , 0 }$ of ${ \bf K } _ { w _ { i } }$ can be regarded as a linear projection function on ${ \bf e } _ { w _ { i } }$ itself, which transforms ${ \bf e } _ { w _ { i } }$ to the same space as other projected embeddings.
+
+# 3.2 WORD-CONTEXT REGION EMBEDDING
+
+We proposed two architectures to perform the region embedding from different perspectives. We consider the semantics of a given region is derived from the mutual influences of the words in this region. In this paper, the regions can be regarded as snapshots of a window sliding on a document, whose middle words are contiguous, hence we can compose the semantics of a give region only by the middle word’s influences on the context words, or the context words’ influences on the middle word.
+
+In the first proposed architecture, we focus on addressing the middle word’s influences on the context words. For example, in the sentence The food is not very good in this hotel, the occurrence of word not might bring a semantic reversal to the local region.
+
+We use the local context unit of the middle word and the original word embeddings in a region to perform the projected embeddings in a word-to-context view, where the projected embeddings can reflect the middle word’s influences on the context words. Once the projected embeddings are obtained, a max pooling operation is applied to extract the most predictive features in the region. The output of the max pooling operation can be regarded as a task related region embedding in a word-to-context view, i.e. Word-Context region embedding.
+
+Formally, we use the context unit ${ \bf K } _ { w _ { i } }$ of middle word $w _ { i }$ and embeddings of all words in a region region $( i , c )$ to compute the projected embedding matrix by equation (1), then the Word-Context region embedding $\mathbf { r } _ { ( i , c ) }$ can be obtained through a max pooling operation on the projected embedding matrix:
+
+$$
+\mathbf { r } _ { ( i , c ) } = m a x \big ( \big [ \mathbf { p } _ { w _ { i - c } } ^ { i } \quad \mathbf { p } _ { w _ { i - c + 1 } } ^ { i } \quad . . . \quad \mathbf { p } _ { w _ { i + c - 1 } } ^ { i } \quad \mathbf { p } _ { w _ { i + c } } ^ { i } \big ] \big )
+$$
+
+where $m a x$ standing for the max pooling operation on the column dimension of the input matrix. Finally, we get $\mathbf { r } _ { ( i , c ) }$ as a vector representation of $r e g i o n ( i , c )$ with dimension $h$ . Figure 1a shows the details of the first model architecture.
+
+For instance, in the sentence The food is not very good in this hotel, the projected word embeddings in the region $( 3 , 2 )$ are composed by the element-wise multiplications between columns in the local
+
+context unit of not and word embeddings of food, is, not, very and good. The embedding $\mathbf { r } _ { 3 , 2 }$ of region $( 3 , 2 )$ can be obtained by max pooling on the projected word embedding matrix.
+
+# 3.3 CONTEXT-WORD REGION EMBEDDING
+
+The second architecture goes as a different view, which addresses the local context words’ influences on the middle word in the region, and we call this Context-Word region embedding. Similarly, for a $r e g i o n ( i , c )$ , the projected embeddings are computed by the original word embedding of the middle word and the context units of all words in the region, then the Context-Word region embedding can be obtained by a max pooling operation through the column dimension of the projected embedding matrix:
+
+$$
+\mathbf { r } _ { ( i , c ) } = m a x \big ( \big [ \mathbf { p } _ { w _ { i } } ^ { i - c } \quad \mathbf { p } _ { w _ { i } } ^ { i - c + 1 } \quad . . . \quad \mathbf { p } _ { w _ { i } } ^ { i + c - 1 } \quad \mathbf { p } _ { w _ { i } } ^ { i + c } \big ] \big )
+$$
+
+Figure 1b shows the details of the second model architecture. our two models take different ways to produce the projected word embeddings, the Word-Context model uses context units of middle words and word embeddings of context words, while the Context-Word model uses context units of context words and word embeddings of the middle word.
+
+# 3.4 REGION EMBEDDING FOR TEXT CLASSIFICATION
+
+For text classification, documents are usually variable-sized, which need to be represented as fixed size vectors. In order to show the effectiveness of our proposed region embedding models, we just sum up the embeddings of all regions to represent a document, and feed it to an upper FullConnected layer for text classification task.
+
+Formally, the model can be represented as following:
+
+$$
+\mathrm { f } ( \mathbf { x } ; \mathbf { E } , \mathbf { U } , \mathbf { W } , \mathbf { b } ) = \mathbf { g } ( \mathbf { W } \sigma ( \sum _ { i = 0 } ^ { n } \mathbf { r } _ { ( i , c ) } ) + \mathbf { b } )
+$$
+
+where $\mathbf { x }$ denotes the input text sequence, W and b denote the weight matrix and bias of the fully connected layer respectively, $\mathbf { g }$ denotes the softmax function of the output layer, $\sigma$ denotes the softsign function and $n$ denotes the number of regions in a document, $\mathbf { r }$ is the region embedding which can be computed by the equation (2) or (3). E, U, W and b can be updated in the training period.
+
+# 4 EXPERIMENTS
+
+We report experiments with proposed models in comparison with previous models.
+
+# 4.1 DATASETS
+
+We use publicly available datasets from Zhang et al. (2015) to evaluate our models. There are in total 8 text classification datasets, corresponding to sentiment analysis, news classification, questionanswer, ontology extraction tasks, respectively. Table 1 shows the descriptive statistics of datasets used in our experiments. To guarantee comparable indications, same evaluation protocol of Zhang et al. (2015) is employed.
+
+# 4.2 BASELINES
+
+Our models are compared with several widely used supervised text classification models. We report the n-grams and TFIDF baselines from Zhang et al. (2015), as well as the character level convolutional model (char-CNN) of Zhang & LeCun (2015), the character based convolution recurrent network (char-CRNN) of Xiao & Cho (2016), the very deep convolutional network (VDCNN) of Conneau et al. (2016), the Discriminative LSTM (D-LSTM) of Yogatama et al. (2017) and the bigram FastText (bigram-FastText) of Joulin et al. (2016).
+
+Table 1: Statistics of Datasets   
+
+<table><tr><td>Dataset</td><td>Classes</td><td>Average Lengths</td><td>Train Samples</td><td>Test Samples</td><td>Tasks</td></tr><tr><td>Yelp Review Polarity Yelp Review Full</td><td>2</td><td>156</td><td>560,000</td><td>38,000</td><td rowspan="3">Sentiment Analysis</td></tr><tr><td></td><td>5</td><td>158</td><td>650,000</td><td>50,000</td></tr><tr><td>Amazon Review Polarity Amazon Review Full</td><td>2</td><td>91</td><td>3,000,000</td><td>650,000</td></tr><tr><td>AG&#x27;s News</td><td>5</td><td>93 44</td><td>3,600,000 120.000</td><td>400,000 7,600</td><td>News</td></tr><tr><td>Sogou News</td><td>4 5</td><td>579</td><td>450,000</td><td>60,000</td><td>Classification</td></tr><tr><td>Yahoo! Answers</td><td>10</td><td>112</td><td>1,400,000</td><td>60,000</td><td>Question Answer</td></tr><tr><td>DBPedia</td><td>14</td><td>55</td><td>560,000</td><td>70,000</td><td>Ontology Extraction</td></tr></table>
+
+# 4.3 IMPLEMENTATION DETAILS
+
+For data preprocessing, all the texts of datasets are tokenized by Stanford tokenizer and all words are converted to lower case. Words that appear only in one document are treated as out-of-vocabulary (OOV) items, and all stop words as well as symbols are kept. Additionally, length of $c$ padding are added to both the head and tail of each document.
+
+For our models, optimal hyperparameters are tuned with $10 \%$ of the training set on Yelp Review Full dataset, and identical hyperparameters are applied to all datasets: the dimension of word embedding is 128, the region size is 7 which means the shape of local context unit matrix of each word is $1 2 8 \times 7$ , the initial learning rate is set to $1 \times 1 0 ^ { - 4 }$ , and the batch size is 16. For optimization, the embeddings of words and the units are randomly initialized with Gaussian Distribution. Adam (Kingma & Ba, 2014) is used as the optimizer. We do not use any extra regularization methods, like L2 normalization or dropout. Algorithms are entirely implemented with TensorFlow and trained on NVIDIA Tesla P40 GPUs. The code 1 is publicly available on the Internet.
+
+# 4.4 RESULTS
+
+Table 2: Test Set Accuracy $[ \% ]$ Compared to other Methods on several Datasets   
+
+<table><tr><td>Model</td><td>Yelp P.</td><td>Yelp F.</td><td>Amz. P.</td><td>Amz. F.</td><td>AG</td><td>Sogou</td><td>Yah. A.</td><td>DBP</td></tr><tr><td>BoW</td><td>92.2</td><td>58.0</td><td>90.4</td><td>54.6</td><td>88.8</td><td>92.9</td><td>68.9</td><td>96.6</td></tr><tr><td>ngrams</td><td>95.6</td><td>56.3</td><td>92.0</td><td>54.3</td><td>92.0</td><td>97.1</td><td>68.5</td><td>98.6</td></tr><tr><td>ngrams TFIDF</td><td>95.4</td><td>54.8</td><td>91.5</td><td>52.4</td><td>92.4</td><td>97.2</td><td>68.5</td><td>98.7</td></tr><tr><td>char-CNN</td><td>94.7</td><td>62.0</td><td>94.5</td><td>59.6</td><td>87.2</td><td>95.1</td><td>71.2</td><td>98.3</td></tr><tr><td>char-CRNN</td><td>94.5</td><td>61.8</td><td>94.1</td><td>59.2</td><td>91.4</td><td>95.2</td><td>71.7</td><td>98.6</td></tr><tr><td>bigram-FastText</td><td>95.7</td><td>63.9</td><td>94.6</td><td>60.2</td><td>92.5</td><td>96.8</td><td>72.3</td><td>98.6</td></tr><tr><td>VDCNN</td><td>95.7</td><td>64.7</td><td>95.7</td><td>63.0</td><td>91.3</td><td>96.8</td><td>73.4</td><td>98.7</td></tr><tr><td>D-LSTM</td><td>92.6</td><td>59.6</td><td>1</td><td>-</td><td>92.1</td><td>94.9</td><td>73.7</td><td>98.7</td></tr><tr><td>W.C.region.emb</td><td>96.4</td><td>64.9</td><td>95.1</td><td>60.9</td><td>92.8</td><td>97.6</td><td>73.7</td><td>98.9</td></tr><tr><td>C.W.region.emb</td><td>96.2</td><td>64.5</td><td>95.3</td><td>60.8</td><td>92.8</td><td>97.3</td><td>73.4</td><td>98.9</td></tr></table>
+
+Table 2 is the summary of the experimental results. We use underscores to represent the best published results, and bold the best records. On six datasets of eight, our models beat or match the state-of-the-art with a performance gain highest to $0 . 7 \%$ . We beat all the previous models on all datasets except VDCNN, while the latter performs almost best on all classification tasks before. As a result, we slightly win VDCNN on six datasets and lost in two of Amazon datasets. Detailed experimental results including best performance epoch and training time for all listed datasets are reported in Appendix A.
+
+Furthermore, the upper layer structure of our models only uses a summing up operation, which is more concise and robust than any other deep or complex models. In fact, both of our two proposed models are effective against previous models.
+
+# 4.5 EXPLORATORY EXPERIMENTS
+
+In this subsection, we are going to do a set of exploratory experiments to study the effect of each component of our model. Typical cases will be analyzed to validate properties of various aspects of our models. Considering the limitation of paper space, we only analyzed the Word-Context region embedding model in our exploratory experiments.
+
+# 4.5.1 EFFECT OF REGION SIZE AND EMBEDDING SIZE
+
+Our method uses a fixed size of region as contextual information just like CNN. So the selection of region size really matters. A small region may lose some long distance patterns, whereas large regions will bring into more noises. Luckily, our models seem to be fairly insensitive towards kinds of datasets. Actually, we just use identical region size 7 for all datasets and it is able to outperform the best published results ever.
+
+Figure 2a describes the performance on Yelp Review Full with different region sizes, and when the size equals to 1, the result is quite close to unigram FastText(accuracy $6 0 . 7 \%$ ), but still gets a $0 . 6 \%$ promotion. Intuitively, the middle word cannot influence other words except itself when the size equals to 1. The performance increases with the growth of region size up to 7.
+
+![](images/39bb20cd81b1b28e61ee38b0e0b72bd1dfaae8572c8dfc73a0815d0a845949ca.jpg)  
+Figure 2: Effect of the hyperparameters (region size and embedding size) on Yelp Review Full dataset. (a) shows the comparison of single fixed region size 7 and multi sizes combination [3,5,7] and (b) shows the effect of different settings of embedding size among four kinds of models, unigram FastText, bigram FastText, CNN and ours. We use region size 7 for CNN and ours.
+
+Furthermore, we experiment our models with the combination of multi region sizes. Here we use the approach of sharing context units among each region, where the parameters of local context units of smaller regions are just the slice of the longest one. Region embeddings of different sizes are concatenated for final classification. In figure 2a, the combination of multi region sizes 3,5,7 is slightly better than the best single region size 7. The effectiveness of multi-size combination can be explained by the difference of influence ranges between words. For example, in sentiment analysis, word very only emphasizes the next word while however may lay stress on a wide range of the following words.
+
+In addition to the analysis of region sizes, we further study the influence of word embedding dimensions. Figure 2b lists the comparative results on Yelp Review Full with different embedding dimensions. The result shows that our model is more robust to overfitting than FastText and CNN with the word embedding dimension increasing. In fact, the amount of parameters in our models is relatively large. Since we learn a specific unit for each word, under the same word embedding dimension, our parameter size has been expanded by region size times, the parameters number is $v \times h + v \times ( 2 \times c + 1 ) \times h + h \times m + m$ , where $m$ is the number of classes. Specific numbers parameters for different region sizes are listed in Appendix A. Notice that the sizes of parameters are relatively consistent among $I O 2 4$ in FastText, 1024 in CNN and 128 in ours.
+
+# 4.5.2 EFFECT OF CONTEXT UNIT
+
+In this section, we explore some comparative experiments to show the effectiveness of our proposed word specific context unit. The experiments are employed based on unigram FastText baseline, which has similar upper layer structure with our models. Table 3 illustrates the results.
+
+Table 3: Comparative decomposition results on Yelp Review Full dataset. For FastText(Unigram), embedding dimension is 10. For FastText(Win-pool), W.C.region.emb(Scalar) and W.C.region.emb(our model), region size is 7 and embedding dimension is 128   
+
+<table><tr><td>Decomposition</td><td>Performance(%)</td></tr><tr><td>FastText(Unigram)</td><td>60.73</td></tr><tr><td>FastText(Win-pool)</td><td>61.01(+0.28)</td></tr><tr><td>W.C.region.emb(Scalar)</td><td>63.18(+2.45)</td></tr><tr><td>W.C.region.emb(Our model)</td><td>64.9(+4.17)</td></tr></table>
+
+Firstly, we remove the entire context units from our model, which means it is just a variant version of unigram FastText, we call it FastText(Win-pool). The difference is that FastText sums up the word embeddings directly while FastText(Win-pool) sums up the window pooled embeddings in a stride of 1. It yields a slightly accuracy gain of $0 . 2 8 \%$ than unigram FastText.
+
+Secondly, we apply a simplified scalar version of context units to FastText(Win-pool). Distinguishable, the context unit of each word has the shape with $1 \times ( 2 \times c + 1 )$ , hence it can be regarded as a broadcasting operation on corresponding word embeddings of its local context. We name this method W.C.region.emb(Scalar). Compared to the non-scalar method, it yields a huge parameter size reduction, but it already yields a significant gain of $2 . 4 5 \%$ .
+
+Furthermore, W.C.region.emb(our model) is the variant version of W.C.region.emb(Scalar) where each column of scalar context unit is expanded to a dense vector. Each word’s context unit has a shape with $h \times ( 2 \times c { + } 1 )$ . Adding the low dimensional dense context unit improves the performance by $4 . 1 7 \%$ . We can sense much from the procedure of decomposition, with the help of context unit, even a simpler scalar version promotes a lot.
+
+To have a better understanding of what context unit actually capture, heat maps are plotted for chosen word samples. Representative adversarial conjunctions like however, but, modifiers like very, good, bad and nouns like food, morning are listed in Figure 3.
+
+For each row of the figure, the intensity of the surrounding color box reflects the emphasis degree in the view of the middle word. Qualitative but not fully rigorous, a normalized L2-norm of each column in context unit is used to render the shade. Region size 7 is adopted default, annotation $l _ { i } ( \mathrm { i } \le 3 )$ is denoted as left columns of the specific context unit, while $r _ { i } ( \mathrm { i } \leq 3 )$ denoted as the right part.
+
+What the figure reflects are consistent with intuitive priors of human beings. In the perspective of however, right contexts play the key role for classification polarity because of the emotional reversal, the color is indeed deeper in $r _ { i }$ than $l _ { i }$ , so does but. For word very, $r _ { 1 }$ is more prominent than the rest of all, which captures some modified patterns like very happy or very sad. For word good, tendencies will be completely different for patterns like not good, very good and not that good, which are intensive negative, intensive positive and slightly hesitated, separately, the position of $l _ { 1 }$ will be strengthened as a result, so does word bad. There are significant differences between two nouns food and morning. The heat map of word food implies patterns like delicious food or food was mediocre, while the word morning has fewer valuable patterns for classification.
+
+Actually, from the motivation of word specified context units, we would like to believe this feature helps capture syntactic and semantic influences of words on surrounding words at relative positions.
+
+# 4.5.3 VISUALIZATION
+
+In this subsection, we will try to visualize the contribution of each word and selected phrase to classification. Detailed visualization techniques have been introduced in Li et al. (2015). Here we generalize it to the color rendering of multi-category version. Notice that for our model, not the original embedding acts here, but the accumulation of the projected embedding of each word on its surrounding words.
+
+![](images/d80f79fd5893ceddc980a9e774ce57d694780e54d6e8c6922edb16fc33afb1b7.jpg)  
+Figure 3: Heat maps of chosen words trained on Yelp Review Polarity, which is a binary sentiment analysis dataset. Each row represent the context unit of the middle word. Region size is 7 and embedding size is 128.
+
+Table 4: Visualization of chosen samples on Yelp Review Polarity dataset. Green denotes positive contribution while red denotes negative. Two methods are compared without context unit(No C-unit) and with context unit(With C-unit).   
+
+<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=8>Sentence Samples</td><td rowspan=1 colspan=3></td><td rowspan=1 colspan=3>Phrase</td></tr><tr><td rowspan=1 colspan=1>No C-unit</td><td rowspan=1 colspan=2>getyour</td><td rowspan=1 colspan=2>wallet</td><td rowspan=1 colspan=1>ready</td><td rowspan=1 colspan=3>theprices</td><td rowspan=1 colspan=1>are</td><td rowspan=1 colspan=1>crazy</td><td rowspan=1 colspan=1>high</td><td rowspan=1 colspan=3> prices are crazy high</td></tr><tr><td rowspan=1 colspan=1>With C-unit</td><td rowspan=1 colspan=4>get your wallet ready</td><td rowspan=1 colspan=4>the prices are crazy</td><td rowspan=1 colspan=1>are</td><td rowspan=1 colspan=1>crazy</td><td rowspan=1 colspan=1>high</td><td rowspan=1 colspan=3> prices are crazy high</td></tr><tr><td rowspan=2 colspan=1>No C-unitWith C-unit</td><td rowspan=2 colspan=1></td><td rowspan=1 colspan=2>nothing</td><td rowspan=1 colspan=3>remarkable</td><td rowspan=1 colspan=1>but</td><td rowspan=1 colspan=1>not</td><td rowspan=1 colspan=1>bad</td><td rowspan=1 colspan=1>either</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>but not bad either</td><td rowspan=2 colspan=1></td></tr><tr><td rowspan=1 colspan=2>nothing</td><td rowspan=1 colspan=4>remarkable   but</td><td rowspan=1 colspan=1>not</td><td rowspan=1 colspan=1>bad</td><td rowspan=1 colspan=1>either</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>but not bad either</td></tr></table>
+
+For clarity, we choose a binary classification task of sentiment analysis. In Table 4, we list two cases in Yelp Review Polarity dataset, in which our model behaves as expected. Words and artificially selected phrases are highlighted green if they are positive factors, red if they are negative. The intensity of the color indicates the degree of the polarity.
+
+To have a better comparison, the results of with and without context unit methods are both visualized. We abbreviate them as With $C$ -unit and No $C$ -unit, respectively. For sentence get your wallet ready, the prices are crazy high, if no context unit is adopted, the word color reflects its word embedding, which is context-free. The polarity of crazy is positive, and high is negative. Because the intensity of crazy is higher than high, the polarity of phrase prices are crazy high is totally positive, which is a mistake. But with context unit, things have changed quite a bit, the polarities of words are context dependent. Under the influence of high, the positive polarity of crazy vanishes and phrase prices are crazy high performs negative overall. For another case nothing remarkable, but not bad either, things seem more interesting. Without context-unit , remarkable is positive, while nothing, not, bad perform negative, respectively. But with context unit, the polarity of the part ahead of but weakens, meanwhile the polarities of not and bad flips. As a result, phrase but not bad either performs positive overall.
+
+# 5 CONCLUSION
+
+This paper proposed two novel architectures for text classification tasks, which learn task specific region embeddings without hand crafted features. To utilize the word specific influences of each word on its context words, a local context unit for each word is learned in addition to word embedding. Our models achieve state-of-the-art performances on six benchmark text classification datasets, and the visualization experiments show that our proposed local context unit can capture the semantic and syntactic information for each word.
+
+Noticed the power of the local context unit on learning task related region embeddings, we are interested in its ability to unsupervised and semi-supervised learning. At the same time, we are also curious about whether we can achieve better results by introducing more complex upper layers on text classification, and other natural language processing tasks.
+
+# ACKNOWLEDGMENTS
+
+This paper is supported by National Basic Research Program of China (973 program No.2014CB340505). We gratefully thank the anonymous reviewers for their insightful comments.
+
+# REFERENCES
+
+Alexis Conneau, Holger Schwenk, Lo¨ıc Barrault, and Yann Lecun. Very deep convolutional networks for natural language processing. arXiv preprint arXiv:1606.01781, 2016.
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+Duyu Tang, Bing Qin, and Ting Liu. Document modeling with gated recurrent neural network for sentiment classification. In EMNLP, pp. 1422–1432, 2015.
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+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (eds.), Advances in Neural Information Processing Systems 30, pp. 6000–6010. Curran Associates, Inc., 2017. URL http://papers.nips.cc/paper/7181-attention-is-all-you-need.pdf.
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+Sida Wang and Christopher D Manning. Baselines and bigrams: Simple, good sentiment and topic classification. In Proceedings of the 50th Annual Meeting of the Association for Computational Linguistics: Short Papers-Volume 2, pp. 90–94. Association for Computational Linguistics, 2012.
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+
+# APPENDIX
+
+# A DETAILED EXPERIMENTAL RESULTS
+
+To have a further insight about our reported results, we list the training time and best testing performance epoch for kinds of region sizes(5,7,9) in detail. For all the 8 datasets in Table 5, hyperparameters are kept in line with section 4.3. The dimension of word embedding is 128, the region size is 7, the initial learning rate is set to $1 \times 1 0 ^ { - 4 }$ , and the batch size is 16. Epoch index starts from 0 and training time is reported per epoch. We choose the model of word-context region embedding here.
+
+Table 5: Experimental detailed records on several datasets   
+
+<table><tr><td>Dataset</td><td>Vocabulary Size</td><td>W.C Region Size</td><td>Parameters Number</td><td>Best Epoch</td><td>Training Time(Mins)</td><td>Accuracy(%)</td></tr><tr><td rowspan="3">Yelp P.</td><td rowspan="3">115298</td><td>5</td><td>88,549,122</td><td>3</td><td>27</td><td>96.34</td></tr><tr><td>7</td><td>118,065,410</td><td>3</td><td>36</td><td>96.39</td></tr><tr><td>9</td><td>147,581,698</td><td>3</td><td>43</td><td>96.38</td></tr><tr><td rowspan="3">Yelp F.</td><td rowspan="3">124273</td><td>5</td><td>95,442,309</td><td>3</td><td>34</td><td>64.73</td></tr><tr><td>7</td><td>127,256,197</td><td>2</td><td>43</td><td>64.90</td></tr><tr><td>9</td><td>159,070,085</td><td>2</td><td>52</td><td>64.74</td></tr><tr><td rowspan="3">Amz. P.</td><td rowspan="3">394385</td><td>5</td><td>302,887,938</td><td>2</td><td>336</td><td>95.07</td></tr><tr><td>7</td><td>403,850,498</td><td>2</td><td>402</td><td>95.23</td></tr><tr><td>9</td><td>504,813,058</td><td>2</td><td>589</td><td>95.06</td></tr><tr><td rowspan="3">Amz. F.</td><td rowspan="3">356312</td><td>5</td><td>273,648,261</td><td>1</td><td>300</td><td>60.83</td></tr><tr><td>7</td><td>364,864,133</td><td>1</td><td>395</td><td>60.93</td></tr><tr><td>9</td><td>456,080,005</td><td>1</td><td>490</td><td>61.05</td></tr><tr><td rowspan="3">AG</td><td rowspan="3">42783</td><td>5</td><td>32,857,860</td><td>6</td><td>2</td><td>92.81</td></tr><tr><td>7</td><td>43,810,308</td><td>4</td><td>3</td><td>92.89</td></tr><tr><td>9</td><td>54,762,756</td><td>5</td><td>4</td><td>92.82</td></tr><tr><td rowspan="3">Sogou</td><td rowspan="3">99394</td><td>5</td><td>76,335,237</td><td>7</td><td>27</td><td>97.6</td></tr><tr><td>7</td><td>101,780,101</td><td>9</td><td>33</td><td>97.63</td></tr><tr><td>9</td><td>127,224,965</td><td>10</td><td>39</td><td>97.56</td></tr><tr><td rowspan="3">Yah.A.</td><td rowspan="3">361926</td><td>5</td><td>277,960,458</td><td>1</td><td>160</td><td>73.42</td></tr><tr><td>7</td><td>370,613,514</td><td>1</td><td>210</td><td>73.66</td></tr><tr><td>9</td><td>463,266,570</td><td>2</td><td>256</td><td>73.68</td></tr><tr><td rowspan="3">DBP</td><td rowspan="3">227863</td><td>5</td><td>175,000,590</td><td>3</td><td>37</td><td>98.87</td></tr><tr><td>7</td><td>233,333,518</td><td>2</td><td>48</td><td>98.89</td></tr><tr><td>9</td><td>291,666,446</td><td>3</td><td>60</td><td>98.94</td></tr></table>
+
+We also report results of several repeated runs in Table 6 to exclude the effect of randomness and ensure reproducibility. Five independent runs are conducted on each dataset of Yelp.P and Yelp.F, where both performance variances are within $0 . 1 1 \%$ on accuracy.
+
+Table 6: Performance variances through several repeated runs on Yelp Datasets   
+
+<table><tr><td>Dataset</td><td>Tries Num.</td><td>W.C region size</td><td>Best Epoch</td><td>Accuracy(%)</td><td>Performance Variance</td></tr><tr><td rowspan="5">Yelp P.</td><td>0</td><td>7</td><td>3</td><td>96.39</td><td rowspan="5">≤%0.11</td></tr><tr><td>1</td><td>7</td><td>4</td><td>96.36</td></tr><tr><td>2</td><td>7</td><td>4</td><td>96.41</td></tr><tr><td>3</td><td>7</td><td>3</td><td>96.38</td></tr><tr><td>4</td><td>7</td><td>2</td><td>96.46</td></tr><tr><td rowspan="5">Yelp F.</td><td>0</td><td>7</td><td>2</td><td>64.90</td><td rowspan="5">≤%0.11</td></tr><tr><td>1</td><td>7</td><td>2</td><td>64.94</td></tr><tr><td>2</td><td>7</td><td>1</td><td>64.87</td></tr><tr><td>3</td><td>7</td><td>1</td><td>64.86</td></tr><tr><td>4</td><td>7</td><td>2</td><td>64.98</td></tr></table>

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+    {
+        "type": "text",
+        "text": "A NEW METHOD OF REGION EMBEDDING FOR TEXT CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            135,
+            821,
+            175
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Chao $\\mathbf { Q } \\mathbf { i } \\mathbf { a } \\mathbf { o } ^ { * \\ddagger }$ , Bo Huang†‡, Guocheng $\\mathbf { N i u } ^ { \\ddag }$ , Daren $\\mathbf { L i } ^ { \\dagger }$ , Daxiang $\\mathbf { D o n g ^ { \\ddagger \\ S } }$ , Wei $\\mathbf { H e } ^ { \\ddagger }$ , Dianhai $\\mathbf { Y } \\mathbf { u } ^ { \\ddag \\ S }$ , Hua $\\mathbf { W _ { u } } ^ { \\ddagger \\ S }$ ",
+        "bbox": [
+            183,
+            197,
+            563,
+            225
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "‡ Baidu Inc., Beijing, China   \n§ National Engineering Laboratory of Deep Learning Technology and Application, China   \n{qiaochao, huangbo02, niuguocheng, lidaren,   \ndaxiangdong, hewei06, yudianhai, wu hua}@baidu.com ",
+        "bbox": [
+            181,
+            226,
+            773,
+            277
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            452,
+            311,
+            542,
+            325
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To represent a text as a bag of properly identified “phrases” and use the representation for processing the text is proved to be useful. The key question here is how to identify the phrases and represent them. The traditional method of utilizing n-grams can be regarded as an approximation of the approach. Such a method can suffer from data sparsity, however, particularly when the length of n-gram is large. In this paper, we propose a new method of learning and utilizing task-specific distributed representations of n-grams, referred to as “region embeddings”. Without loss of generality we address text classification. We specifically propose two models for region embeddings. In our models, the representation of a word has two parts, the embedding of the word itself, and a weighting matrix to interact with the local context, referred to as local context unit. The region embeddings are learned and used in the classification task, as parameters of the neural network classifier. Experimental results show that our proposed method outperforms existing methods in text classification on several benchmark datasets. The results also indicate that our method can indeed capture the salient phrasal expressions in the texts. ",
+        "bbox": [
+            231,
+            343,
+            764,
+            532
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            562,
+            334,
+            577
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Text classification is an important task for many applications, including topic categorization, search query classification, and sentiment analysis, which has been studied for years. A simple yet effective approach for text classification is to represent documents as bag-of-words, and train a classifier on the basis of the representations using methods such as logistic regression, support vector machines (Joachims, 1998; Fan et al., 2008), and naive Bayes (McCallum et al., 1998). Although bag-of-words methods are effective and efficient, they also have limitations. The representations do not take into account the word order information which has been proved to be useful at least in some applications such as sentiment analysis (Pang et al., 2002). ",
+        "bbox": [
+            174,
+            593,
+            823,
+            695
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To make effective use of word order information for text classification, people have traditionally exploited n-grams, i.e., short sequences of words in the texts. Previous work shows that the use of n-grams is effective in the text classification task (Pang et al., 2002; Wang & Manning, 2012; Joulin et al., 2016). Although n-grams are very useful, they have certain limitations. 1) The number of n-grams increases exponentially when the length of n-gram $n$ increases. This makes it difficult to exploit large n-grams (e.g., $n > 4$ ). 2) Since the number of parameters in an n-gram model is very large, the estimation of the parameters usually suffers from the data sparsity problem. ",
+        "bbox": [
+            174,
+            701,
+            823,
+            790
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Recently, the method of FastText has been proposed (Joulin et al., 2016), which can learn and use distributed embeddings of n-grams. More specifically, the embedding of an n-gram is defined as a low-dimensional vector representation of the n-gram. Note that the n-grams in a vocabulary can also be represented as one-hot vectors Wang & Manning (2012). ",
+        "bbox": [
+            174,
+            796,
+            823,
+            849
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose to learn embeddings of n-grams for a specific task (e.g., classification), which are more compact and thus easy to obtain. We call the embeddings region embeddings, following the work in Johnson & Zhang (2015). Our method significantly differs from their method, however, in the sense that the region embeddings in our method are task-dependent and acquired from supervised learning, while those in their method are task-independent and acquired from unsupervised learning. Our method is also largely different from FastText, as it learns richer models for region embeddings. ",
+        "bbox": [
+            173,
+            137,
+            823,
+            226
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Intuitively, the meaning of a word is defined by the meaning of itself as well as the meanings of words in the surrounding context. The extended embedding of a word in an n-gram thus consists of two parts, the embedding of the word itself and a matrix to interact with the local context, named “local context unit”. The embedding of a word is a column vector, and the local context unit of a word is a matrix in which the columns are used to interact with words in the local context. The region embedding of an n-gram is then constructed by the extended embeddings of all words in the n-gram. In this paper, we introduce two models for region embeddings. ",
+        "bbox": [
+            174,
+            232,
+            823,
+            321
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For the text classification task, a document is viewed as a bag of region embeddings, and the bag of region embeddings is fed into a classifier. The parameters of the local context units and word embeddings are trained together with the parameters of the classifier which is a fully connected neural network. Our models achieve better results than the state-of-the-art methods on several benchmark datasets of text classification. Experiments show that our proposed models can really capture important information for the task. ",
+        "bbox": [
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+            328,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            425,
+            342,
+            440
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Text classification has been studied for years, traditional approaches focused on feature engineering and using different types of machine learning algorithms. For feature engineering, bag-of-words features are efficient and popular. In addition, the hand-crafted n-grams or phrases are added to make use of word order in text data, which has been shown effective on Wang & Manning (2012). For machine learning algorithms, linear classifiers are widely used, such as naive bayes (McCallum et al., 1998), logistic regression and support vector machines (Joachims, 1998; Fan et al., 2008). However, these models commonly suffer the data sparsity problem. ",
+        "bbox": [
+            174,
+            454,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, several neural models have been proposed, the pre-trained word embeddings of word2vec (Mikolov et al., 2013) have been widely used as inputs to deep neural models such as recursive tensor networks (Socher et al., 2013). On the other hand, some simple and efficient models which can directly learn task specific word embeddings or fine-tune on pre-trained word embeddings have been proposed recently, such as Deep Averaging Networks (Iyyer et al., 2015), FastText (Joulin et al., 2016). Several neural models have been proposed to make use of word order information, most models are based on convolutional neural network (CNN) (Kim, 2014; Johnson & Zhang, 2014; Zhang et al., 2015) and recurrent neural network (RNN) (Tang et al., 2015; Lai et al., 2015; Yogatama et al., 2017). More recently, the Transformer (Vaswani et al., 2017), a sequence transduction model based solely on attention mechanisms has been proposed. Although Transformer was not designed for the text classification task, it has similarities with our work. In the rest of this section, we will briefly introduce FastText, CNN and Transformer, which are the most relevant to our work. ",
+        "bbox": [
+            173,
+            551,
+            823,
+            714
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "FastText FastText averages the word embeddings to represent a document, and uses a full connected linear layer as the classifier. The word embeddings are trained for each task specifically. To utilize the local word order information of small regions, FastText uses hand-crafted n-grams as features in addition to single words. With the simple architecture, FastText has been proved to be effective and highly efficient on text classification tasks. Similarly, our models use bag of region embeddings to represent a document, and use the same linear classifier. Differently, our models directly learn the semantics of regions based on word sequence, hand-crafted features are not required. ",
+        "bbox": [
+            174,
+            731,
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+            820
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "CNN CNN is a feed-forward network with convolutional layers interleaved with pooling layers, which are originally used for image processing tasks. For natural language processing, words are commonly converted to vectors. CNN directly applies convolutional layer on word vectors, both word vectors and the shared (word independent) kernels are the parameters of CNN, which can be learned to capture the predictive structures of small regions. The essence of CNN is to learn embeddings for small fixed size regions, each kernel of the convolutional layer tries to capture a specific semantic or structural feature. Our purpose is similar with CNN, which tries to learn task specific representations of regions. Unlike CNN, we apply local context units on word vectors, which are word dependent, moreover, the convolution kernels extract the predictive features by applying convolution operation on word sequences, while we use local context units as distinct linear projection functions on context words in corresponding relative positions to get region representations. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "Transformer Vaswani et al. (2017) proposed a sequence transduction model, the Transformer, based solely on attention mechanisms. Both Transformer and our method can capture word order information without any CNN or RNN component, and the scalar form of context units (introduced in our ablation experiments) can be regarded as a kind of local attention. There are also some differences here: the motivation we proposed local context units is to address word specific influence between word and its context, while Vaswani et al. (2017) has proposed a parallelable sequence transduction framework based entirely on attention; To utilize position information, in our method, words are interacted with context words at different relative positions by corresponding columns in their context units, while Transformer use fixed sin and cos function based position encoding. ",
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+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we focus on learning the representations of small text regions which preserve the local internal structural information for text classification. The regions in a document can be considered as fixed length contiguous subsequences of the document. More specifically, with $w _ { i }$ standing for the $i$ -th(starting from 0) word of the document, we use region $( i , c )$ to denote the $2 \\times c + 1$ length region with middle word $w _ { i }$ . For instance, given a sentence such as The food is not very good in this hotel, region $( 3 , 2 )$ means the subsequence food is not very good. ",
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+        "type": "text",
+        "text": "In this work, we use the interactions between words and their local context based on word embeddings as well as the local context units to produce region embeddings. In the rest of this section, we will introduce the local context units firstly, and two architectures to generate the region embeddings through local context units will be introduced, finally we will introduce how we use the region embeddings on text classification. ",
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+        "img_path": "images/cbb613170613bb105975169510719e7d281fcb6e107e0f198c3343b5e22f32c7.jpg",
+        "image_caption": [
+            "Figure 1: Architectures of region embedding using local context units in different perspectives "
+        ],
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+        "type": "text",
+        "text": "3.1 LOCAL CONTEXT UNIT ",
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+        "type": "text",
+        "text": "In natural language processing, words are commonly converted to low dimensional vectors(word embeddings) as the inputs to neural networks. More formally, the embedding ${ \\bf e } _ { w }$ of word $w$ is represented by a column in a matrix $\\mathbf { E } \\in \\mathcal { R } ^ { h \\times v }$ with a look up layer, where $v$ is the size of the vocabulary, $h$ is the embedding size. ",
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+        "type": "text",
+        "text": "To utilize the information of words’ relative positions and local context, we learn a local context unit for each word in addition to the word embedding, and both the unit and word embedding are learned as model parameters. Formally, we define the local context unit ${ \\bf K } _ { w _ { i } } \\in \\mathcal { R } ^ { h \\times ( 2 \\times c + \\bar { 1 } ) }$ of $w _ { i }$ as a matrix which can be looked up in the tensor $\\mathbf { U } \\in \\mathcal { R } ^ { h \\times ( 2 \\times c + 1 ) \\times v }$ by $w _ { i }$ ’s index in the vocabulary. ",
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+        "type": "text",
+        "text": "Each column in ${ \\bf K } _ { w _ { i } }$ can be used to interact with the context word in corresponding relative position of $w _ { i }$ . In fact, the columns of a unit matrix can be regarded as distinctive linear projection functions on the embeddings of words in the local context. The parameters of these projection functions(i.e., columns of each unit matrix) can be learned to capture the semantic and syntactic influence of the word to its context. Word embeddings are used as inputs to the projection functions, and we call the outputs projected word embeddings. ",
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+        "type": "text",
+        "text": "Formally, let $\\mathbf { p } _ { w _ { i + t } } ^ { i }$ be the projected word embedding of $w _ { i + t }$ in $i$ -th word’s view, and ${ \\bf K } _ { w _ { i } , t }$ be the $( c + t )$ -th column in ${ \\bf K } _ { w _ { i } }$ $\\scriptstyle - c < = t < = c )$ , given the unit ${ \\bf K } _ { w _ { i } }$ of $w _ { i }$ and the embedding $\\mathbf { e } _ { w _ { i + t } }$ of $w _ { i + t }$ , we use an element-wise multiplication(denoted by $\\odot$ ) to compute $\\mathbf { p } _ { w _ { i + t } } ^ { i }$ : ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/2c19d24d525b5aafc3c95a1a74a09609372d978eceb8acbcd02b2e4846cd3b86.jpg",
+        "text": "$$\n\\mathbf { p } _ { w _ { i + t } } ^ { i } = \\mathbf { K } _ { w _ { i } , t } \\odot \\mathbf { e } _ { w _ { i + t } }\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "For a context word in a particular relative position of $w _ { i }$ , there is a corresponding linear projection function(a particular column of ${ \\bf K } _ { w _ { i } }$ ), thus our proposed local context units can utilize the local ordered word information in a novel way. Note that the middle column ${ \\bf K } _ { w _ { i } , 0 }$ of ${ \\bf K } _ { w _ { i } }$ can be regarded as a linear projection function on ${ \\bf e } _ { w _ { i } }$ itself, which transforms ${ \\bf e } _ { w _ { i } }$ to the same space as other projected embeddings. ",
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+    {
+        "type": "text",
+        "text": "3.2 WORD-CONTEXT REGION EMBEDDING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We proposed two architectures to perform the region embedding from different perspectives. We consider the semantics of a given region is derived from the mutual influences of the words in this region. In this paper, the regions can be regarded as snapshots of a window sliding on a document, whose middle words are contiguous, hence we can compose the semantics of a give region only by the middle word’s influences on the context words, or the context words’ influences on the middle word. ",
+        "bbox": [
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+        "type": "text",
+        "text": "In the first proposed architecture, we focus on addressing the middle word’s influences on the context words. For example, in the sentence The food is not very good in this hotel, the occurrence of word not might bring a semantic reversal to the local region. ",
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+        "type": "text",
+        "text": "We use the local context unit of the middle word and the original word embeddings in a region to perform the projected embeddings in a word-to-context view, where the projected embeddings can reflect the middle word’s influences on the context words. Once the projected embeddings are obtained, a max pooling operation is applied to extract the most predictive features in the region. The output of the max pooling operation can be regarded as a task related region embedding in a word-to-context view, i.e. Word-Context region embedding. ",
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+        "type": "text",
+        "text": "Formally, we use the context unit ${ \\bf K } _ { w _ { i } }$ of middle word $w _ { i }$ and embeddings of all words in a region region $( i , c )$ to compute the projected embedding matrix by equation (1), then the Word-Context region embedding $\\mathbf { r } _ { ( i , c ) }$ can be obtained through a max pooling operation on the projected embedding matrix: ",
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+    {
+        "type": "equation",
+        "img_path": "images/fe86b31badc2aa9e3f7d86684d4c170252376a733dad45baa1eea31e7637650d.jpg",
+        "text": "$$\n\\mathbf { r } _ { ( i , c ) } = m a x \\big ( \\big [ \\mathbf { p } _ { w _ { i - c } } ^ { i } \\quad \\mathbf { p } _ { w _ { i - c + 1 } } ^ { i } \\quad . . . \\quad \\mathbf { p } _ { w _ { i + c - 1 } } ^ { i } \\quad \\mathbf { p } _ { w _ { i + c } } ^ { i } \\big ] \\big )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "where $m a x$ standing for the max pooling operation on the column dimension of the input matrix. Finally, we get $\\mathbf { r } _ { ( i , c ) }$ as a vector representation of $r e g i o n ( i , c )$ with dimension $h$ . Figure 1a shows the details of the first model architecture. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For instance, in the sentence The food is not very good in this hotel, the projected word embeddings in the region $( 3 , 2 )$ are composed by the element-wise multiplications between columns in the local ",
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+    {
+        "type": "text",
+        "text": "context unit of not and word embeddings of food, is, not, very and good. The embedding $\\mathbf { r } _ { 3 , 2 }$ of region $( 3 , 2 )$ can be obtained by max pooling on the projected word embedding matrix. ",
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+        "type": "text",
+        "text": "3.3 CONTEXT-WORD REGION EMBEDDING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The second architecture goes as a different view, which addresses the local context words’ influences on the middle word in the region, and we call this Context-Word region embedding. Similarly, for a $r e g i o n ( i , c )$ , the projected embeddings are computed by the original word embedding of the middle word and the context units of all words in the region, then the Context-Word region embedding can be obtained by a max pooling operation through the column dimension of the projected embedding matrix: ",
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+    {
+        "type": "equation",
+        "img_path": "images/43fbf8ef405eead8798654c8305313a3ef61a11bb2002bdd1daec43963e5986d.jpg",
+        "text": "$$\n\\mathbf { r } _ { ( i , c ) } = m a x \\big ( \\big [ \\mathbf { p } _ { w _ { i } } ^ { i - c } \\quad \\mathbf { p } _ { w _ { i } } ^ { i - c + 1 } \\quad . . . \\quad \\mathbf { p } _ { w _ { i } } ^ { i + c - 1 } \\quad \\mathbf { p } _ { w _ { i } } ^ { i + c } \\big ] \\big )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "Figure 1b shows the details of the second model architecture. our two models take different ways to produce the projected word embeddings, the Word-Context model uses context units of middle words and word embeddings of context words, while the Context-Word model uses context units of context words and word embeddings of the middle word. ",
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+    {
+        "type": "text",
+        "text": "3.4 REGION EMBEDDING FOR TEXT CLASSIFICATION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For text classification, documents are usually variable-sized, which need to be represented as fixed size vectors. In order to show the effectiveness of our proposed region embedding models, we just sum up the embeddings of all regions to represent a document, and feed it to an upper FullConnected layer for text classification task. ",
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+    },
+    {
+        "type": "text",
+        "text": "Formally, the model can be represented as following: ",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/26bf2ac5ba275e0e50ed5c8aacb7e8e54bc93b32801ff92fbb5a4121faf1f50a.jpg",
+        "text": "$$\n\\mathrm { f } ( \\mathbf { x } ; \\mathbf { E } , \\mathbf { U } , \\mathbf { W } , \\mathbf { b } ) = \\mathbf { g } ( \\mathbf { W } \\sigma ( \\sum _ { i = 0 } ^ { n } \\mathbf { r } _ { ( i , c ) } ) + \\mathbf { b } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { x }$ denotes the input text sequence, W and b denote the weight matrix and bias of the fully connected layer respectively, $\\mathbf { g }$ denotes the softmax function of the output layer, $\\sigma$ denotes the softsign function and $n$ denotes the number of regions in a document, $\\mathbf { r }$ is the region embedding which can be computed by the equation (2) or (3). E, U, W and b can be updated in the training period. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We report experiments with proposed models in comparison with previous models. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 DATASETS ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We use publicly available datasets from Zhang et al. (2015) to evaluate our models. There are in total 8 text classification datasets, corresponding to sentiment analysis, news classification, questionanswer, ontology extraction tasks, respectively. Table 1 shows the descriptive statistics of datasets used in our experiments. To guarantee comparable indications, same evaluation protocol of Zhang et al. (2015) is employed. ",
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+    {
+        "type": "text",
+        "text": "4.2 BASELINES",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our models are compared with several widely used supervised text classification models. We report the n-grams and TFIDF baselines from Zhang et al. (2015), as well as the character level convolutional model (char-CNN) of Zhang & LeCun (2015), the character based convolution recurrent network (char-CRNN) of Xiao & Cho (2016), the very deep convolutional network (VDCNN) of Conneau et al. (2016), the Discriminative LSTM (D-LSTM) of Yogatama et al. (2017) and the bigram FastText (bigram-FastText) of Joulin et al. (2016). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/3694017565e63165bc0ec78d8d1db4c64061fe744dea14ffbfe20d8859d4c263.jpg",
+        "table_caption": [
+            "Table 1: Statistics of Datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Classes</td><td>Average Lengths</td><td>Train Samples</td><td>Test Samples</td><td>Tasks</td></tr><tr><td>Yelp Review Polarity Yelp Review Full</td><td>2</td><td>156</td><td>560,000</td><td>38,000</td><td rowspan=\"3\">Sentiment Analysis</td></tr><tr><td></td><td>5</td><td>158</td><td>650,000</td><td>50,000</td></tr><tr><td>Amazon Review Polarity Amazon Review Full</td><td>2</td><td>91</td><td>3,000,000</td><td>650,000</td></tr><tr><td>AG&#x27;s News</td><td>5</td><td>93 44</td><td>3,600,000 120.000</td><td>400,000 7,600</td><td>News</td></tr><tr><td>Sogou News</td><td>4 5</td><td>579</td><td>450,000</td><td>60,000</td><td>Classification</td></tr><tr><td>Yahoo! Answers</td><td>10</td><td>112</td><td>1,400,000</td><td>60,000</td><td>Question Answer</td></tr><tr><td>DBPedia</td><td>14</td><td>55</td><td>560,000</td><td>70,000</td><td>Ontology Extraction</td></tr></table>",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3 IMPLEMENTATION DETAILS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For data preprocessing, all the texts of datasets are tokenized by Stanford tokenizer and all words are converted to lower case. Words that appear only in one document are treated as out-of-vocabulary (OOV) items, and all stop words as well as symbols are kept. Additionally, length of $c$ padding are added to both the head and tail of each document. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For our models, optimal hyperparameters are tuned with $10 \\%$ of the training set on Yelp Review Full dataset, and identical hyperparameters are applied to all datasets: the dimension of word embedding is 128, the region size is 7 which means the shape of local context unit matrix of each word is $1 2 8 \\times 7$ , the initial learning rate is set to $1 \\times 1 0 ^ { - 4 }$ , and the batch size is 16. For optimization, the embeddings of words and the units are randomly initialized with Gaussian Distribution. Adam (Kingma & Ba, 2014) is used as the optimizer. We do not use any extra regularization methods, like L2 normalization or dropout. Algorithms are entirely implemented with TensorFlow and trained on NVIDIA Tesla P40 GPUs. The code 1 is publicly available on the Internet. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.4 RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/15ee1e55605f089d9ad7f86f9861d1d45e7ccad4ff1e6f3664d6fe2e8c8e7cda.jpg",
+        "table_caption": [
+            "Table 2: Test Set Accuracy $[ \\% ]$ Compared to other Methods on several Datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Yelp P.</td><td>Yelp F.</td><td>Amz. P.</td><td>Amz. F.</td><td>AG</td><td>Sogou</td><td>Yah. A.</td><td>DBP</td></tr><tr><td>BoW</td><td>92.2</td><td>58.0</td><td>90.4</td><td>54.6</td><td>88.8</td><td>92.9</td><td>68.9</td><td>96.6</td></tr><tr><td>ngrams</td><td>95.6</td><td>56.3</td><td>92.0</td><td>54.3</td><td>92.0</td><td>97.1</td><td>68.5</td><td>98.6</td></tr><tr><td>ngrams TFIDF</td><td>95.4</td><td>54.8</td><td>91.5</td><td>52.4</td><td>92.4</td><td>97.2</td><td>68.5</td><td>98.7</td></tr><tr><td>char-CNN</td><td>94.7</td><td>62.0</td><td>94.5</td><td>59.6</td><td>87.2</td><td>95.1</td><td>71.2</td><td>98.3</td></tr><tr><td>char-CRNN</td><td>94.5</td><td>61.8</td><td>94.1</td><td>59.2</td><td>91.4</td><td>95.2</td><td>71.7</td><td>98.6</td></tr><tr><td>bigram-FastText</td><td>95.7</td><td>63.9</td><td>94.6</td><td>60.2</td><td>92.5</td><td>96.8</td><td>72.3</td><td>98.6</td></tr><tr><td>VDCNN</td><td>95.7</td><td>64.7</td><td>95.7</td><td>63.0</td><td>91.3</td><td>96.8</td><td>73.4</td><td>98.7</td></tr><tr><td>D-LSTM</td><td>92.6</td><td>59.6</td><td>1</td><td>-</td><td>92.1</td><td>94.9</td><td>73.7</td><td>98.7</td></tr><tr><td>W.C.region.emb</td><td>96.4</td><td>64.9</td><td>95.1</td><td>60.9</td><td>92.8</td><td>97.6</td><td>73.7</td><td>98.9</td></tr><tr><td>C.W.region.emb</td><td>96.2</td><td>64.5</td><td>95.3</td><td>60.8</td><td>92.8</td><td>97.3</td><td>73.4</td><td>98.9</td></tr></table>",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2 is the summary of the experimental results. We use underscores to represent the best published results, and bold the best records. On six datasets of eight, our models beat or match the state-of-the-art with a performance gain highest to $0 . 7 \\%$ . We beat all the previous models on all datasets except VDCNN, while the latter performs almost best on all classification tasks before. As a result, we slightly win VDCNN on six datasets and lost in two of Amazon datasets. Detailed experimental results including best performance epoch and training time for all listed datasets are reported in Appendix A. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, the upper layer structure of our models only uses a summing up operation, which is more concise and robust than any other deep or complex models. In fact, both of our two proposed models are effective against previous models. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.5 EXPLORATORY EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this subsection, we are going to do a set of exploratory experiments to study the effect of each component of our model. Typical cases will be analyzed to validate properties of various aspects of our models. Considering the limitation of paper space, we only analyzed the Word-Context region embedding model in our exploratory experiments. ",
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+    {
+        "type": "text",
+        "text": "4.5.1 EFFECT OF REGION SIZE AND EMBEDDING SIZE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our method uses a fixed size of region as contextual information just like CNN. So the selection of region size really matters. A small region may lose some long distance patterns, whereas large regions will bring into more noises. Luckily, our models seem to be fairly insensitive towards kinds of datasets. Actually, we just use identical region size 7 for all datasets and it is able to outperform the best published results ever. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Figure 2a describes the performance on Yelp Review Full with different region sizes, and when the size equals to 1, the result is quite close to unigram FastText(accuracy $6 0 . 7 \\%$ ), but still gets a $0 . 6 \\%$ promotion. Intuitively, the middle word cannot influence other words except itself when the size equals to 1. The performance increases with the growth of region size up to 7. ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/39bb20cd81b1b28e61ee38b0e0b72bd1dfaae8572c8dfc73a0815d0a845949ca.jpg",
+        "image_caption": [
+            "Figure 2: Effect of the hyperparameters (region size and embedding size) on Yelp Review Full dataset. (a) shows the comparison of single fixed region size 7 and multi sizes combination [3,5,7] and (b) shows the effect of different settings of embedding size among four kinds of models, unigram FastText, bigram FastText, CNN and ours. We use region size 7 for CNN and ours. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Furthermore, we experiment our models with the combination of multi region sizes. Here we use the approach of sharing context units among each region, where the parameters of local context units of smaller regions are just the slice of the longest one. Region embeddings of different sizes are concatenated for final classification. In figure 2a, the combination of multi region sizes 3,5,7 is slightly better than the best single region size 7. The effectiveness of multi-size combination can be explained by the difference of influence ranges between words. For example, in sentiment analysis, word very only emphasizes the next word while however may lay stress on a wide range of the following words. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In addition to the analysis of region sizes, we further study the influence of word embedding dimensions. Figure 2b lists the comparative results on Yelp Review Full with different embedding dimensions. The result shows that our model is more robust to overfitting than FastText and CNN with the word embedding dimension increasing. In fact, the amount of parameters in our models is relatively large. Since we learn a specific unit for each word, under the same word embedding dimension, our parameter size has been expanded by region size times, the parameters number is $v \\times h + v \\times ( 2 \\times c + 1 ) \\times h + h \\times m + m$ , where $m$ is the number of classes. Specific numbers parameters for different region sizes are listed in Appendix A. Notice that the sizes of parameters are relatively consistent among $I O 2 4$ in FastText, 1024 in CNN and 128 in ours. ",
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+    },
+    {
+        "type": "text",
+        "text": "4.5.2 EFFECT OF CONTEXT UNIT ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this section, we explore some comparative experiments to show the effectiveness of our proposed word specific context unit. The experiments are employed based on unigram FastText baseline, which has similar upper layer structure with our models. Table 3 illustrates the results. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/851d4fdfd2dd8c9354ebfbd907f234e2a8cc364ded839f86f4aa23193f6c0599.jpg",
+        "table_caption": [
+            "Table 3: Comparative decomposition results on Yelp Review Full dataset. For FastText(Unigram), embedding dimension is 10. For FastText(Win-pool), W.C.region.emb(Scalar) and W.C.region.emb(our model), region size is 7 and embedding dimension is 128 "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Decomposition</td><td>Performance(%)</td></tr><tr><td>FastText(Unigram)</td><td>60.73</td></tr><tr><td>FastText(Win-pool)</td><td>61.01(+0.28)</td></tr><tr><td>W.C.region.emb(Scalar)</td><td>63.18(+2.45)</td></tr><tr><td>W.C.region.emb(Our model)</td><td>64.9(+4.17)</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Firstly, we remove the entire context units from our model, which means it is just a variant version of unigram FastText, we call it FastText(Win-pool). The difference is that FastText sums up the word embeddings directly while FastText(Win-pool) sums up the window pooled embeddings in a stride of 1. It yields a slightly accuracy gain of $0 . 2 8 \\%$ than unigram FastText. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Secondly, we apply a simplified scalar version of context units to FastText(Win-pool). Distinguishable, the context unit of each word has the shape with $1 \\times ( 2 \\times c + 1 )$ , hence it can be regarded as a broadcasting operation on corresponding word embeddings of its local context. We name this method W.C.region.emb(Scalar). Compared to the non-scalar method, it yields a huge parameter size reduction, but it already yields a significant gain of $2 . 4 5 \\%$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, W.C.region.emb(our model) is the variant version of W.C.region.emb(Scalar) where each column of scalar context unit is expanded to a dense vector. Each word’s context unit has a shape with $h \\times ( 2 \\times c { + } 1 )$ . Adding the low dimensional dense context unit improves the performance by $4 . 1 7 \\%$ . We can sense much from the procedure of decomposition, with the help of context unit, even a simpler scalar version promotes a lot. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "To have a better understanding of what context unit actually capture, heat maps are plotted for chosen word samples. Representative adversarial conjunctions like however, but, modifiers like very, good, bad and nouns like food, morning are listed in Figure 3. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For each row of the figure, the intensity of the surrounding color box reflects the emphasis degree in the view of the middle word. Qualitative but not fully rigorous, a normalized L2-norm of each column in context unit is used to render the shade. Region size 7 is adopted default, annotation $l _ { i } ( \\mathrm { i } \\le 3 )$ is denoted as left columns of the specific context unit, while $r _ { i } ( \\mathrm { i } \\leq 3 )$ denoted as the right part. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "What the figure reflects are consistent with intuitive priors of human beings. In the perspective of however, right contexts play the key role for classification polarity because of the emotional reversal, the color is indeed deeper in $r _ { i }$ than $l _ { i }$ , so does but. For word very, $r _ { 1 }$ is more prominent than the rest of all, which captures some modified patterns like very happy or very sad. For word good, tendencies will be completely different for patterns like not good, very good and not that good, which are intensive negative, intensive positive and slightly hesitated, separately, the position of $l _ { 1 }$ will be strengthened as a result, so does word bad. There are significant differences between two nouns food and morning. The heat map of word food implies patterns like delicious food or food was mediocre, while the word morning has fewer valuable patterns for classification. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Actually, from the motivation of word specified context units, we would like to believe this feature helps capture syntactic and semantic influences of words on surrounding words at relative positions. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5.3 VISUALIZATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this subsection, we will try to visualize the contribution of each word and selected phrase to classification. Detailed visualization techniques have been introduced in Li et al. (2015). Here we generalize it to the color rendering of multi-category version. Notice that for our model, not the original embedding acts here, but the accumulation of the projected embedding of each word on its surrounding words. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d80f79fd5893ceddc980a9e774ce57d694780e54d6e8c6922edb16fc33afb1b7.jpg",
+        "image_caption": [
+            "Figure 3: Heat maps of chosen words trained on Yelp Review Polarity, which is a binary sentiment analysis dataset. Each row represent the context unit of the middle word. Region size is 7 and embedding size is 128. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/4a0a60d315cde0e9390177ea56c2e4e1eb05d45ed4e0c6c601c0b643c7c7d6e8.jpg",
+        "table_caption": [
+            "Table 4: Visualization of chosen samples on Yelp Review Polarity dataset. Green denotes positive contribution while red denotes negative. Two methods are compared without context unit(No C-unit) and with context unit(With C-unit). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Method</td><td rowspan=1 colspan=8>Sentence Samples</td><td rowspan=1 colspan=3></td><td rowspan=1 colspan=3>Phrase</td></tr><tr><td rowspan=1 colspan=1>No C-unit</td><td rowspan=1 colspan=2>getyour</td><td rowspan=1 colspan=2>wallet</td><td rowspan=1 colspan=1>ready</td><td rowspan=1 colspan=3>theprices</td><td rowspan=1 colspan=1>are</td><td rowspan=1 colspan=1>crazy</td><td rowspan=1 colspan=1>high</td><td rowspan=1 colspan=3> prices are crazy high</td></tr><tr><td rowspan=1 colspan=1>With C-unit</td><td rowspan=1 colspan=4>get your wallet ready</td><td rowspan=1 colspan=4>the prices are crazy</td><td rowspan=1 colspan=1>are</td><td rowspan=1 colspan=1>crazy</td><td rowspan=1 colspan=1>high</td><td rowspan=1 colspan=3> prices are crazy high</td></tr><tr><td rowspan=2 colspan=1>No C-unitWith C-unit</td><td rowspan=2 colspan=1></td><td rowspan=1 colspan=2>nothing</td><td rowspan=1 colspan=3>remarkable</td><td rowspan=1 colspan=1>but</td><td rowspan=1 colspan=1>not</td><td rowspan=1 colspan=1>bad</td><td rowspan=1 colspan=1>either</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>but not bad either</td><td rowspan=2 colspan=1></td></tr><tr><td rowspan=1 colspan=2>nothing</td><td rowspan=1 colspan=4>remarkable   but</td><td rowspan=1 colspan=1>not</td><td rowspan=1 colspan=1>bad</td><td rowspan=1 colspan=1>either</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>but not bad either</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "For clarity, we choose a binary classification task of sentiment analysis. In Table 4, we list two cases in Yelp Review Polarity dataset, in which our model behaves as expected. Words and artificially selected phrases are highlighted green if they are positive factors, red if they are negative. The intensity of the color indicates the degree of the polarity. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To have a better comparison, the results of with and without context unit methods are both visualized. We abbreviate them as With $C$ -unit and No $C$ -unit, respectively. For sentence get your wallet ready, the prices are crazy high, if no context unit is adopted, the word color reflects its word embedding, which is context-free. The polarity of crazy is positive, and high is negative. Because the intensity of crazy is higher than high, the polarity of phrase prices are crazy high is totally positive, which is a mistake. But with context unit, things have changed quite a bit, the polarities of words are context dependent. Under the influence of high, the positive polarity of crazy vanishes and phrase prices are crazy high performs negative overall. For another case nothing remarkable, but not bad either, things seem more interesting. Without context-unit , remarkable is positive, while nothing, not, bad perform negative, respectively. But with context unit, the polarity of the part ahead of but weakens, meanwhile the polarities of not and bad flips. As a result, phrase but not bad either performs positive overall. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This paper proposed two novel architectures for text classification tasks, which learn task specific region embeddings without hand crafted features. To utilize the word specific influences of each word on its context words, a local context unit for each word is learned in addition to word embedding. Our models achieve state-of-the-art performances on six benchmark text classification datasets, and the visualization experiments show that our proposed local context unit can capture the semantic and syntactic information for each word. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+            137,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Noticed the power of the local context unit on learning task related region embeddings, we are interested in its ability to unsupervised and semi-supervised learning. At the same time, we are also curious about whether we can achieve better results by introducing more complex upper layers on text classification, and other natural language processing tasks. ",
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            239,
+            356,
+            254
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "This paper is supported by National Basic Research Program of China (973 program No.2014CB340505). We gratefully thank the anonymous reviewers for their insightful comments. ",
+        "bbox": [
+            173,
+            268,
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+            293
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            135,
+            278,
+            150
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A DETAILED EXPERIMENTAL RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            167,
+            509,
+            181
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "To have a further insight about our reported results, we list the training time and best testing performance epoch for kinds of region sizes(5,7,9) in detail. For all the 8 datasets in Table 5, hyperparameters are kept in line with section 4.3. The dimension of word embedding is 128, the region size is 7, the initial learning rate is set to $1 \\times 1 0 ^ { - 4 }$ , and the batch size is 16. Epoch index starts from 0 and training time is reported per epoch. We choose the model of word-context region embedding here. ",
+        "bbox": [
+            174,
+            195,
+            823,
+            260
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/c7344c3fadf72816e2973c847a64bdb9fa62b548521438748c2139c022e1a8d7.jpg",
+        "table_caption": [
+            "Table 5: Experimental detailed records on several datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Vocabulary Size</td><td>W.C Region Size</td><td>Parameters Number</td><td>Best Epoch</td><td>Training Time(Mins)</td><td>Accuracy(%)</td></tr><tr><td rowspan=\"3\">Yelp P.</td><td rowspan=\"3\">115298</td><td>5</td><td>88,549,122</td><td>3</td><td>27</td><td>96.34</td></tr><tr><td>7</td><td>118,065,410</td><td>3</td><td>36</td><td>96.39</td></tr><tr><td>9</td><td>147,581,698</td><td>3</td><td>43</td><td>96.38</td></tr><tr><td rowspan=\"3\">Yelp F.</td><td rowspan=\"3\">124273</td><td>5</td><td>95,442,309</td><td>3</td><td>34</td><td>64.73</td></tr><tr><td>7</td><td>127,256,197</td><td>2</td><td>43</td><td>64.90</td></tr><tr><td>9</td><td>159,070,085</td><td>2</td><td>52</td><td>64.74</td></tr><tr><td rowspan=\"3\">Amz. P.</td><td rowspan=\"3\">394385</td><td>5</td><td>302,887,938</td><td>2</td><td>336</td><td>95.07</td></tr><tr><td>7</td><td>403,850,498</td><td>2</td><td>402</td><td>95.23</td></tr><tr><td>9</td><td>504,813,058</td><td>2</td><td>589</td><td>95.06</td></tr><tr><td rowspan=\"3\">Amz. F.</td><td rowspan=\"3\">356312</td><td>5</td><td>273,648,261</td><td>1</td><td>300</td><td>60.83</td></tr><tr><td>7</td><td>364,864,133</td><td>1</td><td>395</td><td>60.93</td></tr><tr><td>9</td><td>456,080,005</td><td>1</td><td>490</td><td>61.05</td></tr><tr><td rowspan=\"3\">AG</td><td rowspan=\"3\">42783</td><td>5</td><td>32,857,860</td><td>6</td><td>2</td><td>92.81</td></tr><tr><td>7</td><td>43,810,308</td><td>4</td><td>3</td><td>92.89</td></tr><tr><td>9</td><td>54,762,756</td><td>5</td><td>4</td><td>92.82</td></tr><tr><td rowspan=\"3\">Sogou</td><td rowspan=\"3\">99394</td><td>5</td><td>76,335,237</td><td>7</td><td>27</td><td>97.6</td></tr><tr><td>7</td><td>101,780,101</td><td>9</td><td>33</td><td>97.63</td></tr><tr><td>9</td><td>127,224,965</td><td>10</td><td>39</td><td>97.56</td></tr><tr><td rowspan=\"3\">Yah.A.</td><td rowspan=\"3\">361926</td><td>5</td><td>277,960,458</td><td>1</td><td>160</td><td>73.42</td></tr><tr><td>7</td><td>370,613,514</td><td>1</td><td>210</td><td>73.66</td></tr><tr><td>9</td><td>463,266,570</td><td>2</td><td>256</td><td>73.68</td></tr><tr><td rowspan=\"3\">DBP</td><td rowspan=\"3\">227863</td><td>5</td><td>175,000,590</td><td>3</td><td>37</td><td>98.87</td></tr><tr><td>7</td><td>233,333,518</td><td>2</td><td>48</td><td>98.89</td></tr><tr><td>9</td><td>291,666,446</td><td>3</td><td>60</td><td>98.94</td></tr></table>",
+        "bbox": [
+            179,
+            294,
+            816,
+            630
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We also report results of several repeated runs in Table 6 to exclude the effect of randomness and ensure reproducibility. Five independent runs are conducted on each dataset of Yelp.P and Yelp.F, where both performance variances are within $0 . 1 1 \\%$ on accuracy. ",
+        "bbox": [
+            174,
+            643,
+            823,
+            681
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/ae0c82de8dfce76f2770bd1e9d693b1c71160217f8930efc04d49ddca8b3e217.jpg",
+        "table_caption": [
+            "Table 6: Performance variances through several repeated runs on Yelp Datasets "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Tries Num.</td><td>W.C region size</td><td>Best Epoch</td><td>Accuracy(%)</td><td>Performance Variance</td></tr><tr><td rowspan=\"5\">Yelp P.</td><td>0</td><td>7</td><td>3</td><td>96.39</td><td rowspan=\"5\">≤%0.11</td></tr><tr><td>1</td><td>7</td><td>4</td><td>96.36</td></tr><tr><td>2</td><td>7</td><td>4</td><td>96.41</td></tr><tr><td>3</td><td>7</td><td>3</td><td>96.38</td></tr><tr><td>4</td><td>7</td><td>2</td><td>96.46</td></tr><tr><td rowspan=\"5\">Yelp F.</td><td>0</td><td>7</td><td>2</td><td>64.90</td><td rowspan=\"5\">≤%0.11</td></tr><tr><td>1</td><td>7</td><td>2</td><td>64.94</td></tr><tr><td>2</td><td>7</td><td>1</td><td>64.87</td></tr><tr><td>3</td><td>7</td><td>1</td><td>64.86</td></tr><tr><td>4</td><td>7</td><td>2</td><td>64.98</td></tr></table>",
+        "bbox": [
+            173,
+            723,
+            825,
+            868
+        ],
+        "page_idx": 11
+    }
+]

parse/train/ByeSdsC9Km/ByeSdsC9Km.md

@@ -0,0 +1,302 @@
+# ADAPTIVE POSTERIOR LEARNING: FEW-SHOT LEARNING WITH A SURPRISE-BASED MEMORY MODULE
+
+Tiago Ramalho   
+Cogent Labs   
+tramalho@cogent.co.jp   
+Marta Garnelo   
+DeepMind   
+garnelo@google.com
+
+# ABSTRACT
+
+The ability to generalize quickly from few observations is crucial for intelligent systems. In this paper we introduce APL, an algorithm that approximates probability distributions by remembering the most surprising observations it has encountered. These past observations are recalled from an external memory module and processed by a decoder network that can combine information from different memory slots to generalize beyond direct recall. We show this algorithm can perform as well as state of the art baselines on few-shot classification benchmarks with a smaller memory footprint. In addition, its memory compression allows it to scale to thousands of unknown labels. Finally, we introduce a meta-learning reasoning task which is more challenging than direct classification. In this setting, APL is able to generalize with fewer than one example per class via deductive reasoning.
+
+# 1 INTRODUCTION
+
+Consider the following sequential decision problem: at every iteration of an episode we are provided with an image of a digit (e.g. MNIST) and an unknown symbol. Our goal is to output a digit $Y = X + S$ where $X$ is the value of the MNIST digit, and $S$ is a numerical value that is randomly assigned to the unknown symbol at the beginning of each episode. After seeing only a single instance of a symbol an intelligent system should not only be able to infer the value $S$ of the symbol but also to correctly generalize the operation associated with the symbol to any other digit in the remaining iterations of that episode.
+
+Despite its simplicity, this task emphasizes three cognitive abilities that a generic learning algorithm should display: 1. the algorithm can learn a behaviour and then flexibly apply it to a range of different tasks using only a few context observations at test time; 2. the algorithm can memorize and quickly recall previous experiences for quick adaptation; and 3. the algorithm can process these recalled memories in a non-trivial manner to carry out tasks that require reasoning.
+
+The first point is commonly described as “learning to learn” or meta-learning, and represents a new way of looking at statistical inference (Schmidhuber, 1987; Bengio et al., 1990; Bengio & LeCun, 2007). Traditional neural networks are trained to approximate arbitrary probability distributions with great accuracy by parametric adaptation via gradient descent (LeCun et al., 2015; Schmidhuber, 2015). After training that probability distribution is fixed and neural networks can only generalize well when the testing distribution matches the training distribution (Neyshabur et al., 2017). In contrast, meta-learning systems are trained to learn an algorithm that infers a function directly from the observations it receives at test time. This setup is more flexible than the traditional approach and generalizes better to unseen distributions as it incorporates new information even after the training phase is over. It also allows these models to improve their accuracy as they observe more data, unlike models which learn a fixed distribution.
+
+The second requirement - being able to memorize and efficiently recall previous experience - is another active area of research. Storing information in a model proves especially challenging as we move beyond small toy-examples to tasks with higher dimensional data or real-world problems.
+
+Current methods often work around this by summarizing past experiences in one lower-dimensional representation (Hochreiter & Schmidhuber, 1997; Kingma & Welling, 2013) or using memory modules (Graves et al., 2016). While the former approach can produce good results, the representation and therefore the amount of information we can ultimately encode with such models will be of a fixed and thus limited size. Working with neural memory modules, on the other hand, presents its own challenges as learning to store and keep the right experiences is not trivial. In order to successfully carry out the task defined at the beginning of this paper a model should learn to capture information about a flexible and unbounded number of symbols observed in an episode without storing redundant information.
+
+Finally, reasoning requires processing recalled experiences in order to apply the information they contain to the current data point being processed. In simple cases such as classification, it is enough to simply recall memories of similar data points and directly infer the current class by combining them using a weighted average or a simple kernel (Vinyals et al., 2016; Snell et al., 2017), which limits the models to performing interpolation. In the example mentioned above, more complex reasoning is necessary for human-level generalisation.
+
+In this paper we introduce Approximate Posterior Learning (APL, pronounced like the fruit), a self-contained model and training procedure that address these challenges. APL learns to carry out few-shot approximation of new probability distributions and to store only as few context points as possible in order to carry out the current task. In addition it learns how to process recalled experiences to carry out tasks of varying degrees of complexity. This sequential algorithm was inspired by Bayesian posterior updating (Jaynes, 2003) in the sense that the output probability distribution is updated as more data is observed.
+
+We demonstrate that APL can deliver accuracy comparable to other state-of-the-art algorithms in standard few-shot classification benchmarks while being more data efficient. We also show it can scale to a significantly larger number of classes while retaining good performance. Finally, we apply APL to the reasoning task introduced as motivation and verify that it can perform the strong generalization we desire.
+
+The main contributions of this paper are:
+
+• A simple memory controller design which uses a surprise-based signal to write the most predictive items to memory. By not needing to learn what to write, we avoid costly backpropagation through memory which makes the setup easier and faster to train. This design also minimizes how much data is stored, making our method more memory efficient. • An integrated external and working memory architecture which can take advantage of the best of both worlds: scalability and sparse access provided by the working memory; and all-to-all attention and reasoning provided by a relational reasoning module. • A training setup which steers the system towards learning an algorithm which approximates the posterior without backpropagating through the whole sequence of data in an episode.
+
+# 2 MODEL
+
+# 2.1 ARCHITECTURE
+
+Our proposed model is composed of a number of parts: an encoder that generates a representation for the incoming query data; an external memory store which contains previously seen representation/ data pairings with writing managed by a memory controller; and a decoder that ingests the query representation as well as data from the memory store to generate a probability distribution over targets. We describe each of the parts in detail below1.
+
+Encoder The encoder is a function which takes in arbitrary data $x _ { t }$ and converts it to a representation $e _ { t }$ of (usually) lower dimensionality. In all our experiments $x _ { t }$ is an image, and we therefore choose a convolutional network architecture for the encoder. Architectural details of the encoder used for each of the experiments are provided in the appendix.
+
+![](images/355aa60c9185cd75d6b6a18b73b967f6ed0eaddd8a357d1f8458d35c4561f9d8.jpg)  
+Figure 1: APL model applied to the the classification of an Omniglot image. The encoded image is compared to the entries of the memory and the most relevant ones are passed through a decoder that outputs a probability distribution over the labels. The dotted line indicates the parts of the graph that are not updated via back-propagation.
+
+Memory store The external memory module is a database containing the stored experiences. Each of the columns corresponds to one of the attributes of the data. In the case of classification, for example, we would store two columns: the embedding $e _ { m }$ and the true label $y _ { m }$ . Each of the rows contains the information for one data point. The memory module is queried by finding the k-nearest neighbors between a query and the data in a given column. The full row data for each of the neighbors is returned for later use. The distance metric used to calculate proximity between the points is an open choice, and here we always use euclidean distance.
+
+Since we are not backpropagating through the memory, how do we ensure that the neighbors returned by the querying mechanism contain task-relevant information? We expect that class-discriminative embeddings produced by the encoder should cluster together in representation space, and therefore should be close in the sense of euclidean distance. While this is not mathematically necessary, in the following sections we will show that APL as proposed does work and retrieve the correct neighbors which means that in practice our intuition holds true.
+
+Memory controller We use a simple memory controller which tries to minimize the amount of data points written to memory. Let us define surprise as the quantity associated with the prediction for label $y _ { t }$ as ${ \bf S } = - l n ( y _ { t } )$ . Intuitively, this means that the higher the probability our model assigns to the true class, the less surprised it will be.
+
+This suggests a way of storing the minimal amount of data points in memory which supports maximal classification accuracy. If a data point is ’surprising’, it should be stored in memory; otherwise it can be safely discarded as the model can already classify it correctly.
+
+How should the memory controller decide whether a point is ’surprising’? In this work we choose the simplest possible controller: if the surprise is greater than some hyperparameter $\sigma$ , then that data should be stored in memory. For our experiments, we choose $\sigma \propto - \ln ( N )$ where $N$ is the number of classes under classification which means that if the prediction confidence in the correct class is smaller than the probability assigned by a uniform prediction the value should be written to memory. In the appendix we show that after model training model performance is robust to variations in $\sigma$ , as surprise becomes highly bimodal: a new data point tends to be either highly surprising (never seen something similar before) or not very surprising.
+
+Conveniently, in the case of classification problems the commonly used cross-entropy loss reduces to our measure of surprise directly, and we therefore use the prediction loss as an input to the memory controller directly.
+
+Decoder The decoder takes as input the query representation as well as all the data from the neighbors found in the external memory. We designed a relational feed-forward module with self attention which takes particular advantage of the external memory architecture. In addition we tested two other established decoder architectures: an unrolled relational working memory core and an unrolled LSTM. As all experiments have a classification loss at the end, all the decoders return a vector with logits for the $N$ classes under consideration. Full details of each architecture are provided in the Appendix.
+
+• Relational self-attention feed-forward decoder. The relational feed-forward module (see figure 2, left) processes each of the neighbors individually by comparing them with the query, and then does a cross-element comparison with a self-attention module before reducing the activations with an attention vector calculated from neighbor distances.
+
+![](images/cbfa827ae16bd4a77580ecd8a56b6be593666f81498fc976ee7e7e33bdb298ea.jpg)  
+Figure 2: Two of the three different decoder architectures of APL: relational feed-forward memory (left) and relational working memory (Santoro et al., 2018) (right). In the figure $e _ { t }$ corresponds to the encoded target, $e _ { 1 \dots m }$ to the encoded observations from the memory, $l _ { 1 . . . m } = f ( y _ { 1 . . . m } )$ are the labels processed by an embedding layer and $d _ { 1 \dots m }$ is the distance between $e _ { t }$ and $e _ { 1 \dots m }$ .
+
+• Relational working memory decoder (Santoro et al., 2018) The relational working memory module (figure 2, right) takes in the concatenated neighbor embeddings and corresponding label embeddings as its initial memory state. The query is fed a number $N$ times as input to the relational memory core to unroll the computation.
+
+• LSTM decoder Finally we also test a vanilla LSTM decoder that takes in the query as the initial memory state and is fed each of the concatenated neighbor embeddings and corresponding label embeddings as its input each time step.
+
+# 2.2 TRAINING SETUP
+
+Since we are looking for a system which can update its beliefs in an online manner we need a training procedure that reflect this behaviour. We train the system over a sequence of episodes that are composed of sequences of pairs $( x _ { t } , y _ { t } )$ . At the start of every episode the mapping $x _ { t }  y _ { t }$ is shuffled in a deterministic manner (the exact details are task dependent and will be outlined in the experiments section). The data is then presented to the model sequentially in a random order. The model’s memory is empty at the beginning of the episode.
+
+At each time step, a batch of examples is shown to the model and a prediction is made. We then measure the instantaneous loss $L ( \hat { y } _ { t } , y _ { t } )$ and perform a gradient update step on the network to minimize the loss on that batch alone. The loss is also fed to the memory controller for the network to decide whether to write to memory. In all the experiments below the task is to classify some quantity, therefore we use cross entropy loss throughout.
+
+![](images/d7aad9d64cf23f65f53eb43bab580b91bcd2bf89c273cab89eb5b62d66f32a12.jpg)  
+Figure 3: APL training over several iterations. The encoder $e$ embeds the query image that is compared against the stored experiences in the memory $M$ . Matches are fed alongside the encoded image into a decoder $d$ . Finally, the controller $c$ decides whether the currently observed example should be stored in memory.
+
+APL learns a sequential update algorithm, that is, it minimizes the expected loss over an episode consisting of a number of data elements presented sequentially. However we don’t need to backpropagate through the sequence to learn the algorithm. Rather, the model’s parameters are updated to minimize the cross-entropy loss independently at each time step. Therefore the only pressure to learn a sequential algorithm comes from the fact that episodes are kept small so that the decoder is encouraged to read the information coming from the queried neighbors instead of just learning to fit the current episode’s label mapping in its weights after a few steps of gradient descent (which is what happens in the case of MAML (Finn et al., 2017)).
+
+# 3 RELATED WORK
+
+Meta-learning as a research field covers a large number of areas. The concept of ‘learning to learn’ is not tied to a specific task and thus meta-learning algorithms have been successfully applied to a wide range of challenges like RL (Wang et al., 2016; Finn et al., 2017), program induction (Devlin et al., 2017) few-shot classification (Koch et al., 2015; Vinyals et al., 2016) and scene understanding (Eslami et al., 2018).
+
+Some meta learning models generate predictions in an autoregressive fashion by predicting the next target point from the entire prior sequence of consecutive observations (Reed et al., 2018; Mishra et al., 2018). Algorithms of this kind have delivered state-of-the art results in a range of tasks such as supervised learning to classification. Nonetheless their reliance on the full context history in addition to their autoregressive nature hinders parallelization and hurts performance and scalability.
+
+Another set of methods is based on the nearest neighbours approach (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017). These methods use an encoder to find a suitable embedding and then perform a memory look up based on these representations. The result is a weighted average of the returned labels. As shown in (Mishra et al., 2018) using a pure distance metric to compare neighbors results in worse performance than allowing a network to learn a comparison function. These kinds of methods thus suffer in comparison. Meta Networks (Munkhdalai & Yu, 2017) also use an external memory to enable learning from previous examples combined with a model featuring slow and fast weights to produce the output, enabling them to state-of-the-art performance in several benchmarks.
+
+Conditional neural processes (Garnelo et al., 2018) summarize the data into a fixed representation by averaging over the outputs of an encoder. This representation is fed into a decoder together with a query to produce the output. These methods are more space and compute efficient but given the fixed and averaged representation may not scale to very large problems.
+
+All of the above methods expect a fixed size context, thereby making life-long learning over large time horizons difficult. To enable this, an algorithm must learn to only write observations into memory when they provide additional predictive power. Memory augmented neural networks (MANN) (Santoro et al., 2016) achieve this by learning a controller to write into a differentiable neural dictionary. However, this requires backpropagating through the entire sequence to learn, which makes credit assignment over long time sequences hard and is computationally expensive. The idea of using an external memory module has been explored in (Kaiser et al., 2017) and shown to produce good results. Compared to that work we introduce a simpler writing mechanism and the idea of a relational decoder to exploit the nearest neighbor structure.
+
+# 4 EXPERIMENTS
+
+# 4.1 FEW-SHOT OMNIGLOT CLASSIFICATION
+
+The Omniglot dataset contains 1623 characters with 20 examples each. 1200 of the character classes are assigned to the train set while the remaining 423 are part of the test set. The examples are presented to the model sequentially in batches of 16 examples. For each episode, we choose $N$ classes and shuffle their labels. We then run an episode for a certain number of steps, which is decreased as the model’s accuracy increases to encourage quick adaptation. This means that the model accuracy and number of memories written to memory is time dependent.
+
+We follow an architecture similar to those used in previous work for the image encoder (Vinyals et al., 2016; Mishra et al., 2018), which consists of four convolutional blocks with 3x3 convolutions, relu and batch normalization. We augment the number of classes in the training set by rotating each symbol 90, 180 and 270 degrees as in previous work (Santoro et al., 2016). For this task, we found that all three decoder architectures perform similarly. A detailed comparison and all hyperparameters needed to reproduce this experiment are provided in the Appendix.
+
+In Figure 4a we can see the behavior of the algorithm within a single episode. As it sees more examples its performance increases until it saturates at some point, when additional writes don’t help anymore (assuming the exact same data piece won’t be seen again, which is the regime we always assume here). In the simple case of 5-way Omniglot classification, fewer than 2 examples per class are sufficient to saturate performance.
+
+In Figure 4b we demonstrate the evolution of the posterior distribution in 20-way classification for 3 different, fixed inputs. For the first step, where the memory is empty APL learns to output a uniform distribution $( p \simeq 1 / N$ with $\mathbf { N }$ the number of classes under classification). As more examples are added to memory, its distribution refines until it sees an informative example for that class, at which point its prediction becomes very confident.
+
+In Figure 4c we can see that different numbers of examples are written to memory for different classes, which demonstrates one of the advantages of this framework: we only need to store as many examples as each class requires, therefore if some classes may be more easily classified than others we can optimally use memory. In contrast, other models feed in a fixed context size per class which means they will either suffer in accuracy or use excessive memory.
+
+![](images/a35e3cd15cb2be90e9d7c00eb5e3de8820437e502b78da2c93d1a8eb6c12aaec.jpg)  
+Figure 4: a) Accuracy and size of memory for 5-way Omniglot. APL stops writing to memory after having 2 examples per class for 5-way classification. b), examples of evolution of posterior distribution for 20-way classification for 3 images. The distribution starts as uniform for the very first step, then starts to change as more items are added to memory. When the correct class is seen, the distribution converges. c), the number of labels stored in memory per class is highly heterogeneous. In this 20-way problem, APL stored 44 items in memory and achieved $9 8 . 5 \%$ accuracy, which is higher than its homogeneous 5-shot accuracy. d) Accuracy vs. number of items written to memory for 1000-way classification. Classification accuracy when only 2000 examples have been written to memory (on average 2 examples per class) surpasses the accuracy for a fixed context size of 5 examples per class.
+
+Despite the previous point, it is also worthwhile comparing model accuracy to existing baselines with a fixed context size. To this end, we pre-populate the memory of a trained model with 1 or 5 examples per class and calculate the accuracy over the test set. We emphasize that the model was not trained to do well in this fixed-context scenario, and yet for 1 and 5-shot classification we obtain performance comparable to state-of-the-art models without having extensively tuned hyperparameters. Furthermore we tested our model with a much higher number of classes: 423-way classification where where we can use the whole test set, and 1000-way where the test set is augmented with rotations of the characters as we do in training.
+
+Finally, we test how the model fares on a completely new distribution, MNIST. For 1-shot, 10-way MNIST, APL trained on 20-way omniglot classification obtains $61 \%$ accuracy (compared to $72 \%$ cited by (Vinyals et al., 2016)). Testing our model in the sequential regime, we observe that it continues writing examples to memory as it sees surprising observations, which allows it to correct for the distribution shift. After writing 45 examples per class, it reaches an accuracy of $86 \%$ (there are 1000 examples per class in the MNIST test set, so it is not simply memorizing).
+
+Table 1: Omniglot test accuracies for fixed context sizes compared to other baselines. († For 1000- way classification rotated pseudoclasses are used.)   
+
+<table><tr><td rowspan="2"></td><td colspan="2">5-way</td><td colspan="2">20-way</td><td colspan="2">423-way</td><td colspan="2">1000-way†</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Matching nets</td><td>98.1%</td><td>98.9%</td><td>93.8%</td><td>98.5%</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CNP</td><td>95.3%</td><td>98.5%</td><td>89.9%</td><td>96.8%</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>MANN</td><td>82.2%</td><td>94.9%</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MAML</td><td>98.7%</td><td>99.9%</td><td>95.8%</td><td>98.9%</td><td></td><td>-</td><td>-</td><td></td></tr><tr><td>SNAIL</td><td>99.07%</td><td>99.78%</td><td>97.64%</td><td>99.35%</td><td>-</td><td>-</td><td>1</td><td>-</td></tr><tr><td>APL</td><td>97.9%</td><td>99.9%</td><td>97.2%</td><td>97.6%</td><td>73.5%</td><td>88.0%</td><td>68.9%</td><td>78.9%</td></tr></table>
+
+# 4.2 IMAGENET
+
+![](images/a8720edcb02b5a0aa7780ee57c5c5b415e2b55707ba55a2c1aaba528ab46766c.jpg)  
+Figure 5: Evolution of top-1 accuracy and number of written examples to memory over a single episode for the Imagenet dataset. Curves are averages over 5 test episodes and smoothed with exponential moving average.
+
+We also applied our model to the full scale imagenet dataset. Unlike the above experiments there are no held out classes for testing, as the dataset was not conceived with held out classes in mind. Instead, we rely on shuffling the labels amongst the 1000 Imagenet classes and using the images from the test set for evaluation. This means the generalization results are slightly weaker than in the above sections, but they still provide important insights as to the scalability of our method to thousands of classes and applicability to harder scenarios.
+
+As an encoder we use the pretrained Inception-ResNet-v2 (Szegedy et al., 2017) due to computational constraints. For the fixed label case, this network reaches a top-1 accuracy of $8 0 . 4 \%$ . Training the encoder end-to-end might produce better results, an investigation which we leave to later work.
+
+In the 20-way classification challenge, our method reaches $8 6 . 7 \%$ top-1 accuracy (average accuracy after 50 iterations). Performance remains very high for 100-way $7 2 . 9 \%$ top-1 accuracy). The model’s performance degrades somewhat $( 5 2 . 6 \%$ top-1 accuracy) for 1000-way classification, where all the classes are shuffled. This highlights that large scale meta-learning on real world datasets remains a challenge even when all the classes have been observed by the encoder, as in this case.
+
+# 4.3 NUMBER ANALOGY
+
+The number analogy task challenges a meta-learning model to use logic reasoning to generalize with fewer than 1 example per possible class (Figure 6). At each time step the network is shown two pieces of data, a number $X$ and a symbol $S$ . It is asked to classify the result of $X + S$ based only on the current data and its previous experiments. We experiment with two levels of difficulty for this task: in the first, the number values are fixed and correspond to the MNIST digits, while there are
+
+10 different symbols with unknown values in each episode; in the second, both digits and symbols have shuffled values. We sample the symbol values in the range $[ - 1 0 , 1 0 ]$ .
+
+When querying the memory, we query $k$ neighbors via the number embeddings and $k$ neighbors via the symbol embeddings. This makes sure that any relevant information to the problem is available to the reasoning module. The rest of the training setup is identical to the Omniglot experiments, including the encoder network for the digits.
+
+In the case where the numbers are fixed a human would need only see 10 examples, one for each symbol, to be able to correctly generalize for all 100 possible combinations. With one example per symbol, APL reaches $9 7 . 6 \%$ accuracy on the test set.
+
+When both numbers and symbols are shuffled each episode, a logical deduction process must be performed to infer the correct symbols. Our model is able to generalize using 50 examples written to memory (Figure 6) which is still fewer than seeing one of all 100 possible combinations.
+
+In this complex case, once a symbol’s meaning has been figured out it is no longer necessary to solve the system of equations for that unknown. It would be interesting to explore how a system could additionally store this information in memory for later reuse, a question we leave for later work.
+
+![](images/7c1bcf07a05532ad70c152f3ba9ae1fd0a60a4b9471eff97af48c2059dbc7099.jpg)  
+Figure 6: Left: Number analogy task. The colored symbols have unknown values that are consistent throughout an episode. Right: Accuracy as a function of number of examples seen for the Analogy task where the number meanings are also shuffled each episode. Curves are averages over 10 test episodes and smoothed with exponential moving average. On the left we fix the decoder (relational self-attention feed-forward module) and vary $k$ . As there are 100 possible combinations of symbols (10 numbers $\times 1 0$ symbols), the thick dashed line corresponds to the performance of a model capable of perfect 1-shot generalization. We can see that for $k = 8$ and $k = 1 6$ the decoder can infer the symbol and number meanings to do better than direct 1-shot classifications. On the right we fix $k = 1 6$ and show that the relational self-attention feed-forward module can generalize better from few examples than other decoder architectures.
+
+# 5 CONCLUSION
+
+We introduced a self-contained system which can learn to approximate a probability distribution with as little data and as quickly as it can. This is achieved by putting together the training setup which encourages adaptation; an external memory which allows the system to recall past events; a writing system to adapt the memory to uncertain situations; and a working memory architecture which can efficiently compare items retrieved from memory to produce new predictions.
+
+We showed that the model can:
+
+• Reach state of the art accuracy with a smaller memory footprint than other meta-learning models by efficiently choosing which data points to remember.   
+• Scale to very large problem sizes thanks to the use of an external memory module with sparse access.   
+• Perform fewer than 1-shot generalization thanks to relational reasoning across neighbors.
+
+# ACKNOWLEDGMENTS
+
+The authors thank Elco Bakker, Alex Pritzel and David Raposo for insightful discussions; Paul Komarek, Adrià Puigdomènech for help with writing code; and Kevin McKee for revising the manuscript.
+
+# REFERENCES
+
+Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al. Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261, 2018.
+
+Yoshua Bengio and Yann LeCun. Scaling learning algorithms towards AI. In Large Scale Kernel Machines. MIT Press, 2007.
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+Alex Graves, Greg Wayne, Malcolm Reynolds, Tim Harley, Ivo Danihelka, Agnieszka GrabskaBarwinska, Sergio Gómez Colmenarejo, Edward Grefenstette, Tiago Ramalho, John Agapiou, ´ et al. Hybrid computing using a neural network with dynamic external memory. Nature, 538 (7626):471, 2016.
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+Scott Reed, Yutian Chen, Thomas Paine, Aäron van den Oord, S. M. Ali Eslami, Danilo Rezende, Oriol Vinyals, and Nando de Freitas. Few-shot autoregressive density estimation: Towards learning to learn distributions. In International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id $\underline { { \underline { { \mathbf { \Pi } } } } } =$ r1wEFyWCW.
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+Andrei A Rusu, Neil C Rabinowitz, Guillaume Desjardins, Hubert Soyer, James Kirkpatrick, Koray Kavukcuoglu, Razvan Pascanu, and Raia Hadsell. Progressive neural networks. arXiv preprint arXiv:1606.04671, 2016.
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+Adam Santoro, Sergey Bartunov, Matthew Botvinick, Daan Wierstra, and Timothy Lillicrap. Metalearning with memory-augmented neural networks. In International conference on machine learning, pp. 1842–1850, 2016.
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+Adam Santoro, Ryan Faulkner, David Raposo, Jack Rae, Mike Chrzanowski, Theophane Weber, Daan Wierstra, Oriol Vinyals, Razvan Pascanu, and Timothy Lillicrap. Relational recurrent neural networks. arXiv preprint arXiv:1806.01822, 2018.
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+Jürgen Schmidhuber. Evolutionary principles in self-referential learning, or on learning how to learn: the meta-meta-... hook. PhD thesis, Technische Universität München, 1987.
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+Jürgen Schmidhuber. Deep learning in neural networks: An overview. Neural networks, 61:85–117, 2015.
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+
+Jane X Wang, Zeb Kurth-Nelson, Dhruva Tirumala, Hubert Soyer, Joel Z Leibo, Remi Munos, Charles Blundell, Dharshan Kumaran, and Matt Botvinick. Learning to reinforcement learn. arXiv preprint arXiv:1611.05763, 2016.
+
+Jaehong Yoon, Eunho Yang, Jeongtae Lee, and Sung Ju Hwang. Lifelong learning with dynamically expandable networks. 2018.
+
+# 6 SUPPLEMENTARY MATERIAL
+
+# 6.1 MODEL ARCHITECTURES AND TRAINING DETAILS
+
+For all experiments below we use the same training setup. For each training episode we sample elements from $N$ classes and randomly shuffle them to create training batches. For every batch shown to the model, we do one step of gradient descent with the Adam optimizer. We anneal the learning rate from $1 0 ^ { - 4 }$ to $1 0 ^ { - 5 }$ with exponential decay over 1000 steps (decay rate 0.9).
+
+For all experiments, the query data is passed through an embedding network (described below in), and this vector is used to query an external memory module. The memory module contains multiple columns of data, one of which will be the key and the others will contain data associated with that key. The necessary columns for each experiment are outlined below. The memory size is chosen so that elements will never be overwritten in a single episode (i.e. memory size $>$ batch size $\times$ number of iterations).
+
+The returned memory contents as well as the query are fed to one of the decoder architectures described in section 6.2.
+
+# 6.1.1 OMNIGLOT
+
+For omniglot we encode the images with a convolutional network composed of a single first convolution to map the image to 64 feature channels, followed by 12 convolutional blocks. Each block is made up of a step of Batch Normalization, followed by a ReLU activation and a convolutional layer with kernel size 3. Every three blocks the convolution contains a stride 2 to downsample the image. All layers have 64 features. Finally we flatten the activations to a 1D vector and pass it through a Layer Normalization function.
+
+For all decoders we use a hidden dimensionality of 512, take their final state and pass it through a linear layer to generate the final logits for classification, using a Cross Entropy loss.
+
+# 6.1.2 IMAGENET
+
+The encoder is a pretrained Inception-ResNet-v2 network (Szegedy et al., 2017) with the standard preprocessing as described in the paper. We use as embedding the pre-logit activations. All decoders use a hidden dimensionality of 1024. After the decoder step we take their final state and pass it through a linear layer to generate the final logits for classification, using a Cross Entropy loss.
+
+# 6.1.3 ANALOGY TASK
+
+The encoder for MNIST uses the same convolutional network as described in the Omniglot section. The symbols are one-hot vectors for the first set of experiments. The memory is queried for neighbors both of the digit embeddings as well as the symbols, and found neighbors are concatenated and fed to the decoder.
+
+The decoder process is identical to Omniglot. However, the classification target is now the one-shot encoded version of the result of the computation $X + S$ , where $X$ is the digit value and $S$ is the symbol value. As $S \in [ - 5 , 5 ]$ , we sum 5 to all values to obtain valid one-hot encodings (which means there are 20 possible values in all).
+
+# 6.2 DECODER ARCHITECTURES COMPARISON
+
+# 6.2.1 RELATIONAL SELF-ATTENTION FEED FORWARD MODULE
+
+Consider the set $\{ e _ { t } , e _ { 1 . . . m } , l _ { 1 . . . m } , d _ { 1 . . . m } \}$ , where $e _ { t }$ is the encoded target, $e _ { 1 \dots m }$ the encoded observations from the memory, $l _ { 1 . . . m } = f ( y _ { 1 . . . m } )$ are the labels processed by a simple embedding layer to project the classes into a higher dimensional space, and $d _ { 1 \dots m }$ are the euclidean distances between $e _ { t }$ and $e _ { 1 \ldots m }$ . By concatenating all these vectors, we have a set of inputs to a relational block (Battaglia et al., 2018).
+
+This tensor (of shape [batch size, $\mathbf { k }$ , sum of all embeddings feature sizes]) is fed to what we call a relational self-attentional block: first the tensor is passed through a multihead attention layer (Figure
+
+7), which compares all elements to each other and returns a new tensor of the same shape; then a shared nonlinear layer (ReLU, linear, layer norm) processes each element individually. The selfattentional blocks are repeated 8 times in a residual manner (the dimensionality of the tensor never changes).
+
+Finally, we pass the distances between neighbors and query through a softmax layer to generate an attention vector which is multiplied with the activations tensor over the first axis (this has the effect of weighting closer memories more). The tensor is then summed over that first axis to obtain the final representation.
+
+![](images/5889e06f1272a3cbe821592b0d3cfbaf77d2aab473a3b2c79322aea6081bcef2.jpg)  
+Figure 7: Multihead attention implementation.
+
+# 6.2.2 RELATIONAL WORKING MEMORY
+
+We use a Relational working memory core as described in (Santoro et al., 2018), (figure 2, right). The memory is initialized with the concatenated vectors $\{ e _ { 1 . . . m } , l _ { 1 . . . m } , d _ { 1 . . . m } \}$ . The query $e _ { t }$ is fed a number $N = 5$ times as input to the relational memory core to unroll the computation. The final memory state is passed through a linear layer to obtain the logits.
+
+# 6.2.3 LSTM
+
+We use a standard LSTM module, with initial state equal to the query embedding, and at each time step we feed in the neighbor embedding as concatenated with the embedded label. The LSTM is rolled out for $k$ time steps (i.e. the number of neighbors). Its final output state is taken as input to the logits linear layer.
+
+![](images/b57536a24e844ec7c041ff56eabf513104b3bea405d2f0efc1ab7f25d3f0daf9.jpg)  
+Figure 8: The LSTM decoder for APL.
+
+# 6.2.4 DECODER ARCHITECTURE COMPARISON
+
+We compared all three decoder architectures for the classification case and found they perform equally well for the classification case, as shown in the figure below.
+
+For the analogy task, we found the Relational self-attention feed forward module to work best, as outlined in the main text.
+
+![](images/39189663b0200b4b7fb418498a34fda7fe00fd8b680ed94097c63311911af784.jpg)  
+Figure 9: Accuracy as a function of examples written to memory. We compared relational working memory, LSTM and the relational self-attention feed-forward module for omniglot on the 20-way, 423-way and 1000-way tasks.
+
+![](images/5d5e38917455f1598af040a1769c8d15bedfe06295b4bb1711d885f5bcbba007.jpg)  
+Figure 10: Accuracy as a function of examples written to memory. Each plot corresponds to a different number $k$ of retrieved nearest neighbors. We compared relational working memory, LSTM and the relational self-attention feed-forward module.
+
+# 6.3 EFFECT OF THRESHOLD PARAMETER ON PERFORMANCE
+
+How does the choice of parameter $\sigma$ affect the performance of APL? Empirically we have verified that for a large range of $\sigma$ , memory size and accuracy are largely unchanged. This is due to the feedback loop between the number of items stored and classification accuracy: as more items are stored in memory, the more elements are correctly classified and not stored in memory. Therefore the memory storage mechanism is self-regulating, and the number of elements in memory ends up being largely flat.
+
+In Fig. 11 we show the final memory size and average accuracy for the last 100 data points after showing APL 2000 unique data points for the case of 200-way classification. In this case the ’natural’ (uniform predictions) $\sigma$ is around 5.2, which seems to be close to optimal for accuracy vs. elements in memory. We can increase the value somewhat but eventually the model can’t write to memory any more and performance tanks. On the other side of the curve, for $\sigma = 0$ where we write everything, performance is slightly higher but at a roughly ${ 8 \mathrm { x } }$ memory cost.
+
+![](images/895e37d999f8a7adffb8406f7d1db11d1146682a171b39febe04adaf747a956d.jpg)  
+Figure 11: Accuracy as a function of examples written to memory. Each plot corresponds to a different number $k$ of retrieved nearest neighbors. We compared relational working memory, LSTM and the relational self-attention feed-forward module.
+
+# 6.4 RELATION TO CONTINUAL LEARNING
+
+While we study APL in the few-shot learning setting, the algorithm could also be used in the continual learning setup (Kirkpatrick et al., 2017; Rusu et al., 2016; Yoon et al., 2018; Rebuffi et al., 2017). We consider an experiment where each task consists of learning 10 new and previously unseen classes. For each task we present the models with 200 unique examples, and report the average accuracy for the last 100 examples seen. Examples are drawn from the test set of classes.
+
+In the case of progressive networks, one gradient descent step is taken after each example. For each task, a new logits layer is added on top of a convolutional encoder (same architecuture as APL) pretrained on the omniglot training set. APL is run as described in the main text.
+
+The results are summarized in figure 12: APL can perform as well or better than a progressive network on this kind of task without needing access to gradient information, as its memory store can provide the requisite information to update its predictions to the new task.
+
+![](images/2ada6e4f5074df0eb476a060c43c70bcdaf5f85cce4687b1b49d4d68552be651.jpg)  
+Figure 12: Accuracy of APL on a lifelong learning task where each task corresponds to learning 10 new classes in Omniglot. The baseline is a progressive net where the convolutional encoder is pretrained, and for every task a new logits layer is added and trained to classify the new classes. Results are the average accuracy over 5 runs. While not using any gradient information, APL performs as well or better than progressive networks.

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+        "text": "The ability to generalize quickly from few observations is crucial for intelligent systems. In this paper we introduce APL, an algorithm that approximates probability distributions by remembering the most surprising observations it has encountered. These past observations are recalled from an external memory module and processed by a decoder network that can combine information from different memory slots to generalize beyond direct recall. We show this algorithm can perform as well as state of the art baselines on few-shot classification benchmarks with a smaller memory footprint. In addition, its memory compression allows it to scale to thousands of unknown labels. Finally, we introduce a meta-learning reasoning task which is more challenging than direct classification. In this setting, APL is able to generalize with fewer than one example per class via deductive reasoning. ",
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+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Consider the following sequential decision problem: at every iteration of an episode we are provided with an image of a digit (e.g. MNIST) and an unknown symbol. Our goal is to output a digit $Y = X + S$ where $X$ is the value of the MNIST digit, and $S$ is a numerical value that is randomly assigned to the unknown symbol at the beginning of each episode. After seeing only a single instance of a symbol an intelligent system should not only be able to infer the value $S$ of the symbol but also to correctly generalize the operation associated with the symbol to any other digit in the remaining iterations of that episode. ",
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+        "type": "text",
+        "text": "Despite its simplicity, this task emphasizes three cognitive abilities that a generic learning algorithm should display: 1. the algorithm can learn a behaviour and then flexibly apply it to a range of different tasks using only a few context observations at test time; 2. the algorithm can memorize and quickly recall previous experiences for quick adaptation; and 3. the algorithm can process these recalled memories in a non-trivial manner to carry out tasks that require reasoning. ",
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+        "text": "The first point is commonly described as “learning to learn” or meta-learning, and represents a new way of looking at statistical inference (Schmidhuber, 1987; Bengio et al., 1990; Bengio & LeCun, 2007). Traditional neural networks are trained to approximate arbitrary probability distributions with great accuracy by parametric adaptation via gradient descent (LeCun et al., 2015; Schmidhuber, 2015). After training that probability distribution is fixed and neural networks can only generalize well when the testing distribution matches the training distribution (Neyshabur et al., 2017). In contrast, meta-learning systems are trained to learn an algorithm that infers a function directly from the observations it receives at test time. This setup is more flexible than the traditional approach and generalizes better to unseen distributions as it incorporates new information even after the training phase is over. It also allows these models to improve their accuracy as they observe more data, unlike models which learn a fixed distribution. ",
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+        "type": "text",
+        "text": "The second requirement - being able to memorize and efficiently recall previous experience - is another active area of research. Storing information in a model proves especially challenging as we move beyond small toy-examples to tasks with higher dimensional data or real-world problems. ",
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+        "type": "text",
+        "text": "Current methods often work around this by summarizing past experiences in one lower-dimensional representation (Hochreiter & Schmidhuber, 1997; Kingma & Welling, 2013) or using memory modules (Graves et al., 2016). While the former approach can produce good results, the representation and therefore the amount of information we can ultimately encode with such models will be of a fixed and thus limited size. Working with neural memory modules, on the other hand, presents its own challenges as learning to store and keep the right experiences is not trivial. In order to successfully carry out the task defined at the beginning of this paper a model should learn to capture information about a flexible and unbounded number of symbols observed in an episode without storing redundant information. ",
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+        "type": "text",
+        "text": "Finally, reasoning requires processing recalled experiences in order to apply the information they contain to the current data point being processed. In simple cases such as classification, it is enough to simply recall memories of similar data points and directly infer the current class by combining them using a weighted average or a simple kernel (Vinyals et al., 2016; Snell et al., 2017), which limits the models to performing interpolation. In the example mentioned above, more complex reasoning is necessary for human-level generalisation. ",
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+        "text": "In this paper we introduce Approximate Posterior Learning (APL, pronounced like the fruit), a self-contained model and training procedure that address these challenges. APL learns to carry out few-shot approximation of new probability distributions and to store only as few context points as possible in order to carry out the current task. In addition it learns how to process recalled experiences to carry out tasks of varying degrees of complexity. This sequential algorithm was inspired by Bayesian posterior updating (Jaynes, 2003) in the sense that the output probability distribution is updated as more data is observed. ",
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+        "type": "text",
+        "text": "We demonstrate that APL can deliver accuracy comparable to other state-of-the-art algorithms in standard few-shot classification benchmarks while being more data efficient. We also show it can scale to a significantly larger number of classes while retaining good performance. Finally, we apply APL to the reasoning task introduced as motivation and verify that it can perform the strong generalization we desire. ",
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+        "type": "text",
+        "text": "The main contributions of this paper are: ",
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+        "text": "• A simple memory controller design which uses a surprise-based signal to write the most predictive items to memory. By not needing to learn what to write, we avoid costly backpropagation through memory which makes the setup easier and faster to train. This design also minimizes how much data is stored, making our method more memory efficient. • An integrated external and working memory architecture which can take advantage of the best of both worlds: scalability and sparse access provided by the working memory; and all-to-all attention and reasoning provided by a relational reasoning module. • A training setup which steers the system towards learning an algorithm which approximates the posterior without backpropagating through the whole sequence of data in an episode. ",
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+        "type": "text",
+        "text": "2 MODEL ",
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+        "text": "2.1 ARCHITECTURE ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our proposed model is composed of a number of parts: an encoder that generates a representation for the incoming query data; an external memory store which contains previously seen representation/ data pairings with writing managed by a memory controller; and a decoder that ingests the query representation as well as data from the memory store to generate a probability distribution over targets. We describe each of the parts in detail below1. ",
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+        "text": "Encoder The encoder is a function which takes in arbitrary data $x _ { t }$ and converts it to a representation $e _ { t }$ of (usually) lower dimensionality. In all our experiments $x _ { t }$ is an image, and we therefore choose a convolutional network architecture for the encoder. Architectural details of the encoder used for each of the experiments are provided in the appendix. ",
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+        "image_caption": [
+            "Figure 1: APL model applied to the the classification of an Omniglot image. The encoded image is compared to the entries of the memory and the most relevant ones are passed through a decoder that outputs a probability distribution over the labels. The dotted line indicates the parts of the graph that are not updated via back-propagation. "
+        ],
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+        "type": "text",
+        "text": "Memory store The external memory module is a database containing the stored experiences. Each of the columns corresponds to one of the attributes of the data. In the case of classification, for example, we would store two columns: the embedding $e _ { m }$ and the true label $y _ { m }$ . Each of the rows contains the information for one data point. The memory module is queried by finding the k-nearest neighbors between a query and the data in a given column. The full row data for each of the neighbors is returned for later use. The distance metric used to calculate proximity between the points is an open choice, and here we always use euclidean distance. ",
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+        "text": "Since we are not backpropagating through the memory, how do we ensure that the neighbors returned by the querying mechanism contain task-relevant information? We expect that class-discriminative embeddings produced by the encoder should cluster together in representation space, and therefore should be close in the sense of euclidean distance. While this is not mathematically necessary, in the following sections we will show that APL as proposed does work and retrieve the correct neighbors which means that in practice our intuition holds true. ",
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+        "type": "text",
+        "text": "Memory controller We use a simple memory controller which tries to minimize the amount of data points written to memory. Let us define surprise as the quantity associated with the prediction for label $y _ { t }$ as ${ \\bf S } = - l n ( y _ { t } )$ . Intuitively, this means that the higher the probability our model assigns to the true class, the less surprised it will be. ",
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+        "type": "text",
+        "text": "This suggests a way of storing the minimal amount of data points in memory which supports maximal classification accuracy. If a data point is ’surprising’, it should be stored in memory; otherwise it can be safely discarded as the model can already classify it correctly. ",
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+        "type": "text",
+        "text": "How should the memory controller decide whether a point is ’surprising’? In this work we choose the simplest possible controller: if the surprise is greater than some hyperparameter $\\sigma$ , then that data should be stored in memory. For our experiments, we choose $\\sigma \\propto - \\ln ( N )$ where $N$ is the number of classes under classification which means that if the prediction confidence in the correct class is smaller than the probability assigned by a uniform prediction the value should be written to memory. In the appendix we show that after model training model performance is robust to variations in $\\sigma$ , as surprise becomes highly bimodal: a new data point tends to be either highly surprising (never seen something similar before) or not very surprising. ",
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+        "type": "text",
+        "text": "Conveniently, in the case of classification problems the commonly used cross-entropy loss reduces to our measure of surprise directly, and we therefore use the prediction loss as an input to the memory controller directly. ",
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+        "type": "text",
+        "text": "Decoder The decoder takes as input the query representation as well as all the data from the neighbors found in the external memory. We designed a relational feed-forward module with self attention which takes particular advantage of the external memory architecture. In addition we tested two other established decoder architectures: an unrolled relational working memory core and an unrolled LSTM. As all experiments have a classification loss at the end, all the decoders return a vector with logits for the $N$ classes under consideration. Full details of each architecture are provided in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "• Relational self-attention feed-forward decoder. The relational feed-forward module (see figure 2, left) processes each of the neighbors individually by comparing them with the query, and then does a cross-element comparison with a self-attention module before reducing the activations with an attention vector calculated from neighbor distances. ",
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+    {
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+        "img_path": "images/cbfa827ae16bd4a77580ecd8a56b6be593666f81498fc976ee7e7e33bdb298ea.jpg",
+        "image_caption": [
+            "Figure 2: Two of the three different decoder architectures of APL: relational feed-forward memory (left) and relational working memory (Santoro et al., 2018) (right). In the figure $e _ { t }$ corresponds to the encoded target, $e _ { 1 \\dots m }$ to the encoded observations from the memory, $l _ { 1 . . . m } = f ( y _ { 1 . . . m } )$ are the labels processed by an embedding layer and $d _ { 1 \\dots m }$ is the distance between $e _ { t }$ and $e _ { 1 \\dots m }$ . "
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "• Relational working memory decoder (Santoro et al., 2018) The relational working memory module (figure 2, right) takes in the concatenated neighbor embeddings and corresponding label embeddings as its initial memory state. The query is fed a number $N$ times as input to the relational memory core to unroll the computation. ",
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+        "type": "text",
+        "text": "• LSTM decoder Finally we also test a vanilla LSTM decoder that takes in the query as the initial memory state and is fed each of the concatenated neighbor embeddings and corresponding label embeddings as its input each time step. ",
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+    {
+        "type": "text",
+        "text": "2.2 TRAINING SETUP ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Since we are looking for a system which can update its beliefs in an online manner we need a training procedure that reflect this behaviour. We train the system over a sequence of episodes that are composed of sequences of pairs $( x _ { t } , y _ { t } )$ . At the start of every episode the mapping $x _ { t }  y _ { t }$ is shuffled in a deterministic manner (the exact details are task dependent and will be outlined in the experiments section). The data is then presented to the model sequentially in a random order. The model’s memory is empty at the beginning of the episode. ",
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+    {
+        "type": "text",
+        "text": "At each time step, a batch of examples is shown to the model and a prediction is made. We then measure the instantaneous loss $L ( \\hat { y } _ { t } , y _ { t } )$ and perform a gradient update step on the network to minimize the loss on that batch alone. The loss is also fed to the memory controller for the network to decide whether to write to memory. In all the experiments below the task is to classify some quantity, therefore we use cross entropy loss throughout. ",
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+    {
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+        "img_path": "images/d7aad9d64cf23f65f53eb43bab580b91bcd2bf89c273cab89eb5b62d66f32a12.jpg",
+        "image_caption": [
+            "Figure 3: APL training over several iterations. The encoder $e$ embeds the query image that is compared against the stored experiences in the memory $M$ . Matches are fed alongside the encoded image into a decoder $d$ . Finally, the controller $c$ decides whether the currently observed example should be stored in memory. "
+        ],
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+    {
+        "type": "text",
+        "text": "APL learns a sequential update algorithm, that is, it minimizes the expected loss over an episode consisting of a number of data elements presented sequentially. However we don’t need to backpropagate through the sequence to learn the algorithm. Rather, the model’s parameters are updated to minimize the cross-entropy loss independently at each time step. Therefore the only pressure to learn a sequential algorithm comes from the fact that episodes are kept small so that the decoder is encouraged to read the information coming from the queried neighbors instead of just learning to fit the current episode’s label mapping in its weights after a few steps of gradient descent (which is what happens in the case of MAML (Finn et al., 2017)). ",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "3 RELATED WORK ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Meta-learning as a research field covers a large number of areas. The concept of ‘learning to learn’ is not tied to a specific task and thus meta-learning algorithms have been successfully applied to a wide range of challenges like RL (Wang et al., 2016; Finn et al., 2017), program induction (Devlin et al., 2017) few-shot classification (Koch et al., 2015; Vinyals et al., 2016) and scene understanding (Eslami et al., 2018). ",
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+    {
+        "type": "text",
+        "text": "Some meta learning models generate predictions in an autoregressive fashion by predicting the next target point from the entire prior sequence of consecutive observations (Reed et al., 2018; Mishra et al., 2018). Algorithms of this kind have delivered state-of-the art results in a range of tasks such as supervised learning to classification. Nonetheless their reliance on the full context history in addition to their autoregressive nature hinders parallelization and hurts performance and scalability. ",
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+    {
+        "type": "text",
+        "text": "Another set of methods is based on the nearest neighbours approach (Koch et al., 2015; Vinyals et al., 2016; Snell et al., 2017). These methods use an encoder to find a suitable embedding and then perform a memory look up based on these representations. The result is a weighted average of the returned labels. As shown in (Mishra et al., 2018) using a pure distance metric to compare neighbors results in worse performance than allowing a network to learn a comparison function. These kinds of methods thus suffer in comparison. Meta Networks (Munkhdalai & Yu, 2017) also use an external memory to enable learning from previous examples combined with a model featuring slow and fast weights to produce the output, enabling them to state-of-the-art performance in several benchmarks. ",
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+    {
+        "type": "text",
+        "text": "Conditional neural processes (Garnelo et al., 2018) summarize the data into a fixed representation by averaging over the outputs of an encoder. This representation is fed into a decoder together with a query to produce the output. These methods are more space and compute efficient but given the fixed and averaged representation may not scale to very large problems. ",
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+    {
+        "type": "text",
+        "text": "All of the above methods expect a fixed size context, thereby making life-long learning over large time horizons difficult. To enable this, an algorithm must learn to only write observations into memory when they provide additional predictive power. Memory augmented neural networks (MANN) (Santoro et al., 2016) achieve this by learning a controller to write into a differentiable neural dictionary. However, this requires backpropagating through the entire sequence to learn, which makes credit assignment over long time sequences hard and is computationally expensive. The idea of using an external memory module has been explored in (Kaiser et al., 2017) and shown to produce good results. Compared to that work we introduce a simpler writing mechanism and the idea of a relational decoder to exploit the nearest neighbor structure. ",
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 FEW-SHOT OMNIGLOT CLASSIFICATION ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The Omniglot dataset contains 1623 characters with 20 examples each. 1200 of the character classes are assigned to the train set while the remaining 423 are part of the test set. The examples are presented to the model sequentially in batches of 16 examples. For each episode, we choose $N$ classes and shuffle their labels. We then run an episode for a certain number of steps, which is decreased as the model’s accuracy increases to encourage quick adaptation. This means that the model accuracy and number of memories written to memory is time dependent. ",
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+    {
+        "type": "text",
+        "text": "We follow an architecture similar to those used in previous work for the image encoder (Vinyals et al., 2016; Mishra et al., 2018), which consists of four convolutional blocks with 3x3 convolutions, relu and batch normalization. We augment the number of classes in the training set by rotating each symbol 90, 180 and 270 degrees as in previous work (Santoro et al., 2016). For this task, we found that all three decoder architectures perform similarly. A detailed comparison and all hyperparameters needed to reproduce this experiment are provided in the Appendix. ",
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+    {
+        "type": "text",
+        "text": "In Figure 4a we can see the behavior of the algorithm within a single episode. As it sees more examples its performance increases until it saturates at some point, when additional writes don’t help anymore (assuming the exact same data piece won’t be seen again, which is the regime we always assume here). In the simple case of 5-way Omniglot classification, fewer than 2 examples per class are sufficient to saturate performance. ",
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+    {
+        "type": "text",
+        "text": "In Figure 4b we demonstrate the evolution of the posterior distribution in 20-way classification for 3 different, fixed inputs. For the first step, where the memory is empty APL learns to output a uniform distribution $( p \\simeq 1 / N$ with $\\mathbf { N }$ the number of classes under classification). As more examples are added to memory, its distribution refines until it sees an informative example for that class, at which point its prediction becomes very confident. ",
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+    {
+        "type": "text",
+        "text": "In Figure 4c we can see that different numbers of examples are written to memory for different classes, which demonstrates one of the advantages of this framework: we only need to store as many examples as each class requires, therefore if some classes may be more easily classified than others we can optimally use memory. In contrast, other models feed in a fixed context size per class which means they will either suffer in accuracy or use excessive memory. ",
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+        "img_path": "images/a35e3cd15cb2be90e9d7c00eb5e3de8820437e502b78da2c93d1a8eb6c12aaec.jpg",
+        "image_caption": [
+            "Figure 4: a) Accuracy and size of memory for 5-way Omniglot. APL stops writing to memory after having 2 examples per class for 5-way classification. b), examples of evolution of posterior distribution for 20-way classification for 3 images. The distribution starts as uniform for the very first step, then starts to change as more items are added to memory. When the correct class is seen, the distribution converges. c), the number of labels stored in memory per class is highly heterogeneous. In this 20-way problem, APL stored 44 items in memory and achieved $9 8 . 5 \\%$ accuracy, which is higher than its homogeneous 5-shot accuracy. d) Accuracy vs. number of items written to memory for 1000-way classification. Classification accuracy when only 2000 examples have been written to memory (on average 2 examples per class) surpasses the accuracy for a fixed context size of 5 examples per class. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Despite the previous point, it is also worthwhile comparing model accuracy to existing baselines with a fixed context size. To this end, we pre-populate the memory of a trained model with 1 or 5 examples per class and calculate the accuracy over the test set. We emphasize that the model was not trained to do well in this fixed-context scenario, and yet for 1 and 5-shot classification we obtain performance comparable to state-of-the-art models without having extensively tuned hyperparameters. Furthermore we tested our model with a much higher number of classes: 423-way classification where where we can use the whole test set, and 1000-way where the test set is augmented with rotations of the characters as we do in training. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, we test how the model fares on a completely new distribution, MNIST. For 1-shot, 10-way MNIST, APL trained on 20-way omniglot classification obtains $61 \\%$ accuracy (compared to $72 \\%$ cited by (Vinyals et al., 2016)). Testing our model in the sequential regime, we observe that it continues writing examples to memory as it sees surprising observations, which allows it to correct for the distribution shift. After writing 45 examples per class, it reaches an accuracy of $86 \\%$ (there are 1000 examples per class in the MNIST test set, so it is not simply memorizing). ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/30af0e4ae4e8bc231fa8b4d222fc26e3ebeb7e32db5fcc6f9bdc30fbdb1a529e.jpg",
+        "table_caption": [
+            "Table 1: Omniglot test accuracies for fixed context sizes compared to other baselines. († For 1000- way classification rotated pseudoclasses are used.) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">5-way</td><td colspan=\"2\">20-way</td><td colspan=\"2\">423-way</td><td colspan=\"2\">1000-way†</td></tr><tr><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td><td>1-shot</td><td>5-shot</td></tr><tr><td>Matching nets</td><td>98.1%</td><td>98.9%</td><td>93.8%</td><td>98.5%</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CNP</td><td>95.3%</td><td>98.5%</td><td>89.9%</td><td>96.8%</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>MANN</td><td>82.2%</td><td>94.9%</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MAML</td><td>98.7%</td><td>99.9%</td><td>95.8%</td><td>98.9%</td><td></td><td>-</td><td>-</td><td></td></tr><tr><td>SNAIL</td><td>99.07%</td><td>99.78%</td><td>97.64%</td><td>99.35%</td><td>-</td><td>-</td><td>1</td><td>-</td></tr><tr><td>APL</td><td>97.9%</td><td>99.9%</td><td>97.2%</td><td>97.6%</td><td>73.5%</td><td>88.0%</td><td>68.9%</td><td>78.9%</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "4.2 IMAGENET ",
+        "text_level": 1,
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a8720edcb02b5a0aa7780ee57c5c5b415e2b55707ba55a2c1aaba528ab46766c.jpg",
+        "image_caption": [
+            "Figure 5: Evolution of top-1 accuracy and number of written examples to memory over a single episode for the Imagenet dataset. Curves are averages over 5 test episodes and smoothed with exponential moving average. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We also applied our model to the full scale imagenet dataset. Unlike the above experiments there are no held out classes for testing, as the dataset was not conceived with held out classes in mind. Instead, we rely on shuffling the labels amongst the 1000 Imagenet classes and using the images from the test set for evaluation. This means the generalization results are slightly weaker than in the above sections, but they still provide important insights as to the scalability of our method to thousands of classes and applicability to harder scenarios. ",
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+    {
+        "type": "text",
+        "text": "As an encoder we use the pretrained Inception-ResNet-v2 (Szegedy et al., 2017) due to computational constraints. For the fixed label case, this network reaches a top-1 accuracy of $8 0 . 4 \\%$ . Training the encoder end-to-end might produce better results, an investigation which we leave to later work. ",
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+    {
+        "type": "text",
+        "text": "In the 20-way classification challenge, our method reaches $8 6 . 7 \\%$ top-1 accuracy (average accuracy after 50 iterations). Performance remains very high for 100-way $7 2 . 9 \\%$ top-1 accuracy). The model’s performance degrades somewhat $( 5 2 . 6 \\%$ top-1 accuracy) for 1000-way classification, where all the classes are shuffled. This highlights that large scale meta-learning on real world datasets remains a challenge even when all the classes have been observed by the encoder, as in this case. ",
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+    {
+        "type": "text",
+        "text": "4.3 NUMBER ANALOGY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The number analogy task challenges a meta-learning model to use logic reasoning to generalize with fewer than 1 example per possible class (Figure 6). At each time step the network is shown two pieces of data, a number $X$ and a symbol $S$ . It is asked to classify the result of $X + S$ based only on the current data and its previous experiments. We experiment with two levels of difficulty for this task: in the first, the number values are fixed and correspond to the MNIST digits, while there are ",
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+    },
+    {
+        "type": "text",
+        "text": "10 different symbols with unknown values in each episode; in the second, both digits and symbols have shuffled values. We sample the symbol values in the range $[ - 1 0 , 1 0 ]$ . ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "When querying the memory, we query $k$ neighbors via the number embeddings and $k$ neighbors via the symbol embeddings. This makes sure that any relevant information to the problem is available to the reasoning module. The rest of the training setup is identical to the Omniglot experiments, including the encoder network for the digits. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In the case where the numbers are fixed a human would need only see 10 examples, one for each symbol, to be able to correctly generalize for all 100 possible combinations. With one example per symbol, APL reaches $9 7 . 6 \\%$ accuracy on the test set. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "When both numbers and symbols are shuffled each episode, a logical deduction process must be performed to infer the correct symbols. Our model is able to generalize using 50 examples written to memory (Figure 6) which is still fewer than seeing one of all 100 possible combinations. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this complex case, once a symbol’s meaning has been figured out it is no longer necessary to solve the system of equations for that unknown. It would be interesting to explore how a system could additionally store this information in memory for later reuse, a question we leave for later work. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/7c1bcf07a05532ad70c152f3ba9ae1fd0a60a4b9471eff97af48c2059dbc7099.jpg",
+        "image_caption": [
+            "Figure 6: Left: Number analogy task. The colored symbols have unknown values that are consistent throughout an episode. Right: Accuracy as a function of number of examples seen for the Analogy task where the number meanings are also shuffled each episode. Curves are averages over 10 test episodes and smoothed with exponential moving average. On the left we fix the decoder (relational self-attention feed-forward module) and vary $k$ . As there are 100 possible combinations of symbols (10 numbers $\\times 1 0$ symbols), the thick dashed line corresponds to the performance of a model capable of perfect 1-shot generalization. We can see that for $k = 8$ and $k = 1 6$ the decoder can infer the symbol and number meanings to do better than direct 1-shot classifications. On the right we fix $k = 1 6$ and show that the relational self-attention feed-forward module can generalize better from few examples than other decoder architectures. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We introduced a self-contained system which can learn to approximate a probability distribution with as little data and as quickly as it can. This is achieved by putting together the training setup which encourages adaptation; an external memory which allows the system to recall past events; a writing system to adapt the memory to uncertain situations; and a working memory architecture which can efficiently compare items retrieved from memory to produce new predictions. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We showed that the model can: ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "• Reach state of the art accuracy with a smaller memory footprint than other meta-learning models by efficiently choosing which data points to remember.   \n• Scale to very large problem sizes thanks to the use of an external memory module with sparse access.   \n• Perform fewer than 1-shot generalization thanks to relational reasoning across neighbors. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "The authors thank Elco Bakker, Alex Pritzel and David Raposo for insightful discussions; Paul Komarek, Adrià Puigdomènech for help with writing code; and Kevin McKee for revising the manuscript. ",
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jaehong Yoon, Eunho Yang, Jeongtae Lee, and Sung Ju Hwang. Lifelong learning with dynamically expandable networks. 2018. ",
+        "bbox": [
+            168,
+            666,
+            823,
+            695
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "6 SUPPLEMENTARY MATERIAL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            442,
+            117
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.1 MODEL ARCHITECTURES AND TRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            133,
+            560,
+            147
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For all experiments below we use the same training setup. For each training episode we sample elements from $N$ classes and randomly shuffle them to create training batches. For every batch shown to the model, we do one step of gradient descent with the Adam optimizer. We anneal the learning rate from $1 0 ^ { - 4 }$ to $1 0 ^ { - 5 }$ with exponential decay over 1000 steps (decay rate 0.9). ",
+        "bbox": [
+            174,
+            159,
+            825,
+            214
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For all experiments, the query data is passed through an embedding network (described below in), and this vector is used to query an external memory module. The memory module contains multiple columns of data, one of which will be the key and the others will contain data associated with that key. The necessary columns for each experiment are outlined below. The memory size is chosen so that elements will never be overwritten in a single episode (i.e. memory size $>$ batch size $\\times$ number of iterations). ",
+        "bbox": [
+            174,
+            222,
+            825,
+            305
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The returned memory contents as well as the query are fed to one of the decoder architectures described in section 6.2. ",
+        "bbox": [
+            174,
+            313,
+            823,
+            340
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.1.1 OMNIGLOT ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            356,
+            307,
+            369
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For omniglot we encode the images with a convolutional network composed of a single first convolution to map the image to 64 feature channels, followed by 12 convolutional blocks. Each block is made up of a step of Batch Normalization, followed by a ReLU activation and a convolutional layer with kernel size 3. Every three blocks the convolution contains a stride 2 to downsample the image. All layers have 64 features. Finally we flatten the activations to a 1D vector and pass it through a Layer Normalization function. ",
+        "bbox": [
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+            380,
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+            463
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For all decoders we use a hidden dimensionality of 512, take their final state and pass it through a linear layer to generate the final logits for classification, using a Cross Entropy loss. ",
+        "bbox": [
+            176,
+            470,
+            821,
+            498
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.1.2 IMAGENET ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            513,
+            307,
+            527
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The encoder is a pretrained Inception-ResNet-v2 network (Szegedy et al., 2017) with the standard preprocessing as described in the paper. We use as embedding the pre-logit activations. All decoders use a hidden dimensionality of 1024. After the decoder step we take their final state and pass it through a linear layer to generate the final logits for classification, using a Cross Entropy loss. ",
+        "bbox": [
+            174,
+            537,
+            825,
+            594
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.1.3 ANALOGY TASK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            608,
+            341,
+            622
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The encoder for MNIST uses the same convolutional network as described in the Omniglot section. The symbols are one-hot vectors for the first set of experiments. The memory is queried for neighbors both of the digit embeddings as well as the symbols, and found neighbors are concatenated and fed to the decoder. ",
+        "bbox": [
+            174,
+            632,
+            823,
+            688
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "The decoder process is identical to Omniglot. However, the classification target is now the one-shot encoded version of the result of the computation $X + S$ , where $X$ is the digit value and $S$ is the symbol value. As $S \\in [ - 5 , 5 ]$ , we sum 5 to all values to obtain valid one-hot encodings (which means there are 20 possible values in all). ",
+        "bbox": [
+            174,
+            695,
+            825,
+            752
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.2 DECODER ARCHITECTURES COMPARISON ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            768,
+            504,
+            782
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "6.2.1 RELATIONAL SELF-ATTENTION FEED FORWARD MODULE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            795,
+            622,
+            809
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Consider the set $\\{ e _ { t } , e _ { 1 . . . m } , l _ { 1 . . . m } , d _ { 1 . . . m } \\}$ , where $e _ { t }$ is the encoded target, $e _ { 1 \\dots m }$ the encoded observations from the memory, $l _ { 1 . . . m } = f ( y _ { 1 . . . m } )$ are the labels processed by a simple embedding layer to project the classes into a higher dimensional space, and $d _ { 1 \\dots m }$ are the euclidean distances between $e _ { t }$ and $e _ { 1 \\ldots m }$ . By concatenating all these vectors, we have a set of inputs to a relational block (Battaglia et al., 2018). ",
+        "bbox": [
+            174,
+            818,
+            825,
+            888
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This tensor (of shape [batch size, $\\mathbf { k }$ , sum of all embeddings feature sizes]) is fed to what we call a relational self-attentional block: first the tensor is passed through a multihead attention layer (Figure ",
+        "bbox": [
+            174,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "7), which compares all elements to each other and returns a new tensor of the same shape; then a shared nonlinear layer (ReLU, linear, layer norm) processes each element individually. The selfattentional blocks are repeated 8 times in a residual manner (the dimensionality of the tensor never changes). ",
+        "bbox": [
+            173,
+            103,
+            825,
+            160
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Finally, we pass the distances between neighbors and query through a softmax layer to generate an attention vector which is multiplied with the activations tensor over the first axis (this has the effect of weighting closer memories more). The tensor is then summed over that first axis to obtain the final representation. ",
+        "bbox": [
+            174,
+            166,
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+            222
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/5889e06f1272a3cbe821592b0d3cfbaf77d2aab473a3b2c79322aea6081bcef2.jpg",
+        "image_caption": [
+            "Figure 7: Multihead attention implementation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            235,
+            238,
+            761,
+            392
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "6.2.2 RELATIONAL WORKING MEMORY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            449,
+            459,
+            463
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We use a Relational working memory core as described in (Santoro et al., 2018), (figure 2, right). The memory is initialized with the concatenated vectors $\\{ e _ { 1 . . . m } , l _ { 1 . . . m } , d _ { 1 . . . m } \\}$ . The query $e _ { t }$ is fed a number $N = 5$ times as input to the relational memory core to unroll the computation. The final memory state is passed through a linear layer to obtain the logits. ",
+        "bbox": [
+            173,
+            473,
+            825,
+            530
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "6.2.3 LSTM ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            544,
+            276,
+            559
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We use a standard LSTM module, with initial state equal to the query embedding, and at each time step we feed in the neighbor embedding as concatenated with the embedded label. The LSTM is rolled out for $k$ time steps (i.e. the number of neighbors). Its final output state is taken as input to the logits linear layer. ",
+        "bbox": [
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+            568,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/b57536a24e844ec7c041ff56eabf513104b3bea405d2f0efc1ab7f25d3f0daf9.jpg",
+        "image_caption": [
+            "Figure 8: The LSTM decoder for APL. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            334,
+            638,
+            661,
+            736
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "6.2.4 DECODER ARCHITECTURE COMPARISON ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            789,
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+            803
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We compared all three decoder architectures for the classification case and found they perform equally well for the classification case, as shown in the figure below. ",
+        "bbox": [
+            173,
+            813,
+            823,
+            842
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "For the analogy task, we found the Relational self-attention feed forward module to work best, as outlined in the main text. ",
+        "bbox": [
+            173,
+            848,
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+            877
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/39189663b0200b4b7fb418498a34fda7fe00fd8b680ed94097c63311911af784.jpg",
+        "image_caption": [
+            "Figure 9: Accuracy as a function of examples written to memory. We compared relational working memory, LSTM and the relational self-attention feed-forward module for omniglot on the 20-way, 423-way and 1000-way tasks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/5d5e38917455f1598af040a1769c8d15bedfe06295b4bb1711d885f5bcbba007.jpg",
+        "image_caption": [
+            "Figure 10: Accuracy as a function of examples written to memory. Each plot corresponds to a different number $k$ of retrieved nearest neighbors. We compared relational working memory, LSTM and the relational self-attention feed-forward module. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            309,
+            823,
+            577
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "6.3 EFFECT OF THRESHOLD PARAMETER ON PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            665,
+            602,
+            679
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "How does the choice of parameter $\\sigma$ affect the performance of APL? Empirically we have verified that for a large range of $\\sigma$ , memory size and accuracy are largely unchanged. This is due to the feedback loop between the number of items stored and classification accuracy: as more items are stored in memory, the more elements are correctly classified and not stored in memory. Therefore the memory storage mechanism is self-regulating, and the number of elements in memory ends up being largely flat. ",
+        "bbox": [
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+            690,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "In Fig. 11 we show the final memory size and average accuracy for the last 100 data points after showing APL 2000 unique data points for the case of 200-way classification. In this case the ’natural’ (uniform predictions) $\\sigma$ is around 5.2, which seems to be close to optimal for accuracy vs. elements in memory. We can increase the value somewhat but eventually the model can’t write to memory any more and performance tanks. On the other side of the curve, for $\\sigma = 0$ where we write everything, performance is slightly higher but at a roughly ${ 8 \\mathrm { x } }$ memory cost. ",
+        "bbox": [
+            173,
+            781,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/895e37d999f8a7adffb8406f7d1db11d1146682a171b39febe04adaf747a956d.jpg",
+        "image_caption": [
+            "Figure 11: Accuracy as a function of examples written to memory. Each plot corresponds to a different number $k$ of retrieved nearest neighbors. We compared relational working memory, LSTM and the relational self-attention feed-forward module. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            308,
+            121,
+            691,
+            299
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "6.4 RELATION TO CONTINUAL LEARNING ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            388,
+            473,
+            404
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "While we study APL in the few-shot learning setting, the algorithm could also be used in the continual learning setup (Kirkpatrick et al., 2017; Rusu et al., 2016; Yoon et al., 2018; Rebuffi et al., 2017). We consider an experiment where each task consists of learning 10 new and previously unseen classes. For each task we present the models with 200 unique examples, and report the average accuracy for the last 100 examples seen. Examples are drawn from the test set of classes. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "In the case of progressive networks, one gradient descent step is taken after each example. For each task, a new logits layer is added on top of a convolutional encoder (same architecuture as APL) pretrained on the omniglot training set. APL is run as described in the main text. ",
+        "bbox": [
+            174,
+            492,
+            823,
+            534
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The results are summarized in figure 12: APL can perform as well or better than a progressive network on this kind of task without needing access to gradient information, as its memory store can provide the requisite information to update its predictions to the new task. ",
+        "bbox": [
+            173,
+            540,
+            825,
+            583
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/2ada6e4f5074df0eb476a060c43c70bcdaf5f85cce4687b1b49d4d68552be651.jpg",
+        "image_caption": [
+            "Figure 12: Accuracy of APL on a lifelong learning task where each task corresponds to learning 10 new classes in Omniglot. The baseline is a progressive net where the convolutional encoder is pretrained, and for every task a new logits layer is added and trained to classify the new classes. Results are the average accuracy over 5 runs. While not using any gradient information, APL performs as well or better than progressive networks. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            318,
+            616,
+            656,
+            794
+        ],
+        "page_idx": 13
+    }
+]

parse/train/HJg_ECEKDr/HJg_ECEKDr.md

@@ -0,0 +1,306 @@
+# GENERATIVE TEACHING NETWORKS: ACCELERATING NEURAL ARCHITECTURE SEARCH BY LEARNING TO GENERATE SYNTHETIC TRAINING DATA
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+This paper investigates the intriguing question of whether we can create learning algorithms that automatically generate training data, learning environments, and curricula in order to help AI agents rapidly learn. We show that such algorithms are possible via Generative Teaching Networks (GTNs), a general approach that is, in theory, applicable to supervised, unsupervised, and reinforcement learning, although our experiments only focus on the supervised case. GTNs are deep neural networks that generate data and/or training environments that a learner (e.g. a freshly initialized neural network) trains on for a few SGD steps before being tested on a target task. We then differentiate through the entire learning process via meta-gradients to update the GTN parameters to improve performance on the target task. GTNs have the beneficial property that they can theoretically generate any type of data or training environment, making their potential impact large. This paper introduces GTNs, discusses their potential, and showcases that they can substantially accelerate learning. We also demonstrate a practical and exciting application of GTNs: accelerating the evaluation of candidate architectures for neural architecture search (NAS), which is rate-limited by such evaluations, enabling massive speed-ups in NAS. GTN-NAS improves the NAS state of the art, finding higher performing architectures when controlling for the search proposal mechanism. GTN-NAS also is competitive with the overall state of the art approaches, which achieve top performance while using orders of magnitude less computation than typical NAS methods. Speculating forward, GTNs may represent a first step toward the ambitious goal of algorithms that generate their own training data and, in doing so, open a variety of interesting new research questions and directions.
+
+# 1 INTRODUCTION AND RELATED WORK
+
+Access to vast training data is now common in machine learning. However, to effectively train neural networks (NNs) does not require using all available data. For example, recent work in curriculum learning (Graves et al., 2017), active learning (Konyushkova et al., 2017; Settles, 2010) and core-set selection (Sener & Savarese, 2018; Tsang et al., 2005) demonstrates that a surrogate dataset can be created by intelligently sampling a subset of training data, and that such surrogates enable competitive test performance with less training effort. Being able to more rapidly determine the performance of an architecture in this way could particularly benefit architecture search, where training thousands or millions of candidate NN architectures on full datasets can become prohibitively expensive. From this lens, related work in learning-to-teach has shown promise. For example, the learning to teach (L2T) (Fan et al., 2018) method accelerates learning for a NN learner (hereafter, just learner) through reinforcement learning, by learning how to subsample mini-batches of data.
+
+A key insight in this paper is that the surrogate data need not be drawn from the original data distribution (i.e. they may not need to resemble the original data). For example, humans can learn new skills from reading a book or can prepare for a team game like soccer by practicing skills, such as passing, dribbling, juggling, and shooting. This paper investigates the question of whether we can train a data-generating network that can produce synthetic data that effectively and efficiently teaches a target task to a learner. Related to the idea of generating data, Generative Adversarial Networks (GANs) can produce impressive high-resolution images (Goodfellow et al., 2014; Brock et al., 2018), but they are incentivized to mimic real data (Goodfellow et al., 2014), instead of being optimized to teach learners more efficiently than real data.
+
+Another approach for creating surrogate training data is to treat the training data itself as a hyperparameter of the training process and learn it directly. Such learning can be done through metagradients (also called hyper-gradients), i.e. differentiating through the training process to optimize a meta-objective. This approach was described in Maclaurin et al. (2015), where 10 synthetic training images were learned using meta-gradients such that when a network is trained on these images, the network’s performance on the MNIST validation dataset is maximized. In recent work concurrent with our own, Wang et al. (2019b) scaled this idea to learn 100 synthetic training examples. While the 100 synthetic examples were more effective for training than 100 original (real) MNIST training examples, we show that it is difficult to scale this approach much further without the regularity across samples provided by a generative architecture (Figure 2b, green line).
+
+Being able to very quickly train learners is particularly valuable for neural architecture search (NAS), which is exciting for its potential to automatically discover high-performing architectures, which otherwise must be undertaken through time-consuming manual experimentation for new domains. Many advances in NAS involve accelerating the evaluation of candidate architectures by training a predictor of how well a trained learner would perform, by extrapolating from previously trained architectures (Luo et al., 2018; Liu et al., 2018a; Baker et al., 2017). This approach is still expensive because it requires many architectures to be trained and evaluated to train the predictor. Other approaches accelerate training by sharing training across architectures, either through shared weights (e.g. as in ENAS; Pham et al. (2018)), or Graph HyperNetworks (Zhang et al., 2018).
+
+We propose a scalable, novel, meta-learning approach for creating synthetic data called Generative Teaching Networks (GTNs). GTN training has two nested training loops: an inner loop to train a learner network, and an outer-loop to train a generator network that produces synthetic training data for the learner network. Experiments presented in Section 3 demonstrate that the GTN approach produces synthetic data that enables much faster learning, speeding up the training of a NN by a factor of 9. Importantly, the synthetic data in GTNs is not only agnostic to the weight initialization of the learner network (as in Wang et al. (2019b)), but is also agnostic to the learner’s architecture. As a result, GTNs are a viable method for accelerating evaluation of candidate architectures in NAS. Indeed, controlling for the search algorithm (i.e. using GTN-produced synthetic data as a drop-in replacement for real data when evaluating a candidate architecture’s performance), GTN-NAS improves the NAS state of the art by finding higher-performing architectures than comparable methods like weight sharing (Pham et al., 2018) and Graph HyperNetworks (Zhang et al., 2018); it also is competitive with methods using more sophisticated search algorithms and orders of magnitude more computation. It could also be combined with those methods to provide further gains.
+
+One promising aspect of GTNs is that they make very few assumptions about the learner. In contrast, NAS techniques based on shared training are viable only if the parameterizations of the learners are similar. For example, it is unclear how weight-sharing or HyperNetworks could be applied to architectural search spaces wherein layers could be either convolutional or fully-connected, as there is no obvious way for weights learned for one layer type to inform those of the other. In contrast, GTNs are able to create training data that can generalize between such diverse types of architectures.
+
+GTNs also open up interesting new research questions and applications to be explored by future work. Because they can rapidly train new architectures, GTNs could be used to create NNs ondemand that meet specific design constraints (e.g. a given balance of performance, speed, and energy usage) and/or have a specific subset of skills (e.g. perhaps one needs to rapidly create a compact network capable of three particular skills). Because GTNs can generate virtually any learning environment, they also one day could be a key to creating AI-generating algorithms, which seek to bootstrap themselves from simple initial conditions to powerful forms of AI by creating an openended stream of challenges (learning opportunities) while learning to solve them (Clune, 2019).
+
+# 2 METHODS
+
+The main idea in GTNs is to train a data-generating network such that a learner network trained on data it rapidly produces high accuracy in a target task. Unlike a GAN, here the two networks cooperate (rather than compete) because their interests are aligned towards having the learner perform well on the target task when trained on data produced by the GTN. The generator and the learner networks are trained with meta-learning via nested optimization that consists of inner and outer training loops (Figure 1a). In the inner-loop, the generator $G ( z , y )$ takes Gaussian noise $( z )$ and a label $( y )$ as input and outputs synthetic data $( x )$ . Optionally, the generator could take only noise as input and produce both data and labels as output (Appendix F). The learner is then trained on this synthetic data for a fixed number of inner-loop training steps with any optimizer, such as SGD or Adam (Kingma & Ba, 2014): we use SGD with momentum in this paper. SI Equation 1 defines the inner-loop SGD with momentum update for the learner parameters $\theta _ { t }$ . We sample $\mathbf { z } _ { t }$ (noise vectors input to the generator) from a unit-variance Gaussian and $\mathbf { y } _ { t }$ labels for each generated sample) uniformly from all available class labels. Note that both $\mathbf { z } _ { t }$ and $\mathbf { y } _ { t }$ are batches of samples. We can also learn a curriculum directly by additionally optimizing $\mathbf { z } _ { t }$ directly (instead of sampling it randomly) and keeping $\mathbf { y } _ { t }$ fixed throughout all of training.
+
+The inner-loop loss function $\ell _ { \mathrm { i n n e r } }$ can be cross-entropy for classification problems or mean squared error for regression problems. Note that the inner-loop objective does not depend on the outerloop objective and could even be parameterized and learned through meta-gradients with the rest of the system (Houthooft et al., 2018). In the outer-loop, the learner $\theta _ { T }$ (i.e. the learner parameters trained on synthetic data after the $T$ inner-loop steps) is evaluated on the real training data, which is used to compute the outer-loop loss (aka meta-training loss). The gradient of the meta-training loss with respect to the generator is computed by backpropagating through the entire inner-loop learning process. While computing the gradients for the generator we also compute the gradients of hyperparameters of the inner-loop SGD update rule (its learning rate and momentum), which are updated after each outer-loop at no additional cost. To reduce memory requirements, we leverage gradientcheckpointing (Griewank & Walther, 2000) when computing meta-gradients. The computation and memory complexity of our approach can be found in Appendix D.
+
+![](images/3bb569aff7ce7ba27d1ff13d5c7fd17dea3b3898a66af4476e10cac105840dfd.jpg)  
+(a) Overview of Generative Teaching Networks (b) GTN stability with WN (c) GTN curricula comparison   
+Figure 1: (a) Generative Teaching Network (GTN) Method. The numbers in the figure reflect the order in which a GTN is executed. Noise is fed as an input to the Generator (1), which uses it to generate new data (2). The learner is trained (e.g. using SGD or Adam) to perform well on the generated data (3). The trained learner is then evaluated on the real training data in the outer-loop to compute the outer-loop meta-loss (4). The gradients of the generator parameters are computed w.r.t. to the meta-loss to update the generator (5). Both a learned curriculum and weight normalization substantially improve GTN performance. (b) Weight normalization improves meta-gradient training of GTNs, and makes the method much more robust to different hyperparameter settings. Each boxplot reports the final loss of 20 runs obtained during hyperparameter optimization with Bayesian Optimization (lower is better). (c) shows a comparison between GTNs with different types of curricula. The GTN method with the most control over how samples are presented performs the best.
+
+A key motivation for this work is to generate synthetic data that is learner agnostic, i.e. that generalizes across different potential learner architectures and initializations. To achieve this objective, at the beginning of each new outer-loop training, we choose a new learner architecture according to a predefined set and randomly initialize it (details in Appendix A).
+
+Meta-learning with Weight Normalization. Optimization through meta-gradients is often unstable (Maclaurin et al., 2015). We observed that this instability greatly complicates training because of its hyperparameter sensitivity, and training quickly diverges if they are not well-set. Combining the gradients from Evolution Strategies (Salimans et al., 2017) and backpropagation using inverse variance weighting (Fleiss, 1993; Metz et al., 2019) improved stability in our experiments, but optimization still consistently diverged whenever we increased the number of inner-loop optimization steps. To mitigate this issue, we introduce applying weight normalization (Salimans & Kingma, 2016) to stabilize meta-gradient training by normalizing the generator and learner weights. Instead of updating the weights $( W )$ directly, we parameterize them as $W = g \cdot V / \| V \|$ and instead update the scalar $g$ and vector $V$ . Weight normalization eliminates the need for (and cost of) calculating ES gradients and combining them with backprop gradients, simplifying and speeding up the algorithm.
+
+We hypothesize that weight normalization will help stabilize meta-gradient training more broadly, although future work is required to test this hypothesis in meta-learning contexts besides GTNs. The idea is that applying weight normalization to meta-learning techniques is analogous to batch normalization for deep networks (Ioffe & Szegedy, 2015). Batch normalization normalizes the forward propagation of activations in a long sequence of parameterized operations (a deep NN). In meta-gradient training both the activations and weights result from a long sequence of parameterized operations and thus both should be normalized. Results in section 3.1 support this hypothesis.
+
+Learning a Curriculum with Generative Teaching Networks. Previous work has shown that a learned curriculum can be more effective than training from uniformly sampled data (Graves et al., 2017). A curriculum is usually encoded with indexes to samples from a given dataset, rendering it non-differentiable and thereby complicating the curriculum’s optimization. With GTNs however, a curriculum can be encoded as a series of input vectors to the generator (i.e. instead of sampling the $\mathbf { z } _ { t }$ inputs to the generator from a Gaussian distribution, a sequence of $\mathbf { z } _ { t }$ inputs can be learned). A curriculum can thus be learned by differentiating through the generator to optimize this sequence (in addition to the generator’s parameters). Experiments confirm that GTNs more effectively teach learners when optimizing such a curriculum (Section 3.2).
+
+Accelerating NAS with Generative Teaching Networks. Since GTNs can accelerate learner training, we propose harnessing GTNs to accelerate NAS. Rather than evaluating each architecture in a target task with a standard training procedure, we propose evaluating architectures with a metaoptimized training process (that generates synthetic data in addition to optimizing inner-loop hyperparameters). We show that doing so significantly reduces the cost of running NAS (Section 3.4).
+
+The goal of these experiments is to find a high-performing CNN architecture for the CIFAR10 image-classification task (Krizhevsky et al., 2009) with limited compute costs. We use the same architecture search-space, training procedure, hyperparameters, and code from Neural Architecture Optimization (Luo et al., 2018), a state-of-the-art NAS method. The search space consists of the topology of two cells: a reduction cell and a convolutional cell. Multiple copies of such cells are stacked according to a predefined blueprint to form a full CNN architecture (see Luo et al. (2018) for more details). The blueprint has two hyperparameters $N$ and $F$ that control how many times the convolutional cell is repeated (depth) and the width of each layer, respectively. Each cell contains $B = 5$ nodes. For each node within a cell, the search algorithm has to choose two inputs as well as two operations to apply to those inputs. The inputs to a node can be previous nodes or the outputs of the last two layers. There are 11 operations to choose from (Appendix C).
+
+Following Luo et al. (2018), we report the performance of our best cell instantiated with $N =$ $6 , F = 3 6$ after the resulting architecture is trained for a significant amount of time (600 epochs). Since evaluating each architecture in those settings (named final evaluation from now on) is time consuming, Luo et al. (2018) uses a surrogate evaluation (named search evaluation) to estimate the performance of a given cell wherein a smaller version of the architecture $( N = 3 , F = 3 2 )$ is trained for less epochs (100) on real data. We further reduce the evaluation time of each cell by replacing the training data in the search evaluation with GTN synthetic data, thus reducing the training time per evaluation by $3 0 0 \mathrm { x }$ (which we call GTN evaluation). While we were able to train GTNs directly on the complex architectures from the NAS search space, training was prohibitively slow. Instead, for these experiments, we optimize our GTN ahead of time using proxy learners described in Appendix A.2, which are smaller fully-convolutional networks (this meta-training took 8h on one p6000 GPU). Interestingly, although we never train our GTN on any NAS architectures, because of generalization, synthetic data from GTNs were still effective for training them.
+
+# 3 RESULTS
+
+We first demonstrate that weight normalization significantly improves the stability of meta-learning, an independent contribution of this paper (Section 3.1). We then show that training with synthetic data is more effective when learning such data jointly with a curriculum that orders its presentation to the learner (Section 3.2). We next show that GTNs can generate a synthetic training set that enables more rapid learning in a few SGD steps than real training data in two supervised learning domains (MNIST and CIFAR10) and in a reinforcement learning domain (cart-pole, Appendix H). We then apply GTN-synthetic training data for neural architecture search to find high performing architectures for CIFAR10 with limited compute, outperforming comparable methods like weight sharing (Pham et al., 2018) and Graph HyperNetworks (Zhang et al., 2018) (Section 3.4).
+
+We uniformly split the usual MNIST training set into training (50k) and validation sets (10k). The training set was used for inner-loop training (for the baseline) and to compute meta-gradients for all the treatments. We used the validation set for hyperparameter tuning and report accuracy on the usual MNIST test set (10k images). We followed the same procedure for CIFAR10, resulting in training, validation, and test sets with 45k, 5k, and 10k examples, respectively. Unless otherwise specified, we ran each experiment 5 times and plot the mean and its $9 5 \%$ confidence intervals from $_ { \mathrm { ( n = 1 , 0 0 0 ) } }$ bootstrapping. Appendix A describes additional experimental details.
+
+# 3.1 IMPROVING STABILITY WITH WEIGHT NORMALIZATION
+
+To demonstrate the effectiveness of weight normalization for stabilizing and robustifying metaoptimization, we compare the results of running hyperparameter optimization for GTNs with and without weight normalization on MNIST. Figure 1b shows the distribution of the final performance obtained for 20 runs during hyperparameter tuning, which reflects how sensitive the algorithms are to hyperparameter settings. Overall, weight normalization substantially improved robustness to hyperparameters and final learner performance, supporting the initial hypothesis.
+
+# 3.2 IMPROVING GTNS WITH A CURRICULUM
+
+We experimentally evaluate four different variants of GTNs, each with increasing control over the ordering of the $z$ codes input to the generator, and thus the order of the inputs provided to the learner. The first variant (called GTN - No Curriculum), trains a generator to output synthetic training data by sampling the noise vector $z$ for each sample independently from a Gaussian distribution. In the next three GTN variants, the generator is provided with a fixed set of input samples (instead of a noise vector). These input samples are learned along with the generator parameters during GTN training. The second GTN variant (called GTN - All Shuffled) learns a fixed set of 4,096 input samples that are presented in a random order without replacement (thus learning controls the data, but not the order in which they are presented). The third variant (called GTN - Shuffled Batch) learns 32 batches of 128 samples each (so learning controls which samples coexist within a batch), but the order in which the batches are presented is randomized (without replacement). Finally, the fourth variant (called GTN - Full Curriculum) learns a deterministic sequence of 32 batches of 128 samples, giving learning full control. Learning such a curriculum incurs no additional computational expense, as learning the $\mathbf { z } _ { t }$ tensor is computationally negligible and avoids the cost of repeatedly sampling new Gaussian $z$ codes. We plot the test accuracy of a learner (with random initial weights and architecture) as a function of outer-loop iterations for all four variants in Figure 1c. Although GTNs - No curriculum can seemingly generate endless data (see Appendix G), it performs worse than the other three variants with a fixed set of generator inputs. Overall, training the GTN with exact ordering of input samples (GTN - Full Curriculum) outperforms all other variants.
+
+While curriculum learning usually refers to training on easy tasks first and increasing their difficulty over time, our curriculum goes beyond presenting tasks in a certain order. Specifically, GTN - Full Curriculum learns both the order in which to present samples and the specific group of samples to present at the same time. The ability to learn a full curriculum improves GTN performance. For that reason, we adopt that approach for all GTN experiments.
+
+# 3.3 GTNS FOR SUPERVISED LEARNING
+
+To explore whether GTNs can generate training data that helps networks learn rapidly, we compare to 3 treatments for MNIST classification. 1) Real Data - Training learners with random mini-batches of real data, as is ubiquitous in SGD. 2) Dataset Distillation - Training learners with synthetic data, where training examples are directly encoded as tensors optimized by the meta-objective, as in Wang et al. (2019b). 3) GTN - Our method where the training data presented to the learner is generated by a neural network. Note that all three methods meta-optimize the inner-loop hyperparameters (i.e. the learning rate and momentum of SGD) as part of the meta-optimization.
+
+We emphasize that producing state-of-the-art (SOTA) performance (e.g. on MNIST or CIFAR) when training with GTN-generated data is not important for GTNs. Because the ultimate aim for
+
+GTNs is to accelerate NAS (Section 3.4), what matters is how well and inexpensively we can identify architectures that achieve high asymptotic accuracy when later trained on the full (real) training set. A means to that end is being able to train architectures rapidly, i.e. with very few SGD steps, because doing so allows NAS to rapidly identify promising architectures. We are thus interested in “few-step accuracy (i.e. accuracy after a few–e.g. 32 or 128–SGD steps). Besides, there are many reasons not to expect SOTA performance with GTNs (Appendix B).
+
+Figure 2a shows that the GTN treatment significantly outperforms the other ones $( p < 0 . 0 1 )$ and trains a learner to be much more accurate when in the few-step performance regime. Specifically, for each treatment the figure shows the test performance of a learner following 32 inner-loop training steps with a batch size of 128. We would not expect training on synthetic data to produce higher accuracy than unlimited SGD steps on real data, but here the performance gain comes because GTNs can compress the real training data by producing synthetic data that enables learners to learn more quickly than on real data. For example, the original dataset might contain many similar images, where only a few of them would be sufficient for training (and GTN can produce just these few). GTN could also combine many different things that need to be learned about images into one image.
+
+Figure 2b shows the few-step performance of a learner from each treatment after 2000 total outerloop iterations $\mathord {  } 1$ hour on a p6000 GPU). For reference, Dataset Distillation (Wang et al., 2019b) reported $7 9 . 5 \%$ accuracy for a randomly initialized network (using 100 synthetic images vs. our 4,096) and L2T (Fan et al., 2018) reported needing $3 0 0 \mathrm { x }$ more training iterations to achieve $> 9 8 \%$ MNIST accuracy. Surprisingly, although recognizable as digits and effective for training, GTNgenerated images (Figure 2c) were not visually realistic (see Discussion).
+
+![](images/80c02265c2a3f6a08bffd24c1ddff3b2b3a7007a62fc76ac329482bd3d5d8630.jpg)  
+Figure 2: Teaching MNIST with GTN-generated images. (a) shows MNIST test set few-step accuracy across outer-loop iterations for different sources of inner-loop training data. The inner-loop consists of $3 2 ~ \mathrm { S G D }$ steps and the outer-loop optimizes MNIST validation accuracy. Our method (GTN) outperforms the two controls (dataset distillation and samples from real data). (b) shows, given final meta-training iteration, how iterations of inner-loop training compare between training data sources (measured by MNIST training set accuracy). (c) shows 100 random samples from the trained GTN. Samples are usually recognizable as digits, but are not realistic (see Discussion). Each column contains samples from a different digit class, and each row is taken from different inner-loop iterations (evenly spaced from the 32 total iterations, with early iterations at the top).
+
+# 3.4 ARCHITECTURE SEARCH WITH GTNS
+
+We next test the benefits of GTN for NAS (GTN-NAS) in CIFAR10, a domain where NAS has previously shown significant improvements over the best architectures produced by armies of human scientists. Figure 3a shows the few-step training accuracy of a learner trained with either GTN-synthetic data or real (CIFAR10) data over meta-training iterations. After 8h of meta-training, training with GTN-generated data was significantly faster than with real data, as in MNIST.
+
+To explore the potential for GTN-NAS to accelerate CIFAR10 architecture search, we investigated the Spearman rank correlation (across architectures sampled from the NAS search space) between accelerated GTN-trained network performance (GTN evaluation) and the usual more expensive performance metric used during NAS (search evaluation). A correlation plot is shown in Figure 3c; note that a strong correlation implies we can train architectures using GTN evaluation as an inexpensive surrogate. We find that GTN evaluation enables predicting the performance of an architecture efficiently. The rank-correlation between 128 steps of training with GTN-synthetic data vs. 100 epochs of real data is 0.3606. The correlation improves to 0.5582 when considering the top $50 \%$ of architectures recommended by GTN evaluation scores, which is important because those are the ones that search would select. This improved correlation is slightly stronger than that from 3 epochs of training with real data (0.5235), a $\sim 9 \times$ cost-reduction per trained model.
+
+![](images/4d9cfb5ecebbda63babb0143328f1ad83079642b94679822cb10e2b92b46abdf.jpg)  
+Figure 3: Teaching CIFAR10 with GTN-generated images. (a) CIFAR10 training set performance of the final learner (after 1,700 meta-optimization steps) across inner-loop learning iterations. (b) Samples generated by GTN to teach CIFAR10 are unrecognizable, despite being effective for training. Each column contains a different class, and each row is taken from the same inner-loop iteration (evenly spaced from all 128 iterations, early iterations at the top). (c) Correlation between performance prediction using GTN-data vs. Real Data. When considering the top half of architectures (as ranked by GTN evaluation), correlation between GTN evaluation and search evaluation is strong (0.5582 rank-correlation), suggesting that GTN-NAS has potential to uncover high performing architectures at a significantly lower cost. Architectures shown are uniformly sampled from the NAS search space. The top $10 \%$ of architectures according to the GTN evaluation (blue squares)– those likely to be selected by GTN-NAS–have high true asymptotic accuracy.
+
+Architecture search methods are composed of several semi-independent components, such as the choice of search space, search algorithm, and proxy evaluation of candidate architectures. GTNs are proposed as an improvement to this last component, i.e. as a new way to quickly evaluate a new architecture. Thus we test our method under the standard search space for CIFAR10, using a simple form of search (random search) for which there are previous benchmark results. In particular, we ran an architecture search experiment where we evaluated 800 randomly generated architectures trained with GTN-synthetic data. We present the performance after final evaluation of the best architecture found in Table 1. This experimental setting is similar to that of Zhang et al. (2018). Highlighting the potential of GTNs as an improved proxy evaluation for architectures, we achieve state-of-the-art results when controlling for search algorithm (the choice of which is orthogonal to our contribution). While it is an apples-to-oranges comparison, GTN-NAS is competitive even with methods that use more advanced search techniques than random search to propose architectures (Appendix E). GTN is compatible with such techniques, and would likely improve their performance, an interesting area of future work. Furthermore, because of the NAS search space, the modules GTN found can be used to create even larger networks. A further test of whether GTNs predictions generalize is if such larger networks would continue performing better than architectures generated by the realdata control, similarly scaled. We tried $\mathrm { F } { = } 1 2 8$ and show it indeed does perform better (Table 1), suggesting additional gains can be had by searching post-hoc for the correct F and N settings.
+
+# 4 DISCUSSION, FUTURE WORK, AND CONCLUSION
+
+The results presented here suggest potential future applications and extensions of GTNs. Given the ability of GTNs to rapidly train new models, they are particularly useful when training many independent models is required (as we showed for NAS). Another such application would be to teach networks on demand to realize particular trade-offs between e.g. accuracy, inference time, and memory requirements. While to address a range of such trade-offs would ordinarily require training many models ahead of time and selecting amongst them (Elsken et al., 2019), GTNs could instead rapidly train a new network only when a particular trade-off is needed. Similarly, agents with unique combinations of skills could be created on demand when needed.
+
+Interesting questions are raised by the lack of similarity between the synthetic GTN data and real MNIST and CIFAR10 data. That unrealistic and/or unrecognizable images can meaningfully affect NNs is reminiscent of the finding that deep neural networks are easily fooled by unrecognizable images (Nguyen et al., 2015). It is possible that if neural network architectures were functionally more similar to human brains, GTNs’ synthetic data might more resemble real data. However, an alternate (speculative) hypothesis is that the human brain might also be able to rapidly learn an arbitrary skill by being shown unnatural, unrecognizable data (recalling the novel Snow Crash).
+
+Table 1: Performance of different architecture search methods. Our results report mean $\pm \thinspace \mathrm { S D }$ of 5 evaluations of the same architecture with different initializations. It is common to report scores with and without Cutout (DeVries & Taylor, 2017), a data augmentation technique used during training. We found better architectures compared to other methods that reduce architecture evaluation speed and were tested with random search (Random Search $+ \mathsf { W } \mathsf { S }$ and Random Search+GHN). Increasing the width of the architecture found $\left( \mathrm { F } { = } 1 2 8 \right)$ further improves performance. Because each NAS method finds a different architecture, the number of parameters differs. Each method ran once.   
+
+<table><tr><td>Model</td><td>Error(%)</td><td>#params</td><td>GPU Days</td></tr><tr><td>Random Search + GHN (Zhang et al., 2018)</td><td>4.3± 0.1</td><td>5.1M</td><td>0.42</td></tr><tr><td>Random Search + Weight Sharing (Luo et al., 2018)</td><td>3.92</td><td>3.9M</td><td>0.25</td></tr><tr><td>Random Search + Real Data (baseline)</td><td>3.88± 0.08</td><td>12.4M</td><td>10</td></tr><tr><td>Random Search + GTN (ours)</td><td>3.84 ± 0.06</td><td>8.2M</td><td>0.67</td></tr><tr><td>Random Search + Real Data + Cutout (baseline)</td><td>3.02± 0.03</td><td>12.4M</td><td>10</td></tr><tr><td>Random Search + GTN + Cutout (ours)</td><td>2.92 ± 0.06</td><td>8.2M</td><td>0.67</td></tr><tr><td>Random Search + Real Data + Cutout (F=128) (baseline) Random Search + GTN + Cutout (F=128) (ours)</td><td>2.51±0.13 2.42 ± 0.03</td><td>151.7M 97.9M</td><td>10 0.67</td></tr></table>
+
+The improved stability of training GTNs from weight normalization naturally suggests the hypothesis that weight normalization might similarly stabilize, and thus meaningfully improve, any techniques based on meta-gradients (e.g. MAML (Finn et al., 2017), learned optimizers (Metz et al., 2019), and learned update rules (Metz et al., 2018)). In future work, we will more deeply investigate how consistently, and to what degree, this hypothesis holds.
+
+Both weight sharing and GHNs can be combined with GTNs by using the shared weights or HyperNetwork for initialization of proposed learners and then fine-tuning on GTN-produced data. GTNs could also be combined with more intelligent ways to propose which architecture to sample next such as NAO (Luo et al., 2018). Many other extensions would also be interesting to consider. GTNs could be trained for unsupervised learning, for example by training a useful embedding function. Additionally, they could be used to stabilize GAN training and prevent mode collapse (Appendix I shows encouraging initial results). One particularly promising extension is to introduce a closedloop curriculum (i.e. one that responds dynamically to the performance of the learner throughout training), which we believe could significantly improve performance. For example, a recurrent GTN that is conditioned on previous learner outputs could adapt its samples to be appropriately easier or more difficult depending on an agent’s learning progress, similar in spirit to the approach of a human tutor. Such closed-loop teaching can improve learning (Fan et al., 2018).
+
+An additional interesting direction is having GTNs generate training environments for RL agents. Appendix H shows this works for the simple RL task of CartPole. That could be either for a predefined target task, or could be combined with more open-ended algorithms that attempt to continuously generate new, different, interesting tasks that foster learning (Clune, 2019; Wang et al., 2019a). Because GTNs can encode any possible environment, they (or something similar) may be necessary to have truly unconstrained, open-ended algorithms (Stanley et al., 2017). If techniques could be invented to coax GTNs to produce recognizable, human-meaningful training environments, the technique could also produce interesting virtual worlds for us to learn in, play in, or explore.
+
+This paper introduces a new method called Generative Teaching Networks, wherein data generators are trained to produce effective training data through meta-learning. We have shown that such an approach can produce supervised datasets that yield better few-step accuracy than an equivalent amount of real training data, and generalize across architectures and random initializations. We leverage such efficient training data to create a fast NAS method that generates state-of-the-art architectures (controlling for the search algorithm). While GTNs may be of particular interest to the field of architecture search (where the computational cost to evaluate candidate architectures often limits the scope of its application), we believe that GTNs open up an intriguing and challenging line of research into a variety of algorithms that learn to generate their own training data.
+
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+Hava T Siegelmann and Eduardo D Sontag. On the computational power of neural nets. Journal of computer and system sciences, 50(1):132–150, 1995.
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+Akash Srivastava, Lazar Valkov, Chris Russell, Michael U. Gutmann, and Charles Sutton. Veegan: Reducing mode collapse in gans using implicit variational learning. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (eds.), Advances in Neural Information Processing Systems 30, pp. 3308–3318. Curran Associates, Inc., 2017.
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+Barret Zoph and Quoc V. Le. Neural architecture search with reinforcement learning. 2017. URL https://arxiv.org/abs/1611.01578.
+
+# APPENDIX A ADDITIONAL EXPERIMENTAL DETAILS
+
+The outer loop loss function is domain specific. In the supervised experiments on MNIST and CIFAR, the outer loop loss was cross-entropy for logistic regression on real MNIST or CIFAR data. The inner-loop loss matches the outer-loop loss, but with synthetic data instead of real data. Appendix H describes the losses for the RL experiments.
+
+The following equation defines the inner-loop SGD with momentum update for the learner parameters $\theta _ { t }$ .
+
+$$
+\theta _ { t + 1 } = \theta _ { t } - \alpha \sum _ { 0 \leq t ^ { \prime } \leq t } \beta ^ { t - t ^ { \prime } } \nabla \ell _ { \mathrm { i n n e r } } \bigl ( G ( \mathbf { z } _ { t ^ { \prime } } , \mathbf { y } _ { t ^ { \prime } } ) , \mathbf { y } _ { t ^ { \prime } } , \theta _ { t ^ { \prime } } \bigr ) ,
+$$
+
+where $\alpha$ and $\beta$ are the learning rate and momentum hyperparameters, respectively. $\mathbf { z } _ { t }$ is a batch of noise vectors that are input to the generator and are sampled from a unit-variance Gaussian. $\mathbf { y } _ { t }$ are a batch of labels for each generated sample/input and are sampled uniformly from all available class labels. Instead of randomly sampling $\mathbf { z } _ { t }$ , we can also learn a curriculum by additionally optimizing $\mathbf { z } _ { t }$ directly and keeping $\mathbf { y } _ { t }$ fixed throughout all of training. Results for both approaches (and additional curriculum ablations) are reported in Section 3.2.
+
+# A.1 MNIST EXPERIMENTS:
+
+For the GTN training for MNIST we sampled architectures from a distribution that produces architectures with convolutional (conv) and fully-connectd (FC) layers. All architectures had 2 conv layers, but the number of filters for each layer was sampled uniformly from the ranges $U ( [ 3 2 , 1 2 8 ] )$ and $U ( [ 6 4 , 2 5 6 ] )$ , respectively. After each conv layer there is a max pooling layer for dimensionality reduction. After the last conv layer, there is a fully-connected layer with number of filters sampled uniformly from the range $U ( [ 6 \dot { 4 } , 2 5 6 ] )$ . We used Kaiming Normal initialization (He et al., 2015) and LeakyReLUs (Maas et al., 2013) (with $\alpha = 0 . 1$ ). We use BatchNorm (Ioffe & Szegedy, 2015) for both the generator and the learners. The BatchNorm momentum for the learner was set to 0 (meta-training consistently converged to small values and we saw no significant gain from learning the value).
+
+The generator consisted of 2 FC layers (1024 and $1 2 8 * H / 4 * H / 4$ filters, respectively, where $H$ is the final width of the synthetic image). After the last FC layer there are 2 conv layers. The first conv has 64 filters. The second conv has 1 filter followed by a Tanh. We found it particularly important to normalize (mean of zero and variance of one) all datasets. Hyperparameters are shown in Table 2.
+
+Table 2: Hyperparameters for MNIST experiments   
+
+<table><tr><td rowspan=1 colspan=1>Hyperparameter</td><td rowspan=1 colspan=1>Value</td></tr><tr><td rowspan=1 colspan=1>Learning Rate</td><td rowspan=1 colspan=1>0.01</td></tr><tr><td rowspan=1 colspan=1>Initial LR</td><td rowspan=1 colspan=1>0.02</td></tr><tr><td rowspan=1 colspan=1>InitialMomentum</td><td rowspan=1 colspan=1>0.5</td></tr><tr><td rowspan=1 colspan=1>Adam Beta_1</td><td rowspan=1 colspan=1>0.9</td></tr><tr><td rowspan=1 colspan=1>AdamBeta_2</td><td rowspan=1 colspan=1>0.999</td></tr><tr><td rowspan=1 colspan=1>Size of latent variable</td><td rowspan=1 colspan=1>128</td></tr><tr><td rowspan=1 colspan=1>Inner-Loop Batch Size</td><td rowspan=1 colspan=1>128</td></tr><tr><td rowspan=1 colspan=1>Outer-Loop Batch Size</td><td rowspan=1 colspan=1>128</td></tr></table>
+
+# A.2 CIFAR10 EXPERIMENTS:
+
+For GTN training for CIFAR-10, the template architecture is a small learner with 5 convolutional layers followed by a global average pooling and an FC layer. The second and fourth convolution had stride $^ { \prime = 2 }$ for dimensionality reduction. The number of filters of the first conv layer was sampled uniformly from the range $U ( [ 3 2 , 1 2 8 ] )$ while all others were sampled uniformly from the range $\bar { U } ( [ 6 4 , 2 5 6 ] )$ . Other details including the generator architecture were the same as the MNIST experiments, except the CIFAR generator’s second conv layer had 3 filters instead of 1. Hyperparameters used can be found in Table 3. For CIFAR10 we augmented the real training set when training GTNs with random crops and horizontal flips. We do not add weight normalization to the final architectures found during architecture search, but we do so when we train architectures with GTN-generated data during architecture search to provide an estimate of their asymptotic performance.
+
+Table 3: Hyperparameters for CIFAR10 experiments   
+
+<table><tr><td rowspan=1 colspan=1>Hyperparameter</td><td rowspan=1 colspan=1>Value</td></tr><tr><td rowspan=1 colspan=1>Learning Rate</td><td rowspan=1 colspan=1>0.002</td></tr><tr><td rowspan=1 colspan=1>Initial LR</td><td rowspan=1 colspan=1>0.02</td></tr><tr><td rowspan=1 colspan=1>Initial Momentum</td><td rowspan=1 colspan=1>0.5</td></tr><tr><td rowspan=1 colspan=1>AdamBeta_1</td><td rowspan=1 colspan=1>0.9</td></tr><tr><td rowspan=1 colspan=1>Adam Beta_2</td><td rowspan=1 colspan=1>0.9</td></tr><tr><td rowspan=1 colspan=1>Adam ∈</td><td rowspan=1 colspan=1>1e-5</td></tr><tr><td rowspan=1 colspan=1>Sizeoflatentvariable</td><td rowspan=1 colspan=1>128</td></tr><tr><td rowspan=1 colspan=1>Inner-loop Batch Size</td><td rowspan=1 colspan=1>128</td></tr><tr><td rowspan=1 colspan=1>Outer-loop Batch Size</td><td rowspan=1 colspan=1>256</td></tr></table>
+
+# APPENDIX B REASONS GTNS ARE NOT EXPECTED TO PRODUCE SOTA ACCURACY VS. ASYMPTOTIC PERFORMANCE WHEN TRAINING ON REAL DATA
+
+There are three reasons not to expect SOTA accuracy levels for the learners trained on synthetic data: (1) we train for very few SGD steps (32 or 128 vs. tens of thousands), (2) SOTA performance results from architectures explicitly designed (with much human effort) to achieve record accuracy, whereas GTN produces compressed training data optimized to generalize across diverse architectures with the aim of quickly evaluating a new architecture’s potential, and (3) SOTA methods often use data outside of the benchmark dataset and complex data-augmentation schemes.
+
+# APPENDIX C CELL SEARCH SPACE
+
+When searching for the operations in a CNN cell, the 11 possible operations are listed below.
+
+• identity • $1 \times 1$ convolution • $3 \times 3$ convolution • $1 \times 3 + 3 \times 1$ convolution • $1 \times 7 + 7 \times 1$ convolution • $2 \times 2$ max pooling • $3 \times 3$ max pooling • $5 \times 5$ max pooling • $2 \times 2$ average pooling • $3 \times 3$ average pooling • $5 \times 5$ average pooling
+
+# APPENDIX D COMPUTATION AND MEMORY COMPLEXITY
+
+With the traditional training of DNNs with back-propagation, the memory requirements are proportional to the size of the network because activations during the forward propagation have to be stored for the backward propagation step. With meta-gradients, the memory requirement also grows with the number of inner-loop steps because all activations and weights have to be stored for the
+
+2nd order gradient to be computed. This becomes impractical for large networks and/or many innerloop steps. To reduce the memory requirements, we utilize gradient-checkpointing (Griewank & Walther, 2000) by only storing the computed weights of learner after each inner-loop step and recomputing the activations during the backward pass. This trick allows us to compute meta-gradients for networks with 10s of millions of parameters over hundreds of inner-loop steps in a single GPU. While in theory the computational cost of computing meta-gradients with gradient-checkpointing is $4 \mathbf { x }$ larger than computing gradients (and $1 2 \mathbf { x }$ larger than forward propagation), in our experiments it is about $2 . 5 \mathrm { x }$ slower than gradients through backpropagation due to parallelism. We could further reduce the memory requirements by utilizing reversable hypergradients (Maclaurin et al., 2015), but, in our case, we were not constrained by the number of inner-loop steps we can store in memory.
+
+# APPENDIX E EXTENDED NAS RESULTS
+
+In the limited computation regime (less than 1 day of computation), the best methods were, in order, GHN, ENAS, GTN, and NAONet with a mean error of $2 . 8 4 \%$ , $2 . 8 9 \%$ , $2 . 9 2 \%$ , and $2 . 9 3 \%$ , respectively. A $0 . 0 8 \%$ difference on CIFAR10 represents 8 out of the 10k test samples. For that reason, we consider all of these methods as state of the art. Note that out of the four, GTN is the only one relying on Random Search for architecture proposal.
+
+Table 4: Performance of different architecture search methods. Search with our method required 16h total, of which 8h were spent training the GTN and 8h were spent evaluating 800 architectures with GTN-produced synthetic data. Our results report mean $\pm \thinspace \mathrm { S D }$ of 5 evaluations of the same architecture with different initializations. It is common to report scores with and without Cutout (DeVries & Taylor, 2017), a data augmentation technique used during training.We found better architectures compared to other methods using random search (Random-WS and GHN-Top) and are competitive with algorithms that benefit from more advanced search methods (e.g. NAONet and ENAS employ non-random architecture proposals for performance gains; GTNs could be combined with such nonrandom proposals, which would likely further improve performance). Increasing the width of the architecture found $\left( \mathrm { F } { = } 1 2 8 \right)$ ) further improves performance.
+
+<table><tr><td>Model</td><td>Error(%)</td><td>#params</td><td>Random</td><td>GPU Days</td></tr><tr><td>NASNet-A (Zoph &amp; Le, 2017)</td><td>3.41</td><td>3.3M</td><td>X</td><td>2000</td></tr><tr><td>AmoebaNet-B + Cutout (Real et al., 2019)</td><td>2.13</td><td>34.9M</td><td>X</td><td>3150</td></tr><tr><td>DARTS + Cutout (Liu et al., 2018b)</td><td>2.83</td><td>4.6M</td><td>X</td><td>4</td></tr><tr><td>NAONet + Cutout (Luo et al., 2018)</td><td>2.48</td><td>10.6M</td><td>X</td><td>200</td></tr><tr><td>NAONet-WS (Luo et al., 2018)</td><td>3.53</td><td>2.5M</td><td>X</td><td>0.3</td></tr><tr><td>NAONet-WS + Cutout (Luo et al., 2018)</td><td>2.93</td><td>2.5M</td><td>X</td><td>0.3</td></tr><tr><td>ENAS (Pham et al., 2018)</td><td>3.54</td><td>4.6M</td><td>X</td><td>0.45</td></tr><tr><td>ENAS + Cutout (Pham et al., 2018)</td><td>2.89</td><td>4.6M</td><td>X</td><td>0.45</td></tr><tr><td>GHN Top-Best + Cutout (Zhang et al., 2018)</td><td>2.84 ± 0.07</td><td>5.7M</td><td>X</td><td>0.84</td></tr><tr><td>GHN Top (Zhang et al., 2018)</td><td>4.3± 0.1</td><td>5.1M</td><td>√</td><td>0.42</td></tr><tr><td>Random-WS (Luo et al., 2018)</td><td>3.92</td><td>3.9M</td><td>√</td><td>0.25</td></tr><tr><td>Random Search + Real Data (baseline)</td><td>3.88 ±0.08</td><td>12.4M</td><td>√</td><td>10</td></tr><tr><td>RS + Real Data + Cutout (baseline)</td><td>3.02 ± 0.03</td><td>12.4M</td><td></td><td>10</td></tr><tr><td>RS + Real Data + Cutout (F=128) (baseline)</td><td>2.51 ± 0.13</td><td>151.7M</td><td></td><td>10</td></tr><tr><td>Random Search + GTN (ours)</td><td>3.84 ± 0.06</td><td>8.2M</td><td></td><td>0.67</td></tr><tr><td>Random Search + GTN + Cutout (ours)</td><td>2.92 ± 0.06</td><td>8.2M</td><td></td><td>0.67</td></tr><tr><td>RS + GTN + Cutout (F=128) (ours)</td><td>2.42 ± 0.03</td><td>97.9M</td><td></td><td>0.67</td></tr></table>
+
+# APPENDIX F CONDITIONED GENERATOR VS. XY-GENERATOR
+
+Our experiments in the main paper conditioned the generator to create data with given labels, by concatenating a one-hot encoded label to the input vector. We also explored an alternative approach where the generator itself produced a target probability distribution to label the data it generates. Because more information is encoded into a soft label than a one-hot encoded one, we expected an improved training set to be generated by this variant. Indeed, such a “dark knowledge” distillation setup has been shown to perform better than learning from labels (Hinton et al., 2015).
+
+However, the results in Figure 4 indicate that jointly generating both images and their soft labels under-performs generating only images, although the result could change with different hyperparameter values and/or innovations that improve the stability of training.
+
+![](images/9b996b6986691c1738f020ec4f2d0671edb64b639480d05c302ff2f90234eecf.jpg)  
+Figure 4: Comparison between a conditional generator and a generator that outputs an image/label pair. We expected the latter “dark knowledge” approach to outperform the conditional generator, but that does not seem to be the case. Because initialization and training of the dark knowledge variant were more sensitive, we believe a more rigorous tuning of the process could lead to a different result.
+
+# APPENDIX G GTN GENERATES (SEEMINGLY) ENDLESS DATA
+
+While optimizing images directly (i.e. optimizing a fixed tensor of images) would result in a fixed number of samples, optimizing a generator can potentially result in an unlimited amount of new samples. We tested this generative capability by generating more data during evaluation (i.e. with no change to the meta-optimization procedure) in two ways. In the first experiment, we increase the amount of data in each inner-loop optimization step by increasing the batch size (which results in lower variance gradients). In the second experiment, we keep the number of samples per batch fixed, but increase the number of inner-loop optimization steps for which a new network is trained. Both cases result in an increased amount of training data. If the GTN generator has overfit to the number of inner-loop optimization steps during meta-training and/or the batch size, then we would not expect performance to improve when we have the generator produce more data. However, an alternate hypothesis is that the GTN is producing a healthy distribution of training data, irrespective of exactly how it is being used. Such a hypothesis would be supported by performance increase in these experiments.
+
+Figure 5a shows performance as a function of increasing batch size (beyond the batch size used during meta-optimization, i.e. 128). The increase in performance of GTN means that we can sample larger training sets from our generator (with diminishing returns) and that we are not limited by the choice of batch size during training (which is constrained due to both memory and computation requirements).
+
+Figure 5b shows the results of generating more data by increasing the number of inner-loop optimization steps. Generalization to more inner-loop optimization steps is important when the number of inner-loop optimization steps used during meta-optimization is not enough to achieve maximum performance. This experiment also tests the generalization of the optimizer hyperparameters because they were optimized to maximize learner performance after a fixed number of steps. There is an increase in performance of the learner trained on GTN-generated data as the number of innerloop optimization steps is increased, demonstrating that the GTN is producing generally useful data instead of overfitting to the number of inner-loop optimization steps during training (Figure 5b). Extending the conclusion from Figure 2b, in the very low data regime, GTN is significantly better than training on real data $( p < 0 . 0 5 )$ . However, as more inner-loop optimization steps are taken and thus more unique data is available to the learner, training on the real data becomes more effective than learning from synthetic data $( p < 0 . 0 5 )$ (see Figure 5b).
+
+![](images/5048a5bc42fc2dcce91992eda84da5a48fad172d349edf65eb0135ee0dfb2603.jpg)  
+(a) Increasing inner-loop batch size
+
+![](images/9ffb8c381509897e48fa8227a029e95396f2438001770cd39001f90f9ce3a700.jpg)  
+(b) Increasing inner-loop optimization steps
+
+![](images/928b750db1d9353a8599f9922a2465abd5255f1b26559f9c1d702c4203f6909d.jpg)  
+Figure 5: (a) The left figure shows that even though GTN was meta-trained to generate synthetic data of batch size 128, sampling increasingly larger batches results in improved learner performance (the inner-loop optimization steps are fixed to 16). (b) The right figure shows that increasing the number of inner-loop optimization steps (beyond the 16 steps used during meta-training) improves learner performance. The performance gain with real data is larger in this setting. This improvement shows that GTNs do not overfit to a specific number of inner-loop optimization steps.   
+Figure 6: GTN samples w/o curriculum.
+
+Another interesting test for our generative model is to test the distribution of learners after they have trained on the synthetic data. We want to know, for instance, if training on synthetic samples from one GTN results in a functionally similar set of learner weights regardless of learner initialization (this phenomena can be called learner mode collapse). Learner mode collapse would prevent the performance gains that can be achieved through ensembling diverse learners. We tested for learner mode collapse by evaluating the performance (on held-out data and held-out architecture) of an ensemble of 32 randomly initialized learners that are trained on independent batches from the same GTN. To construct the ensemble, we average the predicted probability distributions across the learners to compute a combined prediction and accuracy. The results of this experiment can be seen in Figure 7, which shows that the combined performance of an ensemble is better (on average) than an individual learner, providing additional evidence that the distribution of synthetic data is healthy and allows ensembles to be harnessed to improve performance, as is standard with networks trained on real data.
+
+# APPENDIX H GTN FOR RL
+
+To demonstrate the potential of GTNs for RL, we tested our approach with a small experiment on the classic CartPole test problem (see Brockman et al. (2016) for details on the domain. We conducted this experiment before the discovery that weight normalization improves GTN training, so these experiments do not feature it; it might further improve performance. For this experiment, the meta-objective the GTN is trained with is the advantage actor-critic formulation: $\log { \bar { \pi } } ( a | \theta _ { \pi } ) ( R -$ $V ( s ; \theta _ { v } ) )$ (Mnih et al., 2016). The state-value $V$ is provided by a separate neural network trained to estimate the average state-value for the learners produced so far during meta-training. The learners train on synthetic data via a single-step of SGD with a batch size of 512 and a mean squared error regression loss, meaning the inner loop is supervised learning. The outer-loop is reinforced because the simulator is non-differentiable. We could have also used an RL algorithm in the inner loop. In that scenario the GTN would have to learn to produce an entire synthetic world an RL agent would learn in. Thus, it would create the initial state and then iteratively receive actions and generate the next state and optionally a reward. For example, a GTN could learn to produce an entire MDP that an agent trains on, with the meta-objective being that the trained agent then performs well on a target task. We consider such synthetic (PO)MDPs an exciting direction for future research.
+
+![](images/022c82203a080f31065c9e19aade071677755fad5c414da6010eba47a5fc3522.jpg)  
+Figure 7: Performance of an ensemble of GTN learners vs. individual GTN learners. Ensembling a set of neural networks that each had different weight initializations, but were trained on data from the same GTN substantially improves performance. This result provides more evidence that GTNs generate a healthy distribution of training data and are not somehow forcing the learners to all learn a functionally equivalent solution.
+
+The score on CartPole is the number of frames out of 200 for which the pole is elevated. Both GTN and an A2C (Mnih et al., 2016) control effectively solve the problem (Figure 8). Interestingly, training GTNs takes the same number of simulator steps as training a single learner with policygradients (Figure 8). Incredibly, however, once trained, the synthetic data from a GTN can be used to train a learner to maximum performance in a single SGD step! While that is unlikely to be true for harder target RL tasks, these results suggest that the speed-up for architecture search from using GTNs in the RL domain can be even greater than in supervised domain.
+
+The CartPole experiments feature a single-layer neural network with 64 hidden units and a tanh activation function for both the policy and the value network. The inner-loop batch size was 512 and the number of inner-loop training iterations was 1. The observation space of this environment consists of a real-valued vector of size 4 (Cart position, Cart velocity, Pole position, Pole velocity). The action space consists of 2 discrete actions (move left or move right). The outer loop loss is the reward function for the target domain (here, pole-balancing). The inner loop loss is mean squared error (i.e. the network is doing supervised learning on the state-action mapping pairs provided by the GTN).
+
+# APPENDIX I SOLVING MODE COLLAPSE IN GANS WITH GTNS
+
+We created an implementation of generative adversarial networks (GANs) (Goodfellow et al., 2014) and found they tend to generate the same class of images (e.g. only 1s, Figure 9), which is a common training pathology in GANs known as mode collapse (Srivastava et al., 2017). While there are techniques to prevent mode collapse (e.g. minibatch discrimination and historical averaging (Salimans et al., 2016)), we hypothesized that combining the ideas behind GTNs and GANs might provide a different, additional technique to help combat mode collapse. The idea is to add a discriminator to the GTN forcing the data it generates to both be realistic and help a learner perform well on the meta-objective of classifying MNIST. The reason this approach should help prevent mode collapse is that if the generator only produces one class of images, a learner trained on that data will not be able to classify all classes of images. This algorithm (GTN-GAN) was able to produce realistic images with no identifiable mode collapse (Figure 10). GTNs offer a different type of solution to the issue of mode collapse than the many that have been proposed, adding a new tool to our toolbox for solving that problem. Note we do not claim this approach is better than other techniques to prevent mode collapse, only that it is an interesting new type of option, perhaps one that could be productively combined with other techniques.
+
+![](images/e3645cc371df475d99759dfb87bf3c100ce93f9621fa407111791ba0fabe5ae7.jpg)  
+Figure 8: An A2C Agent control trains a single policy throughout all of training, while the GTN method starts with a new, randomly initialized network at each iteration and produces the plotted performance after a single step of SGD. This plot is difficult to parse because of that difference: it compares the accumulated performance of A2C across all environment steps up to that point vs. the performance achieved with GTN data in a single step of SGD from a single batch of synthetic data. Thus, at the $1 0 0 { , } 0 0 0 ^ { \mathrm { t h } }$ step of training, GTNs enable training a newly initialized network to the given performance (of around 190) 100,000 times faster with GTN synthetic data than with A2C from scratch. With GTNs, we can therefore train many new, high-performing agents quickly. That would be useful in many ways, such as greatly accelerating architecture search algorithms for RL. Of course, these results are on a simple problem, and (unlike our supervised learning experiments) have not yet shown that the GTN data works with different architectures, but these results demonstrate the intriguing potential of GTNs for RL. One reason we might expect even larger speedups for RL vs. supervised learning is because a major reason RL is sample inefficient is because it requires exploration to figure out how to solve the problem. However, once that exploration has been done, the GTN can produce data to efficiently teach that solution to a new architecture. RL thus represents an exciting area of future research for GTNs. Performing that research is beyond the scope of this paper, but we highlight the intriguing potential here to inspire such future work.
+
+![](images/e893f483d7ce90d347e517ed0e6fc5fc2b292958ead6f238da3df3398eb15144.jpg)  
+Figure 9: Images generated by a basic GAN on MNIST before and after mode collapse. The left image shows GAN-produced images early in GAN training and the right image shows GAN samples later in training after mode collapse has occurred due to training instabilities.
+
+# APPENDIX J ADDITIONAL MOTIVATION
+
+There is an additional motivation for GTNs that involves long-term, ambitious research goals: GTN is a step towards algorithms that generate their own training environments, such that agents trained in them eventually solve tasks we otherwise do not know how to train agents to solve (Clune, 2019). It is important to pursue such algorithms because our capacity to conceive of effective training environments on our own as humans is limited, yet for our learning algorithms to achieve their full potential they will ultimately need to consume vast and complex curricula of learning challenges and data. Algorithms for generating curricula, such as the the paired open-ended trailblazer (POET) algorithm (Wang et al., 2019a), have proven effective for achieving behaviors that would otherwise be out of reach, but no algorithm yet can generate completely unconstrained training conditions. For example, POET searches for training environments within a highly restricted preconceived space of problems. GTNs are exciting because they can encode a rich set of possible environments with minimal assumptions, ranging from labeled data for supervised learning to (in theory) entire complex virtual RL domains (with their own learned internal physics). Because RNNs are Turing-complete (Siegelmann & Sontag, 1995), GTNs should be able to theoretically encode all possible learning environments. Of course, while what is theoretically possible is different from what is achievable in practice, GTNs give us an expressive environmental encoding to begin exploring what potential is unlocked when we can learn to generate sophisticated learning environments. The initial results presented here show that GTNs can be trained end-to-end with gradient descent through the entire learning process; such end-to-end learning has proven highly scalable before, and may similarly in the future enable learning expressive GTNs that encode complex learning environments.
+
+![](images/97ee5c78b530acf710cd8c6412a986e8ce15c10d8c5753395a499ad2b9042422.jpg)  
+Figure 10: Images generated by a GTN with an auxiliary GAN loss. Combining GTNs with GANs produces far more realistic images than GTNs alone (which produced alien, unrecognizable images, Figure 6). The combination also stabilizes GAN training, preventing mode collapse.

parse/train/pULTvw9X313/pULTvw9X313.md

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+# MESHMVS: MULTI-VIEW STEREO GUIDED MESH RECONSTRUCTION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Deep learning based 3D shape generation methods generally utilize latent features extracted from color images to encode the objects’ semantics and guide the shape generation process. These color image semantics only implicitly encode 3D information, potentially limiting the accuracy of the generated shapes. In this paper we propose a multi-view mesh generation method which incorporates geometry information in the color images explicitly by using the features from intermediate 2.5D depth representations of the input images and regularizing the 3D shapes against these depth images. Our system first predicts a coarse 3D volume from the color images by probabilistically merging voxel occupancy grids from individual views. Depth images corresponding to the multi-view color images are predicted which along with the rendered depth images of the coarse shape are used as a contrastive input whose features guide the refinement of the coarse shape through a series of graph convolution networks. Attention-based multi-view feature pooling is proposed to fuse the contrastive depth features from different viewpoints which are fed to the graph convolution networks.
+
+We validate the proposed multi-view mesh generation method on ShapeNet, where we obtain a significant improvement with $34 \%$ decrease in chamfer distance to ground truth and $14 \%$ increase in the F1-score compared with the state-of-the-art multi-view shape generation method.
+
+# 1 INTRODUCTION
+
+3D shape generation is a long-standing research problem in computer vision and computer graphics with applications in autonomous driving, augmented reality, etc. Conventional approaches mainly leverage multi-view geometry based on stereo correspondences between images but are restricted by the coverage provided by the input views. With the availability of large-scale 3D shape datasets and the success of deep learning in several computer vision tasks, 3D representations such as voxel grid Choy et al. (2016); Tulsiani et al. (2017); Yan et al. (2016) and point cloud Yang et al. (2018); Fan et al. (2017) have been explored for single-view 3D reconstruction. Among them, triangle mesh representation has received the most attention as it has various desirable properties for a wide range of applications and is capable of modeling detailed geometry without high memory requirement.
+
+Single-view 3D reconstruction methods Wang et al. (2018); Huang et al. (2015); Kar et al. (2015); Su et al. (2014) generate the 3D shape from merely a single color image but suffer from occlusion and limited visibility which leads to low quality reconstructions in the unseen areas. Multi-view methods Wen et al. (2019); Choy et al. (2016); Kar et al. (2017); Gwak et al. (2017) extend the input to images from different viewpoints which provides more visual information and improves the accuracy of the generated shapes. Recent work in multi-view mesh reconstruction Wen et al. (2019) introduces a multi-view deformation network using perceptual feature from each color image for refining the meshes generated by Pixel2Mesh Wang et al. (2018). Although promising results were obtained, this method relies on perceptual features from color images which do not explicitly encode the objects’ geometry and could restrict the accuracy of the 3D models.
+
+In this work, we present a novel multi-view mesh generation method where we start by predicting coarse volumetric occupancy grid representations for the color images of each input viewpoint independently using a shared fully convolutional network which are merged into a single voxel grid in a probabilistic fashion followed by cubify Gkioxari et al. (2019) operation to convert it to a triangle mesh. We then use Graph Convolutional Network (GCN) Scarselli et al. (2008); Wang et al. (2018) to fine-tune the cubified voxel grid in a coarse-to-fine manner. The GCN refines the coarse mesh by using the feature vector of each graph node (mesh vertices) obtained by projecting the vertices on the 2D contrastive depth features. The contrastive depth features are extracted from the rendered depth maps of the current mesh and predicted depth maps from a multi-view stereo network. We also propose an attention-based method to fuse feature from multiple views that can learn the importance of different views for each of the mesh vertices. Constrains between the intermediate refined mesh from GCN with predicted depth maps of different viewpoints further improve the final mesh quality. By employing multi-view voxel grid generation and refining it using geometry information from both the current mesh (through the rendered depth maps) and predicted depth maps, we are able to generate high-quality meshes. We validate our method on the ShapeNet Chang et al. (2015) benchmark and our method achieves the best performance among all previous multi-view and single-view mesh generation methods.
+
+![](images/02d99d090a9ea2bed535ac9d276d10a485fcea411051838f8d277ebce11a7101.jpg)  
+Figure 1: Architecture of the proposed method. The voxel grid prediction module predicts coarse voxel grid representation which is further refined by a series of GCNs. The GCNs use contrastive depth features from rendered depths of the current shape and the predicted depths from MVSNet. Multi-view features are pooled using a multi-head attention mechanism.
+
+# 2 RELATED WORK
+
+# 2.1 TRADITIONAL SHAPE GENERATION METHODS
+
+3D model generation has traditionally been tackled using multi-view geometry principles. Among them, structure-from-motion (SfM) Schonberger & Frahm (2016); Agarwal et al. (2011); Cui & Tan (2015); Cui et al. (2017) and simultaneous localization and mapping (SLAM) Cadena et al. (2016); Mur-Artal et al. (2015); Engel et al. (2014); Whelan et al. (2015) are popular techniques that perform 3D reconstruction and camera pose estimation at the same time. These methods extract local image features, match them across images and use the matches to estimate camera poses and 3D geometry. Closer to our problem setup, multi-view stereo methods infer 3D geometry from images with known camera parameters. Volumetric methods Kar et al. (2017); Kutulakos & Seitz (2000); Seitz & Dyer (1999) predict voxel grid representation of objects by estimating the relationship between each voxel and object surfaces. Point cloud based methods Furukawa & Ponce (2009); Lhuillier & Quan (2005) start with a sparse point cloud and gradually increase the density of points to obtain a final dense point cloud of the object. Durou et al. (2008); Zhang et al. (1999); Favaro & Soatto (2005) reason about shading, texture and defocus to reason about visible parts of the object and infer its 3D geometry. While the results of these works are impressive in terms of quality and completeness of reconstruction, they still struggle with poorly textured and reflective surfaces and require carefully selected input views.
+
+# 2.2 DEEP SHAPE GENERATION METHODS
+
+Deep learning based approaches can learn to infer 3D structure from training data and can be robust against poorly textured and reflective surfaces as well as limited and arbitrarily selected input views. These methods can be categorized into single view and multi-view methods. Huang et al. (2015); Su et al. (2014) use shape component retrieval and deformation from a large dataset for single-view 3D shape generation. Kurenkov et al. (2018) extend this idea by introducing free-form deformation networks on retrieved object templates from a database. Some work learn shape deformation from ground truth foreground masks of 2D images Kar et al. (2015); Yan et al. (2016); Tulsiani et al. (2017). Recurrent Neural Networks (RNN) based methods Choy et al. (2016); Kar et al. (2017); Gwak et al. (2017) are another popular solution to solve this problem. Gwak et al. (2017); Lin et al. (2019) introduce image silhouettes along with adversarial multi-view constraints and optimize object mesh models using multi-view photometric constraints. Predicting mesh directly from color images was proposed in Wang et al. (2018); Wickramasinghe et al. (2019); Pan et al. (2019); Wen et al. (2019); Gkioxari et al. (2019); Tang et al. (2019). DR-KFS Jin et al. (2019) introduces a differentiable visual similarity metric while SeqXY2SeqZ Han et al. (2020) represents 3D shapes using a set of 2D voxel tubes for shape reconstruction. Front2Back Yao et al. (2020) generates 3D shapes by fusing predicted depth and normal images and DV-Net Jia et al. (2020) predicts dense object point clouds using dual-view RGB images with a gated control network to fuse point clouds from the two views. FoldingNet Yang et al. (2018) learns to reconstruct arbitrary point clouds from a single 2D grid. AtlasNet Groueix et al. (2018) use learned parametric representation while Mescheder et al. (2019); Park et al. (2019); Liu et al. (2019b;a); Murez et al. (2020) employ implicit surface representation to reconstruct 3D shapes.
+
+# 2.3 DEPTH ESTIMATION
+
+Compared to 3D shape generation, depth prediction is an easier problem formulation since it simplifies the task to per-view depth map estimation. Traditional methods Campbell et al. (2008); Galliani et al. (2015); Schönberger et al. (2016) use multi-view stereo principles for depth prediction. Deep learning based multi-view stereo depth estimation was first introduced in Hartmann et al. (2017) where a learned cost metric is used to estimate patch similarities. DeepMVS Huang et al. (2018) warps multi-view images to 3D space and then applies deep networks for regularization and aggregation to estimate depth images. Learned 3D cost volume based depth prediction was proposed in MVSNet Yao et al. (2018) where a 3 dimensional cost volume is built using homographically warped 2D features from multi-view images and 3D CNNs are used for cost regularization and depth regression. This idea was further extended by Chen et al. (2019); Luo et al. (2019); Gu et al. (2019); Yao et al. (2019).
+
+# 3 METHODOLOGY
+
+Figure 1 shows the architecture of the proposed system which takes as input multi-view color images of an object with known poses and outputs a triangle mesh representing the surface of the object.
+
+# 3.1 MULTI-VIEW VOXEL GRID PREDICTION
+
+Single-view Voxel Grid Prediction The single-view voxel branch consists of a ResNet feature extractor and a fully convolutional voxel grid prediction network. It generates the coarse initial shape of an object from one viewpoint as voxel occupancy grid using a color image. Here, we set the resolution of the generated voxel occupancy grid as $3 2 \times 3 2 \times 3 2$ . The voxel prediction networks for all viewpoints share the same weights.
+
+Probabilistic Occupancy Grid Merging Voxel occupancy grid predicted from a single viewpoint suffers from occlusion and limited visibility. In order to fuse voxel grids from different viewpoints, we propose a probabilistic occupancy grid merging method which merges the voxel grids from each input viewpoint probabilistically to obtain the final voxel grid output. This allows occluded regions in one view to be estimated from other views where those regions are visible as well as increase the confidence of prediction in overlapping regions. Occupancy probability of each voxel is represented by $p ( x )$ which is converted to log-odds (logit):
+
+$$
+l ( x ) = l o g { \frac { p ( x ) } { 1 - p ( x ) } }
+$$
+
+Bayesian update on the probabilities reduce to simple summation of log likelihoods Konolige (1997). Hence, the multi-view log-odds of a voxel is given by:
+
+$$
+l ( x ) = l _ { 1 } ( x ) + l _ { 2 } ( x ) + . . . + l _ { n } ( x )
+$$
+
+where $l _ { i }$ is the voxel’s log-odds in view $i$ and $n$ is the number of input views. The final voxel probability $x$ is obtained by applying the inverse function of Equation (1) which is a sigmoid function.
+
+# 3.2 MESH REFINEMENT
+
+The cubified mesh from the voxel branch only provides a coarse reconstruction of the object’s surface. We apply graph convolutional networks which represent each mesh vertex as one graph node and deforms them to more accurate positions.
+
+GCN-based Mesh Deformation The features pooled from multi-view images along with 3D coordinates of the vertices in world frame are used as features of the graph nodes. Series of Graphbased Convolutional Network (GCN) blocks are applied to deform a mesh at the current stage to the next stage, starting with the cubified voxel grids. A graph convolution deforms mesh vertices by propagating features from neighboring vertices by applying $\begin{array} { r } { f _ { i } ^ { ' } = R e L U ( W _ { 0 } f _ { i } + \sum _ { j \in \mathcal { N } ( i ) } W _ { 1 } f _ { j } ) } \end{array}$ where $\mathcal { N } ( i )$ is the set of neighboring vertices of the $i .$ -th vertex in the mesh, $f _ { \{ \} }$ represents the feature vector of a vertex, and $W _ { 0 }$ and $W _ { 1 }$ are learnable parameters of the model. Each GCN block utilizes several graph convolutions to transform the vertex features along with a final vertex refinement operation where the features along with vertex coordinates are further transformed as $v _ { i } ^ { ' } = v _ { i } + t a n h ( W _ { v e r t } [ f _ { i } ; v _ { i } ] )$ where the matrix $W _ { v e r t }$ is another learnable parameter to obtain the deformed mesh.
+
+Contrastive Depth Feature Extraction Yao et al. (2020) demonstrate that using intermediate, image-centric 2.5D representations instead of directly generating 3D shapes in global frame from raw 2D images can improve 3D reconstruction quality. We therefore propose to formulate the features for graph nodes using 2.5D depth maps as input additional inputs alongside the RGB features. Specifically, we render the meshes at different GCN stages to depth image at all the input views using Kato et al. (2018) and use them along with predicted depths for depth feature extraction. We call this form of depth input contrastive depth as it contrasts the rendered depths of the current mesh against the predicted depths and allows the network to reason about the deformation better than when using predicted depth or color images alone. Given the 2D features, corresponding feature vectors of individual vertices can be found by projecting the 3D vertex coordinates to the feature planes using known camera parameters. We use VGG-16 Simonyan & Zisserman (2014) as our contrastive depth feature extraction network.
+
+Multi-View Depth Estimation We extend MVSNet Yao et al. (2018) and predict the depth maps of all views since the original implementation predicts depth of only one reference view. This is achieved by transforming the feature volumes to each view’s coordinate frame using homography warping and applying identical cost volume regularization and depth regression on each view. Detailed network architecture diagram of this module is provided in the appendix.
+
+Attention-based Multi-View Feature Pooling In order to fuse multi-view contrastive depth features, we formulate an attention module by adapting multi-head attention mechanism originally designed for sequence to sequence machine translation using transformer (encoder-decoder) architecture Vaswani et al. (2017). In a transformer architecture the encoder hidden state is mapped to lower dimension key-value pairs $( \mathbf { K } , \mathbf { V } )$ while the decoder hidden state is mapped to a query vector Q using independent fully connected layers. The encoder hidden state in our case is the multi-view features while the decoder hidden state is the mean of the multi-view features. The attention weights are computed using scaled-dot product:
+
+$$
+A t t e n t i o n ( \mathbf { Q } , \mathbf { K } , \mathbf { V } ) = s o f t m a x ( \frac { \mathbf { Q } \mathbf { K } ^ { T } } { \sqrt { N } } ) \mathbf { V }
+$$
+
+![](images/85bfc53cff116373845a2510580033857bbade708c4afa86a5589992859a87b8.jpg)  
+Figure 2: Attention weights visualization. From left to right: input images from 3 viewpoints, corresponding ground truth point clouds color-coded by their view order and the predicted mesh vertices color-coded by the attention weights of the views. Only the view with maximum attention weight is visualized for each predicted points for clarity.
+
+where $N$ is the number of input views.
+
+Multiple attention heads are used which are concatenated and transformed to obtain the final output
+
+$$
+\begin{array} { r } { h e a d _ { i } = A t t e n t i o n ( { \mathbf { Q } } { \mathbf { W } } _ { i } ^ { Q } , { \mathbf { K } } { \mathbf { W } } _ { i } ^ { K } , { \mathbf { V } } { \mathbf { W } } _ { i } ^ { V } ) } \\ { M u l t i H e a d ( { \mathbf { Q } } , { \mathbf { K } } , { \mathbf { V } } ) = [ h e a d _ { 1 } ; . . . ; h e a d _ { h } ] { \mathbf { W } } ^ { 0 } } \end{array}
+$$
+
+where multiple $\mathbf { W }$ are parameters to be learned, $h$ is the number of attention heads and $i \in [ 1 , h ]$
+
+We choose multi-head attention as our feature pooling method since it allows the model to attend information from different representation subspaces of the features by training multiple attentions in parallel. This method is also invariant to the order and number of input views. We visualize the learned attention weights (average of each attention heads) in Figure 2 where we can observe that the attention weights roughly takes into account the visibility/occlusion information from each view.
+
+# 3.3 LOSS FUNCTIONS
+
+Mesh losses The losses which are derived from Wang et al. (2018) to constrain the mesh predicted by each GCN block (P) to resemble the ground truth (Q) include Chamfer distance $\mathcal { L } _ { \mathrm { c h a m f e r } } ( \mathrm { P } , \mathrm { Q } ) =$ $\begin{array} { r } { | \bar { \mathbf { P } } | ^ { - 1 } \sum _ { ( p , q ) \in \Lambda _ { \mathrm { P } , \mathrm { Q } } } | | p - q | | ^ { 2 } + | \mathbf { Q } | ^ { - 1 } \sum _ { ( q , p ) \in \Lambda _ { \mathrm { Q } , \mathrm { P } } } | | q - p | | ^ { 2 } } \end{array}$ and surface normal loss $\mathcal { L } _ { \mathrm { n o r m a l } } ( \mathbf { P } , \mathbf { Q } ) =$ $\begin{array} { r } { - | \mathbf { P } | ^ { - 1 } \sum _ { ( p , q ) \in \Lambda _ { \mathbf { P } , \mathbf { Q } } } | u _ { p } \cdot u _ { q } | - | \mathbf { Q } | ^ { - 1 } \sum _ { ( q , p ) \in \Lambda _ { \mathbf { Q } , \mathbf { P } } } | u _ { q } \cdot u _ { p } | } \end{array}$ with additional regularization in the form of edge length loss $\begin{array} { r } { \mathcal { L } _ { \mathrm { e d g e } } ( \mathrm { V } , \mathrm { E } ) = { \frac { 1 } { | E | } } \sum _ { ( v , v ^ { \prime } ) \in E } | | v - v ^ { \prime } | | ^ { 2 } } \end{array}$ for visually appealing results.
+
+Depth loss Our depth prediction network is supervised using adaptive reversed Huber loss (also known as BerHu criterion) Lambert-Lacroix & Zwald (2016). $\mathcal { L } _ { d e p t h } ~ = ~ | \boldsymbol { x } |$ , if $| x | \ \leq$ c, otherwise x2+c22c where $x$ is the depth error of a pixel and $c$ is a constant set to 0.2. Note that the original MVSNet uses L1-loss, but we used BerHu loss since it gave slightly higher accuracy. Intuitively, this is because BerHu provides a good balance between L1 and L2 loss and has shown similar improvement in Laina et al. (2016).
+
+Contrastive depth loss BerHu loss is also applied between the rendered depth images at different GCN stages and the predicted depth images. $\mathcal { L } _ { c o n t r a s t i v e } = | x | .$ , if $| x | \le c$ , otherwise $\frac { x ^ { 2 } + c ^ { 2 } } { 2 c }$
+
+Voxel loss Binary cross-entropy loss between the predicted voxel occupancy probabilities and the ground truth occupancies is used as voxel loss to supervise the voxel predictions $\mathcal { L } _ { \mathrm { v o x e l } } =$ $- \bar { \Bigl ( p ( x ) l o g \bigl ( p ( x ) \bigr ) + \bigl ( 1 - p ( x ) \bigr ) l o g \bigl ( 1 - p ( x ) \bigr ) \Bigr ) }$
+
+Final loss We use the weighted sum of the individual losses discussed above as the final loss to train our model in an end-to-end fashion. $\mathcal { L } = \lambda _ { \mathrm { c h a m f e r } } \mathcal { L } _ { \mathrm { c h a m f e r } } + \lambda _ { \mathrm { n o r m a l } } \mathcal { L } _ { \mathrm { n o r m a l } } + \lambda _ { \mathrm { e d g e } } \mathcal { L } _ { \mathrm { e d g e } } + \lambda _ { \mathrm { d e p t h } } \mathcal { L } _ { \mathrm { d e p t h } } +$ $\lambda _ { \mathrm { c o n t r a s t i v e } } \mathcal { L } _ { \mathrm { c o n t r a s t i v e } } + \lambda _ { \mathrm { v o x e l } } \mathcal { L } _ { \mathrm { v o x e l } }$ , where $\mathcal { L }$ is the final loss term.
+
+![](images/16e9000814758c5e0f9fc7cafba71cf427150a8b1e28cba393e962fab5a12fac.jpg)  
+Figure 3: Qualitative evaluation on ShapeNet dataset. From top to bottom: one of the input images, ground truth mesh, multi-view extended Pixel2Mesh, Pixel2Mesh $^ { + + }$ , and ours. Our predictions are closer to the actual shape, especially for the objects with more complex topologies.
+
+# 4 EXPERIMENTS
+
+# 4.1 EXPERIMENTAL SETUP
+
+Comparisons We evaluate the proposed method against various multi-view shape generation methods. The state-of-the-art method is Pixel2Mesh $^ { + + }$ Wen et al. (2019) (referred as $P 2 M + +$ ). Wen et al. (2019) also provide a baseline by directly extending Pixel2Mesh Wang et al. (2018) to operate on multi-view images (referred as MVP2M) using their statistical feature pooling method to aggregate features from multiple color images. Results from additional multi-view shape generation baselines 3D-R2N2 Choy et al. (2016) and LSM Kar et al. (2017) are also reported.
+
+Dataset We evaluate our method against the state-of-the-art methods on the dataset from Choy et al. (2016) which is a subset of ShapeNet Chang et al. (2015) and has been widely used by recent 3D shape generation methods. It contains 50K 3D CAD models from 13 categories. Each model is rendered with a transparent background from 24 randomly chosen camera viewpoints to obtain color images. The corresponding camera intrinsics and extrinsics are provided in the dataset. Since the dataset does not contain depth images, we render them using a custom depth renderer at the same viewpoints as the color images and with the same camera intrinsics. We follow the training/testing/validation split of Gkioxari et al. (2019).
+
+Implementation For the depth prediction module, we follow the original MVSNet Yao et al. (2018) implementation. The output depth dimensions reduces by a factor of 4 to $5 6 \times 5 6$ from the $2 2 4 \times 2 2 4$ input image. The number of depth hypotheses is chosen as 48 which offers a balance between accuracy and running/training time efficiency. These depth hypotheses represent values from $0 . 1 { \mathrm { m } }$ to $\mathrm { 1 . 3 } \mathrm { m }$ at an interval of $2 5 \mathrm { m m }$ . These values were chosen based on the range of depths present in the dataset.
+
+The hierarchical features obtained from "Contrastive Depth Features Extractor" are of total 4800 dimensions for each view. The aggregated multi-view features are compressed to 480 dimensional after applying attentive feature pooling. 5 attention heads are used for merging multi-view features. The loss function weights are set as $\lambda _ { \mathrm { c h a m f e r } } = 1$ , $\lambda _ { \mathrm { n o r m a l } } = 1 . 6 \times 1 0 ^ { - 4 }$ , $\lambda _ { \mathrm { d e p t h } } = 0 . 1$ , $\lambda _ { \mathrm { c o n t r a s t i v e } } =$ 0.001 and $\lambda _ { \mathrm { v o x e l } } = 1$ . Two settings of $\lambda _ { \mathrm { e d g e } }$ were used, $\lambda _ { \mathrm { e d g e } } = 0$ (referred as Best) which gives better quantitative results and $\lambda _ { \mathrm { e d g e } } = 0 . 2$ (referred as Pretty) which gives better qualitative results.
+
+Training and Runtime The network is optimized using Adam optimizer with a learning rate of $1 0 ^ { - 4 }$ . The training is done on 5 Nvidia RTX-2080 GPUs with effective batch size 5. The depth prediction network (MVSNet) is trained independently for 30 epochs. Then the whole system is trained for another 40 epochs with the weights of the MVSNet frozen. Our system is implemented in PyTorch deep learning framework and it takes around 60 hours for training.
+
+Evaluation Metric Following Wang et al. (2018); Wen et al. (2019), we use F1-score as our evaluation metric. The F1-score is the harmonic mean of precision and recall where the precision/recall are calculated by finding the percentage of points in the predicted/ground truth that can find a nearest neighbor from the other within a threshold. We provide evaluations with two threshold values: $\tau$ and $2 \tau$ where $\tau = 1 0 ^ { - 4 } ~ \mathrm { m } ^ { 2 }$ .
+
+# 4.2 COMPARISON WITH PREVIOUS MULTI-VIEW SHAPE GENERATION METHODS
+
+We quantitatively compare our method against previous works for multi-view shape generation in Table 1 and show the effectiveness of our methods in improving the shape quality. Our method outperforms the state-of-the-art method Pixel2Mesh $^ { + + }$ Wen et al. (2019) with a decrease in chamfer distance to ground truth by $34 \%$ and $15 \%$ increase in F1-score at threshold $\tau$ . Note that in Table 1 the same model is trained for all the categories but accuracy on individual categories as well as average over the categories are evaluated. We provide the chamfer distances in the appendix.
+
+<table><tr><td rowspan="2">Category</td><td colspan="6">F-score (T)↑</td><td colspan="6">F-score (2τ)↑</td></tr><tr><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++</td><td>Ours (pretty)</td><td>Ours (best)</td><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++</td><td>Ours (pretty)</td><td>Ours (best)</td></tr><tr><td>Couch</td><td>45.47</td><td>43.02</td><td>53.17</td><td>57.56</td><td>71.63</td><td>73.63</td><td>59.97</td><td>55.49</td><td>73.24</td><td>75.33</td><td>85.28</td><td>88.24</td></tr><tr><td>Cabinet</td><td>54.08</td><td>50.80</td><td>56.85</td><td>65.72</td><td>75.91</td><td>76.39</td><td>64.42</td><td>60.72</td><td>76.58</td><td>81.57</td><td>87.61</td><td>88.84</td></tr><tr><td>Bench</td><td>44.56</td><td>49.33</td><td>60.37</td><td>66.24</td><td>81.11</td><td>83.76</td><td>62.47</td><td>65.92</td><td>75.69</td><td>79.67</td><td>90.56</td><td>92.57</td></tr><tr><td>Chair</td><td>37.62</td><td>48.55</td><td>54.19</td><td>62.05</td><td>77.63</td><td>78.69</td><td>54.26</td><td>64.95</td><td>72.36</td><td>77.68</td><td>88.24</td><td>90.02</td></tr><tr><td>Monitor</td><td>36.33</td><td>43.65</td><td>53.41</td><td>60.00</td><td>74.14</td><td>76.64</td><td>48.65</td><td>56.33</td><td>70.63</td><td>75.42</td><td>86.04</td><td>88.89</td></tr><tr><td>Firearm</td><td>55.72</td><td>56.14</td><td>79.67</td><td>80.74</td><td>92.92</td><td>94.32</td><td>76.79</td><td>73.89</td><td>89.08</td><td>89.29</td><td>96.81</td><td>97.67</td></tr><tr><td>Speaker</td><td>41.48</td><td>45.21</td><td>48.90</td><td>54.88</td><td>66.02</td><td>67.83</td><td>52.29</td><td>56.65</td><td>68.29</td><td>71.46</td><td>79.76</td><td>82.34</td></tr><tr><td>Lamp</td><td>32.25</td><td>45.58</td><td>50.82</td><td>62.56</td><td>72.47</td><td>75.93</td><td>49.38</td><td>64.76</td><td>65.72</td><td>74.00</td><td>82.00</td><td>85.33</td></tr><tr><td>Cellphone</td><td>58.09</td><td>60.11</td><td>66.07</td><td>74.36</td><td>85.57</td><td>86.45</td><td>69.66</td><td>71.39</td><td>82.31</td><td>86.16</td><td>93.40</td><td>94.28</td></tr><tr><td>Plane</td><td>47.81</td><td>55.60</td><td>75.16</td><td>76.79</td><td>89.23</td><td>92.13</td><td>70.49</td><td>76.39</td><td>86.38</td><td>86.62</td><td>94.65</td><td>96.57</td></tr><tr><td>Table</td><td>48.78</td><td>48.61</td><td>65.95</td><td>71.89</td><td>82.37</td><td>83.68</td><td>62.67</td><td>62.22</td><td>79.96</td><td>84.19</td><td>90.24</td><td>91.97</td></tr><tr><td>Car</td><td>59.86</td><td>51.91</td><td>67.27</td><td>68.45</td><td>77.01</td><td>80.43</td><td>78.31</td><td>68.20</td><td>84.64</td><td>85.19</td><td>88.99</td><td>92.33</td></tr><tr><td>Watercraft</td><td>40.72</td><td>47.96</td><td>61.85</td><td>62.99</td><td>75.52</td><td>80.48</td><td>63.59</td><td>66.95</td><td>77.49</td><td>77.32</td><td>86.77</td><td>90.35</td></tr><tr><td>Mean</td><td>46.37</td><td>49.73</td><td>61.05</td><td>66.48</td><td>78.58</td><td>80.80</td><td>62.53</td><td>64.91</td><td>77.10</td><td>80.30</td><td>88.49</td><td>90.72</td></tr></table>
+
+Table 1: Qualitative comparison against state-of-the-art multi-view shape generation methods. We report F-score on each semantic category along with the mean over all categories using two thresholds $\tau$ and $2 \tau$ for nearest neighbor match where $\tau { = } 1 0 ^ { - 4 } \mathrm { m } ^ { 2 }$ .
+
+We also provide visual results for qualitative assessment of the generated shapes by our Pretty model in Figure 3 which shows that it is able to more accurately predict topologically diverse shapes.
+
+# 4.3 ABLATION STUDIES
+
+Contrastive Depth Feature Extraction We evaluate several methods for contrastive feature extraction (Sub-section 3.2). These methods are 1) Input Concatenation: using the concatenated rendered and predicted depth maps as input to the VGG feature extractor, 2) Input Difference: using the difference of the two depth maps as input to VGG, 3) Feature Concatenation: concatenating features from rendered and predicted depths extracted by shared VGG, 4) Feature Difference: using difference of the features from the two depth maps extracted by shared VGG, and 5) Predicted depth only: using the VGG features from the predicted depths only. 6) Rendered depth only: using the VGG features from the rendered depths only. The quantitative results are summarized in Table 2 and shows that Input Concatenation method produces better results than other formulations.
+
+Accuracy with different settings Table 3 shows the contribution of different components towards the final accuracy. Naively extending the single-view Mesh R-CNN Gkioxari et al. (2019) to multiple views using statistical feature pooling Wen et al. (2019) for mesh refinement (row 1) gives an F1-score of $7 2 . 7 4 \%$ for threshold $\tau$ which is $6 . 2 6 \%$ improvement over Pixel2Mesh $^ { + + }$ . We further extend the above method with our probabilistic multi-view voxel grid prediction in row 2 and get a $4 . 2 3 \%$ improvement.
+
+In row 3 of Table 3 we use our contrastive depth features instead of RGB features for mesh refinement and get $2 . 7 \%$ improvement. We then replace the statistical feature pooling with the proposed attention method and get $0 . 1 9 \%$ improvement. The improvement is not significant on our final architecture but we found the multi-head attention to perform better on more light-weight architectures. We also evaluate the effect of using additional regularization from contrastive depth losses: rendered depth vs predicted depth in the 5th rows of which improves the score by $0 . 9 8 \%$ . In row 6 we use ground truth instead of predicted depths on our final model which gives the upper bound on our mesh prediction accuracy in relation to the depth prediction accuracy as $8 4 . 5 8 \%$ .
+
+Table 2: Comparisons of different contrastive depth formulations. In 1st and 2nd rows, concatenation and difference of the rendered and predicted depths are fed to VGG feature extractor while in 3rd and 4th rows, concatenation and difference of the VGG features from the depths is used for mesh refinement. 5 uses VGG features from predicted depths only while 6 uses VGG features from rendered depths only.   
+
+<table><tr><td></td><td>F1-T</td><td>F1-2T</td></tr><tr><td>(1) Input Concatenation</td><td>80.80</td><td>90.72</td></tr><tr><td>(2) Input Difference</td><td>80.41</td><td>90.54</td></tr><tr><td>(3) Feature Concatenation</td><td>80.45</td><td>90.54</td></tr><tr><td>(4) Feature Difference</td><td>80.30</td><td>90.40</td></tr><tr><td>(5) Predicted Depth only</td><td>79.40</td><td>89.95</td></tr><tr><td>(6) Rendered Depth only</td><td>78.20</td><td>88.90</td></tr></table>
+
+<table><tr><td></td><td>F1-T</td><td>F1-2T</td></tr><tr><td>(1) Naive multi-view Mesh R-CNN</td><td>72.74</td><td>84.99</td></tr><tr><td>(2) + Multi-view voxel grid prediction</td><td>76.97</td><td>88.24</td></tr><tr><td>(3) + Contrastive depth input</td><td>79.63</td><td>90.10</td></tr><tr><td>(4) + Multi-head attention pooling</td><td>79.82</td><td>90.18</td></tr><tr><td>(5)+ Contrastive depth loss (final model)</td><td>80.80</td><td>90.72</td></tr><tr><td>(6) Using GT depth (final model)</td><td>84.58</td><td>92.86</td></tr></table>
+
+Number of View We test the performance of our framework with respect to the number of views. Table 4 shows that the accuracy of our method increases as we increase the number of input views for training. These experiments also validate that the attention-based feature pooling can efficiently encode features from different views to take advantage of larger number of views.
+
+Table 5 shows the results when using different number of views during testing on our model trained with 3 views which indicates that increasing the number of views during testing does not improve the accuracy while decreasing the number of views can cause a significant drop in accuracy.
+
+Table 4: Accuracy w.r.t the number of views during training. The evaluation was performed on the same number of views as training.   
+
+<table><tr><td>Metric</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>F1-T</td><td>73.60</td><td>80.80</td><td>82.61</td><td>83.76</td><td>84.25</td></tr><tr><td>F1-2T</td><td>85.80</td><td>90.72</td><td>91.78</td><td>92.73</td><td>93.14</td></tr></table>
+
+Table 5: Accuracy w.r.t the number of views during testing. The same model trained with 3 views was used in all of the cases.   
+
+<table><tr><td>Metric</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>F1-T</td><td>72.46</td><td>80.80</td><td>80.98</td><td>80.94</td><td>80.85</td></tr><tr><td>F1-2T</td><td>84.49</td><td>90.72</td><td>91.03</td><td>91.16</td><td>91.20</td></tr></table>
+
+# 5 CONCLUSION
+
+We propose a neural network based solution to predict 3D triangle mesh models of objects from images taken from multiple views. First, we propose a multi-view voxel grid prediction module which probabilistically merges voxel grids predicted from individual input views. We then cubify the merged voxel grid to triangle mesh and apply graph convolutional networks for further refining the mesh. The features for the mesh vertices are extracted from contrastive depth input consisting of rendered depths at each refinement stage along with the predicted depths. The proposed mesh reconstruction method outperforms existing methods with a large margin and is capable of reconstructing objects with more complex topologies.
+
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+
+A APPENDIX
+
+# NETWORK ARCHITECTURE
+
+MVSNET ARCHITECTURE
+
+![](images/e48055ebcff419b4d4a3731091747888bd234fd8debc44af6fd1a3a2716c1c36.jpg)  
+Figure 4: Depth prediction network (MVSNet) architecture
+
+Our depth prediction module is based on MVSNet Yao et al. (2018) which constructs a regularized 3D cost volumes to estimate the depth map of the reference view. Here, we extent MVSNet to predict the depth maps of all views instead of only the reference view. This is achieved by transforming the feature volumes to each view’s coordinate frame using homography warping and applying identical cost volume regularization and depth regression on each view. This allows the reuse of pre-regularization feature volumes for efficient multi-view depth prediction invariant to the order of input images. Figure 4 shows the architecture of the our depth estimation module.
+
+# PROBABILISTIC OCCUPANCY GRID MERGING
+
+We use single-view voxel prediction network from Gkioxari et al. (2019) to predict predicts voxel grids for each of the input images in their respective local coordinate frames. The occupancy grids are transformed to global frame (which is set to the coordinate frame of the first image) by finding the equivalent global grid values in the local grids after applying bilinear interpolation on the closest matches. The voxel grids in global coordinates are then probabilistically merged according to Sub-section 3.1 of the main submission.
+
+# EXPERIMENTS
+
+We quantitatively compare our method against previous works for multi-view shape generation in Table 6 and show effectiveness of our proposed shape generation methods in improving shape quality. Our method outperforms the state-of-the-art method Pixel2Mesh $^ { + + }$ Wen et al. (2019) with decrease in chamfer distance to ground truth by $34 \%$ , which shows the effectiveness of our proposed method. Note that in Table 6 same model is trained for all the categories but accuracy on individual categories as well as average over all the categories are evaluated.
+
+<table><tr><td rowspan="2">Category</td><td colspan="4">Chamfer Distance (CD) ↓</td></tr><tr><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++ Ours</td></tr><tr><td>Couch</td><td>0.806</td><td>0.730</td><td>0.534</td><td>0.439 0.220</td></tr><tr><td>Cabinet</td><td>0.613</td><td>0.634</td><td>0.488 0.337</td><td>0.230</td></tr><tr><td>Bench</td><td>1.362</td><td>0.572</td><td>0.591 0.549</td><td>0.159</td></tr><tr><td>Chair</td><td>1.534</td><td>0.495</td><td>0.583 0.461</td><td>0.201</td></tr><tr><td>Monitor</td><td>1.465</td><td>0.592</td><td>0.658</td><td>0.566 0.217</td></tr><tr><td>Firearm</td><td>0.432</td><td>0.385</td><td>0.305</td><td>0.305 0.123</td></tr><tr><td>Speaker</td><td>1.443</td><td>0.767</td><td>0.745</td><td>0.635 0.402</td></tr><tr><td>Lamp</td><td>6.780</td><td>1.768</td><td>0.980</td><td>1.135 0.755</td></tr><tr><td>Cellphone</td><td>1.161</td><td>0.362</td><td>0.445</td><td>0.325 0.138</td></tr><tr><td>Plane</td><td>0.854</td><td>0.496</td><td>0.403</td><td>0.422 0.084</td></tr><tr><td>Table</td><td>1.243</td><td>0.994</td><td>0.511</td><td>0.388 0.181</td></tr><tr><td>Car</td><td>0.358</td><td>0.326</td><td>0.321</td><td>0.249 0.165</td></tr><tr><td>Watercraft</td><td>0.869</td><td>0.509</td><td>0.463</td><td>0.508 0.175</td></tr><tr><td>Mean</td><td>1.455</td><td>0.664</td><td>0.541</td><td>0.486 0.211</td></tr></table>
+
+Table 6: Qualitative comparison against state-of-the-art multi-view shape generation methods. Following Wen et al. (2019), we report Chamfer Distance in $m ^ { 2 } \times 1 0 0 0$ from ground truth for different methods. Note that same model is trained for all the categories but accuracy on individual categories as well as average over all the categories are evaluated.
+
+# ABLATION STUDIES
+
+Coarse Shape Generation We conduct comparisons on voxel grid predicted from our proposed probabilistically merged voxel grids against single view method Gkioxari et al. (2019). As is shown in Table 7, the accuracy of the initial shape generated from probabilistically merged voxel grid is higher than that from individual views.
+
+Accuracy at Different GCN Stages We analyze the accuracy of meshes at different GCN stages in Table 8. The results validate that our method produces the meshes in a coarse-to-fine manner and multiple GCN refinements improve the mesh quality.
+
+Resolution of Depth Prediction We conduct experiments using different numbers of depth hypotheses in our depth prediction network (Sub-section A), producing depth values at different resolutions. A higher number of depth hypothesis means finer resolution of the predicted depths. The quantitative results with different hypothesis numbers are summarized in Table 9. We set depth hypothesis as 48 for our final architecture which is equivalent to the resolution of $2 5 \mathrm { m m }$ . We observe that the mesh accuracy remain relatively unchanged if we predict depths at finer resolutions.
+
+<table><tr><td>Metric</td><td>Cubified</td><td>Stage-1</td><td>Stage-2</td><td>Stage-3</td></tr><tr><td>F1-T</td><td>31.48</td><td>76.78</td><td>79.88</td><td>80.80</td></tr><tr><td>F1-2T</td><td>44.40</td><td>88.32</td><td>90.19</td><td>90.72</td></tr></table>
+
+Table 7: Accuracy of predicted voxel grids from single-view prediction compared against the proposed probabilistically merged multi-view voxel grids. The voxel branch was trained separately without the mesh refinement and evaluation was performed on the cubified voxel grids. We use three views for probabilistic grid merging.   
+
+<table><tr><td>Metric</td><td>Single-view</td><td>Multi-view</td></tr><tr><td>F1-T</td><td>25.19</td><td>31.27</td></tr><tr><td>F1-2T</td><td>36.75</td><td>44.46</td></tr></table>
+
+Table 8: Accuracy of the refined meshes at different GCN stages. 1, 2 and 3 indicate the performance at the corresponding graph convolution blocks while Cubified is for the cubified voxel grids used as input for the first GCN block. All the stages, including the voxel prediction, were trained jointly and hence the accuracy of voxel predictions varies from that in Table 7.
+
+Table 9: Accuracy w.r.t the number of depth hypothesis. A higher number of depth hypothesis increases the resolution of predicted depth values at the expense of higher memory requirement. The range of depths for all the models are same and based on the minimum/maximum depth in the ShapeNet Chang et al. (2015) dataset.   
+
+<table><tr><td>Metric</td><td>24</td><td>48</td><td>72</td><td>96</td></tr><tr><td>F1-T</td><td>80.29</td><td>80.80</td><td>80.69</td><td>80.34</td></tr><tr><td>F1-2T</td><td>90.43</td><td>90.72</td><td>90.74</td><td>90.47</td></tr></table>
+
+Generalization Capability We conduct experiments to evaluate the generalization capability of our system across the semantic categories. We train our model with only 12 out of the 13 categories and test on the category that was left out. Table 10 shows that the accuracy generally does not decrease significantly when compared with the model that was trained on all 13 categories when using $2 \tau$ threshold for the F-score.
+
+Table 10: Accuracy when a category is excluded during training and evaluation is performed on the category to verify how well training on other categories generalizes to the excluded category.   
+
+<table><tr><td rowspan="2">Category</td><td colspan="2">F-score (T)↑</td><td colspan="2">F-score (2τ)↑</td></tr><tr><td>Excluding</td><td>Including</td><td>Excluding</td><td>Including</td></tr><tr><td>Couch</td><td>63.29</td><td>73.63</td><td>80.79</td><td>88.24</td></tr><tr><td>Cabinet</td><td>68.26</td><td>76.39</td><td>83.10</td><td>88.84</td></tr><tr><td>Bench</td><td>76.08</td><td>83.76</td><td>87.42</td><td>92.57</td></tr><tr><td>Chair</td><td>60.60</td><td>78.69</td><td>75.93</td><td>90.02</td></tr><tr><td>Monitor</td><td>67.26</td><td>76.64</td><td>81.57</td><td>88.89</td></tr><tr><td>Firearm</td><td>78.59</td><td>94.32</td><td>86.28</td><td>97.67</td></tr><tr><td>Speaker</td><td>62.39</td><td>67.83</td><td>77.77</td><td>82.34</td></tr><tr><td>Lamp</td><td>63.50</td><td>75.93</td><td>74.66</td><td>85.33</td></tr><tr><td>Cellphone</td><td>67.24</td><td>86.45</td><td>80.54</td><td>94.28</td></tr><tr><td>Plane</td><td>57.48</td><td>92.13</td><td>67.27</td><td>96.57</td></tr><tr><td>Table</td><td>76.41</td><td>83.68</td><td>86.86</td><td>91.97</td></tr><tr><td>Car</td><td>59.08</td><td>80.43</td><td>75.58</td><td>92.33</td></tr><tr><td>Watercraft</td><td>64.97</td><td>80.48</td><td>78.95</td><td>90.35</td></tr></table>
+
+# B APPENDIX
+
+# BEST VS PRETTY MODELS
+
+We provide qualitative comparison between the our models trained with best and pretty configurations in Figure 5. The best configuration refers to our model trained without edge regularization while pretty refers to the model trained with the regularization (Sub-section 4.1). We observe that without the regularization we get higher score on our evaluation metrics but get degenerate meshes with self-intersections and irregularly sized faces.
+
+![](images/d2afd0508e146a2048b0260560351eca2a72021e6063527c44d85959abc4a970.jpg)  
+Figure 5: Qualitative evaluation: best vs pretty wireframe models. The best models while being preferred by the evaluation metrics lead to degenerate meshes, with irregularly sized faces and self-intersections
+
+# FAILURE CASES
+
+Some failure cases of our model (with pretty setting) are shown in Figure 6. We notice that the rough topology of the mesh is recovered while we failed to reconstruct the fine topology. We can regard the recovery from wrong initial topology as a promising future work.
+
+![](images/ff24da632ff1a17b2967ec106abd663917c046a53d0221503857664f79fc5ef3.jpg)  
+Figure 6: Failure Cases. Our system can struggle to roughly reconstruct shapes with very complex topology while some fine topology of the mesh is missing.

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+    {
+        "type": "text",
+        "text": "MESHMVS: MULTI-VIEW STEREO GUIDED MESH RECONSTRUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            170,
+            398,
+            198
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            234,
+            544,
+            251
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning based 3D shape generation methods generally utilize latent features extracted from color images to encode the objects’ semantics and guide the shape generation process. These color image semantics only implicitly encode 3D information, potentially limiting the accuracy of the generated shapes. In this paper we propose a multi-view mesh generation method which incorporates geometry information in the color images explicitly by using the features from intermediate 2.5D depth representations of the input images and regularizing the 3D shapes against these depth images. Our system first predicts a coarse 3D volume from the color images by probabilistically merging voxel occupancy grids from individual views. Depth images corresponding to the multi-view color images are predicted which along with the rendered depth images of the coarse shape are used as a contrastive input whose features guide the refinement of the coarse shape through a series of graph convolution networks. Attention-based multi-view feature pooling is proposed to fuse the contrastive depth features from different viewpoints which are fed to the graph convolution networks. ",
+        "bbox": [
+            233,
+            267,
+            764,
+            474
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We validate the proposed multi-view mesh generation method on ShapeNet, where we obtain a significant improvement with $34 \\%$ decrease in chamfer distance to ground truth and $14 \\%$ increase in the F1-score compared with the state-of-the-art multi-view shape generation method. ",
+        "bbox": [
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+            479,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            565,
+            336,
+            580
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "3D shape generation is a long-standing research problem in computer vision and computer graphics with applications in autonomous driving, augmented reality, etc. Conventional approaches mainly leverage multi-view geometry based on stereo correspondences between images but are restricted by the coverage provided by the input views. With the availability of large-scale 3D shape datasets and the success of deep learning in several computer vision tasks, 3D representations such as voxel grid Choy et al. (2016); Tulsiani et al. (2017); Yan et al. (2016) and point cloud Yang et al. (2018); Fan et al. (2017) have been explored for single-view 3D reconstruction. Among them, triangle mesh representation has received the most attention as it has various desirable properties for a wide range of applications and is capable of modeling detailed geometry without high memory requirement. ",
+        "bbox": [
+            174,
+            597,
+            825,
+            722
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Single-view 3D reconstruction methods Wang et al. (2018); Huang et al. (2015); Kar et al. (2015); Su et al. (2014) generate the 3D shape from merely a single color image but suffer from occlusion and limited visibility which leads to low quality reconstructions in the unseen areas. Multi-view methods Wen et al. (2019); Choy et al. (2016); Kar et al. (2017); Gwak et al. (2017) extend the input to images from different viewpoints which provides more visual information and improves the accuracy of the generated shapes. Recent work in multi-view mesh reconstruction Wen et al. (2019) introduces a multi-view deformation network using perceptual feature from each color image for refining the meshes generated by Pixel2Mesh Wang et al. (2018). Although promising results were obtained, this method relies on perceptual features from color images which do not explicitly encode the objects’ geometry and could restrict the accuracy of the 3D models. ",
+        "bbox": [
+            174,
+            722,
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+            859
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this work, we present a novel multi-view mesh generation method where we start by predicting coarse volumetric occupancy grid representations for the color images of each input viewpoint independently using a shared fully convolutional network which are merged into a single voxel grid in a probabilistic fashion followed by cubify Gkioxari et al. (2019) operation to convert it to a triangle mesh. We then use Graph Convolutional Network (GCN) Scarselli et al. (2008); Wang et al. (2018) to fine-tune the cubified voxel grid in a coarse-to-fine manner. The GCN refines the coarse mesh by using the feature vector of each graph node (mesh vertices) obtained by projecting the vertices on the 2D contrastive depth features. The contrastive depth features are extracted from the rendered depth maps of the current mesh and predicted depth maps from a multi-view stereo network. We also propose an attention-based method to fuse feature from multiple views that can learn the importance of different views for each of the mesh vertices. Constrains between the intermediate refined mesh from GCN with predicted depth maps of different viewpoints further improve the final mesh quality. By employing multi-view voxel grid generation and refining it using geometry information from both the current mesh (through the rendered depth maps) and predicted depth maps, we are able to generate high-quality meshes. We validate our method on the ShapeNet Chang et al. (2015) benchmark and our method achieves the best performance among all previous multi-view and single-view mesh generation methods. ",
+        "bbox": [
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+            868,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/02d99d090a9ea2bed535ac9d276d10a485fcea411051838f8d277ebce11a7101.jpg",
+        "image_caption": [
+            "Figure 1: Architecture of the proposed method. The voxel grid prediction module predicts coarse voxel grid representation which is further refined by a series of GCNs. The GCNs use contrastive depth features from rendered depths of the current shape and the predicted depths from MVSNet. Multi-view features are pooled using a multi-head attention mechanism. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            666,
+            344,
+            683
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1 TRADITIONAL SHAPE GENERATION METHODS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            700,
+            537,
+            715
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3D model generation has traditionally been tackled using multi-view geometry principles. Among them, structure-from-motion (SfM) Schonberger & Frahm (2016); Agarwal et al. (2011); Cui & Tan (2015); Cui et al. (2017) and simultaneous localization and mapping (SLAM) Cadena et al. (2016); Mur-Artal et al. (2015); Engel et al. (2014); Whelan et al. (2015) are popular techniques that perform 3D reconstruction and camera pose estimation at the same time. These methods extract local image features, match them across images and use the matches to estimate camera poses and 3D geometry. Closer to our problem setup, multi-view stereo methods infer 3D geometry from images with known camera parameters. Volumetric methods Kar et al. (2017); Kutulakos & Seitz (2000); Seitz & Dyer (1999) predict voxel grid representation of objects by estimating the relationship between each voxel and object surfaces. Point cloud based methods Furukawa & Ponce (2009); Lhuillier & Quan (2005) start with a sparse point cloud and gradually increase the density of points to obtain a final dense point cloud of the object. Durou et al. (2008); Zhang et al. (1999); Favaro & Soatto (2005) reason about shading, texture and defocus to reason about visible parts of the object and infer its 3D geometry. While the results of these works are impressive in terms of quality and completeness of reconstruction, they still struggle with poorly textured and reflective surfaces and require carefully selected input views. ",
+        "bbox": [
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+            729,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2 DEEP SHAPE GENERATION METHODS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            150,
+            477,
+            165
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Deep learning based approaches can learn to infer 3D structure from training data and can be robust against poorly textured and reflective surfaces as well as limited and arbitrarily selected input views. These methods can be categorized into single view and multi-view methods. Huang et al. (2015); Su et al. (2014) use shape component retrieval and deformation from a large dataset for single-view 3D shape generation. Kurenkov et al. (2018) extend this idea by introducing free-form deformation networks on retrieved object templates from a database. Some work learn shape deformation from ground truth foreground masks of 2D images Kar et al. (2015); Yan et al. (2016); Tulsiani et al. (2017). Recurrent Neural Networks (RNN) based methods Choy et al. (2016); Kar et al. (2017); Gwak et al. (2017) are another popular solution to solve this problem. Gwak et al. (2017); Lin et al. (2019) introduce image silhouettes along with adversarial multi-view constraints and optimize object mesh models using multi-view photometric constraints. Predicting mesh directly from color images was proposed in Wang et al. (2018); Wickramasinghe et al. (2019); Pan et al. (2019); Wen et al. (2019); Gkioxari et al. (2019); Tang et al. (2019). DR-KFS Jin et al. (2019) introduces a differentiable visual similarity metric while SeqXY2SeqZ Han et al. (2020) represents 3D shapes using a set of 2D voxel tubes for shape reconstruction. Front2Back Yao et al. (2020) generates 3D shapes by fusing predicted depth and normal images and DV-Net Jia et al. (2020) predicts dense object point clouds using dual-view RGB images with a gated control network to fuse point clouds from the two views. FoldingNet Yang et al. (2018) learns to reconstruct arbitrary point clouds from a single 2D grid. AtlasNet Groueix et al. (2018) use learned parametric representation while Mescheder et al. (2019); Park et al. (2019); Liu et al. (2019b;a); Murez et al. (2020) employ implicit surface representation to reconstruct 3D shapes. ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 DEPTH ESTIMATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            487,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Compared to 3D shape generation, depth prediction is an easier problem formulation since it simplifies the task to per-view depth map estimation. Traditional methods Campbell et al. (2008); Galliani et al. (2015); Schönberger et al. (2016) use multi-view stereo principles for depth prediction. Deep learning based multi-view stereo depth estimation was first introduced in Hartmann et al. (2017) where a learned cost metric is used to estimate patch similarities. DeepMVS Huang et al. (2018) warps multi-view images to 3D space and then applies deep networks for regularization and aggregation to estimate depth images. Learned 3D cost volume based depth prediction was proposed in MVSNet Yao et al. (2018) where a 3 dimensional cost volume is built using homographically warped 2D features from multi-view images and 3D CNNs are used for cost regularization and depth regression. This idea was further extended by Chen et al. (2019); Luo et al. (2019); Gu et al. (2019); Yao et al. (2019). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 METHODOLOGY ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            675,
+            341,
+            690
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Figure 1 shows the architecture of the proposed system which takes as input multi-view color images of an object with known poses and outputs a triangle mesh representing the surface of the object. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 MULTI-VIEW VOXEL GRID PREDICTION",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Single-view Voxel Grid Prediction The single-view voxel branch consists of a ResNet feature extractor and a fully convolutional voxel grid prediction network. It generates the coarse initial shape of an object from one viewpoint as voxel occupancy grid using a color image. Here, we set the resolution of the generated voxel occupancy grid as $3 2 \\times 3 2 \\times 3 2$ . The voxel prediction networks for all viewpoints share the same weights. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Probabilistic Occupancy Grid Merging Voxel occupancy grid predicted from a single viewpoint suffers from occlusion and limited visibility. In order to fuse voxel grids from different viewpoints, we propose a probabilistic occupancy grid merging method which merges the voxel grids from each input viewpoint probabilistically to obtain the final voxel grid output. This allows occluded regions in one view to be estimated from other views where those regions are visible as well as increase the confidence of prediction in overlapping regions. Occupancy probability of each voxel is represented by $p ( x )$ which is converted to log-odds (logit): ",
+        "bbox": [
+            174,
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+            922
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            171,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c88231c45176aaa7b6d8bb4f31dc6055bb0e531cee83097465998d8eebaa4b2c.jpg",
+        "text": "$$\nl ( x ) = l o g { \\frac { p ( x ) } { 1 - p ( x ) } }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            429,
+            148,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Bayesian update on the probabilities reduce to simple summation of log likelihoods Konolige (1997). Hence, the multi-view log-odds of a voxel is given by: ",
+        "bbox": [
+            169,
+            190,
+            825,
+            219
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/c34dde1195fc5acdbe36b6bec95589d31c12f6a2d45e575aa3b292b6688d36e5.jpg",
+        "text": "$$\nl ( x ) = l _ { 1 } ( x ) + l _ { 2 } ( x ) + . . . + l _ { n } ( x )\n$$",
+        "text_format": "latex",
+        "bbox": [
+            383,
+            238,
+            614,
+            256
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $l _ { i }$ is the voxel’s log-odds in view $i$ and $n$ is the number of input views. The final voxel probability $x$ is obtained by applying the inverse function of Equation (1) which is a sigmoid function. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 MESH REFINEMENT ",
+        "text_level": 1,
+        "bbox": [
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+            324
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The cubified mesh from the voxel branch only provides a coarse reconstruction of the object’s surface. We apply graph convolutional networks which represent each mesh vertex as one graph node and deforms them to more accurate positions. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "GCN-based Mesh Deformation The features pooled from multi-view images along with 3D coordinates of the vertices in world frame are used as features of the graph nodes. Series of Graphbased Convolutional Network (GCN) blocks are applied to deform a mesh at the current stage to the next stage, starting with the cubified voxel grids. A graph convolution deforms mesh vertices by propagating features from neighboring vertices by applying $\\begin{array} { r } { f _ { i } ^ { ' } = R e L U ( W _ { 0 } f _ { i } + \\sum _ { j \\in \\mathcal { N } ( i ) } W _ { 1 } f _ { j } ) } \\end{array}$ where $\\mathcal { N } ( i )$ is the set of neighboring vertices of the $i .$ -th vertex in the mesh, $f _ { \\{ \\} }$ represents the feature vector of a vertex, and $W _ { 0 }$ and $W _ { 1 }$ are learnable parameters of the model. Each GCN block utilizes several graph convolutions to transform the vertex features along with a final vertex refinement operation where the features along with vertex coordinates are further transformed as $v _ { i } ^ { ' } = v _ { i } + t a n h ( W _ { v e r t } [ f _ { i } ; v _ { i } ] )$ where the matrix $W _ { v e r t }$ is another learnable parameter to obtain the deformed mesh. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Contrastive Depth Feature Extraction Yao et al. (2020) demonstrate that using intermediate, image-centric 2.5D representations instead of directly generating 3D shapes in global frame from raw 2D images can improve 3D reconstruction quality. We therefore propose to formulate the features for graph nodes using 2.5D depth maps as input additional inputs alongside the RGB features. Specifically, we render the meshes at different GCN stages to depth image at all the input views using Kato et al. (2018) and use them along with predicted depths for depth feature extraction. We call this form of depth input contrastive depth as it contrasts the rendered depths of the current mesh against the predicted depths and allows the network to reason about the deformation better than when using predicted depth or color images alone. Given the 2D features, corresponding feature vectors of individual vertices can be found by projecting the 3D vertex coordinates to the feature planes using known camera parameters. We use VGG-16 Simonyan & Zisserman (2014) as our contrastive depth feature extraction network. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Multi-View Depth Estimation We extend MVSNet Yao et al. (2018) and predict the depth maps of all views since the original implementation predicts depth of only one reference view. This is achieved by transforming the feature volumes to each view’s coordinate frame using homography warping and applying identical cost volume regularization and depth regression on each view. Detailed network architecture diagram of this module is provided in the appendix. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Attention-based Multi-View Feature Pooling In order to fuse multi-view contrastive depth features, we formulate an attention module by adapting multi-head attention mechanism originally designed for sequence to sequence machine translation using transformer (encoder-decoder) architecture Vaswani et al. (2017). In a transformer architecture the encoder hidden state is mapped to lower dimension key-value pairs $( \\mathbf { K } , \\mathbf { V } )$ while the decoder hidden state is mapped to a query vector Q using independent fully connected layers. The encoder hidden state in our case is the multi-view features while the decoder hidden state is the mean of the multi-view features. The attention weights are computed using scaled-dot product: ",
+        "bbox": [
+            173,
+            777,
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+            888
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/ce30c38f3d24d3e460aa04b75d98339585004a16874a66f8e1f0d21589f3965f.jpg",
+        "text": "$$\nA t t e n t i o n ( \\mathbf { Q } , \\mathbf { K } , \\mathbf { V } ) = s o f t m a x ( \\frac { \\mathbf { Q } \\mathbf { K } ^ { T } } { \\sqrt { N } } ) \\mathbf { V }\n$$",
+        "text_format": "latex",
+        "bbox": [
+            348,
+            893,
+            648,
+            929
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/85bfc53cff116373845a2510580033857bbade708c4afa86a5589992859a87b8.jpg",
+        "image_caption": [
+            "Figure 2: Attention weights visualization. From left to right: input images from 3 viewpoints, corresponding ground truth point clouds color-coded by their view order and the predicted mesh vertices color-coded by the attention weights of the views. Only the view with maximum attention weight is visualized for each predicted points for clarity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
+            98,
+            823,
+            310
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $N$ is the number of input views. ",
+        "bbox": [
+            176,
+            387,
+            428,
+            401
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Multiple attention heads are used which are concatenated and transformed to obtain the final output ",
+        "bbox": [
+            173,
+            407,
+            823,
+            422
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/622ec6524c1680a41349b3235cfc66afa852421333b4e2e053c48f93a2fc6ebc.jpg",
+        "text": "$$\n\\begin{array} { r } { h e a d _ { i } = A t t e n t i o n ( { \\mathbf { Q } } { \\mathbf { W } } _ { i } ^ { Q } , { \\mathbf { K } } { \\mathbf { W } } _ { i } ^ { K } , { \\mathbf { V } } { \\mathbf { W } } _ { i } ^ { V } ) } \\\\ { M u l t i H e a d ( { \\mathbf { Q } } , { \\mathbf { K } } , { \\mathbf { V } } ) = [ h e a d _ { 1 } ; . . . ; h e a d _ { h } ] { \\mathbf { W } } ^ { 0 } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            334,
+            430,
+            663,
+            473
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where multiple $\\mathbf { W }$ are parameters to be learned, $h$ is the number of attention heads and $i \\in [ 1 , h ]$ ",
+        "bbox": [
+            173,
+            487,
+            808,
+            502
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We choose multi-head attention as our feature pooling method since it allows the model to attend information from different representation subspaces of the features by training multiple attentions in parallel. This method is also invariant to the order and number of input views. We visualize the learned attention weights (average of each attention heads) in Figure 2 where we can observe that the attention weights roughly takes into account the visibility/occlusion information from each view. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3 LOSS FUNCTIONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            590,
+            336,
+            604
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Mesh losses The losses which are derived from Wang et al. (2018) to constrain the mesh predicted by each GCN block (P) to resemble the ground truth (Q) include Chamfer distance $\\mathcal { L } _ { \\mathrm { c h a m f e r } } ( \\mathrm { P } , \\mathrm { Q } ) =$ $\\begin{array} { r } { | \\bar { \\mathbf { P } } | ^ { - 1 } \\sum _ { ( p , q ) \\in \\Lambda _ { \\mathrm { P } , \\mathrm { Q } } } | | p - q | | ^ { 2 } + | \\mathbf { Q } | ^ { - 1 } \\sum _ { ( q , p ) \\in \\Lambda _ { \\mathrm { Q } , \\mathrm { P } } } | | q - p | | ^ { 2 } } \\end{array}$ and surface normal loss $\\mathcal { L } _ { \\mathrm { n o r m a l } } ( \\mathbf { P } , \\mathbf { Q } ) =$ $\\begin{array} { r } { - | \\mathbf { P } | ^ { - 1 } \\sum _ { ( p , q ) \\in \\Lambda _ { \\mathbf { P } , \\mathbf { Q } } } | u _ { p } \\cdot u _ { q } | - | \\mathbf { Q } | ^ { - 1 } \\sum _ { ( q , p ) \\in \\Lambda _ { \\mathbf { Q } , \\mathbf { P } } } | u _ { q } \\cdot u _ { p } | } \\end{array}$ with additional regularization in the form of edge length loss $\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { e d g e } } ( \\mathrm { V } , \\mathrm { E } ) = { \\frac { 1 } { | E | } } \\sum _ { ( v , v ^ { \\prime } ) \\in E } | | v - v ^ { \\prime } | | ^ { 2 } } \\end{array}$ for visually appealing results. ",
+        "bbox": [
+            173,
+            617,
+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Depth loss Our depth prediction network is supervised using adaptive reversed Huber loss (also known as BerHu criterion) Lambert-Lacroix & Zwald (2016). $\\mathcal { L } _ { d e p t h } ~ = ~ | \\boldsymbol { x } |$ , if $| x | \\ \\leq$ c, otherwise x2+c22c where $x$ is the depth error of a pixel and $c$ is a constant set to 0.2. Note that the original MVSNet uses L1-loss, but we used BerHu loss since it gave slightly higher accuracy. Intuitively, this is because BerHu provides a good balance between L1 and L2 loss and has shown similar improvement in Laina et al. (2016). ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Contrastive depth loss BerHu loss is also applied between the rendered depth images at different GCN stages and the predicted depth images. $\\mathcal { L } _ { c o n t r a s t i v e } = | x | .$ , if $| x | \\le c$ , otherwise $\\frac { x ^ { 2 } + c ^ { 2 } } { 2 c }$ ",
+        "bbox": [
+            174,
+            792,
+            820,
+            825
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Voxel loss Binary cross-entropy loss between the predicted voxel occupancy probabilities and the ground truth occupancies is used as voxel loss to supervise the voxel predictions $\\mathcal { L } _ { \\mathrm { v o x e l } } =$ $- \\bar { \\Bigl ( p ( x ) l o g \\bigl ( p ( x ) \\bigr ) + \\bigl ( 1 - p ( x ) \\bigr ) l o g \\bigl ( 1 - p ( x ) \\bigr ) \\Bigr ) }$ ",
+        "bbox": [
+            171,
+            827,
+            825,
+            880
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Final loss We use the weighted sum of the individual losses discussed above as the final loss to train our model in an end-to-end fashion. $\\mathcal { L } = \\lambda _ { \\mathrm { c h a m f e r } } \\mathcal { L } _ { \\mathrm { c h a m f e r } } + \\lambda _ { \\mathrm { n o r m a l } } \\mathcal { L } _ { \\mathrm { n o r m a l } } + \\lambda _ { \\mathrm { e d g e } } \\mathcal { L } _ { \\mathrm { e d g e } } + \\lambda _ { \\mathrm { d e p t h } } \\mathcal { L } _ { \\mathrm { d e p t h } } +$ $\\lambda _ { \\mathrm { c o n t r a s t i v e } } \\mathcal { L } _ { \\mathrm { c o n t r a s t i v e } } + \\lambda _ { \\mathrm { v o x e l } } \\mathcal { L } _ { \\mathrm { v o x e l } }$ , where $\\mathcal { L }$ is the final loss term. ",
+        "bbox": [
+            174,
+            882,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/16e9000814758c5e0f9fc7cafba71cf427150a8b1e28cba393e962fab5a12fac.jpg",
+        "image_caption": [
+            "Figure 3: Qualitative evaluation on ShapeNet dataset. From top to bottom: one of the input images, ground truth mesh, multi-view extended Pixel2Mesh, Pixel2Mesh $^ { + + }$ , and ours. Our predictions are closer to the actual shape, especially for the objects with more complex topologies. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            191,
+            99,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            443,
+            326,
+            458
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            474,
+            375,
+            489
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Comparisons We evaluate the proposed method against various multi-view shape generation methods. The state-of-the-art method is Pixel2Mesh $^ { + + }$ Wen et al. (2019) (referred as $P 2 M + +$ ). Wen et al. (2019) also provide a baseline by directly extending Pixel2Mesh Wang et al. (2018) to operate on multi-view images (referred as MVP2M) using their statistical feature pooling method to aggregate features from multiple color images. Results from additional multi-view shape generation baselines 3D-R2N2 Choy et al. (2016) and LSM Kar et al. (2017) are also reported. ",
+        "bbox": [
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+            502,
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+            585
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Dataset We evaluate our method against the state-of-the-art methods on the dataset from Choy et al. (2016) which is a subset of ShapeNet Chang et al. (2015) and has been widely used by recent 3D shape generation methods. It contains 50K 3D CAD models from 13 categories. Each model is rendered with a transparent background from 24 randomly chosen camera viewpoints to obtain color images. The corresponding camera intrinsics and extrinsics are provided in the dataset. Since the dataset does not contain depth images, we render them using a custom depth renderer at the same viewpoints as the color images and with the same camera intrinsics. We follow the training/testing/validation split of Gkioxari et al. (2019). ",
+        "bbox": [
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+            589,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Implementation For the depth prediction module, we follow the original MVSNet Yao et al. (2018) implementation. The output depth dimensions reduces by a factor of 4 to $5 6 \\times 5 6$ from the $2 2 4 \\times 2 2 4$ input image. The number of depth hypotheses is chosen as 48 which offers a balance between accuracy and running/training time efficiency. These depth hypotheses represent values from $0 . 1 { \\mathrm { m } }$ to $\\mathrm { 1 . 3 } \\mathrm { m }$ at an interval of $2 5 \\mathrm { m m }$ . These values were chosen based on the range of depths present in the dataset. ",
+        "bbox": [
+            174,
+            704,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The hierarchical features obtained from \"Contrastive Depth Features Extractor\" are of total 4800 dimensions for each view. The aggregated multi-view features are compressed to 480 dimensional after applying attentive feature pooling. 5 attention heads are used for merging multi-view features. The loss function weights are set as $\\lambda _ { \\mathrm { c h a m f e r } } = 1$ , $\\lambda _ { \\mathrm { n o r m a l } } = 1 . 6 \\times 1 0 ^ { - 4 }$ , $\\lambda _ { \\mathrm { d e p t h } } = 0 . 1$ , $\\lambda _ { \\mathrm { c o n t r a s t i v e } } =$ 0.001 and $\\lambda _ { \\mathrm { v o x e l } } = 1$ . Two settings of $\\lambda _ { \\mathrm { e d g e } }$ were used, $\\lambda _ { \\mathrm { e d g e } } = 0$ (referred as Best) which gives better quantitative results and $\\lambda _ { \\mathrm { e d g e } } = 0 . 2$ (referred as Pretty) which gives better qualitative results. ",
+        "bbox": [
+            174,
+            794,
+            825,
+            878
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Training and Runtime The network is optimized using Adam optimizer with a learning rate of $1 0 ^ { - 4 }$ . The training is done on 5 Nvidia RTX-2080 GPUs with effective batch size 5. The depth prediction network (MVSNet) is trained independently for 30 epochs. Then the whole system is trained for another 40 epochs with the weights of the MVSNet frozen. Our system is implemented in PyTorch deep learning framework and it takes around 60 hours for training. ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metric Following Wang et al. (2018); Wen et al. (2019), we use F1-score as our evaluation metric. The F1-score is the harmonic mean of precision and recall where the precision/recall are calculated by finding the percentage of points in the predicted/ground truth that can find a nearest neighbor from the other within a threshold. We provide evaluations with two threshold values: $\\tau$ and $2 \\tau$ where $\\tau = 1 0 ^ { - 4 } ~ \\mathrm { m } ^ { 2 }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 COMPARISON WITH PREVIOUS MULTI-VIEW SHAPE GENERATION METHODS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            212,
+            741,
+            227
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We quantitatively compare our method against previous works for multi-view shape generation in Table 1 and show the effectiveness of our methods in improving the shape quality. Our method outperforms the state-of-the-art method Pixel2Mesh $^ { + + }$ Wen et al. (2019) with a decrease in chamfer distance to ground truth by $34 \\%$ and $15 \\%$ increase in F1-score at threshold $\\tau$ . Note that in Table 1 the same model is trained for all the categories but accuracy on individual categories as well as average over the categories are evaluated. We provide the chamfer distances in the appendix. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/501a64ec26e7763e3895a4fb4e169a067f4f3163cb76835189bb2ae644b71499.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Qualitative comparison against state-of-the-art multi-view shape generation methods. We report F-score on each semantic category along with the mean over all categories using two thresholds $\\tau$ and $2 \\tau$ for nearest neighbor match where $\\tau { = } 1 0 ^ { - 4 } \\mathrm { m } ^ { 2 }$ . "
+        ],
+        "table_body": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"6\">F-score (T)↑</td><td colspan=\"6\">F-score (2τ)↑</td></tr><tr><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++</td><td>Ours (pretty)</td><td>Ours (best)</td><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++</td><td>Ours (pretty)</td><td>Ours (best)</td></tr><tr><td>Couch</td><td>45.47</td><td>43.02</td><td>53.17</td><td>57.56</td><td>71.63</td><td>73.63</td><td>59.97</td><td>55.49</td><td>73.24</td><td>75.33</td><td>85.28</td><td>88.24</td></tr><tr><td>Cabinet</td><td>54.08</td><td>50.80</td><td>56.85</td><td>65.72</td><td>75.91</td><td>76.39</td><td>64.42</td><td>60.72</td><td>76.58</td><td>81.57</td><td>87.61</td><td>88.84</td></tr><tr><td>Bench</td><td>44.56</td><td>49.33</td><td>60.37</td><td>66.24</td><td>81.11</td><td>83.76</td><td>62.47</td><td>65.92</td><td>75.69</td><td>79.67</td><td>90.56</td><td>92.57</td></tr><tr><td>Chair</td><td>37.62</td><td>48.55</td><td>54.19</td><td>62.05</td><td>77.63</td><td>78.69</td><td>54.26</td><td>64.95</td><td>72.36</td><td>77.68</td><td>88.24</td><td>90.02</td></tr><tr><td>Monitor</td><td>36.33</td><td>43.65</td><td>53.41</td><td>60.00</td><td>74.14</td><td>76.64</td><td>48.65</td><td>56.33</td><td>70.63</td><td>75.42</td><td>86.04</td><td>88.89</td></tr><tr><td>Firearm</td><td>55.72</td><td>56.14</td><td>79.67</td><td>80.74</td><td>92.92</td><td>94.32</td><td>76.79</td><td>73.89</td><td>89.08</td><td>89.29</td><td>96.81</td><td>97.67</td></tr><tr><td>Speaker</td><td>41.48</td><td>45.21</td><td>48.90</td><td>54.88</td><td>66.02</td><td>67.83</td><td>52.29</td><td>56.65</td><td>68.29</td><td>71.46</td><td>79.76</td><td>82.34</td></tr><tr><td>Lamp</td><td>32.25</td><td>45.58</td><td>50.82</td><td>62.56</td><td>72.47</td><td>75.93</td><td>49.38</td><td>64.76</td><td>65.72</td><td>74.00</td><td>82.00</td><td>85.33</td></tr><tr><td>Cellphone</td><td>58.09</td><td>60.11</td><td>66.07</td><td>74.36</td><td>85.57</td><td>86.45</td><td>69.66</td><td>71.39</td><td>82.31</td><td>86.16</td><td>93.40</td><td>94.28</td></tr><tr><td>Plane</td><td>47.81</td><td>55.60</td><td>75.16</td><td>76.79</td><td>89.23</td><td>92.13</td><td>70.49</td><td>76.39</td><td>86.38</td><td>86.62</td><td>94.65</td><td>96.57</td></tr><tr><td>Table</td><td>48.78</td><td>48.61</td><td>65.95</td><td>71.89</td><td>82.37</td><td>83.68</td><td>62.67</td><td>62.22</td><td>79.96</td><td>84.19</td><td>90.24</td><td>91.97</td></tr><tr><td>Car</td><td>59.86</td><td>51.91</td><td>67.27</td><td>68.45</td><td>77.01</td><td>80.43</td><td>78.31</td><td>68.20</td><td>84.64</td><td>85.19</td><td>88.99</td><td>92.33</td></tr><tr><td>Watercraft</td><td>40.72</td><td>47.96</td><td>61.85</td><td>62.99</td><td>75.52</td><td>80.48</td><td>63.59</td><td>66.95</td><td>77.49</td><td>77.32</td><td>86.77</td><td>90.35</td></tr><tr><td>Mean</td><td>46.37</td><td>49.73</td><td>61.05</td><td>66.48</td><td>78.58</td><td>80.80</td><td>62.53</td><td>64.91</td><td>77.10</td><td>80.30</td><td>88.49</td><td>90.72</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also provide visual results for qualitative assessment of the generated shapes by our Pretty model in Figure 3 which shows that it is able to more accurately predict topologically diverse shapes. ",
+        "bbox": [
+            174,
+            566,
+            823,
+            594
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3 ABLATION STUDIES ",
+        "text_level": 1,
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+        "text": "Contrastive Depth Feature Extraction We evaluate several methods for contrastive feature extraction (Sub-section 3.2). These methods are 1) Input Concatenation: using the concatenated rendered and predicted depth maps as input to the VGG feature extractor, 2) Input Difference: using the difference of the two depth maps as input to VGG, 3) Feature Concatenation: concatenating features from rendered and predicted depths extracted by shared VGG, 4) Feature Difference: using difference of the features from the two depth maps extracted by shared VGG, and 5) Predicted depth only: using the VGG features from the predicted depths only. 6) Rendered depth only: using the VGG features from the rendered depths only. The quantitative results are summarized in Table 2 and shows that Input Concatenation method produces better results than other formulations. ",
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+        "text": "Accuracy with different settings Table 3 shows the contribution of different components towards the final accuracy. Naively extending the single-view Mesh R-CNN Gkioxari et al. (2019) to multiple views using statistical feature pooling Wen et al. (2019) for mesh refinement (row 1) gives an F1-score of $7 2 . 7 4 \\%$ for threshold $\\tau$ which is $6 . 2 6 \\%$ improvement over Pixel2Mesh $^ { + + }$ . We further extend the above method with our probabilistic multi-view voxel grid prediction in row 2 and get a $4 . 2 3 \\%$ improvement. ",
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+        "type": "text",
+        "text": "In row 3 of Table 3 we use our contrastive depth features instead of RGB features for mesh refinement and get $2 . 7 \\%$ improvement. We then replace the statistical feature pooling with the proposed attention method and get $0 . 1 9 \\%$ improvement. The improvement is not significant on our final architecture but we found the multi-head attention to perform better on more light-weight architectures. We also evaluate the effect of using additional regularization from contrastive depth losses: rendered depth vs predicted depth in the 5th rows of which improves the score by $0 . 9 8 \\%$ . In row 6 we use ground truth instead of predicted depths on our final model which gives the upper bound on our mesh prediction accuracy in relation to the depth prediction accuracy as $8 4 . 5 8 \\%$ . ",
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+        "type": "table",
+        "img_path": "images/094ccd58b7015ba66faf7de66d3acb64c2b06a6142fae3e5907067cdb16c6848.jpg",
+        "table_caption": [
+            "Table 2: Comparisons of different contrastive depth formulations. In 1st and 2nd rows, concatenation and difference of the rendered and predicted depths are fed to VGG feature extractor while in 3rd and 4th rows, concatenation and difference of the VGG features from the depths is used for mesh refinement. 5 uses VGG features from predicted depths only while 6 uses VGG features from rendered depths only. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>F1-T</td><td>F1-2T</td></tr><tr><td>(1) Input Concatenation</td><td>80.80</td><td>90.72</td></tr><tr><td>(2) Input Difference</td><td>80.41</td><td>90.54</td></tr><tr><td>(3) Feature Concatenation</td><td>80.45</td><td>90.54</td></tr><tr><td>(4) Feature Difference</td><td>80.30</td><td>90.40</td></tr><tr><td>(5) Predicted Depth only</td><td>79.40</td><td>89.95</td></tr><tr><td>(6) Rendered Depth only</td><td>78.20</td><td>88.90</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "table",
+        "img_path": "images/7119a2639d83768f8037476b4dd40d8e76f198773802d4cc2975d3a525d64a49.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>F1-T</td><td>F1-2T</td></tr><tr><td>(1) Naive multi-view Mesh R-CNN</td><td>72.74</td><td>84.99</td></tr><tr><td>(2) + Multi-view voxel grid prediction</td><td>76.97</td><td>88.24</td></tr><tr><td>(3) + Contrastive depth input</td><td>79.63</td><td>90.10</td></tr><tr><td>(4) + Multi-head attention pooling</td><td>79.82</td><td>90.18</td></tr><tr><td>(5)+ Contrastive depth loss (final model)</td><td>80.80</td><td>90.72</td></tr><tr><td>(6) Using GT depth (final model)</td><td>84.58</td><td>92.86</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Number of View We test the performance of our framework with respect to the number of views. Table 4 shows that the accuracy of our method increases as we increase the number of input views for training. These experiments also validate that the attention-based feature pooling can efficiently encode features from different views to take advantage of larger number of views. ",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "Table 5 shows the results when using different number of views during testing on our model trained with 3 views which indicates that increasing the number of views during testing does not improve the accuracy while decreasing the number of views can cause a significant drop in accuracy. ",
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+    {
+        "type": "table",
+        "img_path": "images/b1e5aff7c4a8fa225533cb238f6303f28efeefd72a7651c36c74a012f9f2b940.jpg",
+        "table_caption": [
+            "Table 4: Accuracy w.r.t the number of views during training. The evaluation was performed on the same number of views as training. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>F1-T</td><td>73.60</td><td>80.80</td><td>82.61</td><td>83.76</td><td>84.25</td></tr><tr><td>F1-2T</td><td>85.80</td><td>90.72</td><td>91.78</td><td>92.73</td><td>93.14</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/18712581ec4f936d9dd3a2a9bcb09f2842f2e142dd093dd71195623fe001abe0.jpg",
+        "table_caption": [
+            "Table 5: Accuracy w.r.t the number of views during testing. The same model trained with 3 views was used in all of the cases. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>F1-T</td><td>72.46</td><td>80.80</td><td>80.98</td><td>80.94</td><td>80.85</td></tr><tr><td>F1-2T</td><td>84.49</td><td>90.72</td><td>91.03</td><td>91.16</td><td>91.20</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We propose a neural network based solution to predict 3D triangle mesh models of objects from images taken from multiple views. First, we propose a multi-view voxel grid prediction module which probabilistically merges voxel grids predicted from individual input views. We then cubify the merged voxel grid to triangle mesh and apply graph convolutional networks for further refining the mesh. The features for the mesh vertices are extracted from contrastive depth input consisting of rendered depths at each refinement stage along with the predicted depths. The proposed mesh reconstruction method outperforms existing methods with a large margin and is capable of reconstructing objects with more complex topologies. ",
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+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "bbox": [
+            176,
+            424,
+            299,
+            440
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "NETWORK ARCHITECTURE ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            459,
+            400,
+            474
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "MVSNET ARCHITECTURE ",
+        "bbox": [
+            174,
+            491,
+            357,
+            505
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/e48055ebcff419b4d4a3731091747888bd234fd8debc44af6fd1a3a2716c1c36.jpg",
+        "image_caption": [
+            "Figure 4: Depth prediction network (MVSNet) architecture "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            245,
+            525,
+            736,
+            796
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Our depth prediction module is based on MVSNet Yao et al. (2018) which constructs a regularized 3D cost volumes to estimate the depth map of the reference view. Here, we extent MVSNet to predict the depth maps of all views instead of only the reference view. This is achieved by transforming the feature volumes to each view’s coordinate frame using homography warping and applying identical cost volume regularization and depth regression on each view. This allows the reuse of pre-regularization feature volumes for efficient multi-view depth prediction invariant to the order of input images. Figure 4 shows the architecture of the our depth estimation module. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "PROBABILISTIC OCCUPANCY GRID MERGING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            103,
+            491,
+            117
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We use single-view voxel prediction network from Gkioxari et al. (2019) to predict predicts voxel grids for each of the input images in their respective local coordinate frames. The occupancy grids are transformed to global frame (which is set to the coordinate frame of the first image) by finding the equivalent global grid values in the local grids after applying bilinear interpolation on the closest matches. The voxel grids in global coordinates are then probabilistically merged according to Sub-section 3.1 of the main submission. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            239,
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+            253
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We quantitatively compare our method against previous works for multi-view shape generation in Table 6 and show effectiveness of our proposed shape generation methods in improving shape quality. Our method outperforms the state-of-the-art method Pixel2Mesh $^ { + + }$ Wen et al. (2019) with decrease in chamfer distance to ground truth by $34 \\%$ , which shows the effectiveness of our proposed method. Note that in Table 6 same model is trained for all the categories but accuracy on individual categories as well as average over all the categories are evaluated. ",
+        "bbox": [
+            173,
+            272,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/05ed8eb9c618464f02b7224b00456f210f47d809d18f15678e836db7df9db06b.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"4\">Chamfer Distance (CD) ↓</td></tr><tr><td>3D-R2N2</td><td>LSM</td><td>MVP2M</td><td>P2M++ Ours</td></tr><tr><td>Couch</td><td>0.806</td><td>0.730</td><td>0.534</td><td>0.439 0.220</td></tr><tr><td>Cabinet</td><td>0.613</td><td>0.634</td><td>0.488 0.337</td><td>0.230</td></tr><tr><td>Bench</td><td>1.362</td><td>0.572</td><td>0.591 0.549</td><td>0.159</td></tr><tr><td>Chair</td><td>1.534</td><td>0.495</td><td>0.583 0.461</td><td>0.201</td></tr><tr><td>Monitor</td><td>1.465</td><td>0.592</td><td>0.658</td><td>0.566 0.217</td></tr><tr><td>Firearm</td><td>0.432</td><td>0.385</td><td>0.305</td><td>0.305 0.123</td></tr><tr><td>Speaker</td><td>1.443</td><td>0.767</td><td>0.745</td><td>0.635 0.402</td></tr><tr><td>Lamp</td><td>6.780</td><td>1.768</td><td>0.980</td><td>1.135 0.755</td></tr><tr><td>Cellphone</td><td>1.161</td><td>0.362</td><td>0.445</td><td>0.325 0.138</td></tr><tr><td>Plane</td><td>0.854</td><td>0.496</td><td>0.403</td><td>0.422 0.084</td></tr><tr><td>Table</td><td>1.243</td><td>0.994</td><td>0.511</td><td>0.388 0.181</td></tr><tr><td>Car</td><td>0.358</td><td>0.326</td><td>0.321</td><td>0.249 0.165</td></tr><tr><td>Watercraft</td><td>0.869</td><td>0.509</td><td>0.463</td><td>0.508 0.175</td></tr><tr><td>Mean</td><td>1.455</td><td>0.664</td><td>0.541</td><td>0.486 0.211</td></tr></table>",
+        "bbox": [
+            281,
+            371,
+            715,
+            598
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Qualitative comparison against state-of-the-art multi-view shape generation methods. Following Wen et al. (2019), we report Chamfer Distance in $m ^ { 2 } \\times 1 0 0 0$ from ground truth for different methods. Note that same model is trained for all the categories but accuracy on individual categories as well as average over all the categories are evaluated. ",
+        "bbox": [
+            173,
+            614,
+            825,
+            670
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            704,
+            313,
+            717
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Coarse Shape Generation We conduct comparisons on voxel grid predicted from our proposed probabilistically merged voxel grids against single view method Gkioxari et al. (2019). As is shown in Table 7, the accuracy of the initial shape generated from probabilistically merged voxel grid is higher than that from individual views. ",
+        "bbox": [
+            174,
+            723,
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+            779
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Accuracy at Different GCN Stages We analyze the accuracy of meshes at different GCN stages in Table 8. The results validate that our method produces the meshes in a coarse-to-fine manner and multiple GCN refinements improve the mesh quality. ",
+        "bbox": [
+            173,
+            790,
+            823,
+            833
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Resolution of Depth Prediction We conduct experiments using different numbers of depth hypotheses in our depth prediction network (Sub-section A), producing depth values at different resolutions. A higher number of depth hypothesis means finer resolution of the predicted depths. The quantitative results with different hypothesis numbers are summarized in Table 9. We set depth hypothesis as 48 for our final architecture which is equivalent to the resolution of $2 5 \\mathrm { m m }$ . We observe that the mesh accuracy remain relatively unchanged if we predict depths at finer resolutions. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/571c4a4e26a7c5f63b6c67294779a3dae4e5fa2363ef876d3aad10b4ebcc22ff.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>Cubified</td><td>Stage-1</td><td>Stage-2</td><td>Stage-3</td></tr><tr><td>F1-T</td><td>31.48</td><td>76.78</td><td>79.88</td><td>80.80</td></tr><tr><td>F1-2T</td><td>44.40</td><td>88.32</td><td>90.19</td><td>90.72</td></tr></table>",
+        "bbox": [
+            508,
+            101,
+            833,
+            142
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/4517204b3b147299904276e071e1e62d4722aae875ce3e70a8c571dc7947cd57.jpg",
+        "table_caption": [
+            "Table 7: Accuracy of predicted voxel grids from single-view prediction compared against the proposed probabilistically merged multi-view voxel grids. The voxel branch was trained separately without the mesh refinement and evaluation was performed on the cubified voxel grids. We use three views for probabilistic grid merging. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>Single-view</td><td>Multi-view</td></tr><tr><td>F1-T</td><td>25.19</td><td>31.27</td></tr><tr><td>F1-2T</td><td>36.75</td><td>44.46</td></tr></table>",
+        "bbox": [
+            218,
+            101,
+            455,
+            142
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Table 8: Accuracy of the refined meshes at different GCN stages. 1, 2 and 3 indicate the performance at the corresponding graph convolution blocks while Cubified is for the cubified voxel grids used as input for the first GCN block. All the stages, including the voxel prediction, were trained jointly and hence the accuracy of voxel predictions varies from that in Table 7. ",
+        "bbox": [
+            506,
+            152,
+            834,
+            263
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/5385f1e59c2d20faee675f4c8da8670a2732c758f3fcc86fe98c1149094ee0ce.jpg",
+        "table_caption": [
+            "Table 9: Accuracy w.r.t the number of depth hypothesis. A higher number of depth hypothesis increases the resolution of predicted depth values at the expense of higher memory requirement. The range of depths for all the models are same and based on the minimum/maximum depth in the ShapeNet Chang et al. (2015) dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Metric</td><td>24</td><td>48</td><td>72</td><td>96</td></tr><tr><td>F1-T</td><td>80.29</td><td>80.80</td><td>80.69</td><td>80.34</td></tr><tr><td>F1-2T</td><td>90.43</td><td>90.72</td><td>90.74</td><td>90.47</td></tr></table>",
+        "bbox": [
+            364,
+            279,
+            633,
+            320
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Generalization Capability We conduct experiments to evaluate the generalization capability of our system across the semantic categories. We train our model with only 12 out of the 13 categories and test on the category that was left out. Table 10 shows that the accuracy generally does not decrease significantly when compared with the model that was trained on all 13 categories when using $2 \\tau$ threshold for the F-score. ",
+        "bbox": [
+            174,
+            420,
+            825,
+            489
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "table",
+        "img_path": "images/2195f0dbd1adba1cfac4fd04eadf53bb3beebb2391b3ed6faa706086b0a1fa6a.jpg",
+        "table_caption": [
+            "Table 10: Accuracy when a category is excluded during training and evaluation is performed on the category to verify how well training on other categories generalizes to the excluded category. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Category</td><td colspan=\"2\">F-score (T)↑</td><td colspan=\"2\">F-score (2τ)↑</td></tr><tr><td>Excluding</td><td>Including</td><td>Excluding</td><td>Including</td></tr><tr><td>Couch</td><td>63.29</td><td>73.63</td><td>80.79</td><td>88.24</td></tr><tr><td>Cabinet</td><td>68.26</td><td>76.39</td><td>83.10</td><td>88.84</td></tr><tr><td>Bench</td><td>76.08</td><td>83.76</td><td>87.42</td><td>92.57</td></tr><tr><td>Chair</td><td>60.60</td><td>78.69</td><td>75.93</td><td>90.02</td></tr><tr><td>Monitor</td><td>67.26</td><td>76.64</td><td>81.57</td><td>88.89</td></tr><tr><td>Firearm</td><td>78.59</td><td>94.32</td><td>86.28</td><td>97.67</td></tr><tr><td>Speaker</td><td>62.39</td><td>67.83</td><td>77.77</td><td>82.34</td></tr><tr><td>Lamp</td><td>63.50</td><td>75.93</td><td>74.66</td><td>85.33</td></tr><tr><td>Cellphone</td><td>67.24</td><td>86.45</td><td>80.54</td><td>94.28</td></tr><tr><td>Plane</td><td>57.48</td><td>92.13</td><td>67.27</td><td>96.57</td></tr><tr><td>Table</td><td>76.41</td><td>83.68</td><td>86.86</td><td>91.97</td></tr><tr><td>Car</td><td>59.08</td><td>80.43</td><td>75.58</td><td>92.33</td></tr><tr><td>Watercraft</td><td>64.97</td><td>80.48</td><td>78.95</td><td>90.35</td></tr></table>",
+        "bbox": [
+            300,
+            503,
+            696,
+            694
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "B APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            776,
+            295,
+            792
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "BEST VS PRETTY MODELS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            810,
+            393,
+            827
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We provide qualitative comparison between the our models trained with best and pretty configurations in Figure 5. The best configuration refers to our model trained without edge regularization while pretty refers to the model trained with the regularization (Sub-section 4.1). We observe that without the regularization we get higher score on our evaluation metrics but get degenerate meshes with self-intersections and irregularly sized faces. ",
+        "bbox": [
+            174,
+            842,
+            825,
+            912
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "image",
+        "img_path": "images/d2afd0508e146a2048b0260560351eca2a72021e6063527c44d85959abc4a970.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative evaluation: best vs pretty wireframe models. The best models while being preferred by the evaluation metrics lead to degenerate meshes, with irregularly sized faces and self-intersections "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            192,
+            101,
+            815,
+            380
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "FAILURE CASES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            440,
+            310,
+            455
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "text",
+        "text": "Some failure cases of our model (with pretty setting) are shown in Figure 6. We notice that the rough topology of the mesh is recovered while we failed to reconstruct the fine topology. We can regard the recovery from wrong initial topology as a promising future work. ",
+        "bbox": [
+            174,
+            472,
+            825,
+            515
+        ],
+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/ff24da632ff1a17b2967ec106abd663917c046a53d0221503857664f79fc5ef3.jpg",
+        "image_caption": [
+            "Figure 6: Failure Cases. Our system can struggle to roughly reconstruct shapes with very complex topology while some fine topology of the mesh is missing. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            184,
+            531,
+            823,
+            742
+        ],
+        "page_idx": 14
+    }
+]

parse/train/r154_g-Rb/r154_g-Rb.md

@@ -0,0 +1,255 @@
+# COMPOSABLE PLANNING WITH ATTRIBUTES
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+The tasks that an agent will need to solve often aren’t known during training. However, if the agent knows which properties of the environment are important, then after learning how its actions affect those properties the agent may be able to use this knowledge to solve complex tasks without training specifically for them. Towards this end, we consider a setup in which an environment is augmented with a set of user defined attributes that parameterize the features of interest. We propose a method that learns a policy for transitioning between “nearby” sets of attributes, and maintains a graph of possible transitions. Given a task at test time that can be expressed in terms of a target set of attributes, and a current state, our model infers the attributes of the current state and searches over paths through attribute space to get a high level plan, and then uses its low level policy to execute the plan. We show in grid-world games and 3D block stacking that our model is able to generalize to longer, more complex tasks at test time even when it only sees short, simple tasks at train time.
+
+# 1 INTRODUCTION
+
+Deep reinforcement learning has demonstrated impressive successes in building agents that can solve difficult tasks, e.g. Mnih et al. (2015); Silver et al. (2016). However, these successes have mostly been confined to situations where it is possible to train a large number of times on a single known task or distribution of tasks. On the other hand, in some situations, the tasks of interest are not known at training time or are too complex to be completed by uninformed exploration on a sparse set of rewards. In these situations, it may be that the cost of the supervision required to identify the important features of the environment, or to describe the space of possible tasks within it, is not so onerous. Recently several papers have taken this approach, for example Reed & de Freitas (2015); Andreas et al. (2017); Oh et al. (2017); Denil et al. (2017).
+
+If we expect an agent to be able to solve many different kinds of tasks, the representation of the task space is particularly important. In this paper, we impose structure on the task space through the use of attribute sets, a high-level abstraction of the environment state. The form of these are chosen by hand to capture task-relevant concepts, allowing both end goals as well as intermediate sub-tasks to be succinctly represented. As in Reed & de Freitas (2015); Andreas et al. (2017); Oh et al. (2017), we thus trade extra supervision for generalization.
+
+The attributes yield a natural space in which to plan: instead of searching over possible sequences of actions, we instead search over attribute sets. Once the agent learns how its actions affect the environment in terms of its relevant attributes, novel tasks can be solved compositionally by executing a plan consisting of a sequence of transitions between abstract states defined by those attributes. In the experiments below, we will show that in various environments, training only on simple tasks, our agents are able to generalize to novel, more complex tasks.
+
+# 2 MODEL
+
+We consider an agent in a Markov environment, i.e. at each time the agent observes the state $s$ and takes action $a$ , which uniquely determines the probability $P ( s , a , s ^ { \prime } )$ of transitioning from $s$ to $s ^ { \prime }$ . We augment the environment with a map $f : S  \{ \rho \}$ from states to a set of user-defined attributes $\rho$ . We assume that either $f$ is provided or a small set of hand-labeled $( s , \rho )$ pairs are provided in order to learning a mapping $\hat { f }$ . Hence, the attributes are human defined and constitute a form of supervision. Here we consider attributes that are sets of binary vectors. These user-specified attributes parameterize the set of goals that can be specified at test time.
+
+![](images/70e696fa0b3d09f6e36b8473581c706861e235d4eeb625aa215f50810ec0ec31.jpg)  
+Figure 1: Solving complex tasks by planning in attribute space. Each state is mapped to a set of binary attributes (orange/purple dots). Our semi-parametric model comprises a graph over sets of attributes (e.g. “there is a blue block left of the red block”), with edge weightings according to the probability that a parametric policy network is able to transition between adjacent pairs. The attributes themselves are manually specified, but inferred from the observation through a neural network; and the graph structure and policy are learned during training via random exploration of the environment. Given a goal attribute set (green), we use the graph to find the shortest path (red) to it in attribute space. The policy network then executes the actions at each stage (gold arrows).
+
+The model has three parts:
+
+1. a neural-net based attribute detector $\hat { f }$ , which maps states $s$ to a set of attributes $\rho$ , i.e. $\rho = f ( s )$ .   
+2. a neural net-based policy $\pi ( s , \rho _ { g } )$ which takes a pair of inputs: the current state $s$ and attributes of the goal state $\rho _ { g }$ . Its output is a distribution over actions.   
+3. a tabular transition function $c _ { \pi } ( \rho _ { i } , \rho _ { j } )$ that scores the possibility of $\pi ( s _ { \rho _ { i } } , \rho _ { j } )$ transiting successfully from $\rho _ { i }$ to $\rho _ { j }$ in a small number of steps.
+
+The transition table keeps track of the transitions seen in training, enabling a transition graph $G$ to be constructed that connects distant pairs of attributes. This high-level attribute graph is then searched at test time to find a path to the goal, with the policy network performing the low-level actions to transition between adjacent attributes.
+
+Since our model uses attributes for planning, we desire a property that we will call “ignorability” which says that the probability of being able to transition from $\rho _ { i }$ to $\rho _ { j }$ should only depend on the attributes $\rho _ { i }$ , not the exact state; i.e. $P _ { \pi } ( f ( s _ { t ^ { \prime } } ) = \rho _ { j } | f ( s _ { t } ) ) = P _ { \pi } ( f ( s _ { t ^ { \prime } } ) = \rho _ { j } | s _ { t } )$ 1. To the extent that this condition is violated, then transitions are aliased, and a planned transition may not be achievable by the policy from the particular state $s$ even though it’s achievable from other states with the same properties, causing the model to fail to achieve its goal. Note that in the experiments in 4.2, there will be nontrivial aliasing.
+
+# 2.1 MODEL TRAINING
+
+# 2.1.1 ATTRIBUTE DETECTOR $\hat { f }$
+
+The first step of training consists of fitting the attribute detectors $\hat { f }$ that map states $s$ to attributes $\rho$ . As mentioned above, we assume that there is a set of labeled (state, attribute) examples we can use for fitting this part of the model. Note that these examples are the only supervision given to the model during the entire training procedure.
+
+# 2.1.2 ATTRIBUTE TRANSITION MODELS $c$ AND $c _ { \pi }$
+
+To construct $c$ , the agent samples transitions from the environment, finding the sets of attributes which actually occur in the environment (from the potentially large number of all possible attributes). In the experiments below, we place the agent in a state at random with attributes $\rho _ { i }$ . It will then take a random action, or short sequence of actions. These lead to a new state with attributes $\rho _ { j }$ , and $c ( \rho _ { i } , \rho _ { j } )$ is incremented. This is repeated many times, building up statistics on possible transitions within attribute space. The resulting table represents a transition graph $G$ with vertices given by all the $\rho$ the agent has seen, and an edge between $\rho _ { i }$ and $\rho _ { j }$ counting the number of times the transition between $\rho _ { i }$ and $\rho _ { j }$ has occurred.
+
+This procedure produces the graph $G$ , but the counts in the graph are not normalized probabilities of transitioning from $\rho _ { i }$ to $\rho _ { j }$ (as we have never seen any negative samples). Therefore, given a low-level policy $\pi$ (see Sec. 2.1.3) we can optionally perform a second phase of training to learn the probability that for each $( \rho _ { i } , \rho _ { j } )$ in the graph, that if $\rho _ { i } = f ( s )$ then $\pi ( s , \rho _ { i } )$ will succeed at transitioning to $\rho _ { j }$ . At a random state $s$ with attributes $\rho _ { i }$ , we pick $\rho _ { j }$ from the set of goals for which $c ( \rho _ { i } , \rho _ { j } ) > 0$ and see if $\pi$ is able to achieve this goal. While doing this, we keep track of the fraction of attempts for which the policy was successful at this transition and store this probability in $c _ { \pi } ( \rho _ { i } , \rho _ { j } )$ .
+
+# 2.1.3 LOW LEVEL POLICY $\pi$
+
+Finally, we need to train a policy network $\pi = \pi ( s , \rho _ { g } )$ to solve simple tasks, i.e. those that require a few actions to move between nearby attribute sets. One way of training $\pi$ is as an “inverse model” in the style of Agrawal et al. (2016); Andrychowicz et al. (2017). In the first phase of training the graph, suppose we sample each initial state $s _ { 0 }$ and an action sequence $[ a _ { 0 } , a _ { 1 } , . . . , a _ { k } ]$ from the exploration policy, causing the agent to arrive at a new state with attributes $\rho _ { 1 }$ . We then treat $a _ { 0 }$ as the “correct” action for $\pi ( s _ { 0 } , \rho _ { 1 } )$ and update its parameters for this target. Alternatively, $\pi$ can be trained using reinforcement learning. After an initial graph $c$ is constructed, tasks can be chosen by sampling from states nearby the initial or current state properties.
+
+# 2.2 EVALUATING THE MODEL
+
+Once the model has been built we can use it for planning. That is, given an input state $s$ and target set of attributes $\rho _ { T }$ , we find a path $[ \rho _ { 0 } , \rho _ { 1 } , . . . , \rho _ { m } ]$ on the graph $G$ with $\rho _ { 0 } = f ( s )$ and $\rho _ { m } = \rho _ { T }$ maximizing
+
+$$
+\sum _ { i = 0 } ^ { m - 1 } \log c _ { \pi } ( \rho _ { i } , \rho _ { i + 1 } ) .
+$$
+
+The optimal path can be found using Dijkstra’s algorithm with a distance metric of $- \log ( c _ { \pi } ( \rho _ { i } , \rho _ { i + 1 } ) )$ . The policy is then used to move along the resulting path between attribute set, i.e. we take actions according to $a = \pi ( s , \rho _ { 1 } )$ , then once ${ \bar { f ( s ) } } = \rho _ { 1 }$ , we change to $a = \pi ( s , \rho _ { 2 } )$ and so on. At each intermediate step, if the current attributes don’t match the attributes on the computed path, then a new path is computed using the current attributes as a starting point (or, equivalently, the whole path is recomputed at each step).
+
+# 3 RELATED WORK
+
+Hierarchical RL Many researchers have recognized the importance of methods that can divide a MDP into subprocesses (Thrun & Schwartz, 1994; Parr & Russell, 1998; Sutton et al., 1999; Dietterich, 2000). Perhaps the most standard formalism today is the options framework of (Sutton et al., 1999), which deals with multistep “macro-actions” in the setting of reinforcement learning. Recent works, like Kulkarni et al. (2016), have shown how options can be used with function approximation via deep learning.
+
+Our work is also a hierarchical approach to controlling an agent in a Markovian environment. However, the paradigm we consider differs from reinforcement learning: we consider a setup where no reward or supervision is provided other than the $( s , \rho ( s ) )$ pairs, and show than an agent can learn to decompose a transition between far away $\rho , \rho ^ { \prime }$ into a sequence of short transitions. If we were to frame the problem as HRL, considering each $\pi ( \cdot , \rho )$ as a macro action2, in order for the agent to learn to sequence the $\pi ( \cdot , \rho _ { i } )$ , the environment would need to give reward for the completion of complex tasks, not just simple ones.
+
+As opposed to e.g. Kulkarni et al. (2016), where additional human supervision is used to allow exploration in the face of extremely sparse rewards, our goal is to show that adding human supervision to parameterize the task space via attributes allows compositionality through planning.
+
+Horde and descendants Our work is related to generalized value functions (Sutton et al., 2011) in that we have policies parameterized by state and target attributes. In particular, if we used a parameterized model for $c$ , it would be similar to the factored state-goal representation in Schaul et al. (2015). Recently, van Seijen et al. (2017) used human provided attributes as a general value function (GVF) in Ms. Pacman, showing that using a weighted combination of these can lead to higher scores than standard rewards. Although the representation used in that work is similar to the one we use, the motivation in our work is to allow generalization to new tasks; and we use the attributes to plan, rather than just as tools for building a reactive policy.
+
+Factored MDP and Relational MDP Our approach is closely related to factored MDP (Boutilier et al., 1995; 2000; Guestrin et al., 2003b). In these works, it is assumed that the environment can be represented by discrete attributes, and that transitions between the attributes by an action can be modeled as a Bayesian network. The value of each attribute after an action is postulated to depend in a known way on attributes from before the action. The present work differs from these in that the attributes do not determine the state and the dependency graph is not assumed to be known. More importantly, the focus in this work is on organizing the space of tasks through the attributes rather than being able to better plan a specific task; and in particular being able to generalize to new, more complex tasks at test time.
+
+Our approach is also related to Relational MDP and Object Oriented MDP (Hernandez-Gardiol & Kaelbling, 2003; van Otterlo, 2005; Diuk et al., 2008; Abel et al., 2015), where states are described as a set of objects, each of which is an instantiation of canonical classes, and each instantiated object has a set of attributes. Our work is especially related to Guestrin et al. (2003a), where the aim is to show that by using a relational representation of an MDP, a policy from one domain can generalize to a new domain. However, in the current work, the attributes are taken directly as functions of the state, as opposed to defined for object classes, and we do not have any explicit encoding of how objects interact. The model is given some examples of various attributes, and builds a parameterized model that maps into the attributes.
+
+The Programmable Agents of Denil et al. (2017) put the notions of objects and attributes (as in relational MDP) into an end-to-end differentiable neural architecture. Our work is similar to this one in that it includes learned mappings from states to attributes $\hat { f }$ in our work, detectors in theirs; although we do not learn these end-to-end), and experiments in the setting of manipulating blocks in a physics simulator. On the other hand, our model uses explicit search instead of an end-to-end neural architecture to reason over attributes. Moreover, in Denil et al. (2017), the agent is trained and tested on similar tasks, but the object properties at test are novel; whereas our model is trained on simple tasks but generalizes to complex ones.
+
+# Lifelong learning, multitask learning, and zero-shot learning
+
+There is a large literature on quickly adapting to a new learning problem given a set or a history of related learning problems. Our approach in this work shares ideas with the one in Isele et al. (2016), where tasks are augmented with descriptors and featurized. Our attributes correspond to these features. In that work, the coefficients of the task features in a sparse dictionary are used to weight a set of vectors defining the model for the associated task. In our work, the low level actor takes in the task features, but we learn how to transit between sets of features, and plan in that space. Similarly, the task is specified by a feature as an input into a model in Lopez-Paz & Ranzato (2017), again this corresponds to the way our low-level actor processes its goal.
+
+Several recent deep reinforcement learning works have used modular architectures and hierarchy to achieve generalization to new tasks. For example, Tessler et al. (2017) uses pre-trained skills for transfer. Oh et al. (2017) uses a meta-controller that selects parameterized skills and analogical supervision on outer-product structured tasks. Our assignments of attributes serves a similar purpose to their analogical supervision, and we use parameterized skills as these works do. However, our “meta-controller” is the search over attributes, rather than a reactive model.
+
+In Andreas et al. (2017), generalization is achieved through supervision in the form of “policy sketches”, which are symbolic representations of the high level steps necessary to complete a given task. The low level steps in executing modules in the sketches are composable. Our work is similar in that high level annotation is used to enable generalization, but the mechanism in this work is different. Note that the approaches in Andreas et al. (2017); Oh et al. (2017) are complementary to the one described here; in future work we wish to explore combining them.
+
+Semiparametric methods In this work we use an explicit memory of sets of attributes the model has seen. Several previous works have used non-parametric memories for lowering the sample complexity of learning, e.g. Blundell et al. (2016); Pritzel et al. (2017). Like these, we lean on the fact that with a good representation of a state, it can be useful to memorize what to do in given situation (having only done it a small number of times) and explicitly look it up. In our case, the “good representation” is informed by the user-specified attributes.
+
+Our approach is also related to Machado et al. (2017), which builds up a multiscale representation of an MDP using Eigenvectors of the transition matrix of the MDP, in the sense that we collect data on possible transitions between attributes in a first phase of training, and then use this knowledge at test time.
+
+Attributes in vision Farhadi et al. (2009) and Lampert et al. (2009) explore visual attributes as a natural intermediate representation for object recognition tasks, demonstrating their effectiveness in one/low-shot settings. Subsequent work has applied the concept to fine-grained recognition (Duan et al., 2012), people’s appearance/clothing (Zhang et al., 2014) and relative judgements (Parikh & Grauman, 2011). However, all these are static I.I.D settings, in contrast to dynamic agent/environment that this work explores.
+
+# 4 EXPERIMENTS
+
+We evaluate our approach (Attribute Planner, abbreviated to $A P$ ) in three different environments. The first two are randomly generated grid-worlds, and the third is a simulation of stacking blocks. In each environment, the goal of the model is to be able to generalize to testing on complex tasks from training on simpler tasks.
+
+We compare against baseline policies trained in several ways. These baseline policies take the state and goal as inputs, and use the same neural network architecture as the policy used for the Attribute Planner.
+
+1. Reinforcement Learning: Policies trained via reinforcement learning with A3C (Mnih et al., 2016) or Reinforce. We consider three variants of training: (i) training only with nearby goals (one attribute transition for grid-world; single actions for block stacking); (ii) training on the evaluation tasks; and (iii) training on a curriculum that transitions from nearby goals to evaluation tasks. Policies (ii) and (iii) are trained on full sequences, thus have an inherent advantage over our model, which only sees short sequences during training.   
+2. Inverse: An inverse model trained in a “supervised” fashion on a dataset of observed trajectories to predict the next action given the state and goal. We train on nearby goals and on longer multi-step tasks.
+
+# 4.1 2-D WORLDS
+
+We implemented two types of small 2- $. D$ environments in Mazebase (Sukhbaatar et al., 2015), where the worlds are randomly generated for each episode. The action space for each consists of movements in the four cardinal directions, and additional environment specific actions.
+
+Colored Switches The first environment consists of four switches, each with four possible colors. An extra toggle action cycles the color of a switch if the agent is standing on it. The attributes for this environment are the states of the switches; and the tasks are to change the switches into a specified configuration, as shown in Fig. 2(right). The locations and colors of the switches are randomly initialized for each episode.
+
+Crafting In the second environment, similar to the one used in Andreas et al. (2017) an agent needs to collect resources and combine them to form items. In addition to moving in the cardinal directions, the agent has a “grab” action that allows it to pick up a resource from the current location and add it to its inventory. If there is no item where the agent is standing, this action does nothing. The agent also has a “craft” action that combines a set of items to create a new item if the agent has the prerequisite items in its inventory and the agent is standing on a special square (a “crafting table”) corresponding to the item to be crafted. If these two conditions are not both met, the “craft” action does nothing. The attributes for this environment are the items in the inventory, and task is to add a specified item to the inventory. In the environment, there are three types of resources and three types of products (see Fig. 2(left)). The episodes are initialized randomly by removing some resources, and adding some items to the inventory.
+
+![](images/90bf30f100a426d3873f3b1558a4c751c1d2761eee1695cfb6bb790c71fe9f95.jpg)  
+! + ! = + + ! =+ + ! =Figure 2: Left: Crafting mazebase game. Right: Colored switches game. See text for details.
+
+1 1The observation is given as a bag of words in both environments, where the words correspond to (feature, location). Features consist of item types, names, and their other properties. The locations 1include position relative to the agent in the maze, and also a few special slots for inventory, current, and target attributes.
+
+The first phase building the high level transitions as in Section 2.1.2 is done by running a random 1 1agent in the environment from a random state until one or more attributes change. Then this change of attribute is recorded as an edge in graph $G$ . The low level policy is trained concurrently with the second phase of Section 2.1.2. We use the current edge estimates in the graph to propose a target set of attributes, and the low level policy is trained with the Reinforce algorithm (Williams, 1992) to reach that set of attributes from the current state. These training episodes terminate when the task completes or after 80 steps; and a reward of -0.1 is given at every step to encourage the agent to complete the task quickly. The policy network is a fully connected network with two hidden layers of 100 units. We run each experiment three times with different random seeds, and report the mean success rate.
+
+In the switches environment, multi-step (test) tasks are generated by setting a random attribute as target, which can require up to 12 attribute transitions. In the crafting environment, multi-step (test) tasks are generated by randomly selecting an item as a target. Since we do not care about other items in the inventory, the target state is underspecified. Some tasks are pre-solved because the randomly chosen target item can already be in the inventory. However, such tasks have no effect on training and are also removed during testing.
+
+In curriculum training which we use as a baseline, we gradually increase the upper bound on the difficulty of tasks. In the switches environment, the difficulty corresponds to the number of toggles necessary for solving the task. The craft environment has two levels of difficulty: tasks can be completed by a single grab or craft action, and tasks that require multiple such actions.
+
+During the second phase of training, we simultaneously compute the transition function $c _ { \pi } ( \rho _ { i } , \rho _ { j } )$ using an exponentially decaying average of success rates of the low level policy $\pi$ :
+
+$$
+c _ { \pi } ( \rho _ { i } , \rho _ { j } ) = \frac { \sum _ { t = 1 } ^ { T } \gamma ^ { T - t } M _ { \pi } ^ { t } ( \rho _ { i } , \rho _ { j } ) } { \sum _ { t = 1 } ^ { T } \gamma ^ { T - t } N _ { \pi } ^ { t } ( \rho _ { i } , \rho _ { j } ) } ,
+$$
+
+where $T$ is the number of training epochs, $N _ { \pi } ^ { t }$ is the number of task $( \rho _ { i } , \rho _ { j } )$ during epoch $t$ , and $M _ { \pi } ^ { t }$ is the number of successful episodes among them. A decay rate of $\gamma = 0 . 9$ is used.
+
+Table 1 compares our Attribute Planner (AP) model to a Reinforce baseline on the Crafting and Colored Switches tasks. In all cases, the baseline performs poorly, while the AP model has a high success rate. The importance of the graph is apparent: when it is removed (Reinforce method) the performance drops significantly on multi-step tasks.
+
+Table 1: Task success rate on Mazebase environments. Our Attribute Planner (AP) approach performs much better than the reactive policies trained with Reinforce. The addition of the attribute graph (over Reinforce only model) is crucial for multi-step evaluation tasks.   
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Training data</td><td colspan="2">Switches</td><td colspan="2">Crafting</td></tr><tr><td>single</td><td>multi</td><td>single</td><td>multi</td></tr><tr><td>Reinforce</td><td>multi-step</td><td>0.0%</td><td>0.0%</td><td>45.7%</td><td>28.6%</td></tr><tr><td>Reinforce</td><td> multi-step + curriculum</td><td>33.6%</td><td>33.3%</td><td>94.9%</td><td>83.9%</td></tr><tr><td>Reinforce</td><td>one-step</td><td>99.0%</td><td>15.4%</td><td>98.7%</td><td>49.0%</td></tr><tr><td>AP</td><td>one-step</td><td>99.0%</td><td>83.1%</td><td>98.7%</td><td>96.2%</td></tr></table>
+
+# 4.2 STACKING BLOCKS
+
+We consider a 3D block stacking task in the Mujoco environment Todorov et al. (2012). There are 4 blocks of different colors, and actions consist of dropping a block in a $3 \times 3$ grid of positions, resulting in 36 total actions. A block cannot be moved when it is underneath another block, so some actions have no effect. The input to the model is the observed image, and there are a total of 36 binary properties corresponding to the relative $\mathbf { X }$ and y positions of the blocks and whether blocks are stacked on one another. For example, one property corresponds to “blue is on top of yellow”. Each training episode is initiated from a random initial state and lasts only one step, i.e. dropping a single block in a new location.
+
+The policy network takes (i) a $1 2 8 \times 1 2 8$ image, which is featurized by a CNN with five convolutional layers and one fully connected (fc) layer to produce a 128d vector; and (ii) goal properties expressed as a 48d binary vector, which are transformed to a 128d vector. The two 128d vectors are concatenated and combined by two fc layers followed by softmax to produce an output distribution over actions. We use an exponential linear nonlinearity after each layer.
+
+Table 2 compares the performance of different models on several block stacking tasks. In the onestep task, a goal is chosen that is the result of taking a single random action. In the multi-step task, the goal is chosen as the properties of a new random initialization. These tasks typically require $3 - 8$ steps to complete. In the 4-stack task, the goal is a vertical stack of blocks in the order red, green, blue, yellow. We compare the performance of our model to reactive policy baselines trained on single-step tasks, complex multi-step tasks or with a curriculum of both. We perform each evaluation task 1000 times.
+
+The single-step reactive policies perform well on single step tasks (which are what it sees at train time), but perform much worse compared to the AP model when transferred to multi-step tasks. The AP model without the second step of training that learns $c _ { \pi }$ also performs substantially worse on multi-step tasks, demonstrating the importance of properly normalized transition probabilities to avoid aliased states.
+
+The rightmost two columns of Table 2 consider underspecified goals, where only a subset of the attributes are provided. These are identical to their fully-specified counterparts, except that each attribute is left unspecified with probability $30 \%$ . The AP model handles these naturally by finding the shorted path to any satisfactory attribute set. We consider reactive baselines that are trained on the same distribution of underspecified attribute sets. Despite this, we observe that reactive policy performance degrades when goals are underspecified, while our AP model does not.
+
+The attribute detector $\hat { f }$ predicts the full attribute set with $< 0 . 1 \%$ error when trained on the full dataset of 1 million examples. If trained on only 10,000 examples, the attribute detector has an error rate of $1 . 4 \%$ . Training the AP model with this less-accurate attribute detector degrades multi-step performance by only $0 . 9 \%$ .
+
+Property Aliasing: The “ignorability” assumption we made in Section 2 is violated in the block stacking task. To see why, consider a transition from “red left of blue and yellow” to “red right of blue and yellow”. This can typically be accomplished in one step, but if blue and yellow are already on the far right, it cannot. Thus, states where this transition are possible and impossible are aliased with the same properties. This is the dominant source of errors on the multi-step task when trained on large sample sizes (in fact, it is the only source of errors as the policy approaches $1 0 0 \%$
+
+Table 2: Model comparison on block stacking task accuracy. Baselines marked ‘multi-step’ or ‘curriculum‘ get to see complex multi-step tasks at train time. The Attribute Planner (AP) generalizes from one-step training to multi-step and underspecified tasks with high accuracy, while reinforcement learning and inverse model training do not. AP outperforms A3C even with a curriculum of tasks. Ablating the normalized graph transition table $c _ { \pi }$ degrades AP performance substantially on multi-step tasks due to aliasing. Inverse one-step model was trained on 2 million examples, inverse multi-step and AP models were trained on 1 million examples, A3C models were trained to convergence.   
+
+<table><tr><td>Model</td><td>Training Data</td><td>one-step</td><td>multi-step</td><td>4-stack</td><td>one-step underspecified</td><td>multi-step</td></tr><tr><td>A3C</td><td>one-step</td><td>98.5%</td><td>8.1%</td><td>1.9%</td><td>65.7%</td><td>6.6%</td></tr><tr><td>A3C</td><td>multi-step</td><td>2.6%</td><td>0%</td><td>0%</td><td>5.3%</td><td>0%</td></tr><tr><td>A3C</td><td>curriculum</td><td>98.2%</td><td>17%</td><td>2.9%</td><td>8.2%</td><td>0.2%</td></tr><tr><td>Inverse</td><td>one-step</td><td>100%</td><td>9.1%</td><td>0.5%</td><td>98.8%</td><td>18.8%</td></tr><tr><td>Inverse</td><td>multi-step</td><td>94.1%</td><td>13.7%</td><td>4.6%</td><td>71.2%</td><td>9.6%</td></tr><tr><td>AP (no Cπ)</td><td> one-step</td><td>74.5%</td><td>29.7%</td><td>62.2%</td><td>81.8%</td><td>28.1%</td></tr><tr><td>AP</td><td>one-step</td><td>98.8%</td><td>66.7%</td><td>98.5%</td><td>97.8%</td><td>63.5%</td></tr></table>
+
+<table><tr><td rowspan="2"># of Training Examples</td><td colspan="2">Inverse</td><td colspan="2">AP</td></tr><tr><td>one-step</td><td>multi-step</td><td>one-step</td><td>multi-step</td></tr><tr><td>10,000</td><td>35.5%</td><td>1.6%</td><td>50.0%</td><td>3.0%</td></tr><tr><td>100,000</td><td>99.9%</td><td>7.8%</td><td>89.0%</td><td>47.0%</td></tr><tr><td>1,000,000</td><td>100%</td><td>9.1%</td><td>98.9%</td><td>66.7%</td></tr><tr><td>10,000,000</td><td>100%</td><td>8.5%</td><td>96.5%</td><td>70.7%</td></tr></table>
+
+Table 3: Effect of the number of (one-step) training examples on one-step and multi-step performance, for an inverse model and the Attribute Planner model. The inverse models are trained on $2 \mathbf { x }$ the samples, including the samples generated from learning $c _ { \pi }$ in our AP method.
+
+accuracy and the graph becomes complete). Figure 4 shows an example plan that becomes stuck due to aliasing.
+
+The second step of training, that computes the probability of $\pi$ transitioning on each edge, is important for mitigating the effects of aliasing in the block stacking task. The graph search finds the path with the highest probability of success (i.e. the product of probabilities on each edge), so it avoids edges that have high aliasing. In the AP model trained on one million samples, the second step of training improves multi-step performance from $2 9 . 7 \%$ to $6 6 . 7 \%$ , as shown in Table 2.
+
+# 5 DISCUSSION
+
+Our results show that structuring the space of tasks with high level attributes allows an agent to compose policies for the solutions of simple tasks into solutions of more complex tasks. The agent plans a path to the final goal at the level of the attributes, and executes the steps in this path with a reactive policy. Thus, supervision of an agent by labeling attributes can lead to generalization from simple tasks at train time to more complex tasks at test time. Nevertheless, there are many fronts for further work:
+
+Sample complexity of the planning module: In Table 5 we can see both the benefits and the liabilities of the explicit non-parametric form for $c$ . By 10K samples, the parametric lower level policy is already able to have a reasonable success rate. However, because in this environment, there are roughly 200K edges in the graph, most of the edges have not been seen, and without any weight-sharing, our model cannot estimate these transition probabilities. On the other hand, by 100K samples the model has seen enough of the graph to make nontrivial plans; and the non-parametric form of the graph makes planning straightforward. In future work, we hope to combine parametric models for $c$ with search to increase the sample efficiency of the planning module. Alternatively, we might hope to make progress on dynamic abstraction (projecting out some of the attributes) depending on the current state and goal, which would make the effective number of edges of the graph smaller.
+
+![](images/28355570631ffc144872cd6f11841f5407f326abc233c5b68f14159249e3594a.jpg)  
+Figure 3: Two examples of block stacking evaluation tasks. The initial/target states are shown in the first/last columns. Successful completions of our Attribute Planner model are shown in rows 1 and 3. By contrast, the A3C baseline is unable to perform the tasks (rows 2 and 4).
+
+![](images/35f4098d826e9a1a5ae3af6917e525e9329c4b3a9e2f382cb0d7bf06f8ec0fc0.jpg)  
+Figure 4: Plans become stuck when states with different transitions map to the same properties. In frame 4 of this example, the policy is directed to place the green block in front of the red and blue blocks, but this is impossible because the blue and red are already in the frontmost position.
+
+Exploration Although we discuss an agent in an environment, we have elided many of the difficult problems of reinforcement learning. In particular, the environments considered in this work allow sampling low level transitions by starting at random states and following random policies, and these are sufficient to cover the state space, although we note that the method for training the model described in Section 2.1 allows for more sophisticated exploration policies. Thus we sidestep the exploration problem, one of the key difficulties of reinforcement learning. Nevertheless, building composable models even in this setting is nontrivial, and our view is that it is important to demonstrate success here (and decouple issues of exploration and composability) before moving on to the full RL problem.
+
+We believe that the attributes $\rho$ and $c$ , in addition to their usefulness for planning, provide a framework for incentivizing exploration. The agent can be rewarded for finding unseen (or rarely-seen) high level transitions, or for validating or falsifying hypotheses about the existence of entries of $c$ .
+
+Learning the attributes: Discovering the attributes automatically would remove much of the need for human supervision. Recent work, such as Thomas et al. (2017), demonstrates how this could be done. Another avenue for discovering attributes is to use a few “seed” attributes; and use aliasing as a signal that some attributes need to be refined.
+
+# REFERENCES
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+Tejas D. Kulkarni, Karthik Narasimhan, Ardavan Saeedi, and Josh Tenenbaum. Hierarchical deep reinforcement learning: Integrating temporal abstraction and intrinsic motivation. In NIPS, pp. 3675–3683, 2016.   
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+David Lopez-Paz and Marc’Aurelio Ranzato. Gradient episodic memory for continuum learning. CoRR, abs/1706.08840, 2017.   
+Marlos C. Machado, Marc G. Bellemare, and Michael H. Bowling. A laplacian framework for option discovery in reinforcement learning. In ICML, volume 70 of Proceedings of Machine Learning Research, pp. 2295–2304. PMLR, 2017.   
+Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Andrei A. Rusu, Joel Veness, Marc G. Bellemare, Alex Graves, Martin Riedmiller, Andreas K. Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wierstra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533, February 2015.   
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+David Silver, Aja Huang, Chris J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of Go with deep neural networks and tree search. Nature, 529(7587):484–489, January 2016.   
+Sainbayar Sukhbaatar, Arthur Szlam, Gabriel Synnaeve, Soumith Chintala, and Rob Fergus. Mazebase: A sandbox for learning from games. arXiv preprint arXiv:1511.07401, 2015.   
+Richard Sutton, Doina Precup, and Satinder Singh. Between mdps and semi-mdps: A framework for temporal abstraction in reinforcement learning. Artificial Intelligence, 112:181–211, 1999.   
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+
+# A ADDING EXPLORATION
+
+We also look into the use of exploration and learn a policy to promote exploration of undiscovered edges in our planning graph. We give a negative reward proportional to $\frac { \mathbf { \dot { \phi } } _ { t } } { \sqrt { n } }$ where $n$ is the number of times that edge has been encountered before and $t$ the time episode. We compare this with a baseline method of single random start and random action selection over $N$ and the method used in the main paper, with $N$ random starts and single rollouts.
+
+# A.1 MAZEBASE RESULTS
+
+Our Mazebase environments in Section 4.1 are designed so that all edges can be discovered without much exploration. So to better test the benefit of exploration, we modified the craft environment to make discovering all edges harder. First, we added 4 new “super” products that can be crafted by combining one normal product with another resource, or three resources. Second, the environment always starts with only 3 resources and an empty inventory. Therefore, it is much harder to discover a super product because it requires agent to craft a product out of two resources, and then pick another resource and craft.
+
+In this hard crafting environment, a random agent discovered 18.6 edges on average, while an agent with the exploration reward discovered all 25 edges of the environment. We used this complete graph to train our AP model and other baselines. Training on one-step tasks require episodes to start from different nodes of the graph, but the environment always initializes at the same node. A simple solution was not to reset the environment between episodes if the previous episode was successful. Thus the next episodes will start from a different node. Table 4 shows the success rates on multi-step tasks, where our AP model clearly outperforms the other baselines.
+
+<table><tr><td>Method</td><td>Training data</td><td>Hard Crafting (multi-step)</td></tr><tr><td>Reinforce</td><td>multi-step + curriculum</td><td>51.5%</td></tr><tr><td>Reinforce</td><td>one-step</td><td>26.0%</td></tr><tr><td>AP</td><td>one-step</td><td>99.8%</td></tr></table>
+
+Table 4: Task success rate on multi-step task in the hard crafting environment. Our Attribute Planner clearly outperforms other baseline approaches.
+
+# A.2 STACKING BLOCKS RESULTS
+
+Table 5: Effect of the number of (one-step) training examples on one-step and multi-step performance, for an inverse model and the Attribute Planner model. The inverse models are trained on $2 \mathbf { x }$ the samples, including the samples generated from learning $c _ { \pi }$ in our AP method.   
+
+<table><tr><td rowspan="2"># of Training Examples</td><td colspan="2">Policy</td><td colspan="2">Random</td><td colspan="2">Main Method</td></tr><tr><td>edges</td><td> accuracy</td><td>edges</td><td>accuracy</td><td>edges</td><td>accuracy</td></tr><tr><td>100,000</td><td>44k</td><td>49.4%</td><td>49k</td><td>49.7%</td><td>38k</td><td>47.0%</td></tr><tr><td>1,000,000</td><td>120k</td><td>67.5%</td><td>130k</td><td>69.8%</td><td>114k</td><td>66.7%</td></tr><tr><td>10,000,000</td><td>139k</td><td>80.6%</td><td>138k</td><td>83.1%</td><td>218k</td><td>70.7%</td></tr></table>

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+        "text": "COMPOSABLE PLANNING WITH ATTRIBUTES ",
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+        "text": "Anonymous authors Paper under double-blind review ",
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "page_idx": 0
+    },
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+        "text": "The tasks that an agent will need to solve often aren’t known during training. However, if the agent knows which properties of the environment are important, then after learning how its actions affect those properties the agent may be able to use this knowledge to solve complex tasks without training specifically for them. Towards this end, we consider a setup in which an environment is augmented with a set of user defined attributes that parameterize the features of interest. We propose a method that learns a policy for transitioning between “nearby” sets of attributes, and maintains a graph of possible transitions. Given a task at test time that can be expressed in terms of a target set of attributes, and a current state, our model infers the attributes of the current state and searches over paths through attribute space to get a high level plan, and then uses its low level policy to execute the plan. We show in grid-world games and 3D block stacking that our model is able to generalize to longer, more complex tasks at test time even when it only sees short, simple tasks at train time. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+            334,
+            478
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+        "page_idx": 0
+    },
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+        "type": "text",
+        "text": "Deep reinforcement learning has demonstrated impressive successes in building agents that can solve difficult tasks, e.g. Mnih et al. (2015); Silver et al. (2016). However, these successes have mostly been confined to situations where it is possible to train a large number of times on a single known task or distribution of tasks. On the other hand, in some situations, the tasks of interest are not known at training time or are too complex to be completed by uninformed exploration on a sparse set of rewards. In these situations, it may be that the cost of the supervision required to identify the important features of the environment, or to describe the space of possible tasks within it, is not so onerous. Recently several papers have taken this approach, for example Reed & de Freitas (2015); Andreas et al. (2017); Oh et al. (2017); Denil et al. (2017). ",
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+    {
+        "type": "text",
+        "text": "If we expect an agent to be able to solve many different kinds of tasks, the representation of the task space is particularly important. In this paper, we impose structure on the task space through the use of attribute sets, a high-level abstraction of the environment state. The form of these are chosen by hand to capture task-relevant concepts, allowing both end goals as well as intermediate sub-tasks to be succinctly represented. As in Reed & de Freitas (2015); Andreas et al. (2017); Oh et al. (2017), we thus trade extra supervision for generalization. ",
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+    {
+        "type": "text",
+        "text": "The attributes yield a natural space in which to plan: instead of searching over possible sequences of actions, we instead search over attribute sets. Once the agent learns how its actions affect the environment in terms of its relevant attributes, novel tasks can be solved compositionally by executing a plan consisting of a sequence of transitions between abstract states defined by those attributes. In the experiments below, we will show that in various environments, training only on simple tasks, our agents are able to generalize to novel, more complex tasks. ",
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+        "text": "2 MODEL ",
+        "text_level": 1,
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+    {
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+        "text": "We consider an agent in a Markov environment, i.e. at each time the agent observes the state $s$ and takes action $a$ , which uniquely determines the probability $P ( s , a , s ^ { \\prime } )$ of transitioning from $s$ to $s ^ { \\prime }$ . We augment the environment with a map $f : S  \\{ \\rho \\}$ from states to a set of user-defined attributes $\\rho$ . We assume that either $f$ is provided or a small set of hand-labeled $( s , \\rho )$ pairs are provided in order to learning a mapping $\\hat { f }$ . Hence, the attributes are human defined and constitute a form of supervision. Here we consider attributes that are sets of binary vectors. These user-specified attributes parameterize the set of goals that can be specified at test time. ",
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+        "image_caption": [
+            "Figure 1: Solving complex tasks by planning in attribute space. Each state is mapped to a set of binary attributes (orange/purple dots). Our semi-parametric model comprises a graph over sets of attributes (e.g. “there is a blue block left of the red block”), with edge weightings according to the probability that a parametric policy network is able to transition between adjacent pairs. The attributes themselves are manually specified, but inferred from the observation through a neural network; and the graph structure and policy are learned during training via random exploration of the environment. Given a goal attribute set (green), we use the graph to find the shortest path (red) to it in attribute space. The policy network then executes the actions at each stage (gold arrows). "
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+        "text": "The model has three parts: ",
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+    {
+        "type": "text",
+        "text": "1. a neural-net based attribute detector $\\hat { f }$ , which maps states $s$ to a set of attributes $\\rho$ , i.e. $\\rho = f ( s )$ .   \n2. a neural net-based policy $\\pi ( s , \\rho _ { g } )$ which takes a pair of inputs: the current state $s$ and attributes of the goal state $\\rho _ { g }$ . Its output is a distribution over actions.   \n3. a tabular transition function $c _ { \\pi } ( \\rho _ { i } , \\rho _ { j } )$ that scores the possibility of $\\pi ( s _ { \\rho _ { i } } , \\rho _ { j } )$ transiting successfully from $\\rho _ { i }$ to $\\rho _ { j }$ in a small number of steps. ",
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+    {
+        "type": "text",
+        "text": "The transition table keeps track of the transitions seen in training, enabling a transition graph $G$ to be constructed that connects distant pairs of attributes. This high-level attribute graph is then searched at test time to find a path to the goal, with the policy network performing the low-level actions to transition between adjacent attributes. ",
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+        "type": "text",
+        "text": "Since our model uses attributes for planning, we desire a property that we will call “ignorability” which says that the probability of being able to transition from $\\rho _ { i }$ to $\\rho _ { j }$ should only depend on the attributes $\\rho _ { i }$ , not the exact state; i.e. $P _ { \\pi } ( f ( s _ { t ^ { \\prime } } ) = \\rho _ { j } | f ( s _ { t } ) ) = P _ { \\pi } ( f ( s _ { t ^ { \\prime } } ) = \\rho _ { j } | s _ { t } )$ 1. To the extent that this condition is violated, then transitions are aliased, and a planned transition may not be achievable by the policy from the particular state $s$ even though it’s achievable from other states with the same properties, causing the model to fail to achieve its goal. Note that in the experiments in 4.2, there will be nontrivial aliasing. ",
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+        "type": "text",
+        "text": "2.1 MODEL TRAINING ",
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+        "type": "text",
+        "text": "2.1.1 ATTRIBUTE DETECTOR $\\hat { f }$ ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The first step of training consists of fitting the attribute detectors $\\hat { f }$ that map states $s$ to attributes $\\rho$ . As mentioned above, we assume that there is a set of labeled (state, attribute) examples we can use for fitting this part of the model. Note that these examples are the only supervision given to the model during the entire training procedure. ",
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+    {
+        "type": "text",
+        "text": "2.1.2 ATTRIBUTE TRANSITION MODELS $c$ AND $c _ { \\pi }$ ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "To construct $c$ , the agent samples transitions from the environment, finding the sets of attributes which actually occur in the environment (from the potentially large number of all possible attributes). In the experiments below, we place the agent in a state at random with attributes $\\rho _ { i }$ . It will then take a random action, or short sequence of actions. These lead to a new state with attributes $\\rho _ { j }$ , and $c ( \\rho _ { i } , \\rho _ { j } )$ is incremented. This is repeated many times, building up statistics on possible transitions within attribute space. The resulting table represents a transition graph $G$ with vertices given by all the $\\rho$ the agent has seen, and an edge between $\\rho _ { i }$ and $\\rho _ { j }$ counting the number of times the transition between $\\rho _ { i }$ and $\\rho _ { j }$ has occurred. ",
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "This procedure produces the graph $G$ , but the counts in the graph are not normalized probabilities of transitioning from $\\rho _ { i }$ to $\\rho _ { j }$ (as we have never seen any negative samples). Therefore, given a low-level policy $\\pi$ (see Sec. 2.1.3) we can optionally perform a second phase of training to learn the probability that for each $( \\rho _ { i } , \\rho _ { j } )$ in the graph, that if $\\rho _ { i } = f ( s )$ then $\\pi ( s , \\rho _ { i } )$ will succeed at transitioning to $\\rho _ { j }$ . At a random state $s$ with attributes $\\rho _ { i }$ , we pick $\\rho _ { j }$ from the set of goals for which $c ( \\rho _ { i } , \\rho _ { j } ) > 0$ and see if $\\pi$ is able to achieve this goal. While doing this, we keep track of the fraction of attempts for which the policy was successful at this transition and store this probability in $c _ { \\pi } ( \\rho _ { i } , \\rho _ { j } )$ . ",
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+    {
+        "type": "text",
+        "text": "2.1.3 LOW LEVEL POLICY $\\pi$ ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Finally, we need to train a policy network $\\pi = \\pi ( s , \\rho _ { g } )$ to solve simple tasks, i.e. those that require a few actions to move between nearby attribute sets. One way of training $\\pi$ is as an “inverse model” in the style of Agrawal et al. (2016); Andrychowicz et al. (2017). In the first phase of training the graph, suppose we sample each initial state $s _ { 0 }$ and an action sequence $[ a _ { 0 } , a _ { 1 } , . . . , a _ { k } ]$ from the exploration policy, causing the agent to arrive at a new state with attributes $\\rho _ { 1 }$ . We then treat $a _ { 0 }$ as the “correct” action for $\\pi ( s _ { 0 } , \\rho _ { 1 } )$ and update its parameters for this target. Alternatively, $\\pi$ can be trained using reinforcement learning. After an initial graph $c$ is constructed, tasks can be chosen by sampling from states nearby the initial or current state properties. ",
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+        "type": "text",
+        "text": "2.2 EVALUATING THE MODEL ",
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+        "type": "text",
+        "text": "Once the model has been built we can use it for planning. That is, given an input state $s$ and target set of attributes $\\rho _ { T }$ , we find a path $[ \\rho _ { 0 } , \\rho _ { 1 } , . . . , \\rho _ { m } ]$ on the graph $G$ with $\\rho _ { 0 } = f ( s )$ and $\\rho _ { m } = \\rho _ { T }$ maximizing ",
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+        "text": "$$\n\\sum _ { i = 0 } ^ { m - 1 } \\log c _ { \\pi } ( \\rho _ { i } , \\rho _ { i + 1 } ) .\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "The optimal path can be found using Dijkstra’s algorithm with a distance metric of $- \\log ( c _ { \\pi } ( \\rho _ { i } , \\rho _ { i + 1 } ) )$ . The policy is then used to move along the resulting path between attribute set, i.e. we take actions according to $a = \\pi ( s , \\rho _ { 1 } )$ , then once ${ \\bar { f ( s ) } } = \\rho _ { 1 }$ , we change to $a = \\pi ( s , \\rho _ { 2 } )$ and so on. At each intermediate step, if the current attributes don’t match the attributes on the computed path, then a new path is computed using the current attributes as a starting point (or, equivalently, the whole path is recomputed at each step). ",
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+    {
+        "type": "text",
+        "text": "3 RELATED WORK ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Hierarchical RL Many researchers have recognized the importance of methods that can divide a MDP into subprocesses (Thrun & Schwartz, 1994; Parr & Russell, 1998; Sutton et al., 1999; Dietterich, 2000). Perhaps the most standard formalism today is the options framework of (Sutton et al., 1999), which deals with multistep “macro-actions” in the setting of reinforcement learning. Recent works, like Kulkarni et al. (2016), have shown how options can be used with function approximation via deep learning. ",
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+    {
+        "type": "text",
+        "text": "Our work is also a hierarchical approach to controlling an agent in a Markovian environment. However, the paradigm we consider differs from reinforcement learning: we consider a setup where no reward or supervision is provided other than the $( s , \\rho ( s ) )$ pairs, and show than an agent can learn to decompose a transition between far away $\\rho , \\rho ^ { \\prime }$ into a sequence of short transitions. If we were to frame the problem as HRL, considering each $\\pi ( \\cdot , \\rho )$ as a macro action2, in order for the agent to learn to sequence the $\\pi ( \\cdot , \\rho _ { i } )$ , the environment would need to give reward for the completion of complex tasks, not just simple ones. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "As opposed to e.g. Kulkarni et al. (2016), where additional human supervision is used to allow exploration in the face of extremely sparse rewards, our goal is to show that adding human supervision to parameterize the task space via attributes allows compositionality through planning. ",
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+    {
+        "type": "text",
+        "text": "Horde and descendants Our work is related to generalized value functions (Sutton et al., 2011) in that we have policies parameterized by state and target attributes. In particular, if we used a parameterized model for $c$ , it would be similar to the factored state-goal representation in Schaul et al. (2015). Recently, van Seijen et al. (2017) used human provided attributes as a general value function (GVF) in Ms. Pacman, showing that using a weighted combination of these can lead to higher scores than standard rewards. Although the representation used in that work is similar to the one we use, the motivation in our work is to allow generalization to new tasks; and we use the attributes to plan, rather than just as tools for building a reactive policy. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Factored MDP and Relational MDP Our approach is closely related to factored MDP (Boutilier et al., 1995; 2000; Guestrin et al., 2003b). In these works, it is assumed that the environment can be represented by discrete attributes, and that transitions between the attributes by an action can be modeled as a Bayesian network. The value of each attribute after an action is postulated to depend in a known way on attributes from before the action. The present work differs from these in that the attributes do not determine the state and the dependency graph is not assumed to be known. More importantly, the focus in this work is on organizing the space of tasks through the attributes rather than being able to better plan a specific task; and in particular being able to generalize to new, more complex tasks at test time. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our approach is also related to Relational MDP and Object Oriented MDP (Hernandez-Gardiol & Kaelbling, 2003; van Otterlo, 2005; Diuk et al., 2008; Abel et al., 2015), where states are described as a set of objects, each of which is an instantiation of canonical classes, and each instantiated object has a set of attributes. Our work is especially related to Guestrin et al. (2003a), where the aim is to show that by using a relational representation of an MDP, a policy from one domain can generalize to a new domain. However, in the current work, the attributes are taken directly as functions of the state, as opposed to defined for object classes, and we do not have any explicit encoding of how objects interact. The model is given some examples of various attributes, and builds a parameterized model that maps into the attributes. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The Programmable Agents of Denil et al. (2017) put the notions of objects and attributes (as in relational MDP) into an end-to-end differentiable neural architecture. Our work is similar to this one in that it includes learned mappings from states to attributes $\\hat { f }$ in our work, detectors in theirs; although we do not learn these end-to-end), and experiments in the setting of manipulating blocks in a physics simulator. On the other hand, our model uses explicit search instead of an end-to-end neural architecture to reason over attributes. Moreover, in Denil et al. (2017), the agent is trained and tested on similar tasks, but the object properties at test are novel; whereas our model is trained on simple tasks but generalizes to complex ones. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Lifelong learning, multitask learning, and zero-shot learning ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "There is a large literature on quickly adapting to a new learning problem given a set or a history of related learning problems. Our approach in this work shares ideas with the one in Isele et al. (2016), where tasks are augmented with descriptors and featurized. Our attributes correspond to these features. In that work, the coefficients of the task features in a sparse dictionary are used to weight a set of vectors defining the model for the associated task. In our work, the low level actor takes in the task features, but we learn how to transit between sets of features, and plan in that space. Similarly, the task is specified by a feature as an input into a model in Lopez-Paz & Ranzato (2017), again this corresponds to the way our low-level actor processes its goal. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Several recent deep reinforcement learning works have used modular architectures and hierarchy to achieve generalization to new tasks. For example, Tessler et al. (2017) uses pre-trained skills for transfer. Oh et al. (2017) uses a meta-controller that selects parameterized skills and analogical supervision on outer-product structured tasks. Our assignments of attributes serves a similar purpose to their analogical supervision, and we use parameterized skills as these works do. However, our “meta-controller” is the search over attributes, rather than a reactive model. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In Andreas et al. (2017), generalization is achieved through supervision in the form of “policy sketches”, which are symbolic representations of the high level steps necessary to complete a given task. The low level steps in executing modules in the sketches are composable. Our work is similar in that high level annotation is used to enable generalization, but the mechanism in this work is different. Note that the approaches in Andreas et al. (2017); Oh et al. (2017) are complementary to the one described here; in future work we wish to explore combining them. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Semiparametric methods In this work we use an explicit memory of sets of attributes the model has seen. Several previous works have used non-parametric memories for lowering the sample complexity of learning, e.g. Blundell et al. (2016); Pritzel et al. (2017). Like these, we lean on the fact that with a good representation of a state, it can be useful to memorize what to do in given situation (having only done it a small number of times) and explicitly look it up. In our case, the “good representation” is informed by the user-specified attributes. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our approach is also related to Machado et al. (2017), which builds up a multiscale representation of an MDP using Eigenvectors of the transition matrix of the MDP, in the sense that we collect data on possible transitions between attributes in a first phase of training, and then use this knowledge at test time. ",
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+    {
+        "type": "text",
+        "text": "Attributes in vision Farhadi et al. (2009) and Lampert et al. (2009) explore visual attributes as a natural intermediate representation for object recognition tasks, demonstrating their effectiveness in one/low-shot settings. Subsequent work has applied the concept to fine-grained recognition (Duan et al., 2012), people’s appearance/clothing (Zhang et al., 2014) and relative judgements (Parikh & Grauman, 2011). However, all these are static I.I.D settings, in contrast to dynamic agent/environment that this work explores. ",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate our approach (Attribute Planner, abbreviated to $A P$ ) in three different environments. The first two are randomly generated grid-worlds, and the third is a simulation of stacking blocks. In each environment, the goal of the model is to be able to generalize to testing on complex tasks from training on simpler tasks. ",
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+    {
+        "type": "text",
+        "text": "We compare against baseline policies trained in several ways. These baseline policies take the state and goal as inputs, and use the same neural network architecture as the policy used for the Attribute Planner. ",
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+    {
+        "type": "text",
+        "text": "1. Reinforcement Learning: Policies trained via reinforcement learning with A3C (Mnih et al., 2016) or Reinforce. We consider three variants of training: (i) training only with nearby goals (one attribute transition for grid-world; single actions for block stacking); (ii) training on the evaluation tasks; and (iii) training on a curriculum that transitions from nearby goals to evaluation tasks. Policies (ii) and (iii) are trained on full sequences, thus have an inherent advantage over our model, which only sees short sequences during training.   \n2. Inverse: An inverse model trained in a “supervised” fashion on a dataset of observed trajectories to predict the next action given the state and goal. We train on nearby goals and on longer multi-step tasks. ",
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+        "type": "text",
+        "text": "4.1 2-D WORLDS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We implemented two types of small 2- $. D$ environments in Mazebase (Sukhbaatar et al., 2015), where the worlds are randomly generated for each episode. The action space for each consists of movements in the four cardinal directions, and additional environment specific actions. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Colored Switches The first environment consists of four switches, each with four possible colors. An extra toggle action cycles the color of a switch if the agent is standing on it. The attributes for this environment are the states of the switches; and the tasks are to change the switches into a specified configuration, as shown in Fig. 2(right). The locations and colors of the switches are randomly initialized for each episode. ",
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+    {
+        "type": "text",
+        "text": "Crafting In the second environment, similar to the one used in Andreas et al. (2017) an agent needs to collect resources and combine them to form items. In addition to moving in the cardinal directions, the agent has a “grab” action that allows it to pick up a resource from the current location and add it to its inventory. If there is no item where the agent is standing, this action does nothing. The agent also has a “craft” action that combines a set of items to create a new item if the agent has the prerequisite items in its inventory and the agent is standing on a special square (a “crafting table”) corresponding to the item to be crafted. If these two conditions are not both met, the “craft” action does nothing. The attributes for this environment are the items in the inventory, and task is to add a specified item to the inventory. In the environment, there are three types of resources and three types of products (see Fig. 2(left)). The episodes are initialized randomly by removing some resources, and adding some items to the inventory. ",
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+    {
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+        "img_path": "images/90bf30f100a426d3873f3b1558a4c751c1d2761eee1695cfb6bb790c71fe9f95.jpg",
+        "image_caption": [
+            "! + ! = + + ! =+ + ! =Figure 2: Left: Crafting mazebase game. Right: Colored switches game. See text for details. "
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+        "image_footnote": [],
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+        "type": "text",
+        "text": "1 1The observation is given as a bag of words in both environments, where the words correspond to (feature, location). Features consist of item types, names, and their other properties. The locations 1include position relative to the agent in the maze, and also a few special slots for inventory, current, and target attributes. ",
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+    {
+        "type": "text",
+        "text": "The first phase building the high level transitions as in Section 2.1.2 is done by running a random 1 1agent in the environment from a random state until one or more attributes change. Then this change of attribute is recorded as an edge in graph $G$ . The low level policy is trained concurrently with the second phase of Section 2.1.2. We use the current edge estimates in the graph to propose a target set of attributes, and the low level policy is trained with the Reinforce algorithm (Williams, 1992) to reach that set of attributes from the current state. These training episodes terminate when the task completes or after 80 steps; and a reward of -0.1 is given at every step to encourage the agent to complete the task quickly. The policy network is a fully connected network with two hidden layers of 100 units. We run each experiment three times with different random seeds, and report the mean success rate. ",
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+        "type": "text",
+        "text": "In the switches environment, multi-step (test) tasks are generated by setting a random attribute as target, which can require up to 12 attribute transitions. In the crafting environment, multi-step (test) tasks are generated by randomly selecting an item as a target. Since we do not care about other items in the inventory, the target state is underspecified. Some tasks are pre-solved because the randomly chosen target item can already be in the inventory. However, such tasks have no effect on training and are also removed during testing. ",
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+    {
+        "type": "text",
+        "text": "In curriculum training which we use as a baseline, we gradually increase the upper bound on the difficulty of tasks. In the switches environment, the difficulty corresponds to the number of toggles necessary for solving the task. The craft environment has two levels of difficulty: tasks can be completed by a single grab or craft action, and tasks that require multiple such actions. ",
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+        "type": "text",
+        "text": "During the second phase of training, we simultaneously compute the transition function $c _ { \\pi } ( \\rho _ { i } , \\rho _ { j } )$ using an exponentially decaying average of success rates of the low level policy $\\pi$ : ",
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+    {
+        "type": "equation",
+        "img_path": "images/77129c3880f0194beedf8e4e4d006ca6fc8f5bfcd1a0b98c75d6b36bad52d10f.jpg",
+        "text": "$$\nc _ { \\pi } ( \\rho _ { i } , \\rho _ { j } ) = \\frac { \\sum _ { t = 1 } ^ { T } \\gamma ^ { T - t } M _ { \\pi } ^ { t } ( \\rho _ { i } , \\rho _ { j } ) } { \\sum _ { t = 1 } ^ { T } \\gamma ^ { T - t } N _ { \\pi } ^ { t } ( \\rho _ { i } , \\rho _ { j } ) } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $T$ is the number of training epochs, $N _ { \\pi } ^ { t }$ is the number of task $( \\rho _ { i } , \\rho _ { j } )$ during epoch $t$ , and $M _ { \\pi } ^ { t }$ is the number of successful episodes among them. A decay rate of $\\gamma = 0 . 9$ is used. ",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1 compares our Attribute Planner (AP) model to a Reinforce baseline on the Crafting and Colored Switches tasks. In all cases, the baseline performs poorly, while the AP model has a high success rate. The importance of the graph is apparent: when it is removed (Reinforce method) the performance drops significantly on multi-step tasks. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a4c3024cf16429bb6f83f8d8e6bc2af3fac2e6327a0aed3a75f8e3f2c9a78093.jpg",
+        "table_caption": [
+            "Table 1: Task success rate on Mazebase environments. Our Attribute Planner (AP) approach performs much better than the reactive policies trained with Reinforce. The addition of the attribute graph (over Reinforce only model) is crucial for multi-step evaluation tasks. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">Training data</td><td colspan=\"2\">Switches</td><td colspan=\"2\">Crafting</td></tr><tr><td>single</td><td>multi</td><td>single</td><td>multi</td></tr><tr><td>Reinforce</td><td>multi-step</td><td>0.0%</td><td>0.0%</td><td>45.7%</td><td>28.6%</td></tr><tr><td>Reinforce</td><td> multi-step + curriculum</td><td>33.6%</td><td>33.3%</td><td>94.9%</td><td>83.9%</td></tr><tr><td>Reinforce</td><td>one-step</td><td>99.0%</td><td>15.4%</td><td>98.7%</td><td>49.0%</td></tr><tr><td>AP</td><td>one-step</td><td>99.0%</td><td>83.1%</td><td>98.7%</td><td>96.2%</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.2 STACKING BLOCKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We consider a 3D block stacking task in the Mujoco environment Todorov et al. (2012). There are 4 blocks of different colors, and actions consist of dropping a block in a $3 \\times 3$ grid of positions, resulting in 36 total actions. A block cannot be moved when it is underneath another block, so some actions have no effect. The input to the model is the observed image, and there are a total of 36 binary properties corresponding to the relative $\\mathbf { X }$ and y positions of the blocks and whether blocks are stacked on one another. For example, one property corresponds to “blue is on top of yellow”. Each training episode is initiated from a random initial state and lasts only one step, i.e. dropping a single block in a new location. ",
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+    {
+        "type": "text",
+        "text": "The policy network takes (i) a $1 2 8 \\times 1 2 8$ image, which is featurized by a CNN with five convolutional layers and one fully connected (fc) layer to produce a 128d vector; and (ii) goal properties expressed as a 48d binary vector, which are transformed to a 128d vector. The two 128d vectors are concatenated and combined by two fc layers followed by softmax to produce an output distribution over actions. We use an exponential linear nonlinearity after each layer. ",
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+    },
+    {
+        "type": "text",
+        "text": "Table 2 compares the performance of different models on several block stacking tasks. In the onestep task, a goal is chosen that is the result of taking a single random action. In the multi-step task, the goal is chosen as the properties of a new random initialization. These tasks typically require $3 - 8$ steps to complete. In the 4-stack task, the goal is a vertical stack of blocks in the order red, green, blue, yellow. We compare the performance of our model to reactive policy baselines trained on single-step tasks, complex multi-step tasks or with a curriculum of both. We perform each evaluation task 1000 times. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The single-step reactive policies perform well on single step tasks (which are what it sees at train time), but perform much worse compared to the AP model when transferred to multi-step tasks. The AP model without the second step of training that learns $c _ { \\pi }$ also performs substantially worse on multi-step tasks, demonstrating the importance of properly normalized transition probabilities to avoid aliased states. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The rightmost two columns of Table 2 consider underspecified goals, where only a subset of the attributes are provided. These are identical to their fully-specified counterparts, except that each attribute is left unspecified with probability $30 \\%$ . The AP model handles these naturally by finding the shorted path to any satisfactory attribute set. We consider reactive baselines that are trained on the same distribution of underspecified attribute sets. Despite this, we observe that reactive policy performance degrades when goals are underspecified, while our AP model does not. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The attribute detector $\\hat { f }$ predicts the full attribute set with $< 0 . 1 \\%$ error when trained on the full dataset of 1 million examples. If trained on only 10,000 examples, the attribute detector has an error rate of $1 . 4 \\%$ . Training the AP model with this less-accurate attribute detector degrades multi-step performance by only $0 . 9 \\%$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Property Aliasing: The “ignorability” assumption we made in Section 2 is violated in the block stacking task. To see why, consider a transition from “red left of blue and yellow” to “red right of blue and yellow”. This can typically be accomplished in one step, but if blue and yellow are already on the far right, it cannot. Thus, states where this transition are possible and impossible are aliased with the same properties. This is the dominant source of errors on the multi-step task when trained on large sample sizes (in fact, it is the only source of errors as the policy approaches $1 0 0 \\%$ ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/97cefae6f4a25c134baed4690fefe030b065d411d2535d16a47dea4aa6161483.jpg",
+        "table_caption": [
+            "Table 2: Model comparison on block stacking task accuracy. Baselines marked ‘multi-step’ or ‘curriculum‘ get to see complex multi-step tasks at train time. The Attribute Planner (AP) generalizes from one-step training to multi-step and underspecified tasks with high accuracy, while reinforcement learning and inverse model training do not. AP outperforms A3C even with a curriculum of tasks. Ablating the normalized graph transition table $c _ { \\pi }$ degrades AP performance substantially on multi-step tasks due to aliasing. Inverse one-step model was trained on 2 million examples, inverse multi-step and AP models were trained on 1 million examples, A3C models were trained to convergence. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Training Data</td><td>one-step</td><td>multi-step</td><td>4-stack</td><td>one-step underspecified</td><td>multi-step</td></tr><tr><td>A3C</td><td>one-step</td><td>98.5%</td><td>8.1%</td><td>1.9%</td><td>65.7%</td><td>6.6%</td></tr><tr><td>A3C</td><td>multi-step</td><td>2.6%</td><td>0%</td><td>0%</td><td>5.3%</td><td>0%</td></tr><tr><td>A3C</td><td>curriculum</td><td>98.2%</td><td>17%</td><td>2.9%</td><td>8.2%</td><td>0.2%</td></tr><tr><td>Inverse</td><td>one-step</td><td>100%</td><td>9.1%</td><td>0.5%</td><td>98.8%</td><td>18.8%</td></tr><tr><td>Inverse</td><td>multi-step</td><td>94.1%</td><td>13.7%</td><td>4.6%</td><td>71.2%</td><td>9.6%</td></tr><tr><td>AP (no Cπ)</td><td> one-step</td><td>74.5%</td><td>29.7%</td><td>62.2%</td><td>81.8%</td><td>28.1%</td></tr><tr><td>AP</td><td>one-step</td><td>98.8%</td><td>66.7%</td><td>98.5%</td><td>97.8%</td><td>63.5%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/d94ce6877d1871186eb83817ffa1d1a005b5a2ab4d985ac0b3c9929066073333.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"># of Training Examples</td><td colspan=\"2\">Inverse</td><td colspan=\"2\">AP</td></tr><tr><td>one-step</td><td>multi-step</td><td>one-step</td><td>multi-step</td></tr><tr><td>10,000</td><td>35.5%</td><td>1.6%</td><td>50.0%</td><td>3.0%</td></tr><tr><td>100,000</td><td>99.9%</td><td>7.8%</td><td>89.0%</td><td>47.0%</td></tr><tr><td>1,000,000</td><td>100%</td><td>9.1%</td><td>98.9%</td><td>66.7%</td></tr><tr><td>10,000,000</td><td>100%</td><td>8.5%</td><td>96.5%</td><td>70.7%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Effect of the number of (one-step) training examples on one-step and multi-step performance, for an inverse model and the Attribute Planner model. The inverse models are trained on $2 \\mathbf { x }$ the samples, including the samples generated from learning $c _ { \\pi }$ in our AP method. ",
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "accuracy and the graph becomes complete). Figure 4 shows an example plan that becomes stuck due to aliasing. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The second step of training, that computes the probability of $\\pi$ transitioning on each edge, is important for mitigating the effects of aliasing in the block stacking task. The graph search finds the path with the highest probability of success (i.e. the product of probabilities on each edge), so it avoids edges that have high aliasing. In the AP model trained on one million samples, the second step of training improves multi-step performance from $2 9 . 7 \\%$ to $6 6 . 7 \\%$ , as shown in Table 2. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our results show that structuring the space of tasks with high level attributes allows an agent to compose policies for the solutions of simple tasks into solutions of more complex tasks. The agent plans a path to the final goal at the level of the attributes, and executes the steps in this path with a reactive policy. Thus, supervision of an agent by labeling attributes can lead to generalization from simple tasks at train time to more complex tasks at test time. Nevertheless, there are many fronts for further work: ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Sample complexity of the planning module: In Table 5 we can see both the benefits and the liabilities of the explicit non-parametric form for $c$ . By 10K samples, the parametric lower level policy is already able to have a reasonable success rate. However, because in this environment, there are roughly 200K edges in the graph, most of the edges have not been seen, and without any weight-sharing, our model cannot estimate these transition probabilities. On the other hand, by 100K samples the model has seen enough of the graph to make nontrivial plans; and the non-parametric form of the graph makes planning straightforward. In future work, we hope to combine parametric models for $c$ with search to increase the sample efficiency of the planning module. Alternatively, we might hope to make progress on dynamic abstraction (projecting out some of the attributes) depending on the current state and goal, which would make the effective number of edges of the graph smaller. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/28355570631ffc144872cd6f11841f5407f326abc233c5b68f14159249e3594a.jpg",
+        "image_caption": [
+            "Figure 3: Two examples of block stacking evaluation tasks. The initial/target states are shown in the first/last columns. Successful completions of our Attribute Planner model are shown in rows 1 and 3. By contrast, the A3C baseline is unable to perform the tasks (rows 2 and 4). "
+        ],
+        "image_footnote": [],
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/35f4098d826e9a1a5ae3af6917e525e9329c4b3a9e2f382cb0d7bf06f8ec0fc0.jpg",
+        "image_caption": [
+            "Figure 4: Plans become stuck when states with different transitions map to the same properties. In frame 4 of this example, the policy is directed to place the green block in front of the red and blue blocks, but this is impossible because the blue and red are already in the frontmost position. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Exploration Although we discuss an agent in an environment, we have elided many of the difficult problems of reinforcement learning. In particular, the environments considered in this work allow sampling low level transitions by starting at random states and following random policies, and these are sufficient to cover the state space, although we note that the method for training the model described in Section 2.1 allows for more sophisticated exploration policies. Thus we sidestep the exploration problem, one of the key difficulties of reinforcement learning. Nevertheless, building composable models even in this setting is nontrivial, and our view is that it is important to demonstrate success here (and decouple issues of exploration and composability) before moving on to the full RL problem. ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We believe that the attributes $\\rho$ and $c$ , in addition to their usefulness for planning, provide a framework for incentivizing exploration. The agent can be rewarded for finding unseen (or rarely-seen) high level transitions, or for validating or falsifying hypotheses about the existence of entries of $c$ . ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Learning the attributes: Discovering the attributes automatically would remove much of the need for human supervision. Recent work, such as Thomas et al. (2017), demonstrates how this could be done. Another avenue for discovering attributes is to use a few “seed” attributes; and use aliasing as a signal that some attributes need to be refined. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
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Fidjeland, Georg Ostrovski, Stig Petersen, Charles Beattie, Amir Sadik, Ioannis Antonoglou, Helen King, Dharshan Kumaran, Daan Wierstra, Shane Legg, and Demis Hassabis. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533, February 2015.   \nVolodymyr Mnih, Adria Puigdomenech Badia, Mehdi Mirza, Alex Graves, Timothy Lillicrap, Tim Harley, David Silver, and Koray Kavukcuoglu. Asynchronous methods for deep reinforcement learning. In International Conference on Machine Learning, pp. 1928–1937, 2016.   \nJunhyuk Oh, Satinder P. Singh, Honglak Lee, and Pushmeet Kohli. Zero-shot task generalization with multi-task deep reinforcement learning. In ICML, volume 70 of Proceedings of Machine Learning Research, pp. 2661–2670. PMLR, 2017.   \nDevi Parikh and Kristen Grauman. Relative attributes. In Computer Vision (ICCV), 2011 IEEE International Conference on, pp. 503–510. IEEE, 2011.   \nRonald Parr and Stuart Russell. 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Centre for Telematics and Information Technology University of Twente, 2005.   \nHarm van Seijen, Mehdi Fatemi, Joshua Romoff, Romain Laroche, Tavian Barnes, and Jeffrey Tsang. Hybrid reward architecture for reinforcement learning. CoRR, abs/1706.04208, 2017.   \nRonald J. Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. In Machine Learning, pp. 229–256, 1992.   \nNing Zhang, Manohar Paluri, Marc’Aurelio Ranzato, Trevor Darrell, and Lubomir Bourdev. Panda: Pose aligned networks for deep attribute modeling. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2014. ",
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+        "text": "A ADDING EXPLORATION ",
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+        "text": "We also look into the use of exploration and learn a policy to promote exploration of undiscovered edges in our planning graph. We give a negative reward proportional to $\\frac { \\mathbf { \\dot { \\phi } } _ { t } } { \\sqrt { n } }$ where $n$ is the number of times that edge has been encountered before and $t$ the time episode. We compare this with a baseline method of single random start and random action selection over $N$ and the method used in the main paper, with $N$ random starts and single rollouts. ",
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+        "text": "A.1 MAZEBASE RESULTS ",
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+        "text": "Our Mazebase environments in Section 4.1 are designed so that all edges can be discovered without much exploration. So to better test the benefit of exploration, we modified the craft environment to make discovering all edges harder. First, we added 4 new “super” products that can be crafted by combining one normal product with another resource, or three resources. Second, the environment always starts with only 3 resources and an empty inventory. Therefore, it is much harder to discover a super product because it requires agent to craft a product out of two resources, and then pick another resource and craft. ",
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+        "text": "In this hard crafting environment, a random agent discovered 18.6 edges on average, while an agent with the exploration reward discovered all 25 edges of the environment. We used this complete graph to train our AP model and other baselines. Training on one-step tasks require episodes to start from different nodes of the graph, but the environment always initializes at the same node. A simple solution was not to reset the environment between episodes if the previous episode was successful. Thus the next episodes will start from a different node. Table 4 shows the success rates on multi-step tasks, where our AP model clearly outperforms the other baselines. ",
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+        "table_body": "<table><tr><td>Method</td><td>Training data</td><td>Hard Crafting (multi-step)</td></tr><tr><td>Reinforce</td><td>multi-step + curriculum</td><td>51.5%</td></tr><tr><td>Reinforce</td><td>one-step</td><td>26.0%</td></tr><tr><td>AP</td><td>one-step</td><td>99.8%</td></tr></table>",
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+        "text": "Table 4: Task success rate on multi-step task in the hard crafting environment. Our Attribute Planner clearly outperforms other baseline approaches. ",
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+        "text": "A.2 STACKING BLOCKS RESULTS ",
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+        "table_caption": [
+            "Table 5: Effect of the number of (one-step) training examples on one-step and multi-step performance, for an inverse model and the Attribute Planner model. The inverse models are trained on $2 \\mathbf { x }$ the samples, including the samples generated from learning $c _ { \\pi }$ in our AP method. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"># of Training Examples</td><td colspan=\"2\">Policy</td><td colspan=\"2\">Random</td><td colspan=\"2\">Main Method</td></tr><tr><td>edges</td><td> accuracy</td><td>edges</td><td>accuracy</td><td>edges</td><td>accuracy</td></tr><tr><td>100,000</td><td>44k</td><td>49.4%</td><td>49k</td><td>49.7%</td><td>38k</td><td>47.0%</td></tr><tr><td>1,000,000</td><td>120k</td><td>67.5%</td><td>130k</td><td>69.8%</td><td>114k</td><td>66.7%</td></tr><tr><td>10,000,000</td><td>139k</td><td>80.6%</td><td>138k</td><td>83.1%</td><td>218k</td><td>70.7%</td></tr></table>",
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