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DEEP NEURAL NETWORKS + +Anonymous authors Paper under double-blind review + +# ABSTRACT + +We present a radial basis function solver for convolutional neural networks that can be directly applied to both distance metric learning and classification problems. Our method treats all training features from a deep neural network as radial basis function centres and computes loss by summing the influence of a feature’s nearby centres in the embedding space. Having a radial basis function centred on each training feature is made scalable by treating it as an approximate nearest neighbour search problem. End-to-end learning of the network and solver is carried out, mapping high dimensional features into clusters of the same class. This results in a well formed embedding space, where semantically related instances are likely to be located near one another, regardless of whether or not the network was trained on those classes. The same loss function is used for both the metric learning and classification problems. We show that our radial basis function solver outperforms state-of-the-art embedding approaches on the Stanford Cars196 and CUB-200- 2011 datasets. Additionally, we show that when used as a classifier, our method outperforms a conventional softmax classifier on the CUB-200-2011, Stanford Cars196, Oxford 102 Flowers and Leafsnap fine-grained classification datasets. + +# 1 INTRODUCTION + +The solver of a neural network is vital to its performance, as it defines the objective and drives the learning. We define a solver as the layers of the network that are aware of the class labels of the data. In the domain of image classification, a softmax solver is conventionally used to transform activations into a distribution across class labels (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016). While in the domain of distance metric learning, a Siamese (Chopra et al., 2005) or triplet (Hoffer & Ailon, 2015; Schroff et al., 2015; Kumar et al., 2017) solver, with contrastive or hinge loss, is commonly used to pull embeddings of the same class together and push embeddings of different classes apart. The two tasks of classification and metric learning are related but distinct. Conventional classification learning is generally used when the objective is to associate data with a pre-defined set of classes and there is sufficient data to train or fine-tune a network to do so. Distance metric learning, or embedding space building, aims to learn an embedding space where samples with similar semantic meaning are located near one another. Applications for learning such effective embeddings include transfer learning, retrieval, clustering and weakly supervised or self-supervised learning. + +In this paper, we present a deep neural network solver that can be applied to both embedding space building and classification problems. The solver defines training features in the embedding space as radial basis function (RBF) centres, which are used to push or pull features in a local neighbourhood, depending on the labels of the associated training samples. The same loss function is used for both classification and metric learning problems. This means that a network trained for the classification task results in feature embeddings of the same class being located near one another and similarly, a network trained for metric learning results in feature embeddings that can be well classified by our RBF solver. Fast approximate nearest neighbour search is used to provide an efficient and scalable solution. + +The best success on embedding building tasks has been achieved by deep metric learning methods (Hoffer & Ailon, 2015; Schroff et al., 2015; Song et al., 2016a; Sohn, 2016; Kumar et al., 2017), which make use of deep neural networks. Such approaches may indiscriminately pull samples of the same class together, regardless of whether the two samples were already within well defined local clusters of like samples. These methods aim to form a single cluster per class. In contrast, our approach pushes a feature around the embedding space based only on the local neighbourhood of that feature. This means that the current structure of the space is considered, allowing multiple clusters to form for a single class, if that is appropriate. Our radial basis function solver is able to learn embeddings that result in samples of similar semantic meaning being located near one another. Our experiments show that the RBF solver is able to do this better than existing deep metric learning methods. + +Softmax solvers have been a mainstay of the standard classification problem (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016). Such an approach is inefficient as classes must be axis-aligned and the number of classes is baked into the network. Our RBF approach is free to position clusters such that the intrinsic structure of the data can be better represented. This may involve multiple clusters forming for a single class. The nearest neighbour RBF solver outperforms conventional softmax solvers in our experiments and provides additional adaptability and flexibility, as new classes can be added to the problem with no updates to the network weights required to obtain reasonable results. This performance improvement is obtained despite smaller model capacity. The RBF solver by its very nature is a classifier, but learns the classification problem in the exact same way it learns the embedding space building problem. + +The main advantages of our novel radial basis function solver for neural networks can be summarised as follows: + +• Our solver can be directly applied to two previously separate problems; classification and embedding space learning. +• End-to-end learning can be made scalable by leveraging fast approximate nearest neighbour search (as seen in Section 3.2). Our approach outperforms current state-of-the-art deep metric learning algorithms on the Stanford Cars196 and CUB-200-2011 datasets (as seen in Section 4.1). Finally, our radial basis function classifier outperforms a conventional softmax classifier on the fine-grained classification datasets CUB-200-2011, Stanford Cars196, Oxford 102 Flowers and Leafsnap (as seen in Section 4.2). + +# 2 RELATED WORK + +Radial Basis Functions in Neural Networks Radial basis function networks were introduced by Broomhead & Lowe (1988). The networks formulate activation functions as RBFs, resulting in an output that is a sum of radial basis function values between the input and network parameters. In contrast to these radial basis function networks, our approach uses RBFs in the solver of a deep convolutional neural network and our radial basis function centres are coupled to high dimensional embeddings of training samples, rather than being network parameters. Radial basis functions have been used as neural network solvers in the form of support vector machines. In one such formulation, a neural network is used as a fixed feature extractor and separate support vector machines are trained to classify the features (Razavian et al., 2014; Donahue et al., 2014). No joint training occurs between the solver (classifier) and network. Such an approach is often used for transfer learning, where the network is trained on vast amounts of data and the support vector machines are trained for problems in which labelled training data is scarce. Tang (2013) replaces the typical softmax classifier with linear support vector machines. In this case, the solver and network are trained jointly, meaning the loss that is minimised is margin based. + +Metric Learning Early methods in the domain of metric learning include those that use Siamese networks (Bromley et al., 1993) and contrastive loss (Hadsell et al., 2006; Chopra et al., 2005). The objective of these approaches is to pull pairwise samples of the same class together and push pairwise samples of different classes apart. Such methods work on absolute distances, while triplet networks with hinge loss (Weinberger et al., 2006) work on relative distance. Triplet loss approaches take a trio of inputs; an anchor, a positive sample of the same class as the anchor and a negative sample of a different class. Triplet loss aims to pull the positive sample closer to the anchor than the negative sample. Several deep metric learning approaches make use of, or generalise deep triplet neural networks (Hoffer & Ailon, 2015; Wang et al., 2014; Schroff et al., 2015; Song et al., 2016a; Sohn, 2016; Kumar et al., 2017). Schroff et al. (2015) perform semi-hard mining within a mini-batch, while Song et al. (2016a) propose a lifted structured embedding with efficient computation of the full distance matrix within a mini-batch. This allows comparisons between all positive and negative pairs in the batch. Similarly, Sohn (2016) proposes an approach that allows multiple intra-batch distance comparisons, but optimises a generalisation of triplet loss, named N-pair loss, rather than a max-margin based objective, as in Song et al. (2016a). The global embedding structure is considered in Song et al. (2016b) by directly minimising a global clustering metric, while a combination of global and triplet loss is shown to be beneficial in Kumar et al. (2016). Finally, Kumar et al. (2017) introduce a smart mining technique that mines for triplets over the entire dataset. A Fast Approximate Nearest Neighbour Graph (FANNG) (Harwood & Drummond, 2016) is leveraged for computational efficiently. Beyond triplet loss, Rippel et al. (2016) introduce a loss function that allows multiple clusters to form per class. Rather than only penalising a single triplet at a time, the neighbourhood densities are considered and overlaps between classes penalised. + +![](images/73dfcbed79adccb1fa69d2669a2d68b8d5ca02240c86bd7a56aab148be320002.jpg) +Figure 1: Overview of our radial basis function solver. + +# 3 RADIAL BASIS FUNCTION SOLVERS + +A radial basis function returns a value that depends only on the distance between two points, one of which is commonly referred to as a centre. Although several radial basis functions exist, in this paper we use RBF to refer to a Gaussian radial basis function, which returns a value based on the Euclidean distance between a point $\mathbf { X }$ and the RBF centre c. The radial basis function, $f$ , is calculated as: + +$$ +f ( \mathbf { x } , \mathbf { c } ) = \exp \left( \frac { - \| \mathbf { x } - \mathbf { c } \| ^ { 2 } } { 2 \sigma ^ { 2 } } \right) +$$ + +where $\sigma$ is standard deviation that controls the width of the Gaussian curve, that is, the region around the RBF centre deemed to be of importance. + +In the context of our neural network solver, we define the deep feature embeddings of each training set sample as radial basis function centres. Specifically, we take the layer in a network immediately before the solver as the embedding layer. For example, in a VGG architecture, this may be FC7 (fully connected layer 7), forming a 4096 dimension embedding. In general, however, the embedding may be of any size. An overview of this approach is seen in Figure 1. + +# 3.1 CLASSIFIER AND LOSS FUNCTION + +A radial basis function classifier can be formed by the weighted sum of the RBF distance calculations between a sample feature embedding and the centres. Classification of a sample is achieved by passing the input through the network, resulting in a feature embedding in the same space as the RBF centres. A probability distribution over class labels is found by summing the influence of each centre and normalising. A centre contributes only to the probability of the ground truth label of the training sample coupled to that centre. For example, the probability that the feature embedding $\mathbf { X }$ has class label $Q$ is: + +$$ +P r ( \mathbf { x } \in \operatorname { c l a s s } Q ) = \frac { \sum _ { i \in Q } w _ { i } f ( \mathbf { x } , \mathbf { c _ { i } } ) } { \sum _ { j = 1 } ^ { m } w _ { j } f ( \mathbf { x } , \mathbf { c _ { j } } ) } , +$$ + +where $f$ is the RBF, $i \in Q$ are the centres with label $Q$ , $m$ is the number of training samples and $w _ { i }$ is a learnable weight for RBF centre $i$ . Of course, if a sample is in the training set and has a corresponding RBF centre, the distance calculation to itself is omitted during the computation of the classification distribution, the loss function and the derivatives. + +The loss function used for optimisation is simply the summed negative logarithm of the probabilities of the true class labels. For example, the loss $L$ for sample $\mathbf { X }$ with ground truth label $R$ is: + +$$ +L ( \mathbf { x } ) = - \ln \left( P r ( \mathbf { x } \in \operatorname { c l a s s } R ) \right) . +$$ + +The same loss function is used regardless of whether the network is being trained for classification, as above, or for embedding space building (distance metric learning). This is possible since the RBF classifier is directly computed from distances between features in the embedding space. This means that a network trained for classification will result in features of the same class being located near one another, and similarly a network trained for metric learning will result in an embedding space in which features can be well classified using RBFs. + +# 3.2 NEAREST NEIGHBOUR RBF SOLVER + +In Equation 2, the distribution is calculated by summing over all RBF centres. However, since these centres are attached to training samples, of which there could be any large number, computing that sum is both intractable and unnecessary. The majority of RBF values for a given feature embedding will be effectively zero, as the sample feature will lie only within a subset of the RBF centres’ Gaussian windows. As such, only the local neighbourhood around a feature embedding should be considered. Operating on the set of the nearest RBF centres to a feature ensures that most of the distance values computed are pertinent to the loss calculation. The classifier equation becomes: + +$$ +P r ( \mathbf x \in \mathrm { c l a s s } Q ) = \frac { \sum _ { i \in Q \cap \mathcal { N } } w _ { i } f ( \mathbf x , \mathbf c _ { \mathbf i } ) } { \sum _ { j \in \mathcal { N } } w _ { j } f ( \mathbf x , \mathbf c _ { \mathbf j } ) } , +$$ + +where $\mathcal { N }$ is the set of approximate nearest neighbours for sample $\mathbf { X }$ and therefore $i \in Q \cap \mathcal N$ is the set of approximate nearest neighbours that have label $Q$ . Again, we note that training set samples exclude their own RBF centre from their nearest neighbour list. + +In the interest of providing a scalable solution, we use approximate nearest neighbour search to obtain candidate nearest neighbour lists. This allows for a trade off between precision and computational efficiency. Specifically, we use a Fast Approximate Nearest Neighbour Graph (FANNG) (Harwood & Drummond, 2016), as it provides the most efficiency when needing a high probability of finding the true nearest neighbours of a query point. Importantly, FANNG provides scalability in terms of the number of dimensions and the number of training samples. + +# 3.3 END-TO-END LEARNING + +The network and solver weights are learned end-to-end. As the weights are constantly being updated during training, the locations of the RBF centres are changing. This leads to complications in the computation of the derivatives of the loss with respect to the embeddings. This calculation requires dimension by dimension differences between the training embeddings and the RBF centres. The centres are moving as the network is being updated, but computing the current RBF centre locations online is intractable. For example, if considering 100 nearest neighbours, 101 samples would need to be forward propagated through the network for each training sample. However, we find that is is not necessary for the RBF centres to be up to date at all times in order for the model to converge. A bank of the RBF centres is stored and updated at a fixed interval. + +A further consequence of the RBF centres moving during training is that the nearest neighbours also change. It is intractable to find to correct nearest neighbours each time the weights are updated. This is simply remedied by considering a larger number of nearest neighbours than would be required if all centres and neighbour lists were up-to-date at all times. The embedding space changes slowly enough that it is highly likely many of the previously neighbouring RBF centres will remain relevant. Since the Gaussian RBF decays to zero as the distance between the points becomes large, it does not matter if an RBF centre that is no longer near the sample remains a candidate nearest neighbour. + +We call the frequency at which the RBF centres are updated and the nearest neighbours found the update interval. During training, at a fixed number of epochs we forward pass the entire training set through the network, storing the new RBF centres. The up-to-date nearest neighbours can now be found. If FANNG is used, a rebuild of the graph is required. Note that the stored RBF centres do not have dropout (Srivastava et al., 2014) applied, but the current training embeddings may. The effect of the number of nearest neighbours considered and the update interval are discussed in Section 4.2. + +Radial Basis Function Parameters A global standard deviation parameter $\sigma$ is shared amongst the RBFs. This ensures that the assumption made about samples only being influenced by their nearest RBF centres holds. Although the parameter is learnable, we find that fixing the standard deviation value before training is a suitable approach. We treat the standard deviation as an additional hyperparameter to tune, however it can also be learned independently before full network training commences. As seen in Equation 4, each RBF centre has a weight, which is learned end-to-end with the network weights. These weights are initialised at values of one. Note that in our experiments we only tune the RBF weights for the classification task; they remain fixed for metric learning problems. + +# 4 EXPERIMENTS + +We detail our experimental results in two tasks; distance metric learning and image classification. + +# 4.1 DISTANCE METRIC LEARNING + +Experimental Set-up We evaluate our approach on two datasets; Stanford Cars196 (Krause et al., 2013) and CUB-200-2011 (Birds200) (Welinder et al., 2010). Cars196 consists of 16,185 images of 196 different car makes and models, while Birds200 consists of 11,788 images of 200 different bird species. In this problem, the network is trained and evaluated on different sets of classes. We follow the experimental set-up used in Song et al. (2016a); Sohn (2016); Song et al. (2016b); Kumar et al. (2017). For the Cars196 dataset, we train the network on the first 98 classes and evaluate on the remaining 98. For the Birds200 dataset we train on the first 100 classes and evaluate on the remaining 100. Stochastic gradient descent optimisation is used. All images are first resized to be 256x256 and data is augmented by random cropping and horizontal mirroring. Note that we do not crop the images using the provided bounding boxes. + +Our method is compared to state-of-the-art approaches on the considered datasets; semi-hard mining for triplet networks (Schroff et al., 2015), lifted structured feature embedding (Song et al., 2016a), N-pair loss (Sohn, 2016), clustering (Song et al., 2016b), global loss with triplet networks (Kumar et al., 2016) and smart mining for triplet networks (Kumar et al., 2017). For fair comparison to these methods, we use the same base architecture for our experiments; GoogLeNet (Szegedy et al., 2015). Network weights are initialised from ImageNet (Russakovsky et al., 2015) pre-trained weights. We use 100 nearest neighbours and an update interval of 10 epochs. RBF weights are fixed at a value of one for this task. We train for 50 epochs on Cars196 and 30 epochs on Birds200. A batch size of 20, base learning of 0.00001 and weight decay of 0.0002 are used. The RBF standard deviation used depends on size of the embedding dimension. We find values between 10 and 30 work well for this task. + +Evaluation Metrics Following Song et al. (2016a), we evaluate the embedding space using two metrics; Normalised Mutual Information (NMI) (Manning et al., 2008) and Recall $@ \mathrm { K }$ . The NMI score is the ratio of mutual information and average entropy of a set of clusters and labels. It evaluates only for the number of clusters equal to the number of classes. As discussed in Section 1, a good embedding space does not necessarily have only one cluster per class, but may have multiple well formed clusters in the space. This means that our mutual information may be higher than reported with this metric. Nevertheless, we present results on the NMI score in the interest of comparing to existing methods that evaluate on this metric. The Recall $@ \mathrm { K }$ $( \mathbb { R } ^ { \ @ \mathbb { K } ) }$ metric is better suited for evaluating an embedding space. A true positive is defined as a sample that has at least one of its true nearest K neighbours in the embedding space with the same class as itself. + +Embedding Space Dimension We investigate the importance of the embedding dimension. A similar study in Song et al. (2016a) suggests that the number of dimensions is not important for triplet networks, in fact, increasing the number of dimensions can be detrimental to performance. We compare our method with increasing dimension size against triplet loss (Weinberger et al., 2006; + +![](images/c12dcaaee4263341e5a94a15e639afe7c1aabf716e1c6bfa48752a0b28b68e8c.jpg) +Figure 2: Effect of embedding size on NMI score on the test set of Cars196 (left) and Birds200 (right). The NMI of our RBF approach improves with increasing embedding size, while performance degrades or oscillates for triplet (Weinberger et al., 2006; Schroff et al., 2015) and lifted structured embedding (Song et al., 2016a). + +![](images/6ee4762a10f3fa17ca4f97739f1a0d53a7d49d6330e5cecafd50aaa8f77d629c.jpg) +Figure 3: Recall of our RBF solver at 1, 2, 4 and 8 nearest neighbours on the test set of Cars196 (left) and Birds200 (right). Recall performance of our approach increases with embedding size. + +Schroff et al., 2015) and lifted structured embedding (Song et al., 2016a), both taken from the study in Song et al. (2016a). Figure 2 shows the effect of the embedding size on NMI score. It’s clear that while increasing the number of dimensions does not necessarily improve performance for triplet-based networks, the dimensionality is important for our RBF approach. The NMI score for our approach improves with increasing numbers of dimensions. Similar behaviour is seen in Figure 3, which shows the Recall $@ \mathrm { K }$ metric for our RBF method with varying numbers of dimensions. Again, this shows that the dimensionality is an important factor for our approach. + +Comparison of Results Our approach is compared to the state-of-the-art in Table 1, with the compared results taken from Song et al. (2016b) and Kumar et al. (2017). Since, as discussed above, the number of embedding dimensions does not have much impact on the other approaches, all results in Song et al. (2016b) and Kumar et al. (2017) are reported using 64 dimensions. For fair comparison, we report our results at 64 dimensions, but also at the better performing higher dimensions. Our approach outperforms the other methods in both the NMI and Recall $@ \mathrm { K }$ measures, at all embedding sizes presented. Our approach is able to produce better compact embeddings than existing methods, but can also take advantage of a larger embedding space. Figure 4 shows a t-SNE (van der Maaten & Hinton, 2008) visualisation of the Birds200 test set embedding space. Despite the test classes being withheld during training, bird species are well clustered. + +![](images/9ad95d5dfa4f101642116b32c7576560527f37481ecf02e7b0a2c6153c559e48.jpg) +Figure 4: Visualisation of the Birds200 test set embedding space, using the t-SNE algorithm (van der Maaten & Hinton, 2008). Despite not being trained on the test classes, bird species are well clustered. Best viewed in colour and zoomed in on a monitor. + +# 4.2 IMAGE CLASSIFICATION + +Experimental Set-up We evaluate our solver in the domain of image classification, comparing performance with conventional softmax loss. For all experiments, images are resized to $2 5 6 \mathbf { x } 2 5 6$ and random cropping and horizontal mirroring is used for data augmentation. Unlike in Section 4.1, we crop Birds200 and Cars196 images using the provided bounding boxes before resizing. The same classes are used for training and testing. All datasets are split in to training, validation and test sets. We select softmax and RBF hyperparameters that minimise the validation loss. The FC7 layer (4096 dimensions), with dropout and without a ReLU, is used as the embedding layer for our RBF solver when using a VGG (Simonyan & Zisserman, 2014) or AlexNet (Krizhevsky et al., 2012) architecture. For a ResNet architecture (He et al., 2016), we use the final pooling layer (2048 dimensions). We find that following the ResNet embedding layer with a dropout layer results in a small performance gain for both RBF and softmax solvers. A batch size of 20 is used and an update interval of 10 epochs, unless otherwise noted. We use stochastic gradient descent optimisation. In general, we find a base learning rate of 0.00001 to be appropriate for our approach. A standard deviation of around 100 for the RBFs is found to be suitable for the 4096 dimension VGG16 embeddings on Birds200. Networks are initialised with ImageNet (Russakovsky et al., 2015) pre-trained weights. + +![](images/b82bff4ec4bcfa40985140153ccd5b9e8ccc7a88ed46ec80451369726237ca81.jpg) +Figure 5: Effect of the number of training samples per class on the test set accuracy of Birds200, using a VGG16 architecture. Note that the final data point in the plot refers to the entire training set; while most classes have 24 training samples per class, some have only 23. + +Table 2: Birds200 test set accuracy. + +
Base NetworkSolver
SoftmaxRBF (Ours)
AlexNet62.4166.95
VGG1675.3778.63
ResNet5078.0578.98
+ +Evaluation on Birds200 We carry out detailed evaluation of our approach on the Birds200 dataset. Since there is no standard validation set for this dataset, we take $20 \%$ of the training data as validation data. In Table 2, we evaluate with three network architectures; AlexNet (Krizhevsky et al., 2012), VGG16 (Simonyan & Zisserman, 2014) and ResNet50 (He et al., 2016). Our approach outperforms the softmax counterpart for each network. The performance gain over softmax is larger for AlexNet and VGG than for ResNet. This is likely because ResNet has significantly more non-linear activation function layers, meaning there is less improvement seen when using the highly non-linear RBF solver. The effect of the number of training samples per class is shown in Figure 5. Our RBF approach outperforms softmax loss at all numbers of training images, with a particularly large gain when training data is scarce. + +Results from ablation experiments on our RBF approach are shown in Table 3. The importance of the following components of learning are shown; tuning the RBF standard deviation $\sigma$ , learning the RBF weights and fine-tuning the network weights. Figure 6a shows the impact of the number of nearest neighbours used for each sample during training. There is a clear lower bound required for good performance. As discussed in Section 3.3, this is because the network weights are constantly being updated, but the stored RBF centres are not. As such, we need to consider a larger number of neighbours than if the centres were always up-to-date. Figure 6b shows the average distance from each training sample to its nearest RBF centres at different points during training. Similarly, Figure 6c shows the average radial basis function values between training samples and their nearest centres. These experiments use a VGG16 architecture. + +Table 3: Ablation study on Birds200. + +
Initial Network WeightsTune σLearn RBF WeightsFine-tune Network WeightsTest Accuracy
RandomYesNoNo1.35
ImageNetYesNoNo47.32
ImageNetYesYesNo49.22
ImageNetYesNoYes77.94
ImageNetYesYesYes78.63
+ +![](images/b4f1926e93fd86b15012674b1408c4e84caeaf5b21bca4425d0de792ca91fecc.jpg) +Figure 6: (a) The effect of the number of nearest neighbours considered during training. (b) The average distance from training samples to their nearest RBF centres. (c) The average RBF value between training samples and their nearest RBF centres. + +When training with softmax loss on a VGG16 architecture, validation loss plateaus at around 7000 iterations. For our RBF solver, the number of iterations taken for validation loss to stop improving depends on the update interval, that is, the interval at which the RBF centres are updated and the nearest neighbours computed. For update intervals of 1, 5 and 10, validation loss stops improving at around 8500, 12000 and 15000 iterations, respectively. Since nearest neighbour search becomes the bottleneck as the dataset size increases, a less frequent update interval should be used for large datasets, allowing for a faster overall training time. The softmax solver is able to converge in fewer iterations than our approach. This is likely due to the RBF centres not being up-to-date at all times, leading to weight updates that are less effective than in the ideal scenario. However, as discussed in Section 3.3, keeping the RBF centres up-to-date at all times in intractable. + +Our RBF approach allows clusters to position themselves freely in the embedding space, such that the intrinsic structure of the data can be represented. As a result, we expect the embeddings to be co-located based not only in terms of class, but also in terms of more fine-grained information, such as attributes. We use the 312 binary attributes of Birds200 to confirm this expectation. For each 4096 dimension VGG16 test set embedding, we propagate attributes by computing the density of each attribute label present in the neighbouring test embeddings. This is done using Gaussian radial basis functions, treating each attribute as a binary classification problem. We find the best Gaussian standard deviation for softmax and our RBF learned embeddings separately. A precision and recall curve, shown in Figure 7, is generated by sweeping the classification discrimination threshold from zero to one. We find that for a given precision, the RBF solver results in an embedding space with better attribute recall than softmax. Note that we do not train the models using the attribute labels. + +Other Datasets We further evaluate our approach on three other fine-grained classification datasets; Oxford 102 Flowers (Nilsback & Zisserman, 2008), Stanford Cars196 (Krause et al., 2013) and + +![](images/da213ab32b744bcc91a0ebcedb139e9d3e3f2409ebcc52d565034950822f1a9c.jpg) +Figure 7: Attribute precision and recall on the 312 binary attributes of Birds200. The attributes are propagated from neighbouring test embeddings and the curves are generated by sweeping the classification discrimination threshold. The ideal standard deviation is found for the RBF and softmax approaches separately. No training was carried out on the attribute labels. + +Table 4: Test accuracy on fine-grained classification datasets. + +
DatasetSoftmaxRBF (Ours)
Oxford 102 Flowers82.7986.26
Stanford Cars19685.6786.52
Leafsnap Field73.8075.96
+ +Leafsnap (Kumar et al., 2012). We use the standard training, validation and test splits for Oxford 102 Flowers. For Stanford Cars196, we take $30 \%$ of the training set as validation data. We use the challenging field images from Leafsnap, which are taken in uncontrolled conditions. The dataset contains 185 classes of leaf species and we split the data into $50 \%$ , $20 \%$ and $30 \%$ for training, validation and testing, respectively. Again, hyperparameters are selected based on validation loss and a VGG16 architecture is used. Results are shown in Table 4. + +# 5 DISCUSSION AND CONCLUSION + +Our approach is designed to address two problems; metric space learning and classification. The use of RBFs arises very naturally in the context of the first problem because metric spaces are defined and measured in terms of Euclidean distance. It is perhaps more surprising that the classification problem also benefits from using a metric space kernel density approach, rather than softmax. This appears to hold independently of the base network architecture (Table 2) and the improvement is particularly strong when limited quantities of training data are available (Figure 5). + +Metric learning inherently pulls samples together into high density regions of the embedding space, whereas softmax is content to allow samples to fill a very large region of space, provided that the logit dimension corresponding to the correct class is larger than the others. This suggests that metric learning is able to provide some regularisation, because classification is driven by multiple nearby samples, whereas samples may be well separated in logit space for softmax. In turn, this leads to increased robustness for the metric space approach, particularly when training data is impoverished. Additionally, softmax is constrained to push samples into regions of space determined by the locations of the logit axes, whereas our metric learning approach is free to position clusters in a way that may more naturally reflect the intrinsic structure of the data. Finally, our approach is also free to create multiple clusters for each class, if this is appropriate. As a result of these factors, our RBF solver is able to outperform state-of-the-art approaches in the metric learning problem, as well as provide benefit over softmax in the classification problem. + +# REFERENCES + +Jane Bromley, I Guyon, Yann Lecun, Eduard Sackinger, and R Shah. Signature verification using a Siamese time delay neural network. In Advances in neural information processing systems (NIPS 1993), 1993. + +David S Broomhead and David Lowe. Radial basis functions, multi-variable functional interpolation and adaptive networks. Technical report, DTIC Document, 1988. + +S Chopra, R Hadsell, and Y LeCun. Learning a similarity metric discriminatively, with application to face verification. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), volume 1, pp. 539–546, 2005. + +Jeff Donahue, Yangqing Jia, Oriol Vinyals, Judy Hoffman, Ning Zhang, Eric Tzeng, and Trevor Darrell. DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition. In Icml, volume 32, pp. 647–655, 2014. + +R Hadsell, S Chopra, and Y LeCun. Dimensionality Reduction by Learning an Invariant Mapping. In 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’06), volume 2, pp. 1735–1742, 2006. + +B Harwood and T Drummond. FANNG: Fast Approximate Nearest Neighbour Graphs. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5713–5722, 2016. + +K He, X Zhang, S Ren, and J Sun. Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778, 2016. + +Elad Hoffer and Nir Ailon. Deep metric learning using triplet network. In International Workshop on Similarity-Based Pattern Recognition, pp. 84–92, 2015. + +Jonathan Krause, Michael Stark, Jia Deng, and Li Fei-Fei. 3d object representations for finegrained categorization. In Proceedings of the IEEE International Conference on Computer Vision Workshops, pp. 554–561, 2013. + +Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. ImageNet Classification with Deep Convolutional Neural Networks. In Advances in Neural Information Processing Systems, pp. 1097–1105. 2012. + +Neeraj Kumar, Peter N Belhumeur, Arijit Biswas, David W Jacobs, W John Kress, Ida Lopez, and João V B Soares. Leafsnap: A Computer Vision System for Automatic Plant Species Identification. In The 12th European Conference on Computer Vision (ECCV), 2012. + +Vijay B G Kumar, G Carneiro, and I Reid. Learning Local Image Descriptors with Deep Siamese and Triplet Convolutional Networks by Minimizing Global Loss Functions. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5385–5394, 2016. + +Vijay B G Kumar, Ben Harwood, Gustavo Carneiro, Ian Reid, and Tom Drummond. Smart Mining for Deep Metric Learning. arXiv preprint arXiv:1704.01285, 2017. + +Christopher D Manning, Prabhakar Raghavan, and Hinrich Schütze. Introduction to information retrieval, volume 1. Cambridge university press Cambridge, 2008. + +M-E. Nilsback and A Zisserman. Automated Flower Classification over a Large Number of Classes. In Proceedings of the Indian Conference on Computer Vision, Graphics and Image Processing, 2008. + +Ali Sharif Razavian, Hossein Azizpour, Josephine Sullivan, and Stefan Carlsson. CNN Features Offthe-Shelf: An Astounding Baseline for Recognition. In Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 512–519, 2014. + +Oren Rippel, Manohar Paluri, Piotr Dollar, and Lubomir Bourdev. Metric learning with adaptive density discrimination. International Conference on Learning Representations, 2016. + +Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. Imagenet large scale visual recognition challenge. International Journal of Computer Vision, 115(3):211–252, 2015. + +F Schroff, D Kalenichenko, and J Philbin. FaceNet: A unified embedding for face recognition and clustering. In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 815–823, 2015. + +K Simonyan and A Zisserman. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv preprint arXiv:1409.1556, 2014. + +Kihyuk Sohn. Improved Deep Metric Learning with Multi-class N-pair Loss Objective. In Advances in Neural Information Processing Systems 29, pp. 1857–1865. 2016. + +H O Song, Y Xiang, S Jegelka, and S Savarese. Deep Metric Learning via Lifted Structured Feature Embedding. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4004–4012, 2016a. + +Hyun Oh Song, Stefanie Jegelka, Vivek Rathod, and Kevin Murphy. Learnable Structured Clustering Framework for Deep Metric Learning. arXiv preprint arXiv:1612.01213, 2016b. + +Nitish Srivastava, Geoffrey E Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15(1):1929–1958, 2014. + +C Szegedy, Wei Liu, Yangqing Jia, P Sermanet, S Reed, D Anguelov, D Erhan, V Vanhoucke, and A Rabinovich. Going deeper with convolutions. In 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1–9, 2015. + +Yichuan Tang. Deep learning using linear support vector machines. arXiv preprint arXiv:1306.0239, 2013. + +Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-SNE. Journal of Machine Learning Research, 9(Nov):2579–2605, 2008. + +J Wang, Y Song, T Leung, C Rosenberg, J Wang, J Philbin, B Chen, and Y Wu. Learning FineGrained Image Similarity with Deep Ranking. In 2014 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1386–1393, 2014. + +Kilian Q Weinberger, John Blitzer, and Lawrence Saul. Distance metric learning for large margin nearest neighbor classification. Advances in neural information processing systems, 2006. + +P Welinder, S Branson, T Mita, C Wah, F Schroff, S Belongie, and P Perona. Caltech-UCSD Birds 200. Technical Report CNS-TR-2010-001, California Institute of Technology, 2010. \ No newline at end of file diff --git a/parse/train/SkFEGHx0Z/SkFEGHx0Z_content_list.json b/parse/train/SkFEGHx0Z/SkFEGHx0Z_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..99fd8c3483e4b1b67ea5d6222aa05040e22cba1d --- /dev/null +++ b/parse/train/SkFEGHx0Z/SkFEGHx0Z_content_list.json @@ -0,0 +1,1188 @@ +[ + { + "type": "text", + "text": "NEAREST NEIGHBOUR RADIAL BASIS FUNCTION SOLVERS FOR DEEP NEURAL NETWORKS ", + "text_level": 1, + "bbox": [ + 176, + 98, + 808, + 146 + ], + "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": "We present a radial basis function solver for convolutional neural networks that can be directly applied to both distance metric learning and classification problems. Our method treats all training features from a deep neural network as radial basis function centres and computes loss by summing the influence of a feature’s nearby centres in the embedding space. Having a radial basis function centred on each training feature is made scalable by treating it as an approximate nearest neighbour search problem. End-to-end learning of the network and solver is carried out, mapping high dimensional features into clusters of the same class. This results in a well formed embedding space, where semantically related instances are likely to be located near one another, regardless of whether or not the network was trained on those classes. The same loss function is used for both the metric learning and classification problems. We show that our radial basis function solver outperforms state-of-the-art embedding approaches on the Stanford Cars196 and CUB-200- 2011 datasets. Additionally, we show that when used as a classifier, our method outperforms a conventional softmax classifier on the CUB-200-2011, Stanford Cars196, Oxford 102 Flowers and Leafsnap fine-grained classification datasets. ", + "bbox": [ + 233, + 267, + 766, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 516, + 336, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The solver of a neural network is vital to its performance, as it defines the objective and drives the learning. We define a solver as the layers of the network that are aware of the class labels of the data. In the domain of image classification, a softmax solver is conventionally used to transform activations into a distribution across class labels (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016). While in the domain of distance metric learning, a Siamese (Chopra et al., 2005) or triplet (Hoffer & Ailon, 2015; Schroff et al., 2015; Kumar et al., 2017) solver, with contrastive or hinge loss, is commonly used to pull embeddings of the same class together and push embeddings of different classes apart. The two tasks of classification and metric learning are related but distinct. Conventional classification learning is generally used when the objective is to associate data with a pre-defined set of classes and there is sufficient data to train or fine-tune a network to do so. Distance metric learning, or embedding space building, aims to learn an embedding space where samples with similar semantic meaning are located near one another. Applications for learning such effective embeddings include transfer learning, retrieval, clustering and weakly supervised or self-supervised learning. ", + "bbox": [ + 174, + 547, + 825, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present a deep neural network solver that can be applied to both embedding space building and classification problems. The solver defines training features in the embedding space as radial basis function (RBF) centres, which are used to push or pull features in a local neighbourhood, depending on the labels of the associated training samples. The same loss function is used for both classification and metric learning problems. This means that a network trained for the classification task results in feature embeddings of the same class being located near one another and similarly, a network trained for metric learning results in feature embeddings that can be well classified by our RBF solver. Fast approximate nearest neighbour search is used to provide an efficient and scalable solution. ", + "bbox": [ + 174, + 750, + 825, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The best success on embedding building tasks has been achieved by deep metric learning methods (Hoffer & Ailon, 2015; Schroff et al., 2015; Song et al., 2016a; Sohn, 2016; Kumar et al., 2017), which make use of deep neural networks. Such approaches may indiscriminately pull samples of the same class together, regardless of whether the two samples were already within well defined local clusters of like samples. These methods aim to form a single cluster per class. In contrast, our approach pushes a feature around the embedding space based only on the local neighbourhood of that feature. This means that the current structure of the space is considered, allowing multiple clusters to form for a single class, if that is appropriate. Our radial basis function solver is able to learn embeddings that result in samples of similar semantic meaning being located near one another. Our experiments show that the RBF solver is able to do this better than existing deep metric learning methods. ", + "bbox": [ + 176, + 882, + 825, + 924 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 825, + 214 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Softmax solvers have been a mainstay of the standard classification problem (Krizhevsky et al., 2012; Simonyan & Zisserman, 2014; Szegedy et al., 2015; He et al., 2016). Such an approach is inefficient as classes must be axis-aligned and the number of classes is baked into the network. Our RBF approach is free to position clusters such that the intrinsic structure of the data can be better represented. This may involve multiple clusters forming for a single class. The nearest neighbour RBF solver outperforms conventional softmax solvers in our experiments and provides additional adaptability and flexibility, as new classes can be added to the problem with no updates to the network weights required to obtain reasonable results. This performance improvement is obtained despite smaller model capacity. The RBF solver by its very nature is a classifier, but learns the classification problem in the exact same way it learns the embedding space building problem. ", + "bbox": [ + 174, + 222, + 825, + 361 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main advantages of our novel radial basis function solver for neural networks can be summarised as follows: ", + "bbox": [ + 173, + 367, + 823, + 395 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• Our solver can be directly applied to two previously separate problems; classification and embedding space learning. \n• End-to-end learning can be made scalable by leveraging fast approximate nearest neighbour search (as seen in Section 3.2). Our approach outperforms current state-of-the-art deep metric learning algorithms on the Stanford Cars196 and CUB-200-2011 datasets (as seen in Section 4.1). Finally, our radial basis function classifier outperforms a conventional softmax classifier on the fine-grained classification datasets CUB-200-2011, Stanford Cars196, Oxford 102 Flowers and Leafsnap (as seen in Section 4.2). ", + "bbox": [ + 215, + 409, + 825, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 570, + 344, + 587 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Radial Basis Functions in Neural Networks Radial basis function networks were introduced by Broomhead & Lowe (1988). The networks formulate activation functions as RBFs, resulting in an output that is a sum of radial basis function values between the input and network parameters. In contrast to these radial basis function networks, our approach uses RBFs in the solver of a deep convolutional neural network and our radial basis function centres are coupled to high dimensional embeddings of training samples, rather than being network parameters. Radial basis functions have been used as neural network solvers in the form of support vector machines. In one such formulation, a neural network is used as a fixed feature extractor and separate support vector machines are trained to classify the features (Razavian et al., 2014; Donahue et al., 2014). No joint training occurs between the solver (classifier) and network. Such an approach is often used for transfer learning, where the network is trained on vast amounts of data and the support vector machines are trained for problems in which labelled training data is scarce. Tang (2013) replaces the typical softmax classifier with linear support vector machines. In this case, the solver and network are trained jointly, meaning the loss that is minimised is margin based. ", + "bbox": [ + 174, + 602, + 825, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Metric Learning Early methods in the domain of metric learning include those that use Siamese networks (Bromley et al., 1993) and contrastive loss (Hadsell et al., 2006; Chopra et al., 2005). The objective of these approaches is to pull pairwise samples of the same class together and push pairwise samples of different classes apart. Such methods work on absolute distances, while triplet networks with hinge loss (Weinberger et al., 2006) work on relative distance. Triplet loss approaches take a trio of inputs; an anchor, a positive sample of the same class as the anchor and a negative sample of a different class. Triplet loss aims to pull the positive sample closer to the anchor than the negative sample. Several deep metric learning approaches make use of, or generalise deep triplet neural networks (Hoffer & Ailon, 2015; Wang et al., 2014; Schroff et al., 2015; Song et al., 2016a; Sohn, 2016; Kumar et al., 2017). Schroff et al. (2015) perform semi-hard mining within a mini-batch, while Song et al. (2016a) propose a lifted structured embedding with efficient computation of the full distance matrix within a mini-batch. This allows comparisons between all positive and negative pairs in the batch. Similarly, Sohn (2016) proposes an approach that allows multiple intra-batch distance comparisons, but optimises a generalisation of triplet loss, named N-pair loss, rather than a max-margin based objective, as in Song et al. (2016a). The global embedding structure is considered in Song et al. (2016b) by directly minimising a global clustering metric, while a combination of global and triplet loss is shown to be beneficial in Kumar et al. (2016). Finally, Kumar et al. (2017) introduce a smart mining technique that mines for triplets over the entire dataset. A Fast Approximate Nearest Neighbour Graph (FANNG) (Harwood & Drummond, 2016) is leveraged for computational efficiently. Beyond triplet loss, Rippel et al. (2016) introduce a loss function that allows multiple clusters to form per class. Rather than only penalising a single triplet at a time, the neighbourhood densities are considered and overlaps between classes penalised. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/73dfcbed79adccb1fa69d2669a2d68b8d5ca02240c86bd7a56aab148be320002.jpg", + "image_caption": [ + "Figure 1: Overview of our radial basis function solver. " + ], + "image_footnote": [], + "bbox": [ + 174, + 99, + 823, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 304, + 825, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 RADIAL BASIS FUNCTION SOLVERS ", + "text_level": 1, + "bbox": [ + 174, + 518, + 506, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A radial basis function returns a value that depends only on the distance between two points, one of which is commonly referred to as a centre. Although several radial basis functions exist, in this paper we use RBF to refer to a Gaussian radial basis function, which returns a value based on the Euclidean distance between a point $\\mathbf { X }$ and the RBF centre c. The radial basis function, $f$ , is calculated as: ", + "bbox": [ + 173, + 549, + 825, + 606 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/0b9dec16d20b8f7d28f3b2653f10a9acd994feafcdb638316cb0f5a5693741e3.jpg", + "text": "$$\nf ( \\mathbf { x } , \\mathbf { c } ) = \\exp \\left( \\frac { - \\| \\mathbf { x } - \\mathbf { c } \\| ^ { 2 } } { 2 \\sigma ^ { 2 } } \\right)\n$$", + "text_format": "latex", + "bbox": [ + 397, + 609, + 601, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma$ is standard deviation that controls the width of the Gaussian curve, that is, the region around the RBF centre deemed to be of importance. ", + "bbox": [ + 176, + 647, + 826, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the context of our neural network solver, we define the deep feature embeddings of each training set sample as radial basis function centres. Specifically, we take the layer in a network immediately before the solver as the embedding layer. For example, in a VGG architecture, this may be FC7 (fully connected layer 7), forming a 4096 dimension embedding. In general, however, the embedding may be of any size. An overview of this approach is seen in Figure 1. ", + "bbox": [ + 174, + 683, + 825, + 752 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 CLASSIFIER AND LOSS FUNCTION ", + "text_level": 1, + "bbox": [ + 176, + 768, + 450, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A radial basis function classifier can be formed by the weighted sum of the RBF distance calculations between a sample feature embedding and the centres. Classification of a sample is achieved by passing the input through the network, resulting in a feature embedding in the same space as the RBF centres. A probability distribution over class labels is found by summing the influence of each centre and normalising. A centre contributes only to the probability of the ground truth label of the training sample coupled to that centre. For example, the probability that the feature embedding $\\mathbf { X }$ has class label $Q$ is: ", + "bbox": [ + 173, + 794, + 825, + 891 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/c99b5f94e1bec4588b5d8120c9f4f6a0833844fafd8a9e96c24ba09352dbd282.jpg", + "text": "$$\nP r ( \\mathbf { x } \\in \\operatorname { c l a s s } Q ) = \\frac { \\sum _ { i \\in Q } w _ { i } f ( \\mathbf { x } , \\mathbf { c _ { i } } ) } { \\sum _ { j = 1 } ^ { m } w _ { j } f ( \\mathbf { x } , \\mathbf { c _ { j } } ) } ,\n$$", + "text_format": "latex", + "bbox": [ + 367, + 888, + 627, + 929 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f$ is the RBF, $i \\in Q$ are the centres with label $Q$ , $m$ is the number of training samples and $w _ { i }$ is a learnable weight for RBF centre $i$ . Of course, if a sample is in the training set and has a corresponding RBF centre, the distance calculation to itself is omitted during the computation of the classification distribution, the loss function and the derivatives. ", + "bbox": [ + 174, + 103, + 823, + 160 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss function used for optimisation is simply the summed negative logarithm of the probabilities of the true class labels. For example, the loss $L$ for sample $\\mathbf { X }$ with ground truth label $R$ is: ", + "bbox": [ + 171, + 166, + 823, + 195 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/9bb32f330f211af7618a01c37cd98921b95b2bf14d564756505ef2e151c55f82.jpg", + "text": "$$\nL ( \\mathbf { x } ) = - \\ln \\left( P r ( \\mathbf { x } \\in \\operatorname { c l a s s } R ) \\right) .\n$$", + "text_format": "latex", + "bbox": [ + 387, + 198, + 609, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The same loss function is used regardless of whether the network is being trained for classification, as above, or for embedding space building (distance metric learning). This is possible since the RBF classifier is directly computed from distances between features in the embedding space. This means that a network trained for classification will result in features of the same class being located near one another, and similarly a network trained for metric learning will result in an embedding space in which features can be well classified using RBFs. ", + "bbox": [ + 173, + 217, + 825, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 NEAREST NEIGHBOUR RBF SOLVER ", + "text_level": 1, + "bbox": [ + 176, + 316, + 468, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Equation 2, the distribution is calculated by summing over all RBF centres. However, since these centres are attached to training samples, of which there could be any large number, computing that sum is both intractable and unnecessary. The majority of RBF values for a given feature embedding will be effectively zero, as the sample feature will lie only within a subset of the RBF centres’ Gaussian windows. As such, only the local neighbourhood around a feature embedding should be considered. Operating on the set of the nearest RBF centres to a feature ensures that most of the distance values computed are pertinent to the loss calculation. The classifier equation becomes: ", + "bbox": [ + 173, + 343, + 825, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/325b18d1e53eff7c6d216b7383e0c9df86986896d30805f7d46d60dbc51063fc.jpg", + "text": "$$\nP r ( \\mathbf x \\in \\mathrm { c l a s s } Q ) = \\frac { \\sum _ { i \\in Q \\cap \\mathcal { N } } w _ { i } f ( \\mathbf x , \\mathbf c _ { \\mathbf i } ) } { \\sum _ { j \\in \\mathcal { N } } w _ { j } f ( \\mathbf x , \\mathbf c _ { \\mathbf j } ) } ,\n$$", + "text_format": "latex", + "bbox": [ + 356, + 443, + 637, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal { N }$ is the set of approximate nearest neighbours for sample $\\mathbf { X }$ and therefore $i \\in Q \\cap \\mathcal N$ is the set of approximate nearest neighbours that have label $Q$ . Again, we note that training set samples exclude their own RBF centre from their nearest neighbour list. ", + "bbox": [ + 174, + 484, + 825, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the interest of providing a scalable solution, we use approximate nearest neighbour search to obtain candidate nearest neighbour lists. This allows for a trade off between precision and computational efficiency. Specifically, we use a Fast Approximate Nearest Neighbour Graph (FANNG) (Harwood & Drummond, 2016), as it provides the most efficiency when needing a high probability of finding the true nearest neighbours of a query point. Importantly, FANNG provides scalability in terms of the number of dimensions and the number of training samples. ", + "bbox": [ + 174, + 532, + 825, + 617 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3 END-TO-END LEARNING ", + "text_level": 1, + "bbox": [ + 174, + 633, + 385, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The network and solver weights are learned end-to-end. As the weights are constantly being updated during training, the locations of the RBF centres are changing. This leads to complications in the computation of the derivatives of the loss with respect to the embeddings. This calculation requires dimension by dimension differences between the training embeddings and the RBF centres. The centres are moving as the network is being updated, but computing the current RBF centre locations online is intractable. For example, if considering 100 nearest neighbours, 101 samples would need to be forward propagated through the network for each training sample. However, we find that is is not necessary for the RBF centres to be up to date at all times in order for the model to converge. A bank of the RBF centres is stored and updated at a fixed interval. ", + "bbox": [ + 174, + 659, + 825, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A further consequence of the RBF centres moving during training is that the nearest neighbours also change. It is intractable to find to correct nearest neighbours each time the weights are updated. This is simply remedied by considering a larger number of nearest neighbours than would be required if all centres and neighbour lists were up-to-date at all times. The embedding space changes slowly enough that it is highly likely many of the previously neighbouring RBF centres will remain relevant. Since the Gaussian RBF decays to zero as the distance between the points becomes large, it does not matter if an RBF centre that is no longer near the sample remains a candidate nearest neighbour. ", + "bbox": [ + 174, + 790, + 825, + 888 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We call the frequency at which the RBF centres are updated and the nearest neighbours found the update interval. During training, at a fixed number of epochs we forward pass the entire training set through the network, storing the new RBF centres. The up-to-date nearest neighbours can now be found. If FANNG is used, a rebuild of the graph is required. Note that the stored RBF centres do not have dropout (Srivastava et al., 2014) applied, but the current training embeddings may. The effect of the number of nearest neighbours considered and the update interval are discussed in Section 4.2. ", + "bbox": [ + 174, + 895, + 823, + 924 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 159 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Radial Basis Function Parameters A global standard deviation parameter $\\sigma$ is shared amongst the RBFs. This ensures that the assumption made about samples only being influenced by their nearest RBF centres holds. Although the parameter is learnable, we find that fixing the standard deviation value before training is a suitable approach. We treat the standard deviation as an additional hyperparameter to tune, however it can also be learned independently before full network training commences. As seen in Equation 4, each RBF centre has a weight, which is learned end-to-end with the network weights. These weights are initialised at values of one. Note that in our experiments we only tune the RBF weights for the classification task; they remain fixed for metric learning problems. ", + "bbox": [ + 174, + 175, + 825, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 308, + 326, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We detail our experimental results in two tasks; distance metric learning and image classification. ", + "bbox": [ + 176, + 339, + 808, + 353 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1 DISTANCE METRIC LEARNING ", + "text_level": 1, + "bbox": [ + 176, + 372, + 426, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experimental Set-up We evaluate our approach on two datasets; Stanford Cars196 (Krause et al., 2013) and CUB-200-2011 (Birds200) (Welinder et al., 2010). Cars196 consists of 16,185 images of 196 different car makes and models, while Birds200 consists of 11,788 images of 200 different bird species. In this problem, the network is trained and evaluated on different sets of classes. We follow the experimental set-up used in Song et al. (2016a); Sohn (2016); Song et al. (2016b); Kumar et al. (2017). For the Cars196 dataset, we train the network on the first 98 classes and evaluate on the remaining 98. For the Birds200 dataset we train on the first 100 classes and evaluate on the remaining 100. Stochastic gradient descent optimisation is used. All images are first resized to be 256x256 and data is augmented by random cropping and horizontal mirroring. Note that we do not crop the images using the provided bounding boxes. ", + "bbox": [ + 174, + 398, + 825, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our method is compared to state-of-the-art approaches on the considered datasets; semi-hard mining for triplet networks (Schroff et al., 2015), lifted structured feature embedding (Song et al., 2016a), N-pair loss (Sohn, 2016), clustering (Song et al., 2016b), global loss with triplet networks (Kumar et al., 2016) and smart mining for triplet networks (Kumar et al., 2017). For fair comparison to these methods, we use the same base architecture for our experiments; GoogLeNet (Szegedy et al., 2015). Network weights are initialised from ImageNet (Russakovsky et al., 2015) pre-trained weights. We use 100 nearest neighbours and an update interval of 10 epochs. RBF weights are fixed at a value of one for this task. We train for 50 epochs on Cars196 and 30 epochs on Birds200. A batch size of 20, base learning of 0.00001 and weight decay of 0.0002 are used. The RBF standard deviation used depends on size of the embedding dimension. We find values between 10 and 30 work well for this task. ", + "bbox": [ + 174, + 544, + 825, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics Following Song et al. (2016a), we evaluate the embedding space using two metrics; Normalised Mutual Information (NMI) (Manning et al., 2008) and Recall $@ \\mathrm { K }$ . The NMI score is the ratio of mutual information and average entropy of a set of clusters and labels. It evaluates only for the number of clusters equal to the number of classes. As discussed in Section 1, a good embedding space does not necessarily have only one cluster per class, but may have multiple well formed clusters in the space. This means that our mutual information may be higher than reported with this metric. Nevertheless, we present results on the NMI score in the interest of comparing to existing methods that evaluate on this metric. The Recall $@ \\mathrm { K }$ $( \\mathbb { R } ^ { \\ @ \\mathbb { K } ) }$ metric is better suited for evaluating an embedding space. A true positive is defined as a sample that has at least one of its true nearest K neighbours in the embedding space with the same class as itself. ", + "bbox": [ + 174, + 712, + 825, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Embedding Space Dimension We investigate the importance of the embedding dimension. A similar study in Song et al. (2016a) suggests that the number of dimensions is not important for triplet networks, in fact, increasing the number of dimensions can be detrimental to performance. We compare our method with increasing dimension size against triplet loss (Weinberger et al., 2006; ", + "bbox": [ + 176, + 867, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c12dcaaee4263341e5a94a15e639afe7c1aabf716e1c6bfa48752a0b28b68e8c.jpg", + "image_caption": [ + "Figure 2: Effect of embedding size on NMI score on the test set of Cars196 (left) and Birds200 (right). The NMI of our RBF approach improves with increasing embedding size, while performance degrades or oscillates for triplet (Weinberger et al., 2006; Schroff et al., 2015) and lifted structured embedding (Song et al., 2016a). " + ], + "image_footnote": [], + "bbox": [ + 171, + 98, + 823, + 290 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6ee4762a10f3fa17ca4f97739f1a0d53a7d49d6330e5cecafd50aaa8f77d629c.jpg", + "image_caption": [ + "Figure 3: Recall of our RBF solver at 1, 2, 4 and 8 nearest neighbours on the test set of Cars196 (left) and Birds200 (right). Recall performance of our approach increases with embedding size. " + ], + "image_footnote": [], + "bbox": [ + 173, + 382, + 825, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Schroff et al., 2015) and lifted structured embedding (Song et al., 2016a), both taken from the study in Song et al. (2016a). Figure 2 shows the effect of the embedding size on NMI score. It’s clear that while increasing the number of dimensions does not necessarily improve performance for triplet-based networks, the dimensionality is important for our RBF approach. The NMI score for our approach improves with increasing numbers of dimensions. Similar behaviour is seen in Figure 3, which shows the Recall $@ \\mathrm { K }$ metric for our RBF method with varying numbers of dimensions. Again, this shows that the dimensionality is an important factor for our approach. ", + "bbox": [ + 174, + 655, + 825, + 752 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison of Results Our approach is compared to the state-of-the-art in Table 1, with the compared results taken from Song et al. (2016b) and Kumar et al. (2017). Since, as discussed above, the number of embedding dimensions does not have much impact on the other approaches, all results in Song et al. (2016b) and Kumar et al. (2017) are reported using 64 dimensions. For fair comparison, we report our results at 64 dimensions, but also at the better performing higher dimensions. Our approach outperforms the other methods in both the NMI and Recall $@ \\mathrm { K }$ measures, at all embedding sizes presented. Our approach is able to produce better compact embeddings than existing methods, but can also take advantage of a larger embedding space. Figure 4 shows a t-SNE (van der Maaten & Hinton, 2008) visualisation of the Birds200 test set embedding space. Despite the test classes being withheld during training, bird species are well clustered. ", + "bbox": [ + 173, + 785, + 826, + 924 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9ad95d5dfa4f101642116b32c7576560527f37481ecf02e7b0a2c6153c559e48.jpg", + "image_caption": [ + "Figure 4: Visualisation of the Birds200 test set embedding space, using the t-SNE algorithm (van der Maaten & Hinton, 2008). Despite not being trained on the test classes, bird species are well clustered. Best viewed in colour and zoomed in on a monitor. " + ], + "image_footnote": [], + "bbox": [ + 174, + 155, + 825, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2 IMAGE CLASSIFICATION ", + "text_level": 1, + "bbox": [ + 176, + 840, + 383, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experimental Set-up We evaluate our solver in the domain of image classification, comparing performance with conventional softmax loss. For all experiments, images are resized to $2 5 6 \\mathbf { x } 2 5 6$ and random cropping and horizontal mirroring is used for data augmentation. Unlike in Section 4.1, we crop Birds200 and Cars196 images using the provided bounding boxes before resizing. The same classes are used for training and testing. All datasets are split in to training, validation and test sets. We select softmax and RBF hyperparameters that minimise the validation loss. The FC7 layer (4096 dimensions), with dropout and without a ReLU, is used as the embedding layer for our RBF solver when using a VGG (Simonyan & Zisserman, 2014) or AlexNet (Krizhevsky et al., 2012) architecture. For a ResNet architecture (He et al., 2016), we use the final pooling layer (2048 dimensions). We find that following the ResNet embedding layer with a dropout layer results in a small performance gain for both RBF and softmax solvers. A batch size of 20 is used and an update interval of 10 epochs, unless otherwise noted. We use stochastic gradient descent optimisation. In general, we find a base learning rate of 0.00001 to be appropriate for our approach. A standard deviation of around 100 for the RBFs is found to be suitable for the 4096 dimension VGG16 embeddings on Birds200. Networks are initialised with ImageNet (Russakovsky et al., 2015) pre-trained weights. ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b82bff4ec4bcfa40985140153ccd5b9e8ccc7a88ed46ec80451369726237ca81.jpg", + "image_caption": [ + "Figure 5: Effect of the number of training samples per class on the test set accuracy of Birds200, using a VGG16 architecture. Note that the final data point in the plot refers to the entire training set; while most classes have 24 training samples per class, some have only 23. " + ], + "image_footnote": [], + "bbox": [ + 316, + 111, + 658, + 325 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/dda7b3a083cd96dd0fa18c6ac34446fd185bc66592fe00f371081e2cb4c84e88.jpg", + "table_caption": [ + "Table 2: Birds200 test set accuracy. " + ], + "table_footnote": [], + "table_body": "
Base NetworkSolver
SoftmaxRBF (Ours)
AlexNet62.4166.95
VGG1675.3778.63
ResNet5078.0578.98
", + "bbox": [ + 334, + 419, + 656, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 539, + 826, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation on Birds200 We carry out detailed evaluation of our approach on the Birds200 dataset. Since there is no standard validation set for this dataset, we take $20 \\%$ of the training data as validation data. In Table 2, we evaluate with three network architectures; AlexNet (Krizhevsky et al., 2012), VGG16 (Simonyan & Zisserman, 2014) and ResNet50 (He et al., 2016). Our approach outperforms the softmax counterpart for each network. The performance gain over softmax is larger for AlexNet and VGG than for ResNet. This is likely because ResNet has significantly more non-linear activation function layers, meaning there is less improvement seen when using the highly non-linear RBF solver. The effect of the number of training samples per class is shown in Figure 5. Our RBF approach outperforms softmax loss at all numbers of training images, with a particularly large gain when training data is scarce. ", + "bbox": [ + 174, + 708, + 825, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results from ablation experiments on our RBF approach are shown in Table 3. The importance of the following components of learning are shown; tuning the RBF standard deviation $\\sigma$ , learning the RBF weights and fine-tuning the network weights. Figure 6a shows the impact of the number of nearest neighbours used for each sample during training. There is a clear lower bound required for good performance. As discussed in Section 3.3, this is because the network weights are constantly being updated, but the stored RBF centres are not. As such, we need to consider a larger number of neighbours than if the centres were always up-to-date. Figure 6b shows the average distance from each training sample to its nearest RBF centres at different points during training. Similarly, Figure 6c shows the average radial basis function values between training samples and their nearest centres. These experiments use a VGG16 architecture. ", + "bbox": [ + 174, + 854, + 825, + 924 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/58475954d1a3dfc4e6587bfbbe68e7f922e085c3912341d6e8b6b09781e1ca13.jpg", + "table_caption": [ + "Table 3: Ablation study on Birds200. " + ], + "table_footnote": [], + "table_body": "
Initial Network WeightsTune σLearn RBF WeightsFine-tune Network WeightsTest Accuracy
RandomYesNoNo1.35
ImageNetYesNoNo47.32
ImageNetYesYesNo49.22
ImageNetYesNoYes77.94
ImageNetYesYesYes78.63
", + "bbox": [ + 272, + 126, + 722, + 256 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/b4f1926e93fd86b15012674b1408c4e84caeaf5b21bca4425d0de792ca91fecc.jpg", + "image_caption": [ + "Figure 6: (a) The effect of the number of nearest neighbours considered during training. (b) The average distance from training samples to their nearest RBF centres. (c) The average RBF value between training samples and their nearest RBF centres. " + ], + "image_footnote": [], + "bbox": [ + 176, + 273, + 808, + 417 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 501, + 825, + 570 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "When training with softmax loss on a VGG16 architecture, validation loss plateaus at around 7000 iterations. For our RBF solver, the number of iterations taken for validation loss to stop improving depends on the update interval, that is, the interval at which the RBF centres are updated and the nearest neighbours computed. For update intervals of 1, 5 and 10, validation loss stops improving at around 8500, 12000 and 15000 iterations, respectively. Since nearest neighbour search becomes the bottleneck as the dataset size increases, a less frequent update interval should be used for large datasets, allowing for a faster overall training time. The softmax solver is able to converge in fewer iterations than our approach. This is likely due to the RBF centres not being up-to-date at all times, leading to weight updates that are less effective than in the ideal scenario. However, as discussed in Section 3.3, keeping the RBF centres up-to-date at all times in intractable. ", + "bbox": [ + 174, + 578, + 825, + 717 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our RBF approach allows clusters to position themselves freely in the embedding space, such that the intrinsic structure of the data can be represented. As a result, we expect the embeddings to be co-located based not only in terms of class, but also in terms of more fine-grained information, such as attributes. We use the 312 binary attributes of Birds200 to confirm this expectation. For each 4096 dimension VGG16 test set embedding, we propagate attributes by computing the density of each attribute label present in the neighbouring test embeddings. This is done using Gaussian radial basis functions, treating each attribute as a binary classification problem. We find the best Gaussian standard deviation for softmax and our RBF learned embeddings separately. A precision and recall curve, shown in Figure 7, is generated by sweeping the classification discrimination threshold from zero to one. We find that for a given precision, the RBF solver results in an embedding space with better attribute recall than softmax. Note that we do not train the models using the attribute labels. ", + "bbox": [ + 174, + 723, + 825, + 877 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Other Datasets We further evaluate our approach on three other fine-grained classification datasets; Oxford 102 Flowers (Nilsback & Zisserman, 2008), Stanford Cars196 (Krause et al., 2013) and ", + "bbox": [ + 174, + 895, + 823, + 922 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/da213ab32b744bcc91a0ebcedb139e9d3e3f2409ebcc52d565034950822f1a9c.jpg", + "image_caption": [ + "Figure 7: Attribute precision and recall on the 312 binary attributes of Birds200. The attributes are propagated from neighbouring test embeddings and the curves are generated by sweeping the classification discrimination threshold. The ideal standard deviation is found for the RBF and softmax approaches separately. No training was carried out on the attribute labels. " + ], + "image_footnote": [], + "bbox": [ + 312, + 113, + 658, + 325 + ], + "page_idx": 9 + }, + { + "type": "table", + "img_path": "images/363bd419a5669c40976f6328e56b3952870f2458087f76b315aebde1beea313c.jpg", + "table_caption": [ + "Table 4: Test accuracy on fine-grained classification datasets. " + ], + "table_footnote": [], + "table_body": "
DatasetSoftmaxRBF (Ours)
Oxford 102 Flowers82.7986.26
Stanford Cars19685.6786.52
Leafsnap Field73.8075.96
", + "bbox": [ + 302, + 433, + 691, + 507 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Leafsnap (Kumar et al., 2012). We use the standard training, validation and test splits for Oxford 102 Flowers. For Stanford Cars196, we take $30 \\%$ of the training set as validation data. We use the challenging field images from Leafsnap, which are taken in uncontrolled conditions. The dataset contains 185 classes of leaf species and we split the data into $50 \\%$ , $20 \\%$ and $30 \\%$ for training, validation and testing, respectively. Again, hyperparameters are selected based on validation loss and a VGG16 architecture is used. Results are shown in Table 4. ", + "bbox": [ + 173, + 531, + 826, + 614 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "5 DISCUSSION AND CONCLUSION ", + "text_level": 1, + "bbox": [ + 178, + 635, + 468, + 651 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Our approach is designed to address two problems; metric space learning and classification. The use of RBFs arises very naturally in the context of the first problem because metric spaces are defined and measured in terms of Euclidean distance. It is perhaps more surprising that the classification problem also benefits from using a metric space kernel density approach, rather than softmax. This appears to hold independently of the base network architecture (Table 2) and the improvement is particularly strong when limited quantities of training data are available (Figure 5). ", + "bbox": [ + 174, + 666, + 825, + 750 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Metric learning inherently pulls samples together into high density regions of the embedding space, whereas softmax is content to allow samples to fill a very large region of space, provided that the logit dimension corresponding to the correct class is larger than the others. This suggests that metric learning is able to provide some regularisation, because classification is driven by multiple nearby samples, whereas samples may be well separated in logit space for softmax. In turn, this leads to increased robustness for the metric space approach, particularly when training data is impoverished. Additionally, softmax is constrained to push samples into regions of space determined by the locations of the logit axes, whereas our metric learning approach is free to position clusters in a way that may more naturally reflect the intrinsic structure of the data. 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Initial Network WeightsTune σLearn RBF WeightsFine-tune Network WeightsTest Accuracy
RandomYesNoNo1.35
ImageNetYesNoNo47.32
ImageNetYesYesNo49.22
ImageNetYesNoYes77.94
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DatasetSoftmaxRBF (Ours)
Oxford 102 Flowers82.7986.26
Stanford Cars19685.6786.52
Leafsnap Field73.8075.96
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Yet little research has been done regarding the scenario where each client learns on a sequence of tasks from a private local data stream. This problem of federated continual learning poses new challenges to continual learning, such as utilizing knowledge from other clients, while preventing interference from irrelevant knowledge. To resolve these issues, we propose a novel federated continual learning framework, Federated Weighted Inter-client Transfer (FedWeIT), which decomposes the network weights into global federated parameters and sparse task-specific parameters, and each client receives selective knowledge from other clients by taking a weighted combination of their task-specific parameters. FedWeIT minimizes interference between incompatible tasks, and also allows positive knowledge transfer across clients during learning. We validate our FedWeIT against existing federated learning and continual learning methods under varying degrees of task similarity across clients, and our model significantly outperforms them with a large reduction in the communication cost. + +# 1 INTRODUCTION + +Continual learning (Thrun, 1995; Kumar & Daume III, 2012; Ruvolo & Eaton, 2013; Kirkpatrick et al., 2017; Schwarz et al., 2018) describes a learning scenario where a model continuously trains on a sequence of tasks; it is inspired by the human learning process, as a person learns to perform numerous tasks with large diversity over his/her lifespan, making use of the past knowledge to learn about new tasks without forgetting previously learned ones. Continual learning is a long-studied topic since having such an ability leads to the potential of building a general artificial intelligence. However, there are crucial challenges in implementing it with conventional models such as deep neural networks (DNNs), such as catastrophic forgetting, which describes the problem where parameters or semantic representations learned for the past tasks drift to the direction of new tasks during training. The problem has been tackled by various prior work (Kirkpatrick et al., 2017; Lee et al., 2017; Shin et al., 2017; Riemer et al., 2019). More recent works tackle other issues, such as scalability or order-robustness (Schwarz et al., 2018; Hung et al., 2019; Yoon et al., 2020). + +However, all of these models are fundamentally limited in that the models can only learn from its direct experience - they only learn from the sequence of the tasks they have trained on. Contrarily, humans can learn from indirect experience from others, through different means (e.g. verbal communications, books, or various media). Then wouldn’t it be beneficial to implement such an ability to a continual learning framework, such that multiple models learning on different machines can learn from the knowledge of the tasks that have been already experienced by other clients? One problem that arises here, is that due to data privacy on individual clients and exorbitant communication cost, it may not be possible to communicate data directly between the clients or between the server and clients. Federated learning (McMahan et al., 2016; Li et al., 2018; Yurochkin et al., 2019) is a learning paradigm that tackles this issue by communicating the parameters instead of the raw data itself. We may have a server that receives the parameters locally trained on multiple clients, aggregates it into a single model parameter, and sends it back to the clients. Motivated by our intuition on learning from indirect experience, we tackle the problem of Federated Continual Learning (FCL) where we perform continual learning with multiple clients trained on private task sequences, which communicate their task-specific parameters via a global server. Figure 1 (a) depicts an example scenario of FCL. Suppose that we are building a network of hospitals, each of which has a disease diagnosis model which continuously learns to perform diagnosis given CT scans, for new types of diseases. Then, under our framework, any diagnosis model which has learned about a new type of disease (e.g. COVID-19) will transmit the task-specific parameters to the global server, which will redistribute them to other hospitals for the local models to utilize. This allows all participants to benefit from the new task knowledge without compromising the data privacy. + +![](images/6998a6802da248658c2a2e9155a1bc0fe3e656e424795ecf911b7107c7f66236.jpg) +Figure 1: (a): Concept. A continual learner at a hospital which learns on sequence of disease prediction tasks may want to utilize relevant task parameters from other hospitals. FCL allows such inter-client knowledge transfer via the communication of task-decomposed parameters. (b): Challenge of FCL. Interference from other clients, resulting from sharing irrelevant knowledge, may hinder an optimal training of target clients (Red) while relevant knowledge from other clients will be beneficial for their learning (Green). + +Yet, the problem of federated continual learning also brings new challenges. First, there is not only the catastrophic forgetting from continual learning, but also the threat of potential interference from other clients. Figure 1 (b) describes this challenge with the results of a simple experiment. Here, we train a model for MNIST digit recognition while communicating the parameters from another client trained on a different dataset. When the knowledge transferred from the other client is relevant to the target task (SVHN), the model starts with high accuracy, converge faster and reach higher accuracy (green line), whereas the model underperforms the base model if the transferred knowledge is from a task highly different from the target task (CIFAR-10, red line). Thus, we need to selective utilize knowledge from other clients to minimize the inter-client interference and maximize inter-client knowledge transfer. Another problem with the federated learning is efficient communication, as communication cost could become excessively large when utilizing the knowledge of the other clients, since the communication cost could be the main bottleneck in practical scenarios when working with edge devices. Thus we want the knowledge to be represented as compactly as possible. + +To tackle these challenges, we propose a novel framework for federated continual learning, Federated Weighted Inter-client Transfer (FedWeIT), which decomposes the local model parameters into a dense base parameter and sparse task-adaptive parameters. FedWeIT reduces the interference between different tasks since the base parameters will encode task-generic knowledge, while the task-specific knowledge will be encoded into the task-adaptive parameters. When we utilize the generic knowledge, we also want the client to selectively utilize task-specific knowledge obtained at other clients. To this end, we allow each model to take a weighted combination of the task-adaptive parameters broadcast from the server, such that it can select task-specific knowledge helpful for the task at hand. FedWeIT is communication-efficient, since the task-adaptive parameters are highly sparse and only need to be communicated once when created. Moreover, when communication efficiency is not a critical issue as in cross-silo federated learning (Kairouz et al., 2019), we can use our framework to incentivize each client based on the attention weights on its task-adaptive parameters. We validate our method on multiple different scenarios with varying degree of task similarity across clients against various federated learning and local continual learning models. The results show that our model obtains significantly superior performance over all baselines, adapts faster to new tasks, with largely reduced communication cost. The main contributions of this paper are as follows: + +• We introduce a new problem of Federated Continual Learning (FCL), where multiple models continuously learn on distributed clients, which poses new challenges such as prevention of inter-client interference and inter-client knowledge transfer. We propose a novel and communication-efficient framework for federated continual learning, which allows each client to adaptively update the federated parameter and selectively utilize the past knowledge from other clients, by communicating sparse parameters. + +# 2 RELATED WORK + +Continual learning While continual learning (Kumar & Daume III, 2012; Ruvolo & Eaton, 2013) is a long-studied topic with a vast literature, we only discuss recent relevant works. Regularizationbased: EWC (Kirkpatrick et al., 2017) leverages Fisher Information Matrix to restrict the change of the model parameters such that the model finds solution that is good for both previous and the current task, and IMM (Lee et al., 2017) proposes to learn the posterior distribution for multiple tasks as a mixture of Gaussians. Architecture-based: DEN (Yoon et al., 2018) tackles this issue by expanding the networks size that are necessary via iterative neuron/filter pruning and splitting, and RCL (Xu & Zhu, 2018) tackles the same problem using reinforcement learning. APD (Yoon et al., 2020) additively decomposes the parameters into shared and task-specific parameters to minimize the increase in the network complexity. Coreset-based: GEM variants (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019) minimize the loss on both of actual dataset and stored episodic memory. FRCL (Titsias et al., 2020) memorizes approximated posteriors of previous tasks with sophisticatedly constructed inducing points. To the best of our knowledge, none of the existing approaches considered the communicability for continual learning of deep neural networks, which we tackle. CoLLA (Rostami et al., 2018) aims at solving multi-agent lifelong learning with sparse dictionary learning, but it is not applicable to federated learning or continual deep learning. + +Federated learning Federated learning is a distributed learning framework under differential privacy, which aims to learn a global model on a server while aggregating the parameters learned at the clients on their private data. FedAvg (McMahan et al., 2016) aggregates the model trained across multiple clients by computing a weighted average of them based on the number of data points trained. FedProx (Li et al., 2018) trains the local models with a proximal term which restricts their updates to be close to the global model. FedCurv (Shoham et al., 2019) aims to minimize the model disparity across clients during federated learning by adopting a modified version of EWC. Recent works Yurochkin et al. (2019); Wang et al. (2020) introduce well-designed aggregation policies by leveraging Bayesian non-parametric methods. A crucial challenge of federated learning is the reduction of communication cost. TWAFL (Chen et al., 2019) tackles this problem by performing layer-wise parameter aggregation, where shallow layers are aggregated at every step, but deep layers are aggregated in the last few steps of a loop. Karimireddy et al. (2020) suggests an algorithm for rapid convergence, which minimizes the interference among discrepant tasks at clients by sacrificing the local optimality. This is an opposite direction from personalized federated learning methods (Fallah et al., 2020; Lange et al., 2020; Deng et al., 2020) which put more emphasis on the performance of local models. FCL is a parallel research direction to both, and to the best of our knowledge, ours is the first work that considers task-incremental learning of clients under federated learning framework. + +# 3 FEDERATED CONTINUAL LEARNING WITH FEDWEIT + +Motivated by the human learning process from indirect experiences, we introduce a novel continual learning under federated learning setting, which we refer to as Federated Continual Learning (FCL). FCL assumes that multiple clients are trained on a sequence of tasks from private data stream, while communicating the learned parameters with a global server. We first formally define the problem in Section 3.1, and then propose naive solutions that straightforwardly combine the existing federated learning and continual learning methods in Section 3.2. Then, following Section 3.3 and 3.4, we discuss about two novel challenges that are introduced by federated continual learning, and propose a novel framework, Federated Weighted Inter-client Transfer (FedWeIT) which can effectively handle the two problems while also reducing the client-to-sever communication cost. + +# 3.1 PROBLEM DEFINITION + +In the stof tasks $\{ \mathcal { T } ^ { ( 1 ) } , \mathcal { T } ^ { ( 2 ) } , . . . , \mathcal { T } ^ { ( T ) } \}$ ng (on a where $\mathcal { T } ^ { ( t ) }$ le machine), the model i is a labeled dataset of $t ^ { t h }$ tivelytask, $\mathcal { T } ^ { ( t ) } = \{ \mathbf { x } _ { i } ^ { ( t ) } , \mathbf { y } _ { i } ^ { ( \bar { t } ) } \} _ { i = 1 } ^ { N _ { t } }$ which consists of $N _ { t }$ pairs of instances $\mathbf { x } _ { i } ^ { ( t ) }$ and their corresponding labels ${ \bf y } _ { i } ^ { ( t ) }$ . Assuming the most realistic situation, we consider the case where the task sequence is a task stream with an unknown arriving order, such that the model can access $\mathcal { T } ^ { ( t ) }$ only at the training period of task $t$ which becomes inaccessible afterwards. Given $\mathcal { T } ^ { ( t ) }$ and the model learned so far, the learning objective at task $t$ is as follows: $\mathrm { m i n i m i z e } _ { \theta ^ { ( t } }$ ) $\mathscr { L } ( \pmb { \theta } ^ { ( t ) } ; \pmb { \theta } ^ { ( t - 1 ) } , \tau ^ { ( t ) } )$ , where ${ \pmb \theta } ^ { ( t ) }$ is a set of the model parameters at task $t$ . + +We now extend the conventional continual learning to the federated learning setting with multiple clients and a global server. Let us assume that we have $C$ clients, where at each client $c _ { c } \in$ $\{ c _ { 1 } , \ldots , c _ { C } \}$ trains a model on a privately accessible sequence of tasks $\{ \mathcal { T } _ { c } ^ { ( 1 ) } , \mathcal { T } _ { c } ^ { ( 2 ) } , . . . , \mathcal { T } _ { c } ^ { ( t ) } \} \subseteq \mathcal { T }$ . Please note that there is no relation among the tasks $\mathcal { T } _ { 1 : c } ^ { ( t ) }$ received at step $t$ , across clients. Now the goal is to effectively train $C$ continual learning models on their own private task streams, via communicating the model parameters with the global server, which aggregates the parameters sent from each client, and redistributes them to clients. + +# 3.2 COMMUNICABLE CONTINUAL LEARNING + +In conventional federated learning settings, the learning is done with multiple rounds of local learning and parameter aggregation. At each round of communication $r$ , each client $c _ { c }$ and the server $s$ perform the following two procedures: local parameter transmission and parameter aggregation $\&$ broadcasting. In the local parameter transmission step, for a randomly selected subset of clients at round $r$ , $\mathcal { C } ^ { ( r ) } \subseteq \{ c _ { 1 } , c _ { 2 } , . . . , c _ { C } \}$ , each client $c _ { c }$ sends updated parameters $\pmb \theta ^ { ( r ) }$ to the server. The server-clients transmission is not done at every client because some of the clients may be temporarily disconnected. Then the server aggregates the parameters $\pmb { \theta } _ { c } ^ { ( r ) }$ sent from the clients into a single parameter. The most popular frameworks for this aggregation are FedAvg (McMahan et al., 2016) and FedProx (Li et al., 2018). However, naive federated continual learning with these two algorithms on local sequences of tasks may result in catastrophic forgetting. One simple solution is to use a regularization-based, such as Elastic Weight Consolidation (EWC) (Kirkpatrick et al., 2017), which allows the model to obtain a solution that is optimal for both the previous and the current tasks. There exist other advanced solutions (Rusu et al., 2016; Nguyen et al., 2018; Chaudhry et al., 2019) that successfully prevents catastrophic forgetting. However, the prevention of catastrophic forgetting at the client level is an orthogonal problem from federated learning. + +Thus we focus on challenges that newly arise in this federated continual learning setting. In the federated continual learning framework, the aggregation of the parameters into a global parameter $\theta _ { G }$ allows inter-client knowledge transfer across clients, since a task $\mathcal { T } _ { i } ^ { ( q ) }$ learned at client $c _ { i }$ at round $q$ may be similar or related to $\mathcal { T } _ { j } ^ { ( r ) }$ learned at client $c _ { j }$ at round $r$ . Yet, using a single aggregated parameter $\theta _ { G }$ may be suboptimal in achieving this goal since knowledge from irrelevant tasks may not to be useful or even hinder the training at each client by altering its parameters into incorrect directions, which we describe as inter-client interference. Another problem that is also practically important, is the communication-efficiency. Both the parameter transmission from the client to the server, and server to client will incur large communication cost, which will be problematic for the continual learning setting, since the clients may train on possibly unlimited streams of tasks. + +# 3.3 FEDERATED WEIGHTED INTER-CLIENT TRANSFER + +How can we then maximize the knowledge transfer between clients while minimizing the inter-client interference, and communication cost? We now describe our model, Federated Weighted Inter-client Transfer (FedWeIT), which can resolve the these two problems that arise with a naive combination of continual learning approaches with federated learning framework. + +The main cause of the problems, as briefly alluded to earlier, is that the knowledge of all tasks learned at multiple clients is stored into a single set of parameters $\theta _ { G }$ . However, for the knowledge transfer to be effective, each client should selectively utilize only the knowledge of the relevant tasks that is trained at other clients. This selective transfer is also the key to minimize the inter-client interference as well as it will disregard the knowledge of irrelevant tasks that may interfere with learning. + +We tackle this problem by decomposing the parameters, into three different types of the parameters with different roles: global parameters $( \pmb \theta _ { G } )$ that capture the global and generic knowledge across all clients, local base parameters $\mathbf { \delta } ( \mathbf { B } )$ which capture generic knowledge for each client, and task-adaptive parameters (A) for each specific task per client, motivated by Yoon et al. (2020). A set of the model parameters $\pmb { \theta } _ { c } ^ { ( t ) }$ for task $t$ at continual learning client $c _ { c }$ is then defined as follows: + +$$ +\pmb { \theta } _ { c } ^ { ( t ) } = \mathbf { B } _ { c } ^ { ( t ) } \odot \mathbf { m } _ { c } ^ { ( t ) } + \mathbf { A } _ { c } ^ { ( t ) } + \sum _ { i \in \mathcal { C } _ { \backslash c } } \sum _ { j < | t | } \alpha _ { i , j } ^ { ( t ) } \mathbf { A } _ { i } ^ { ( j ) } +$$ + +where $\mathbf { B } _ { c } ^ { ( t ) } \in \{ \mathbb { R } ^ { I _ { l } \times O _ { l } } \} _ { l = 1 } ^ { L }$ is the set of base parameters for $c ^ { t h }$ client shared across all tasks in the client, $\mathbf { m } _ { c } ^ { ( t ) } \in \{ \mathbb { R } ^ { O _ { l } } \} _ { l = 1 } ^ { L }$ is the set of sparse vector masks which allows to adaptively transform $\mathbf { B } _ { c } ^ { ( t ) }$ for the task t, A(t)c ∈ {RIl×Ol }Ll=1 is the set of a sparse task-adaptive parameters at client cc. Here, $L$ is the number of the layer in the neural network, and $I _ { l } , O _ { l }$ are input and output dimension of the weights at layer $l$ , respectively. + +![](images/502254cbcb197ea4db1cf249ff75854e1847b1d40e294b6cac2fee19b1406f51.jpg) +Figure 2: Updates of FedWeIT. (a) A client sends sparsified federated parameter $\mathbf { B } _ { c } \odot \mathbf { m } _ { c } ^ { ( t ) }$ . After that, the server redistributes aggregated parameters to the clients. (b) The knowledge base stores previous tasks-adaptive parameters of clients, and each client selectively utilizes them with an attention mask. + +The first term allows selective utilization of the global knowledge. We want the base parameter $\mathbf { B } _ { c } ^ { ( t ) }$ at each client to capture generic knowledge across all tasks across all clients. In Figure 2 (a), we initialize it at each round $t$ with the global parameter from the previous iteration, $\theta _ { G } ^ { ( t - 1 ) }$ which aggregates the parameters sent from the client. This allows $\mathbf { B } _ { c } ^ { ( t ) }$ to also benefit from the global knowledge about all the tasks. However, since $\theta _ { G } ^ { ( t - 1 ) }$ also contains knowledge irrelevant to the current task, instead of using it as is, we learn the sparse mask $\mathbf { m } _ { c } ^ { ( t ) }$ to select only the relevant parameters for the given task. This sparse parameter selection helps minimize inter-client interference, and also allows for efficient communication. The second term is the task-adaptive parameters $\mathbf { A } _ { c } ^ { ( t ) }$ . Since we additively decompose the parameters, this will learn to capture knowledge about the task that is not captured by the first term, and thus will capture specific knowledge about the task ${ \mathcal T } _ { c } ^ { ( t ) }$ . The final term describes weighted inter-client knowledge transfer. We have a set of parameters that are transmitted from the server, which contain all task-adaptive parameters from all the clients. To selectively utilizes these indirect experiences from other clients, we further allocate attention $\alpha _ { c } ^ { ( t ) }$ on these parameters, to take a weighted combination of them. By learning this attention, each client can select only the relevant task-adaptive parameters that help learn the given task. Although we design $A _ { i } ^ { ( j ) }$ to be highly sparse, using about $2 - 3 \%$ of memory of full parameter in practice, sending all task knowledge is not desirable. Thus we only transmit the task-adaptive parameter of the previous task $( t - 1 )$ , which we empirically find to achieve good results in practice. + +Training. We learn the decomposable parameter $\pmb { \theta } _ { c } ^ { ( t ) }$ by optimizing for the following objective: + +$$ +\operatorname* { m i n i m i z e } _ { \mathbf { B } _ { c } ^ { ( t ) } , \ \mathbf { m } _ { c } ^ { ( t ) } , \ \mathbf { A } _ { c } ^ { ( t + 1 ) } , \ \alpha _ { c } ^ { ( t ) } } \ \mathcal { L } \left( \pmb { \theta } _ { c } ^ { ( t ) } ; \mathcal { T } _ { c } ^ { ( t ) } \right) + \lambda _ { 1 } \Omega ( \{ \mathbf { m } _ { c } ^ { ( t ) } , \mathbf { A } _ { c } ^ { ( 1 : t ) } \} ) + \lambda _ { 2 } \sum _ { i = 1 } ^ { t - 1 } \| \Delta \mathbf { B } _ { c } ^ { ( t ) } \odot \mathbf { m } _ { c } ^ { ( i ) } + \Delta \mathbf { A } _ { c } ^ { ( i ) } \| _ { 2 } ^ { 2 } , +$$ + +where $\mathcal { L }$ is a loss function and $\Omega ( \cdot )$ is a sparsity-inducing regularization term for all task-adaptive parameters and the masking variable (we use $\ell _ { 1 }$ -norm regularization), to make them sparse. The second regularization term is used for retroactive update of the past task-adaptive parameters, which helps the task-adaptive parameters to maintain the original solutions for the target tasks, by reflecting the change of the base parameter. Here, $\Delta \mathbf { B } _ { c } ^ { ( t ) } = \mathbf { B } _ { c } ^ { ( t ) } - \mathbf { B } _ { c } ^ { ( t - 1 ) }$ is the difference between the base parameter at the current and previous timestep, and $\Delta \mathbf { A } _ { c } ^ { ( i ) }$ is the difference between the task-adaptive parameter for task $i$ at the current and previous timestep. This regularization is essential for preventing catastrophic forgetting. $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are hyperparameters controlling the effect of the two regularizers. + +# 3.4 EFFICIENT COMMUNICATION VIA SPARSE PARAMETERS + +FedWeIT learns via server-to-client communication. As discussed earlier, a crucial challenge here is to reduce the communication cost. We describe what happens at the client and the server at each step. + +Algorithm 1 Federated Weighted Inter-client Transfer +input Dataset {D(1:t)c }Cc=1 , and Global Parameter $\theta _ { G }$ +output $\{ \mathbf { B } _ { c } , \mathbf { m } _ { c } ^ { ( 1 : t ) }$ , $\alpha _ { c } ^ { ( 1 : t ) }$ , ${ \bf A } _ { c } ^ { ( 1 : t ) } \} _ { c = 1 } ^ { C }$ 1: Initialize $\mathbf { B } _ { c }$ to $\theta _ { G }$ for all $c \in \mathcal { C } \equiv \{ 1 , . . . , C \}$ 2: for task $t = 1 , 2 , \dots \mathbf { d o }$ 3: for round $r = 1 , 2 , . . . , R$ do 4: Transmit Bb(t,r)c a nd A(t−1,R)c o f client cc to server 5: Compute $\begin{array} { r } { \pmb { \theta } _ { G } ^ { ( r ) } \frac { 1 } { | \mathcal { C } | } \sum _ { c \in \mathcal { C } } \widehat { \mathbf { B } } _ { c } ^ { ( t , r ) } } \end{array}$ 6: Distribute $\theta _ { G } ^ { ( r ) }$ ) and {A(t−1,R)} to client $c$ 7: Minimize Eq. (2) for solving each local CL problems 8: end for +9: end for + +![](images/4a433d57d9642d510b139cc97c019e10c193a5a9a99bb9571a0f4b8c8aedff61.jpg) +Figure 3: Configuration of task sequences: We first split a dataset $D$ into multiple sub-tasks in non-IID manner ((a) and (b)). Then, we distribute them to multiple clients $( C _ { \# } )$ . Mixed tasks from multiple datasets (colored circles) are distributed across all clients ((c)). + +Client: At each round $r$ , each client $c _ { c }$ partially updates its base parameter with the nonzero components of the global parameter sent from the server; that is, $\bar { \mathbf { B } _ { c } } ( n ) = \pmb { \theta } _ { G } ( n )$ where $n$ is a nonzero element of the global parameter. After training the model using Eq. (2), it obtains a sparsified base parameter $\widehat { \mathbf { B } } _ { c } ^ { ( t ) } = \mathbf { B } _ { c } ^ { ( t ) } \odot \mathbf { m } _ { c } ^ { ( t ) }$ and task-adaptive parameter $\mathbf { A } _ { c } ^ { ( t ) }$ for the new task, both of which are sent to the server, at smaller cost compared to naive FCL baselines. While naive FCL baselines require $\vert { \mathcal { C } } \vert \times R \times \vert \theta \vert$ for client-to-server communication, FedWeIT requires $| { \mathcal { C } } | \times \left( R \times | { \widehat { \mathbf { B } } } | + | \mathbf { A } | \right)$ where $R$ is the number of communication round per task and $| \cdot |$ is the number of parameters. + +Server: The server first aggregates the base parameters sent from all the clients by taking an weighted average of them: $\begin{array} { r } { \pmb { \theta } _ { G } = \frac { 1 } { \mathcal { C } } \sum _ { c } \widehat { \mathbf { B } } _ { i } ^ { ( t ) } } \end{array}$ . Then, it broadcasts $\theta _ { G }$ to all the clients. Task adaptive parameters of t − 1, {A(t−1)i }C\ci=1 a re broadcast at once per client during training task $t$ . While naive FCL baselines requires $\lvert \mathcal { C } \rvert \times \bar { R ^ { \prime } } \times \lvert \pmb { \theta } \rvert$ for server-to-client communication cost, FedWeIT requires $| { \mathcal { C } } | \times ( R \times | \pmb { \theta } _ { G } | + ( | { \mathcal { C } } | - 1 ) \times | \mathbf { A } | )$ in which $\theta _ { G } , \mathbf { A }$ are highly sparse. We describe the FedWeIT algorithm in Algorithm 1. For a detailed version of the algorithm, please see Section D in appendix. + +# 4 EXPERIMENTS + +We validate our FedWeIT under different configurations of task sequences against baselines which are namely Overlapped-CIFAR-100 and NonIID-50. 1) Overlapped-CIFAR-100: We group 100 classes of CIFAR-100 dataset into 20 non-iid superclasses tasks. Then, we randomly sample 10 tasks out of 20 tasks and split instances to create a task sequence for each of the clients with overlapping tasks. 2) NonIID-50: We use the following eight benchmark datasets: MNIST (LeCun et al., 1998), CIFAR10/-100 (Krizhevsky & Hinton, 2009), SVHN (Netzer et al., 2011), Fashion-MNIST (Xiao et al., 2017), Not-MNIST (Bulatov, 2011), FaceScrub $\mathrm { N g }$ & Winkler, 2014), and TrafficSigns (Stallkamp et al., 2011). We split the classes in the 8 datasets into 50 non-IID tasks, each of which is composed of 5 classes that are disjoint from the classes used for the other tasks. This is a large-scale experiment, containing 280, 000 images of 293 classes from 8 heterogeneous datasets. After generating and processing tasks, we randomly distribute them to multiple clients as illustrated in Figure 3. + +Experimental setup We use a modified version of LeNet (LeCun et al., 1998) for the experiments with both Overlapped-CIFAR-100 and NonIID-50 dataset. Further, we use ResNet-18 He et al. (2016) with NonIID-50 dataset. We followed other experimental setups from Serrà et al. (2018) and Yoon et al. (2020). For detailed descriptions of the task configuration and hyperparameters used, please see Section B in appendix. Also, for more ablation studies, please see Section C in appendix. + +Baselines and our model 1) STL: Single Task Learning at each arriving task. 2) Local-EWC: Individual continual learning with EWC (Kirkpatrick et al., 2017) per client. 3) Local-APD: Individual continual learning with APD (Yoon et al., 2020) per client. 4) FedProx: FCL using FedProx (Li et al., 2018) algorithm. 5) Scaffold: FCL using Scaffold (Karimireddy et al., 2020) algorithm. 6) FedCurv: FCL using FedCurv (Shoham et al., 2019) algorithm. 7) FedProx-[model]: FCL, that is trained using FedProx algorithm with [model]. 8) FedWeIT: Our FedWeIT algorithm. + +Table 1: Averaged Per-task performance on both dataset during FCL with 5 clients (fraction $\scriptstyle 1 = 1 . 0$ ). We measured task accuracy and model size after completing all learning phases over 3 individual trials. We also measured C2S/S2C communication cost for training each task. + +
NonIID-50Dataset (F=1.0, R=20)Overlapped CIFAR-100 (F=1.0,R=20)
MethodsAccuracyModel SizeC2S/S2C CostAccuracyModel SizeC2S/S2C Cost
STL85.78 ±0.170.610GBN/A57.15 ±0.070.610 GBN/A
Local-EWC74.30±0.080.061GB- -N/A44.26±0.430.061GBN7A
Local-APD81.42 ± 0.720.090 GBN/A50.82 ± 0.330.073 GBN/A
FedProx63.691.750.061GB1.22/1.22GB33.83±0.480.061GB1.22/1.22GB
Scaffold30.84 ± 1.410.061 GB2.44 /2.44 GB22.80 ±0.470.061 GB2.44/2.44 GB
FedCurv72.39 ±0.320.061GB1.22/1.22 GB40.36 ±0.440.061GB1.22/1.22 GB
FedProx-EWC68.18 ± 0.580.061 GB1.22/1.22 GB41.91 ± 0.470.061 GB1.22/1.22 GB
FedProx-APD81.20 ± 1.240.079 GB1.22/1.22 GB52.20 ± 0.410.075 GB1.22/1.22 GB
FedWeIT84.11 ± 0.270.078 GB0.37/1.07 GB55.16 ± 0.190.075 GB0.37/1.07 GB
+ +![](images/16f3d871fde0d78f4c6941c6e95eaa8bb16972c0eeda1361c502d7518d17b655.jpg) + +
100 clients (F=0.05,R=20,1,000 tasks in total)
MethodsAccuracyModel SizeC2S/S2C Cost
STL32.96 ±0.2312.20 GBN/A
Local-APD37.50 ±0.174.01GBN/A
FedProx24.11 ±0.441.22 GB1.2271.22 GB
FedCurv29.11 ± 0.201.22 GB1.22 /1.22 GB
FedCurv-EWC29.72 ± 0.201.22 GB1.22 /1.22 GB
FedWeIT39.58 ± 0.274.03 GB0.38 /1.10 GB
+ +Figure 4: Left: Averaged task adaptation during training last two ${ \mathfrak { g } } ^ { t h }$ and $1 0 ^ { t h }$ ) tasks with 5 and 100 clients. Right: Average Per-task Performance on Overlapped-CIFAR-100 during FCL with 100 clients. + +# 4.1 EXPERIMENTAL RESULTS + +We first validate our model on both Overlapped-CIFAR-100 and NonIID-50 task sequences against single task learning (STL), continual learning (EWC, APD), federated learning (FedProx, Scaffold, FedCurv), and naive federated continual learning (FedProx-based) baselines. Table 1 shows the final average per-task performance after the completion of (federated) continual learning on both datasets. We observe that FedProx-based federated continual learning (FCL) approaches degenerate the performance of continual learning (CL) methods over the same methods without federated learning. This is because the aggregation of all client parameters that are learned on irrelevant tasks results in severe interference in the learning for each task, which leads to catastrophic forgetting and suboptimal task adaptation. Scaffold achieves poor performance on FCL, as its regularization on the local gradients is harmful for FCL, where all clients learn from a different task sequences. While FedCurv reduces inter-task disparity in parameters, it cannot minimize inter-task interference, which results it to underperform single-machine CL methods. On the other hand, FedWeIT significantly outperforms both single-machine CL baselines and naive FCL baselines on both datasets. Even with larger number of clients $C = 1 0 0$ ), FedWeIT consistently outperforms all baselines (Figure 4). This improvement largely owes to FedWeIT’s ability to selectively utilize the knowledge from other clients to rapidly adapt to the target task, and obtain better final performance (Figure 4 Left). + +The fast adaptation to new task is another clear advantage of inter-client knowledge transfer. To further demonstrate the practicality of our method with larger networks, we experiment on Non-IID dtaset with ResNet-18 (Table 2), on which FedWeIT still significantly outperforms the strongest baseline (FedProx-APD) while using fewer parameters. Also, our model is not sensitive to the hyperparameters $\lambda _ { 1 }$ and $\lambda _ { 2 }$ , if they are within reasonable scales (Figure 6 Left). + +Table 2: FCL results on NonIID-50 dataset with ResNet-18. + +
ResNet-18
MethodsAcc.M Size
Local-APDFedProx-APDFedWeIT92.44 %92.89%94.86 %1.86 GB2.05GB1.84 GB
+ +Efficiency of FedWeIT We also report the accuracy as a function of network capacity in Table 1, 2, which we measure by the number of parameters used. We observe that FedWeIT obtains much higher accuracy while utilizing less number of parameters compared to FedProx-APD. This efficiency mainly comes from the reuse of task-adaptive parameters from other clients, which is not possible with single-machine CL methods or naive FCL methods. We also examine the communication cost (the size of non-zero parameters transmitted) of each method. Table 1 reports both the client-to-server (C2S) / server-to-client (S2C) communication cost at training each task. FedWeIT, uses only $3 0 \%$ and $3 \%$ of parameters for $\widehat { \mathbf B }$ and A of the dense models respectively. We observe that FedWeIT is significantly more communication-efficient than FCL baselines although it broadcasts task-adaptive parameters, due to high sparsity of the parameters. Figure 5 (a) shows the accuracy as a function of C2S cost according to a transmission of top- $\kappa \%$ informative parameters. Since FedWeIT selectively utilizes task-specific parameters learned from other clients, it results in superior performance over APD-baselines especially with sparse communication of model parameters. + +![](images/42b7c39389253e8c6b14218f62c8e3c835b18e61b7312d3849dc060008c81811.jpg) +Figure 5: (a) Accuracy over C2S cost. We report the relative communication cost to the original network. All results are averaged over the 5 clients. (b) Inter-client transfer for NonIID-50. We compare the scale of the attentions at first FC layer which gives the weights on transferred task-adaptive parameters from other clients. + +![](images/b48b317b40e852b5ce1c0fd7677219d4191234672dc950bc7d939cfbf41b0cf8.jpg) +Figure 6: Left: Performance of FedWeIT with different scale of hyperparameters on Non-iid 50. Middle: Performance comparison about current task adaptation at $6 ^ { t h }$ and $8 ^ { t h }$ tasks during federated continual learning on NonIID-50. Right: Forgetting measure using Backward Transfer (BWT). + +Catastrophic forgetting Further, we examine how the performance of the past tasks change during continual learning, to see the severity of catastrophic forgetting with each method. Figure 6 Left shows the performance of FedWeIT and FCL baselines on the $6 ^ { t h }$ and $8 ^ { t h }$ tasks, at the end of training for later tasks. We observe that naive FCL baselines suffer from more severe catastrophic forgetting than local continual learning with EWC because of the inter-client interference, where the knowledge of irrelevant tasks from other clients overwrites the knowledge of the past tasks. Contrarily, our model shows no sign of catastrophic forgetting. This is mainly due to the selective utilization of the prior knowledge learned from other clients through the global/task-adaptive parameters, which allows it to effectively alleviate inter-client interference. FedProx-APD also does not suffer from catastrophic forgetting, but they yield inferior performance due to ineffective knowledge transfer. We also report Backward Transfer (BWT), which is a measure on catastrophic forgetting for all models (more positive the better). We provide the details of BWT in the Section B in appendix. + +Weighted inter-client knowledge transfer By analyzing the attention $_ \alpha$ in Eq. (1), we examine which task parameters from other clients each client selected. Figure 5 (b), shows example of the attention weights that are learned for the $0 ^ { t h }$ split of MNIST and $1 0 ^ { \hat { t h } }$ split of CIFAR-100. We observe that large attentions are allocated to the task parameters from the same dataset (CIFAR-100 utilizes parameters from CIFAR-100 tasks with disjoint classes), or from a similar dataset (MNIST utilizes parameters from Traffic Sign and SVHN). This shows that FedWeIT effectively selects beneficial parameters to maximize inter-client knowledge transfer. This is an impressive result since it does not know which datasets the parameters are trained on. + +# 5 CONCLUSION + +We tackled a novel problem of federated continual learning, whose goal is to continuously learn local models at each client while allowing it to utilize indirect experience (task knowledge) from other clients. This poses new challenges such as inter-client knowledge transfer and prevention of interclient interference between irrelevant tasks. To tackle these challenges, we additively decomposed the model parameters at each client into the global parameters that are shared across all clients, and sparse local task-adaptive parameters that are specific to each task. Further, we allowed each model to selectively update the global task-shared parameters and selectively utilize the task-adaptive parameters from other clients. The experimental validation of our model under various task similarity across clients, against existing federated learning and continual learning baselines shows that our model obtains significantly outperforms baselines with reduced communication cost. We believe that federated continual learning is a practically important topic of large interests to both research communities of continual learning and federated learning, that will lead to new research directions. + +# REFERENCES + +Yaroslav Bulatov. Not-mnist dataset. 2011. + +Arslan Chaudhry, Marc’Aurelio Ranzato, Marcus Rohrbach, and Mohamed Elhoseiny. 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In Advances in Neural Information Processing Systems (NIPS), 2016. + +Paul Ruvolo and Eric Eaton. Ella: An efficient lifelong learning algorithm. In Proceedings of the International Conference on Machine Learning (ICML), 2013. + +Jonathan Schwarz, Jelena Luketina, Wojciech M Czarnecki, Agnieszka Grabska-Barwinska, Yee Whye Teh, Razvan Pascanu, and Raia Hadsell. Progress & compress: A scalable framework for continual learning. arXiv preprint arXiv:1805.06370, 2018. + +Joan Serrà, Dídac Surís, Marius Miron, and Alexandros Karatzoglou. Overcoming catastrophic forgetting with hard attention to the task. In Proceedings of the International Conference on Machine Learning (ICML), 2018. + +Hanul Shin, Jung Kwon Lee, Jaehon Kim, and Jiwon Kim. Continual learning with deep generative replay. In Advances in Neural Information Processing Systems (NIPS), 2017. + +Neta Shoham, Tomer Avidor, Aviv Keren, Nadav Israel, Daniel Benditkis, Liron Mor-Yosef, and Itai Zeitak. Overcoming forgetting in federated learning on non-iid data. arXiv preprint arXiv:1910.07796, 2019. + +Johannes Stallkamp, Marc Schlipsing, Jan Salmen, and Christian Igel. The german traffic sign recognition benchmark: a multi-class classification competition. In The 2011 international joint conference on neural networks, 2011. + +Sebastian Thrun. A Lifelong Learning Perspective for Mobile Robot Control. Elsevier, 1995. + +Michalis K Titsias, Jonathan Schwarz, Alexander G de G Matthews, Razvan Pascanu, and Yee Whye Teh. Functional regularisation for continual learning with gaussian processes. In Proceedings of the International Conference on Learning Representations (ICLR), 2020. + +Hongyi Wang, Mikhail Yurochkin, Yuekai Sun, Dimitris Papailiopoulos, and Yasaman Khazaeni. Federated learning with matched averaging. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id=BkluqlSFDS. + +Han Xiao, Kashif Rasul, and Roland Vollgraf. Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747, 2017. + +Ju Xu and Zhanxing Zhu. Reinforced continual learning. In Advances in Neural Information Processing Systems (NIPS), 2018. + +Jaehong Yoon, Eunho Yang, Jeongtae Lee, and Sung Ju Hwang. Lifelong learning with dynamically expandable networks. In Proceedings of the International Conference on Learning Representations (ICLR), 2018. + +Jaehong Yoon, Saehoon Kim, Eunho Yang, and Sung Ju Hwang. Scalable and order-robust continual learning with additive parameter decomposition. In Proceedings of the International Conference on Learning Representations (ICLR), 2020. + +Mikhail Yurochkin, Mayank Agarwal, Soumya Ghosh, Kristjan Greenewald, Trong Nghia Hoang, and Yasaman Khazaeni. Bayesian nonparametric federated learning of neural networks. Proceedings of the International Conference on Machine Learning (ICML), 2019. + +# A APPENDIX + +Organization The appendix is organized as follows: In Section B, we further describe the experimental details, including the network architecture, hyper-parameter configurations, forgetting measures, and datasets. Also, we report additional experimental results in Section C about the effect of the communication frequency (Section C.1) and an additional ablation studies for model components on Overlapped-CIFAR-100 dataset (Section C.2). We include a detailed algorithm for our FedWeIT in Section D. + +# B EXPERIMENTAL DETAILS + +We further provide the experimental settings in detail, including the descriptions of the network architectures, hyperparameters, and dataset configuration. + +Network architecture We utilize a modified version of LeNet and a conventional ResNet-18 as the backbone network architectures for validation. In the LeNet, the first two layers are convolutional neural layers of 20 and 50 filters with the $5 \times 5$ convolutional kernels, which are followed by the two fully-connected layers of 800 and 500 units each. Rectified linear units activations and local response normalization are subsequently applied to each layers. We use $2 \times 2$ max-pooling after each convolutional layer. All layers are initialized based on the variance scaling method. Detailed description of the architecture for LeNet is given in Table 3. + +Table 3: Base Network Architecture (LeNet) and Total Number of Parameters of both FedWeIT and All Baseline Models. $T$ describes the number of arrived tasks in continual learning. + +
LayerFilter ShapeStrideOutput
Input Conv 1N/A 5×5×20N/A32×32×3 32×32 ×20
Max Pooling 13×31 216 ×16× 20
Conv 25×5×50116 ×16× 50
Max Pooling 23×328×8×50
Flatten3200N/A1×1×3200
FC1800N/A1×1×800
FC2500N/A1×1× 500
SoftmaxClassifierN/A1×1×5×T
TotalNumberofParameters3,012,920
+ +Configurations We use an Adam optimizer with adaptive learning rate decay, which decays the learning rate by a factor of 3 for every 5 epochs with no consecutive decrease in the validation loss. We stop training in advance and start learning the next task (if available) when the learning rate reaches $\rho$ . The experiment for LeNet with 5 clients, we initialize by $1 e ^ { - 3 } \times \frac { 1 } { 3 }$ at the beginning of each new task and $\rho = 1 e ^ { - 7 }$ . Mini-batch size is 100, the rounds per task is 20, an the epoch per round is 1. The setting for ResNet-18 is identical, excluding the initial learning rate, $1 e ^ { - 4 }$ . In the case of + +experiments with 20 and 100 clients, we set the same settings except reducing minibatch size from 100 to 10 with an initial learning rate $1 e ^ { - 4 }$ . We use client fraction 0.25 and 0.05, respectively, at each communication round. we set $\lambda _ { 1 } = [ 1 e ^ { - 1 } , 4 e ^ { - 1 } ]$ and $\lambda _ { 2 } = 1 0 0$ for all experiments. Further, we use $\mu = 5 e ^ { - 3 }$ for FedProx, $\lambda = [ 1 e ^ { - 2 } , 1 . 0 ]$ for EWC and FedCurv. We initialize the attention parameter $\alpha _ { c } ^ { ( t ) }$ as sum to one, $\alpha _ { c , j } ^ { ( t ) } 1 / | \alpha _ { c } ^ { ( t ) } |$ . + +Backward-transfer (BWT) Backward transfer (BWT) is a measure for catastrophic forgetting. BWT compares the performance disparity of previous tasks after learning current task as follows: + +$$ +\mathrm { B W T } = \frac { 1 } { T - 1 } \sum _ { i < T } P _ { i } ^ { ( T ) } - P _ { i } ^ { ( i ) } , +$$ + +where P (T ) is the performance of task $i$ after task $T$ is learned $( i < T )$ ). Thus, a large negative backward transfer value indicates that the performance has been substantially reduced, in which case catastrophic forgetting has happened. + +For NonIID-50 dataset, we utilize 8 heterogenous datasets and create 50 non-iid tasks in total as shown in Table 4. Then we arbitrarily select 10 tasks without duplication and distribtue them to 5 clients. The average performance of single task learning on the dataset is $8 5 . 7 8 \pm 0 . 1 7 ( \% )$ , measured by our base LeNet architecture. + +Table 4: Detailed configuration of NonIID-50 Dataset. + +
NonIID-50
Dataset#Classes#Tasks#Classes (Task)#Train Set#Valid Set#Test Set
CIFAR-100Face Scrub10015536,75010,5005,250
10016513,8593,9591,979
Traffic SignsSVHNMNIST4395 (3)32,1709,1914,595
102561,81017,6608,830
102542,70012,2006,100
CIFAR-10Not MNIST102536,75010,5005,250
102511,3393,2391,619
Fashion MNIST102542,70012,2006,100
Total29350248278,07839,72379,449
+ +Datasets We create both Overlapped-CIFAR-100 and NonIID-50 datasets. For Overlapped-CIFAR100, we generate 20 non-iid tasks based on 20 superclasses, which hold 5 subclasses. We split instances of 20 tasks according to the number of clients (5, 20, and 100) and then distribute the tasks across all clients. + +
Overlapped-CIFAR-100
MethodsAccuracyModel SizeC2S/S2C CostEpochs /Round
FedWeIT55.16 ± 0.190.075 GB0.37/1.07 GB1
FedWeIT55.18 ± 0.080.077GB0.19/0.53GB2
FedWeIT53.73 ± 0.440.083 GB0.08/0.22 GB5
FedWeIT53.22 ±0.140.088 GB0.02 /0.07 GB20
+ +![](images/915f5727b0c2c60f49a80c4777cc099c5baea8fa8f149347e3ff1e59614a69e2.jpg) +Figure 7: Average Per-task Performance with error bars over the number of training epochs per communication rounds on Overlapped-CIFAR-100 for FedWeIT with 5 clients. All models transmit full of local base parameters and highly sparse task-adaptive parameters. All results are the mean accuracy over 5 clients and we run 3 individual trials. Red arrows at each point describes the standard deviation of the performance. + +# C ADDITIONAL EXPERIMENTAL RESULTS + +We further include a quantitative analysis about the communication round frequency and additional experimental results across the number of clients. + +# C.1 EFFECT OF THE COMMUNICATION FREQUENCY + +We provide an analysis on the effect of the communication frequency by comparing the performance of the model, measured by the number of training epochs per communication round. We run the 4 different FedWeIT with 1, 2, 5, and 20 training epochs per round. Figure 7 shows the performance of our FedWeIT variants. As clients frequently update the model pa + +Table 5: Experimental results on the Overlapped-CIFAR-100 dataset with 20 tasks. All results are the mean accuracies over 5 clients, averaged over 3 individual trials. + +
Overlapped-CIFAR-100 with 20 tasks
MethodsAccuracyM SizeC2S/S2C Cost
FedProx29.76 ± 0.390.061GB1.22/1.22 GB
FedProx-EWC27.80 ± 0.580.061 GB1.22 / 1.22 GB
FedProx-APD43.80 ±0.760.093 GB1.22 / 1.22 GB
FedWeIT46.78 ±0.1470.092 GB0.3771.07 GB
+ +rameters through the communication with the central server, the model gets higher performance while maintaining smaller network capacity since the model with a frequent communication efficiently updates the model parameters as transferring the inter-client knowledge. However, it requires much heavier communication costs than the model with sparser communication. For example, the model trained for 1 epochs at each round may need to about 16.9 times larger entire communication cost than the model trained for 20 epochs at each round. Hence, there is a trade-off between model performance of federated continual learning and communication efficiency, whereas FedWeIT variants consistently outperform (federated) continual learning baselines. + +![](images/3b657f592fdd90c124b41dc16b9b78e2bc01a6bed1984f8f97607761c7fd63ee.jpg) +Figure 8: (a) Comparison of adaption for tasks between FedWeIT and APD with 20 clients in federated continual learning scenario (b) Comparison of adaptation for tasks between FedWeIT and APD with 100 clients in federated continual learning scenario. We visualize the last 5 tasks out of 10 tasks per client. Overlapped-CIFAR-100 dataset are used after splitting instances according to the number of clients (20 and 100). + +![](images/32f8172baf1860a819de6a58939b25386f9df87f5382ad5dc1d63dd285ae73e1.jpg) +Figure 9: Forgetting analysis. Performance change over the increasing number of tasks for all tasks except the last task $1 ^ { s t }$ to $9 ^ { t h }$ ) during federated continual learning on NonIID-50. We observe that our method does not suffer from task forgetting on any tasks. + +# C.2 ABLATION STUDY FOR MODEL COMPONENTS + +We perform an ablation study to analyze the role of each component of our FedWeIT. We compare the performance of four different variations of our model. w/o B communication describes the model that does not transfer the base parameter $\mathbf { B }$ and only communicates task-adaptive ones. w/o A communication is the model that does not communicate task-adaptive parameters. w/o A is the model which trains the model only with sparse transmission of local base parameter, and w/o m is the model without the sparse vector mask. + +As shown in Table 6, without communicating $\mathbf { B }$ or A, the model yields significantly lower performance compared to the full model since they do not benefit from inter-client knowledge transfer. The model w/o A obtains very low performance due to catastrophic forgetting, and the model w/o sparse mask m achieves lower accuracy with larger capacity and cost, which demonstrates the importance of performing selective transmission. + +Table 6: Ablation studies to analyze the effectiveness of parameter decomposition on WeIT. All experiments performed on NonIID-50 dataset. + +
NonIID-50
MethodsAcc.M SizeC2S/S2C Cost
FedWeIT w/o B comm.84.11% 77.88%0.078 GB 0.070GB0.37/1.07 GB 0.0170.01 GB
w/o A comm.79.21%0.079 GB0.37 /1.04 GB
w/o A w/0 m65.66% 78.71%0.061 GB 0.087 GB0.37 / 1.04 GB 1.23 / 1.25 GB
+ +# D DETAILED ALGORITHM FOR FEDWEIT + +# Algorithm 2 Algorithm for FedWeIT + +input Dataset {D(1:t)c }Cc=1 , and Global Parameter $\theta _ { G }$ +output $\{ \mathbf { B } _ { c } , \mathbf { m } _ { c } ^ { ( 1 : t ) }$ , , α(1:c ), A(1:t)c }Cc=1 +1: Initialize $\mathbf { B } _ { c }$ to $\theta _ { G }$ for all $c \in \mathcal { C } \equiv \{ 1 , . . . , C \}$ +2: for task $t = 1 , 2 , \dots$ do +3: for round $r = 1 , 2 , . . . , R$ do +4: Select communicable clients ${ \mathcal { C } } ^ { ( r ) } \subseteq { \mathcal { C } }$ +5: if $r = 1$ then +6: A(t−1,R) c∈C(r) and $\hat { \mathbf { B } } _ { c \in \mathcal { C } ^ { ( r ) } } ^ { ( t , r ) }$ are transmitted from $\mathcal { C } ^ { ( r ) }$ to the central server +7: Set a new knowledge base $k b ^ { ( t - 1 ) } = \{ \mathbf { A } _ { j } ^ { ( t - 1 , R ) } \} _ { j \in \mathcal { C } ^ { ( 1 ) } }$ +9: 8: el $\hat { \mathbf { B } } _ { c \in \mathcal { C } ^ { ( r ) } } ^ { ( t , r ) }$ are transmitted from $\mathcal { C } ^ { ( r ) }$ to the central server +10: end if +11: Update 1|C(r)| Pc∈C(r) Bˆ (t,r)c +12: Distribute $\theta _ { G } ^ { ( r ) }$ and $k b ^ { ( t - 1 ) }$ to client $c \in \mathcal { C } ^ { ( r ) }$ if $c _ { c }$ meets $k b ^ { ( t - 1 ) }$ first, otherwise distribute only $\theta _ { G } ^ { ( r ) }$ +13: Minimize Eq. (2) for solving each local CL problems +14: end for +15: end for + +# E FEDWEIT FOR ASYNCHRONOUS FEDERATED CONTINUAL LEARNING + +# Algorithm 3 Algorithm for Asynchronous FedWeIT + +input Dataset {D(1:t)c }Cc=1 , and Global Parameter θG +output $\{ \mathbf { B } _ { c } , \mathbf { m } _ { c } ^ { ( 1 : t ) }$ , $\pmb { \alpha } _ { c } ^ { ( 1 : t ) }$ , ${ \bf A } _ { c } ^ { ( 1 : t ) } \} _ { c = 1 } ^ { C }$ +1: Initialize $\mathbf { B } _ { c }$ to $\theta _ { G }$ for all $c \in \mathcal { C } \equiv \{ 1 , . . . , C \}$ +2: the knowledge base $k b \gets \{ \}$ +3: for round $r = 1 , 2 , \ldots$ do +4: if all clients finished the training then +5: break +6: else +7: Select communicable clients ${ \mathcal { C } } ^ { ( r ) } \subseteq { \mathcal { C } }$ +8: for $c \in \mathcal { C } ^ { ( r ) }$ do +9: if new task $t ^ { \prime }$ is arrived at the client $c _ { c }$ then +10: Update the knowledge base $k b \gets k b \cup \{ { \bf A } _ { c } ^ { ( t ^ { \prime } - 1 ) } \}$ at the central server +11: end if +12: $\widehat { \mathbf { B } } _ { c } ^ { ( r ) }$ are transmitted from the client $c _ { c }$ to the central server +13: 14: end forUpdate $\begin{array} { r } { \pmb { \theta } _ { G } ^ { ( r ) } \frac { 1 } { | \mathcal { C } ^ { ( r ) } | } \sum _ { c \in \mathcal { C } ^ { ( r ) } } \widehat { \mathbf { B } } _ { c } ^ { ( r ) } } \end{array}$ +15: if a client $c _ { c \in { \mathcal { C } } ^ { ( r ) } }$ still learn then +16: Distribute $\theta _ { G } ^ { ( r ) }$ and $k b ^ { \prime } \subseteq k b$ to the client $c _ { c }$ if new task is arrived, otherwise distribute $\theta _ { G } ^ { ( r ) }$ +17: Minimize Eq. (2) for solving local CL problems at the client $c _ { c }$ +18: end if +19: end if +20: end for + +We now consider FedWeIT under the asynchronous federated continual learning scenario, where there is no synchronization across clients for each task. This is a more realistic scenario since each task may require different training rounds to converge during federated continual learning. Here, asynchronous implies that each task requires different training costs (i.e., time, epochs, or rounds) for training. Under the asynchronous federated learning scenario, FedWeIT transfers any available task-adaptive parameters from the knowledge base $( k b ^ { \prime } )$ to each client. We provide the detailed algorithm in Algorithm 3. In Table 7 and Figure 10, we plot the average test accuracy over all tasks during synchronous / asynchronous federated continual learning. As shown in Figure 10, different tasks across clients at the same timestep require the same number of training rounds, receiving new tasks and task-adaptive parameters from the knowledge base simultaneously with the synchronous FedWeIT. On the other hand, with asynchronous FedWeIT, each task requires different training rounds and receives new tasks and task-adaptive parameters in an asynchronous manner. The results in Table 7 shows that the performance of asynchronous FedWeIT is almost similar to that of the synchronous FedWeIT. + +Table 7: Averaged performance of FedWeIT with synchronous and asynchronous federated continual learning scenario. + +
NonIID-50
FedWeITAccuracy (%)
Synchronous84.11 ± 0.27
Asynchronous84.40 ± 0.41
+ +![](images/345bee7f94e9da58f53b79209b11767056060b036018900f29baf9c0068f0802.jpg) +Figure 10: FedWeIT with asynchronous federated continual learning on Non-iid 50 dataset. We measure the test accuracy of all tasks per client. \ No newline at end of file diff --git a/parse/train/Svfh1_hYEtF/Svfh1_hYEtF_content_list.json b/parse/train/Svfh1_hYEtF/Svfh1_hYEtF_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d1def30e4c717c8a1dd39f7aa98566eba56b77f5 --- /dev/null +++ b/parse/train/Svfh1_hYEtF/Svfh1_hYEtF_content_list.json @@ -0,0 +1,1629 @@ +[ + { + "type": "text", + "text": "FEDERATED CONTINUAL LEARNING WITHWEIGHTED INTER-CLIENT TRANSFER", + "text_level": 1, + "bbox": [ + 173, + 99, + 681, + 146 + ], + "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": "There has been a surge of interest in continual learning and federated learning, both of which are important in deep neural networks in real-world scenarios. Yet little research has been done regarding the scenario where each client learns on a sequence of tasks from a private local data stream. This problem of federated continual learning poses new challenges to continual learning, such as utilizing knowledge from other clients, while preventing interference from irrelevant knowledge. To resolve these issues, we propose a novel federated continual learning framework, Federated Weighted Inter-client Transfer (FedWeIT), which decomposes the network weights into global federated parameters and sparse task-specific parameters, and each client receives selective knowledge from other clients by taking a weighted combination of their task-specific parameters. FedWeIT minimizes interference between incompatible tasks, and also allows positive knowledge transfer across clients during learning. We validate our FedWeIT against existing federated learning and continual learning methods under varying degrees of task similarity across clients, and our model significantly outperforms them with a large reduction in the communication cost. ", + "bbox": [ + 233, + 265, + 766, + 486 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 511, + 336, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continual learning (Thrun, 1995; Kumar & Daume III, 2012; Ruvolo & Eaton, 2013; Kirkpatrick et al., 2017; Schwarz et al., 2018) describes a learning scenario where a model continuously trains on a sequence of tasks; it is inspired by the human learning process, as a person learns to perform numerous tasks with large diversity over his/her lifespan, making use of the past knowledge to learn about new tasks without forgetting previously learned ones. Continual learning is a long-studied topic since having such an ability leads to the potential of building a general artificial intelligence. However, there are crucial challenges in implementing it with conventional models such as deep neural networks (DNNs), such as catastrophic forgetting, which describes the problem where parameters or semantic representations learned for the past tasks drift to the direction of new tasks during training. The problem has been tackled by various prior work (Kirkpatrick et al., 2017; Lee et al., 2017; Shin et al., 2017; Riemer et al., 2019). More recent works tackle other issues, such as scalability or order-robustness (Schwarz et al., 2018; Hung et al., 2019; Yoon et al., 2020). ", + "bbox": [ + 174, + 541, + 825, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, all of these models are fundamentally limited in that the models can only learn from its direct experience - they only learn from the sequence of the tasks they have trained on. Contrarily, humans can learn from indirect experience from others, through different means (e.g. verbal communications, books, or various media). Then wouldn’t it be beneficial to implement such an ability to a continual learning framework, such that multiple models learning on different machines can learn from the knowledge of the tasks that have been already experienced by other clients? One problem that arises here, is that due to data privacy on individual clients and exorbitant communication cost, it may not be possible to communicate data directly between the clients or between the server and clients. Federated learning (McMahan et al., 2016; Li et al., 2018; Yurochkin et al., 2019) is a learning paradigm that tackles this issue by communicating the parameters instead of the raw data itself. We may have a server that receives the parameters locally trained on multiple clients, aggregates it into a single model parameter, and sends it back to the clients. Motivated by our intuition on learning from indirect experience, we tackle the problem of Federated Continual Learning (FCL) where we perform continual learning with multiple clients trained on private task sequences, which communicate their task-specific parameters via a global server. Figure 1 (a) depicts an example scenario of FCL. Suppose that we are building a network of hospitals, each of which has a disease diagnosis model which continuously learns to perform diagnosis given CT scans, for new types of diseases. Then, under our framework, any diagnosis model which has learned about a new type of disease (e.g. COVID-19) will transmit the task-specific parameters to the global server, which will redistribute them to other hospitals for the local models to utilize. This allows all participants to benefit from the new task knowledge without compromising the data privacy. ", + "bbox": [ + 174, + 715, + 825, + 924 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6998a6802da248658c2a2e9155a1bc0fe3e656e424795ecf911b7107c7f66236.jpg", + "image_caption": [ + "Figure 1: (a): Concept. A continual learner at a hospital which learns on sequence of disease prediction tasks may want to utilize relevant task parameters from other hospitals. FCL allows such inter-client knowledge transfer via the communication of task-decomposed parameters. (b): Challenge of FCL. Interference from other clients, resulting from sharing irrelevant knowledge, may hinder an optimal training of target clients (Red) while relevant knowledge from other clients will be beneficial for their learning (Green). " + ], + "image_footnote": [], + "bbox": [ + 179, + 90, + 795, + 231 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 319, + 825, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Yet, the problem of federated continual learning also brings new challenges. First, there is not only the catastrophic forgetting from continual learning, but also the threat of potential interference from other clients. Figure 1 (b) describes this challenge with the results of a simple experiment. Here, we train a model for MNIST digit recognition while communicating the parameters from another client trained on a different dataset. When the knowledge transferred from the other client is relevant to the target task (SVHN), the model starts with high accuracy, converge faster and reach higher accuracy (green line), whereas the model underperforms the base model if the transferred knowledge is from a task highly different from the target task (CIFAR-10, red line). Thus, we need to selective utilize knowledge from other clients to minimize the inter-client interference and maximize inter-client knowledge transfer. Another problem with the federated learning is efficient communication, as communication cost could become excessively large when utilizing the knowledge of the other clients, since the communication cost could be the main bottleneck in practical scenarios when working with edge devices. Thus we want the knowledge to be represented as compactly as possible. ", + "bbox": [ + 174, + 409, + 825, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle these challenges, we propose a novel framework for federated continual learning, Federated Weighted Inter-client Transfer (FedWeIT), which decomposes the local model parameters into a dense base parameter and sparse task-adaptive parameters. FedWeIT reduces the interference between different tasks since the base parameters will encode task-generic knowledge, while the task-specific knowledge will be encoded into the task-adaptive parameters. When we utilize the generic knowledge, we also want the client to selectively utilize task-specific knowledge obtained at other clients. To this end, we allow each model to take a weighted combination of the task-adaptive parameters broadcast from the server, such that it can select task-specific knowledge helpful for the task at hand. FedWeIT is communication-efficient, since the task-adaptive parameters are highly sparse and only need to be communicated once when created. Moreover, when communication efficiency is not a critical issue as in cross-silo federated learning (Kairouz et al., 2019), we can use our framework to incentivize each client based on the attention weights on its task-adaptive parameters. We validate our method on multiple different scenarios with varying degree of task similarity across clients against various federated learning and local continual learning models. The results show that our model obtains significantly superior performance over all baselines, adapts faster to new tasks, with largely reduced communication cost. The main contributions of this paper are as follows: ", + "bbox": [ + 173, + 597, + 825, + 818 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• We introduce a new problem of Federated Continual Learning (FCL), where multiple models continuously learn on distributed clients, which poses new challenges such as prevention of inter-client interference and inter-client knowledge transfer. We propose a novel and communication-efficient framework for federated continual learning, which allows each client to adaptively update the federated parameter and selectively utilize the past knowledge from other clients, by communicating sparse parameters. ", + "bbox": [ + 187, + 830, + 826, + 920 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 102, + 344, + 117 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continual learning While continual learning (Kumar & Daume III, 2012; Ruvolo & Eaton, 2013) is a long-studied topic with a vast literature, we only discuss recent relevant works. Regularizationbased: EWC (Kirkpatrick et al., 2017) leverages Fisher Information Matrix to restrict the change of the model parameters such that the model finds solution that is good for both previous and the current task, and IMM (Lee et al., 2017) proposes to learn the posterior distribution for multiple tasks as a mixture of Gaussians. Architecture-based: DEN (Yoon et al., 2018) tackles this issue by expanding the networks size that are necessary via iterative neuron/filter pruning and splitting, and RCL (Xu & Zhu, 2018) tackles the same problem using reinforcement learning. APD (Yoon et al., 2020) additively decomposes the parameters into shared and task-specific parameters to minimize the increase in the network complexity. Coreset-based: GEM variants (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2019) minimize the loss on both of actual dataset and stored episodic memory. FRCL (Titsias et al., 2020) memorizes approximated posteriors of previous tasks with sophisticatedly constructed inducing points. To the best of our knowledge, none of the existing approaches considered the communicability for continual learning of deep neural networks, which we tackle. CoLLA (Rostami et al., 2018) aims at solving multi-agent lifelong learning with sparse dictionary learning, but it is not applicable to federated learning or continual deep learning. ", + "bbox": [ + 174, + 131, + 826, + 353 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Federated learning Federated learning is a distributed learning framework under differential privacy, which aims to learn a global model on a server while aggregating the parameters learned at the clients on their private data. FedAvg (McMahan et al., 2016) aggregates the model trained across multiple clients by computing a weighted average of them based on the number of data points trained. FedProx (Li et al., 2018) trains the local models with a proximal term which restricts their updates to be close to the global model. FedCurv (Shoham et al., 2019) aims to minimize the model disparity across clients during federated learning by adopting a modified version of EWC. Recent works Yurochkin et al. (2019); Wang et al. (2020) introduce well-designed aggregation policies by leveraging Bayesian non-parametric methods. A crucial challenge of federated learning is the reduction of communication cost. TWAFL (Chen et al., 2019) tackles this problem by performing layer-wise parameter aggregation, where shallow layers are aggregated at every step, but deep layers are aggregated in the last few steps of a loop. Karimireddy et al. (2020) suggests an algorithm for rapid convergence, which minimizes the interference among discrepant tasks at clients by sacrificing the local optimality. This is an opposite direction from personalized federated learning methods (Fallah et al., 2020; Lange et al., 2020; Deng et al., 2020) which put more emphasis on the performance of local models. FCL is a parallel research direction to both, and to the best of our knowledge, ours is the first work that considers task-incremental learning of clients under federated learning framework. ", + "bbox": [ + 173, + 359, + 825, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 FEDERATED CONTINUAL LEARNING WITH FEDWEIT ", + "text_level": 1, + "bbox": [ + 176, + 621, + 645, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by the human learning process from indirect experiences, we introduce a novel continual learning under federated learning setting, which we refer to as Federated Continual Learning (FCL). FCL assumes that multiple clients are trained on a sequence of tasks from private data stream, while communicating the learned parameters with a global server. We first formally define the problem in Section 3.1, and then propose naive solutions that straightforwardly combine the existing federated learning and continual learning methods in Section 3.2. Then, following Section 3.3 and 3.4, we discuss about two novel challenges that are introduced by federated continual learning, and propose a novel framework, Federated Weighted Inter-client Transfer (FedWeIT) which can effectively handle the two problems while also reducing the client-to-sever communication cost. ", + "bbox": [ + 174, + 650, + 825, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 PROBLEM DEFINITION ", + "text_level": 1, + "bbox": [ + 174, + 791, + 370, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the stof tasks $\\{ \\mathcal { T } ^ { ( 1 ) } , \\mathcal { T } ^ { ( 2 ) } , . . . , \\mathcal { T } ^ { ( T ) } \\}$ ng (on a where $\\mathcal { T } ^ { ( t ) }$ le machine), the model i is a labeled dataset of $t ^ { t h }$ tivelytask, $\\mathcal { T } ^ { ( t ) } = \\{ \\mathbf { x } _ { i } ^ { ( t ) } , \\mathbf { y } _ { i } ^ { ( \\bar { t } ) } \\} _ { i = 1 } ^ { N _ { t } }$ which consists of $N _ { t }$ pairs of instances $\\mathbf { x } _ { i } ^ { ( t ) }$ and their corresponding labels ${ \\bf y } _ { i } ^ { ( t ) }$ . Assuming the most realistic situation, we consider the case where the task sequence is a task stream with an unknown arriving order, such that the model can access $\\mathcal { T } ^ { ( t ) }$ only at the training period of task $t$ which becomes inaccessible afterwards. Given $\\mathcal { T } ^ { ( t ) }$ and the model learned so far, the learning objective at task $t$ is as follows: $\\mathrm { m i n i m i z e } _ { \\theta ^ { ( t } }$ ) $\\mathscr { L } ( \\pmb { \\theta } ^ { ( t ) } ; \\pmb { \\theta } ^ { ( t - 1 ) } , \\tau ^ { ( t ) } )$ , where ${ \\pmb \\theta } ^ { ( t ) }$ is a set of the model parameters at task $t$ . ", + "bbox": [ + 174, + 814, + 825, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now extend the conventional continual learning to the federated learning setting with multiple clients and a global server. Let us assume that we have $C$ clients, where at each client $c _ { c } \\in$ $\\{ c _ { 1 } , \\ldots , c _ { C } \\}$ trains a model on a privately accessible sequence of tasks $\\{ \\mathcal { T } _ { c } ^ { ( 1 ) } , \\mathcal { T } _ { c } ^ { ( 2 ) } , . . . , \\mathcal { T } _ { c } ^ { ( t ) } \\} \\subseteq \\mathcal { T }$ . Please note that there is no relation among the tasks $\\mathcal { T } _ { 1 : c } ^ { ( t ) }$ received at step $t$ , across clients. Now the goal is to effectively train $C$ continual learning models on their own private task streams, via communicating the model parameters with the global server, which aggregates the parameters sent from each client, and redistributes them to clients. ", + "bbox": [ + 173, + 103, + 826, + 208 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 COMMUNICABLE CONTINUAL LEARNING ", + "text_level": 1, + "bbox": [ + 173, + 220, + 503, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In conventional federated learning settings, the learning is done with multiple rounds of local learning and parameter aggregation. At each round of communication $r$ , each client $c _ { c }$ and the server $s$ perform the following two procedures: local parameter transmission and parameter aggregation $\\&$ broadcasting. In the local parameter transmission step, for a randomly selected subset of clients at round $r$ , $\\mathcal { C } ^ { ( r ) } \\subseteq \\{ c _ { 1 } , c _ { 2 } , . . . , c _ { C } \\}$ , each client $c _ { c }$ sends updated parameters $\\pmb \\theta ^ { ( r ) }$ to the server. The server-clients transmission is not done at every client because some of the clients may be temporarily disconnected. Then the server aggregates the parameters $\\pmb { \\theta } _ { c } ^ { ( r ) }$ sent from the clients into a single parameter. The most popular frameworks for this aggregation are FedAvg (McMahan et al., 2016) and FedProx (Li et al., 2018). However, naive federated continual learning with these two algorithms on local sequences of tasks may result in catastrophic forgetting. One simple solution is to use a regularization-based, such as Elastic Weight Consolidation (EWC) (Kirkpatrick et al., 2017), which allows the model to obtain a solution that is optimal for both the previous and the current tasks. There exist other advanced solutions (Rusu et al., 2016; Nguyen et al., 2018; Chaudhry et al., 2019) that successfully prevents catastrophic forgetting. However, the prevention of catastrophic forgetting at the client level is an orthogonal problem from federated learning. ", + "bbox": [ + 173, + 242, + 825, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus we focus on challenges that newly arise in this federated continual learning setting. In the federated continual learning framework, the aggregation of the parameters into a global parameter $\\theta _ { G }$ allows inter-client knowledge transfer across clients, since a task $\\mathcal { T } _ { i } ^ { ( q ) }$ learned at client $c _ { i }$ at round $q$ may be similar or related to $\\mathcal { T } _ { j } ^ { ( r ) }$ learned at client $c _ { j }$ at round $r$ . Yet, using a single aggregated parameter $\\theta _ { G }$ may be suboptimal in achieving this goal since knowledge from irrelevant tasks may not to be useful or even hinder the training at each client by altering its parameters into incorrect directions, which we describe as inter-client interference. Another problem that is also practically important, is the communication-efficiency. Both the parameter transmission from the client to the server, and server to client will incur large communication cost, which will be problematic for the continual learning setting, since the clients may train on possibly unlimited streams of tasks. ", + "bbox": [ + 173, + 462, + 825, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3 FEDERATED WEIGHTED INTER-CLIENT TRANSFER", + "text_level": 1, + "bbox": [ + 174, + 622, + 565, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "How can we then maximize the knowledge transfer between clients while minimizing the inter-client interference, and communication cost? We now describe our model, Federated Weighted Inter-client Transfer (FedWeIT), which can resolve the these two problems that arise with a naive combination of continual learning approaches with federated learning framework. ", + "bbox": [ + 174, + 643, + 825, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The main cause of the problems, as briefly alluded to earlier, is that the knowledge of all tasks learned at multiple clients is stored into a single set of parameters $\\theta _ { G }$ . However, for the knowledge transfer to be effective, each client should selectively utilize only the knowledge of the relevant tasks that is trained at other clients. This selective transfer is also the key to minimize the inter-client interference as well as it will disregard the knowledge of irrelevant tasks that may interfere with learning. ", + "bbox": [ + 173, + 705, + 825, + 776 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We tackle this problem by decomposing the parameters, into three different types of the parameters with different roles: global parameters $( \\pmb \\theta _ { G } )$ that capture the global and generic knowledge across all clients, local base parameters $\\mathbf { \\delta } ( \\mathbf { B } )$ which capture generic knowledge for each client, and task-adaptive parameters (A) for each specific task per client, motivated by Yoon et al. (2020). A set of the model parameters $\\pmb { \\theta } _ { c } ^ { ( t ) }$ for task $t$ at continual learning client $c _ { c }$ is then defined as follows: ", + "bbox": [ + 173, + 782, + 825, + 856 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/e9fa79e8d9e76fe428194db35faadc7881639a065831ccd0d94f3c86bd92fce6.jpg", + "text": "$$\n\\pmb { \\theta } _ { c } ^ { ( t ) } = \\mathbf { B } _ { c } ^ { ( t ) } \\odot \\mathbf { m } _ { c } ^ { ( t ) } + \\mathbf { A } _ { c } ^ { ( t ) } + \\sum _ { i \\in \\mathcal { C } _ { \\backslash c } } \\sum _ { j < | t | } \\alpha _ { i , j } ^ { ( t ) } \\mathbf { A } _ { i } ^ { ( j ) }\n$$", + "text_format": "latex", + "bbox": [ + 339, + 862, + 656, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf { B } _ { c } ^ { ( t ) } \\in \\{ \\mathbb { R } ^ { I _ { l } \\times O _ { l } } \\} _ { l = 1 } ^ { L }$ is the set of base parameters for $c ^ { t h }$ client shared across all tasks in the client, $\\mathbf { m } _ { c } ^ { ( t ) } \\in \\{ \\mathbb { R } ^ { O _ { l } } \\} _ { l = 1 } ^ { L }$ is the set of sparse vector masks which allows to adaptively transform $\\mathbf { B } _ { c } ^ { ( t ) }$ for the task t, A(t)c ∈ {RIl×Ol }Ll=1 is the set of a sparse task-adaptive parameters at client cc. Here, $L$ is the number of the layer in the neural network, and $I _ { l } , O _ { l }$ are input and output dimension of the weights at layer $l$ , respectively. ", + "bbox": [ + 178, + 907, + 821, + 925 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/502254cbcb197ea4db1cf249ff75854e1847b1d40e294b6cac2fee19b1406f51.jpg", + "image_caption": [ + "Figure 2: Updates of FedWeIT. (a) A client sends sparsified federated parameter $\\mathbf { B } _ { c } \\odot \\mathbf { m } _ { c } ^ { ( t ) }$ . After that, the server redistributes aggregated parameters to the clients. (b) The knowledge base stores previous tasks-adaptive parameters of clients, and each client selectively utilizes them with an attention mask. " + ], + "image_footnote": [], + "bbox": [ + 223, + 101, + 766, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 308, + 825, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The first term allows selective utilization of the global knowledge. We want the base parameter $\\mathbf { B } _ { c } ^ { ( t ) }$ at each client to capture generic knowledge across all tasks across all clients. In Figure 2 (a), we initialize it at each round $t$ with the global parameter from the previous iteration, $\\theta _ { G } ^ { ( t - 1 ) }$ which aggregates the parameters sent from the client. This allows $\\mathbf { B } _ { c } ^ { ( t ) }$ to also benefit from the global knowledge about all the tasks. However, since $\\theta _ { G } ^ { ( t - 1 ) }$ also contains knowledge irrelevant to the current task, instead of using it as is, we learn the sparse mask $\\mathbf { m } _ { c } ^ { ( t ) }$ to select only the relevant parameters for the given task. This sparse parameter selection helps minimize inter-client interference, and also allows for efficient communication. The second term is the task-adaptive parameters $\\mathbf { A } _ { c } ^ { ( t ) }$ . Since we additively decompose the parameters, this will learn to capture knowledge about the task that is not captured by the first term, and thus will capture specific knowledge about the task ${ \\mathcal T } _ { c } ^ { ( t ) }$ . The final term describes weighted inter-client knowledge transfer. We have a set of parameters that are transmitted from the server, which contain all task-adaptive parameters from all the clients. To selectively utilizes these indirect experiences from other clients, we further allocate attention $\\alpha _ { c } ^ { ( t ) }$ on these parameters, to take a weighted combination of them. By learning this attention, each client can select only the relevant task-adaptive parameters that help learn the given task. Although we design $A _ { i } ^ { ( j ) }$ to be highly sparse, using about $2 - 3 \\%$ of memory of full parameter in practice, sending all task knowledge is not desirable. Thus we only transmit the task-adaptive parameter of the previous task $( t - 1 )$ , which we empirically find to achieve good results in practice. ", + "bbox": [ + 173, + 378, + 826, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. We learn the decomposable parameter $\\pmb { \\theta } _ { c } ^ { ( t ) }$ by optimizing for the following objective: ", + "bbox": [ + 176, + 669, + 810, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/392869cf1289509af548aaacad72a0231e91d48abff406f9e9648b72413e53fc.jpg", + "text": "$$\n\\operatorname* { m i n i m i z e } _ { \\mathbf { B } _ { c } ^ { ( t ) } , \\ \\mathbf { m } _ { c } ^ { ( t ) } , \\ \\mathbf { A } _ { c } ^ { ( t + 1 ) } , \\ \\alpha _ { c } ^ { ( t ) } } \\ \\mathcal { L } \\left( \\pmb { \\theta } _ { c } ^ { ( t ) } ; \\mathcal { T } _ { c } ^ { ( t ) } \\right) + \\lambda _ { 1 } \\Omega ( \\{ \\mathbf { m } _ { c } ^ { ( t ) } , \\mathbf { A } _ { c } ^ { ( 1 : t ) } \\} ) + \\lambda _ { 2 } \\sum _ { i = 1 } ^ { t - 1 } \\| \\Delta \\mathbf { B } _ { c } ^ { ( t ) } \\odot \\mathbf { m } _ { c } ^ { ( i ) } + \\Delta \\mathbf { A } _ { c } ^ { ( i ) } \\| _ { 2 } ^ { 2 } ,\n$$", + "text_format": "latex", + "bbox": [ + 194, + 689, + 781, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal { L }$ is a loss function and $\\Omega ( \\cdot )$ is a sparsity-inducing regularization term for all task-adaptive parameters and the masking variable (we use $\\ell _ { 1 }$ -norm regularization), to make them sparse. The second regularization term is used for retroactive update of the past task-adaptive parameters, which helps the task-adaptive parameters to maintain the original solutions for the target tasks, by reflecting the change of the base parameter. Here, $\\Delta \\mathbf { B } _ { c } ^ { ( t ) } = \\mathbf { B } _ { c } ^ { ( t ) } - \\mathbf { B } _ { c } ^ { ( t - 1 ) }$ is the difference between the base parameter at the current and previous timestep, and $\\Delta \\mathbf { A } _ { c } ^ { ( i ) }$ is the difference between the task-adaptive parameter for task $i$ at the current and previous timestep. This regularization is essential for preventing catastrophic forgetting. $\\lambda _ { 1 }$ and $\\lambda _ { 2 }$ are hyperparameters controlling the effect of the two regularizers. ", + "bbox": [ + 173, + 734, + 825, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4 EFFICIENT COMMUNICATION VIA SPARSE PARAMETERS ", + "text_level": 1, + "bbox": [ + 174, + 869, + 602, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FedWeIT learns via server-to-client communication. As discussed earlier, a crucial challenge here is to reduce the communication cost. We describe what happens at the client and the server at each step. ", + "bbox": [ + 173, + 895, + 823, + 924 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Federated Weighted Inter-client Transfer \ninput Dataset {D(1:t)c }Cc=1 , and Global Parameter $\\theta _ { G }$ \noutput $\\{ \\mathbf { B } _ { c } , \\mathbf { m } _ { c } ^ { ( 1 : t ) }$ , $\\alpha _ { c } ^ { ( 1 : t ) }$ , ${ \\bf A } _ { c } ^ { ( 1 : t ) } \\} _ { c = 1 } ^ { C }$ 1: Initialize $\\mathbf { B } _ { c }$ to $\\theta _ { G }$ for all $c \\in \\mathcal { C } \\equiv \\{ 1 , . . . , C \\}$ 2: for task $t = 1 , 2 , \\dots \\mathbf { d o }$ 3: for round $r = 1 , 2 , . . . , R$ do 4: Transmit Bb(t,r)c a nd A(t−1,R)c o f client cc to server 5: Compute $\\begin{array} { r } { \\pmb { \\theta } _ { G } ^ { ( r ) } \\frac { 1 } { | \\mathcal { C } | } \\sum _ { c \\in \\mathcal { C } } \\widehat { \\mathbf { B } } _ { c } ^ { ( t , r ) } } \\end{array}$ 6: Distribute $\\theta _ { G } ^ { ( r ) }$ ) and {A(t−1,R)} to client $c$ 7: Minimize Eq. (2) for solving each local CL problems 8: end for \n9: end for ", + "bbox": [ + 166, + 103, + 522, + 284 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4a433d57d9642d510b139cc97c019e10c193a5a9a99bb9571a0f4b8c8aedff61.jpg", + "image_caption": [ + "Figure 3: Configuration of task sequences: We first split a dataset $D$ into multiple sub-tasks in non-IID manner ((a) and (b)). Then, we distribute them to multiple clients $( C _ { \\# } )$ . Mixed tasks from multiple datasets (colored circles) are distributed across all clients ((c)). " + ], + "image_footnote": [], + "bbox": [ + 526, + 103, + 812, + 184 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Client: At each round $r$ , each client $c _ { c }$ partially updates its base parameter with the nonzero components of the global parameter sent from the server; that is, $\\bar { \\mathbf { B } _ { c } } ( n ) = \\pmb { \\theta } _ { G } ( n )$ where $n$ is a nonzero element of the global parameter. After training the model using Eq. (2), it obtains a sparsified base parameter $\\widehat { \\mathbf { B } } _ { c } ^ { ( t ) } = \\mathbf { B } _ { c } ^ { ( t ) } \\odot \\mathbf { m } _ { c } ^ { ( t ) }$ and task-adaptive parameter $\\mathbf { A } _ { c } ^ { ( t ) }$ for the new task, both of which are sent to the server, at smaller cost compared to naive FCL baselines. While naive FCL baselines require $\\vert { \\mathcal { C } } \\vert \\times R \\times \\vert \\theta \\vert$ for client-to-server communication, FedWeIT requires $| { \\mathcal { C } } | \\times \\left( R \\times | { \\widehat { \\mathbf { B } } } | + | \\mathbf { A } | \\right)$ where $R$ is the number of communication round per task and $| \\cdot |$ is the number of parameters. ", + "bbox": [ + 173, + 308, + 825, + 415 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Server: The server first aggregates the base parameters sent from all the clients by taking an weighted average of them: $\\begin{array} { r } { \\pmb { \\theta } _ { G } = \\frac { 1 } { \\mathcal { C } } \\sum _ { c } \\widehat { \\mathbf { B } } _ { i } ^ { ( t ) } } \\end{array}$ . Then, it broadcasts $\\theta _ { G }$ to all the clients. Task adaptive parameters of t − 1, {A(t−1)i }C\\ci=1 a re broadcast at once per client during training task $t$ . While naive FCL baselines requires $\\lvert \\mathcal { C } \\rvert \\times \\bar { R ^ { \\prime } } \\times \\lvert \\pmb { \\theta } \\rvert$ for server-to-client communication cost, FedWeIT requires $| { \\mathcal { C } } | \\times ( R \\times | \\pmb { \\theta } _ { G } | + ( | { \\mathcal { C } } | - 1 ) \\times | \\mathbf { A } | )$ in which $\\theta _ { G } , \\mathbf { A }$ are highly sparse. We describe the FedWeIT algorithm in Algorithm 1. For a detailed version of the algorithm, please see Section D in appendix. ", + "bbox": [ + 173, + 420, + 825, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 545, + 326, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We validate our FedWeIT under different configurations of task sequences against baselines which are namely Overlapped-CIFAR-100 and NonIID-50. 1) Overlapped-CIFAR-100: We group 100 classes of CIFAR-100 dataset into 20 non-iid superclasses tasks. Then, we randomly sample 10 tasks out of 20 tasks and split instances to create a task sequence for each of the clients with overlapping tasks. 2) NonIID-50: We use the following eight benchmark datasets: MNIST (LeCun et al., 1998), CIFAR10/-100 (Krizhevsky & Hinton, 2009), SVHN (Netzer et al., 2011), Fashion-MNIST (Xiao et al., 2017), Not-MNIST (Bulatov, 2011), FaceScrub $\\mathrm { N g }$ & Winkler, 2014), and TrafficSigns (Stallkamp et al., 2011). We split the classes in the 8 datasets into 50 non-IID tasks, each of which is composed of 5 classes that are disjoint from the classes used for the other tasks. This is a large-scale experiment, containing 280, 000 images of 293 classes from 8 heterogeneous datasets. After generating and processing tasks, we randomly distribute them to multiple clients as illustrated in Figure 3. ", + "bbox": [ + 173, + 580, + 826, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental setup We use a modified version of LeNet (LeCun et al., 1998) for the experiments with both Overlapped-CIFAR-100 and NonIID-50 dataset. Further, we use ResNet-18 He et al. (2016) with NonIID-50 dataset. We followed other experimental setups from Serrà et al. (2018) and Yoon et al. (2020). For detailed descriptions of the task configuration and hyperparameters used, please see Section B in appendix. Also, for more ablation studies, please see Section C in appendix. ", + "bbox": [ + 173, + 751, + 825, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines and our model 1) STL: Single Task Learning at each arriving task. 2) Local-EWC: Individual continual learning with EWC (Kirkpatrick et al., 2017) per client. 3) Local-APD: Individual continual learning with APD (Yoon et al., 2020) per client. 4) FedProx: FCL using FedProx (Li et al., 2018) algorithm. 5) Scaffold: FCL using Scaffold (Karimireddy et al., 2020) algorithm. 6) FedCurv: FCL using FedCurv (Shoham et al., 2019) algorithm. 7) FedProx-[model]: FCL, that is trained using FedProx algorithm with [model]. 8) FedWeIT: Our FedWeIT algorithm. ", + "bbox": [ + 173, + 840, + 826, + 924 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7a8de8b1f6504d1d1bf3c8aeae2eeb39507986e27170b111dbed770185dedb12.jpg", + "table_caption": [ + "Table 1: Averaged Per-task performance on both dataset during FCL with 5 clients (fraction $\\scriptstyle 1 = 1 . 0$ ). We measured task accuracy and model size after completing all learning phases over 3 individual trials. We also measured C2S/S2C communication cost for training each task. " + ], + "table_footnote": [], + "table_body": "
NonIID-50Dataset (F=1.0, R=20)Overlapped CIFAR-100 (F=1.0,R=20)
MethodsAccuracyModel SizeC2S/S2C CostAccuracyModel SizeC2S/S2C Cost
STL85.78 ±0.170.610GBN/A57.15 ±0.070.610 GBN/A
Local-EWC74.30±0.080.061GB- -N/A44.26±0.430.061GBN7A
Local-APD81.42 ± 0.720.090 GBN/A50.82 ± 0.330.073 GBN/A
FedProx63.691.750.061GB1.22/1.22GB33.83±0.480.061GB1.22/1.22GB
Scaffold30.84 ± 1.410.061 GB2.44 /2.44 GB22.80 ±0.470.061 GB2.44/2.44 GB
FedCurv72.39 ±0.320.061GB1.22/1.22 GB40.36 ±0.440.061GB1.22/1.22 GB
FedProx-EWC68.18 ± 0.580.061 GB1.22/1.22 GB41.91 ± 0.470.061 GB1.22/1.22 GB
FedProx-APD81.20 ± 1.240.079 GB1.22/1.22 GB52.20 ± 0.410.075 GB1.22/1.22 GB
FedWeIT84.11 ± 0.270.078 GB0.37/1.07 GB55.16 ± 0.190.075 GB0.37/1.07 GB
", + "bbox": [ + 173, + 156, + 831, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16f3d871fde0d78f4c6941c6e95eaa8bb16972c0eeda1361c502d7518d17b655.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 168, + 287, + 418, + 412 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/039998d424871c7ec8845e5c6ac7ba6ad952ae879ae709ab993495884ba8de23.jpg", + "table_caption": [], + "table_footnote": [ + "Figure 4: Left: Averaged task adaptation during training last two ${ \\mathfrak { g } } ^ { t h }$ and $1 0 ^ { t h }$ ) tasks with 5 and 100 clients. Right: Average Per-task Performance on Overlapped-CIFAR-100 during FCL with 100 clients. " + ], + "table_body": "
100 clients (F=0.05,R=20,1,000 tasks in total)
MethodsAccuracyModel SizeC2S/S2C Cost
STL32.96 ±0.2312.20 GBN/A
Local-APD37.50 ±0.174.01GBN/A
FedProx24.11 ±0.441.22 GB1.2271.22 GB
FedCurv29.11 ± 0.201.22 GB1.22 /1.22 GB
FedCurv-EWC29.72 ± 0.201.22 GB1.22 /1.22 GB
FedWeIT39.58 ± 0.274.03 GB0.38 /1.10 GB
", + "bbox": [ + 431, + 297, + 833, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1 EXPERIMENTAL RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 460, + 392, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We first validate our model on both Overlapped-CIFAR-100 and NonIID-50 task sequences against single task learning (STL), continual learning (EWC, APD), federated learning (FedProx, Scaffold, FedCurv), and naive federated continual learning (FedProx-based) baselines. Table 1 shows the final average per-task performance after the completion of (federated) continual learning on both datasets. We observe that FedProx-based federated continual learning (FCL) approaches degenerate the performance of continual learning (CL) methods over the same methods without federated learning. This is because the aggregation of all client parameters that are learned on irrelevant tasks results in severe interference in the learning for each task, which leads to catastrophic forgetting and suboptimal task adaptation. Scaffold achieves poor performance on FCL, as its regularization on the local gradients is harmful for FCL, where all clients learn from a different task sequences. While FedCurv reduces inter-task disparity in parameters, it cannot minimize inter-task interference, which results it to underperform single-machine CL methods. On the other hand, FedWeIT significantly outperforms both single-machine CL baselines and naive FCL baselines on both datasets. Even with larger number of clients $C = 1 0 0$ ), FedWeIT consistently outperforms all baselines (Figure 4). This improvement largely owes to FedWeIT’s ability to selectively utilize the knowledge from other clients to rapidly adapt to the target task, and obtain better final performance (Figure 4 Left). ", + "bbox": [ + 173, + 488, + 825, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The fast adaptation to new task is another clear advantage of inter-client knowledge transfer. To further demonstrate the practicality of our method with larger networks, we experiment on Non-IID dtaset with ResNet-18 (Table 2), on which FedWeIT still significantly outperforms the strongest baseline (FedProx-APD) while using fewer parameters. Also, our model is not sensitive to the hyperparameters $\\lambda _ { 1 }$ and $\\lambda _ { 2 }$ , if they are within reasonable scales (Figure 6 Left). ", + "bbox": [ + 174, + 710, + 562, + 821 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ed525339e278ad372705bcd6d62b6727ca278f2a0145c9d02491a78246372094.jpg", + "table_caption": [ + "Table 2: FCL results on NonIID-50 dataset with ResNet-18. " + ], + "table_footnote": [], + "table_body": "
ResNet-18
MethodsAcc.M Size
Local-APDFedProx-APDFedWeIT92.44 %92.89%94.86 %1.86 GB2.05GB1.84 GB
", + "bbox": [ + 573, + 747, + 821, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Efficiency of FedWeIT We also report the accuracy as a function of network capacity in Table 1, 2, which we measure by the number of parameters used. We observe that FedWeIT obtains much higher accuracy while utilizing less number of parameters compared to FedProx-APD. This efficiency mainly comes from the reuse of task-adaptive parameters from other clients, which is not possible with single-machine CL methods or naive FCL methods. We also examine the communication cost (the size of non-zero parameters transmitted) of each method. Table 1 reports both the client-to-server (C2S) / server-to-client (S2C) communication cost at training each task. FedWeIT, uses only $3 0 \\%$ and $3 \\%$ of parameters for $\\widehat { \\mathbf B }$ and A of the dense models respectively. We observe that FedWeIT is significantly more communication-efficient than FCL baselines although it broadcasts task-adaptive parameters, due to high sparsity of the parameters. Figure 5 (a) shows the accuracy as a function of C2S cost according to a transmission of top- $\\kappa \\%$ informative parameters. Since FedWeIT selectively utilizes task-specific parameters learned from other clients, it results in superior performance over APD-baselines especially with sparse communication of model parameters. ", + "bbox": [ + 173, + 825, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/42b7c39389253e8c6b14218f62c8e3c835b18e61b7312d3849dc060008c81811.jpg", + "image_caption": [ + "Figure 5: (a) Accuracy over C2S cost. We report the relative communication cost to the original network. All results are averaged over the 5 clients. (b) Inter-client transfer for NonIID-50. We compare the scale of the attentions at first FC layer which gives the weights on transferred task-adaptive parameters from other clients. " + ], + "image_footnote": [], + "bbox": [ + 192, + 104, + 797, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b48b317b40e852b5ce1c0fd7677219d4191234672dc950bc7d939cfbf41b0cf8.jpg", + "image_caption": [ + "Figure 6: Left: Performance of FedWeIT with different scale of hyperparameters on Non-iid 50. Middle: Performance comparison about current task adaptation at $6 ^ { t h }$ and $8 ^ { t h }$ tasks during federated continual learning on NonIID-50. Right: Forgetting measure using Backward Transfer (BWT). " + ], + "image_footnote": [], + "bbox": [ + 176, + 261, + 799, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 412, + 825, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Catastrophic forgetting Further, we examine how the performance of the past tasks change during continual learning, to see the severity of catastrophic forgetting with each method. Figure 6 Left shows the performance of FedWeIT and FCL baselines on the $6 ^ { t h }$ and $8 ^ { t h }$ tasks, at the end of training for later tasks. We observe that naive FCL baselines suffer from more severe catastrophic forgetting than local continual learning with EWC because of the inter-client interference, where the knowledge of irrelevant tasks from other clients overwrites the knowledge of the past tasks. Contrarily, our model shows no sign of catastrophic forgetting. This is mainly due to the selective utilization of the prior knowledge learned from other clients through the global/task-adaptive parameters, which allows it to effectively alleviate inter-client interference. FedProx-APD also does not suffer from catastrophic forgetting, but they yield inferior performance due to ineffective knowledge transfer. We also report Backward Transfer (BWT), which is a measure on catastrophic forgetting for all models (more positive the better). We provide the details of BWT in the Section B in appendix. ", + "bbox": [ + 173, + 506, + 825, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Weighted inter-client knowledge transfer By analyzing the attention $_ \\alpha$ in Eq. (1), we examine which task parameters from other clients each client selected. Figure 5 (b), shows example of the attention weights that are learned for the $0 ^ { t h }$ split of MNIST and $1 0 ^ { \\hat { t h } }$ split of CIFAR-100. We observe that large attentions are allocated to the task parameters from the same dataset (CIFAR-100 utilizes parameters from CIFAR-100 tasks with disjoint classes), or from a similar dataset (MNIST utilizes parameters from Traffic Sign and SVHN). This shows that FedWeIT effectively selects beneficial parameters to maximize inter-client knowledge transfer. This is an impressive result since it does not know which datasets the parameters are trained on. ", + "bbox": [ + 174, + 680, + 825, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 CONCLUSION ", + "text_level": 1, + "bbox": [ + 176, + 810, + 318, + 827 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We tackled a novel problem of federated continual learning, whose goal is to continuously learn local models at each client while allowing it to utilize indirect experience (task knowledge) from other clients. This poses new challenges such as inter-client knowledge transfer and prevention of interclient interference between irrelevant tasks. To tackle these challenges, we additively decomposed the model parameters at each client into the global parameters that are shared across all clients, and sparse local task-adaptive parameters that are specific to each task. Further, we allowed each model to selectively update the global task-shared parameters and selectively utilize the task-adaptive parameters from other clients. The experimental validation of our model under various task similarity across clients, against existing federated learning and continual learning baselines shows that our model obtains significantly outperforms baselines with reduced communication cost. We believe that federated continual learning is a practically important topic of large interests to both research communities of continual learning and federated learning, that will lead to new research directions. 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Lifelong learning with dynamically expandable networks. In Proceedings of the International Conference on Learning Representations (ICLR), 2018. ", + "bbox": [ + 173, + 140, + 823, + 183 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Jaehong Yoon, Saehoon Kim, Eunho Yang, and Sung Ju Hwang. Scalable and order-robust continual learning with additive parameter decomposition. In Proceedings of the International Conference on Learning Representations (ICLR), 2020. ", + "bbox": [ + 173, + 193, + 823, + 234 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Mikhail Yurochkin, Mayank Agarwal, Soumya Ghosh, Kristjan Greenewald, Trong Nghia Hoang, and Yasaman Khazaeni. Bayesian nonparametric federated learning of neural networks. Proceedings of the International Conference on Machine Learning (ICML), 2019. ", + "bbox": [ + 173, + 244, + 825, + 286 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "A APPENDIX ", + "text_level": 1, + "bbox": [ + 176, + 102, + 297, + 117 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Organization The appendix is organized as follows: In Section B, we further describe the experimental details, including the network architecture, hyper-parameter configurations, forgetting measures, and datasets. Also, we report additional experimental results in Section C about the effect of the communication frequency (Section C.1) and an additional ablation studies for model components on Overlapped-CIFAR-100 dataset (Section C.2). We include a detailed algorithm for our FedWeIT in Section D. ", + "bbox": [ + 174, + 133, + 825, + 218 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "B EXPERIMENTAL DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 239, + 419, + 256 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "We further provide the experimental settings in detail, including the descriptions of the network architectures, hyperparameters, and dataset configuration. ", + "bbox": [ + 174, + 272, + 825, + 300 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Network architecture We utilize a modified version of LeNet and a conventional ResNet-18 as the backbone network architectures for validation. In the LeNet, the first two layers are convolutional neural layers of 20 and 50 filters with the $5 \\times 5$ convolutional kernels, which are followed by the two fully-connected layers of 800 and 500 units each. Rectified linear units activations and local response normalization are subsequently applied to each layers. We use $2 \\times 2$ max-pooling after each convolutional layer. All layers are initialized based on the variance scaling method. Detailed description of the architecture for LeNet is given in Table 3. ", + "bbox": [ + 173, + 316, + 825, + 415 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/7664297c72439ca0a1ecc746f5b3b71b4ee1c97800bed2ac4ddc10820c2a74c7.jpg", + "table_caption": [ + "Table 3: Base Network Architecture (LeNet) and Total Number of Parameters of both FedWeIT and All Baseline Models. $T$ describes the number of arrived tasks in continual learning. " + ], + "table_footnote": [], + "table_body": "
LayerFilter ShapeStrideOutput
Input Conv 1N/A 5×5×20N/A32×32×3 32×32 ×20
Max Pooling 13×31 216 ×16× 20
Conv 25×5×50116 ×16× 50
Max Pooling 23×328×8×50
Flatten3200N/A1×1×3200
FC1800N/A1×1×800
FC2500N/A1×1× 500
SoftmaxClassifierN/A1×1×5×T
TotalNumberofParameters3,012,920
", + "bbox": [ + 450, + 489, + 823, + 635 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Configurations We use an Adam optimizer with adaptive learning rate decay, which decays the learning rate by a factor of 3 for every 5 epochs with no consecutive decrease in the validation loss. We stop training in advance and start learning the next task (if available) when the learning rate reaches $\\rho$ . The experiment for LeNet with 5 clients, we initialize by $1 e ^ { - 3 } \\times \\frac { 1 } { 3 }$ at the beginning of each new task and $\\rho = 1 e ^ { - 7 }$ . Mini-batch size is 100, the rounds per task is 20, an the epoch per round is 1. The setting for ResNet-18 is identical, excluding the initial learning rate, $1 e ^ { - 4 }$ . In the case of ", + "bbox": [ + 174, + 433, + 437, + 641 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "experiments with 20 and 100 clients, we set the same settings except reducing minibatch size from 100 to 10 with an initial learning rate $1 e ^ { - 4 }$ . We use client fraction 0.25 and 0.05, respectively, at each communication round. we set $\\lambda _ { 1 } = [ 1 e ^ { - 1 } , 4 e ^ { - 1 } ]$ and $\\lambda _ { 2 } = 1 0 0$ for all experiments. Further, we use $\\mu = 5 e ^ { - 3 }$ for FedProx, $\\lambda = [ 1 e ^ { - 2 } , 1 . 0 ]$ for EWC and FedCurv. We initialize the attention parameter $\\alpha _ { c } ^ { ( t ) }$ as sum to one, $\\alpha _ { c , j } ^ { ( t ) } 1 / | \\alpha _ { c } ^ { ( t ) } |$ . ", + "bbox": [ + 174, + 642, + 826, + 717 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Backward-transfer (BWT) Backward transfer (BWT) is a measure for catastrophic forgetting. BWT compares the performance disparity of previous tasks after learning current task as follows: ", + "bbox": [ + 173, + 732, + 823, + 762 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/c8dd0dda2d56295603b67e679da3083dee89231904bf67b481d700f96c927a44.jpg", + "text": "$$\n\\mathrm { B W T } = \\frac { 1 } { T - 1 } \\sum _ { i < T } P _ { i } ^ { ( T ) } - P _ { i } ^ { ( i ) } ,\n$$", + "text_format": "latex", + "bbox": [ + 387, + 768, + 607, + 806 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where P (T ) is the performance of task $i$ after task $T$ is learned $( i < T )$ ). Thus, a large negative backward transfer value indicates that the performance has been substantially reduced, in which case catastrophic forgetting has happened. ", + "bbox": [ + 174, + 815, + 825, + 861 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "For NonIID-50 dataset, we utilize 8 heterogenous datasets and create 50 non-iid tasks in total as shown in Table 4. Then we arbitrarily select 10 tasks without duplication and distribtue them to 5 clients. The average performance of single task learning on the dataset is $8 5 . 7 8 \\pm 0 . 1 7 ( \\% )$ , measured by our base LeNet architecture. ", + "bbox": [ + 174, + 867, + 823, + 924 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/8c8fe29895f27ba09e81e78a736dfe5e0a5489ccfe992a69e97f29788f767c59.jpg", + "table_caption": [ + "Table 4: Detailed configuration of NonIID-50 Dataset. " + ], + "table_footnote": [], + "table_body": "
NonIID-50
Dataset#Classes#Tasks#Classes (Task)#Train Set#Valid Set#Test Set
CIFAR-100Face Scrub10015536,75010,5005,250
10016513,8593,9591,979
Traffic SignsSVHNMNIST4395 (3)32,1709,1914,595
102561,81017,6608,830
102542,70012,2006,100
CIFAR-10Not MNIST102536,75010,5005,250
102511,3393,2391,619
Fashion MNIST102542,70012,2006,100
Total29350248278,07839,72379,449
", + "bbox": [ + 174, + 128, + 820, + 272 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Datasets We create both Overlapped-CIFAR-100 and NonIID-50 datasets. For Overlapped-CIFAR100, we generate 20 non-iid tasks based on 20 superclasses, which hold 5 subclasses. We split instances of 20 tasks according to the number of clients (5, 20, and 100) and then distribute the tasks across all clients. ", + "bbox": [ + 173, + 285, + 825, + 342 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/b35bb7726c0fdbb48921b525d2777205cbf4d00d339ee6a9cdb7ffa2131d9725.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Overlapped-CIFAR-100
MethodsAccuracyModel SizeC2S/S2C CostEpochs /Round
FedWeIT55.16 ± 0.190.075 GB0.37/1.07 GB1
FedWeIT55.18 ± 0.080.077GB0.19/0.53GB2
FedWeIT53.73 ± 0.440.083 GB0.08/0.22 GB5
FedWeIT53.22 ±0.140.088 GB0.02 /0.07 GB20
", + "bbox": [ + 377, + 375, + 820, + 474 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/915f5727b0c2c60f49a80c4777cc099c5baea8fa8f149347e3ff1e59614a69e2.jpg", + "image_caption": [ + "Figure 7: Average Per-task Performance with error bars over the number of training epochs per communication rounds on Overlapped-CIFAR-100 for FedWeIT with 5 clients. All models transmit full of local base parameters and highly sparse task-adaptive parameters. All results are the mean accuracy over 5 clients and we run 3 individual trials. Red arrows at each point describes the standard deviation of the performance. " + ], + "image_footnote": [], + "bbox": [ + 171, + 364, + 362, + 479 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "C ADDITIONAL EXPERIMENTAL RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 571, + 537, + 588 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We further include a quantitative analysis about the communication round frequency and additional experimental results across the number of clients. ", + "bbox": [ + 174, + 607, + 823, + 635 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "C.1 EFFECT OF THE COMMUNICATION FREQUENCY ", + "text_level": 1, + "bbox": [ + 174, + 659, + 544, + 672 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "We provide an analysis on the effect of the communication frequency by comparing the performance of the model, measured by the number of training epochs per communication round. We run the 4 different FedWeIT with 1, 2, 5, and 20 training epochs per round. Figure 7 shows the performance of our FedWeIT variants. As clients frequently update the model pa", + "bbox": [ + 174, + 688, + 444, + 813 + ], + "page_idx": 12 + }, + { + "type": "table", + "img_path": "images/5517932fdc9493a7a748b653993c5d6938845f22ca899810d79ae30fcb595467.jpg", + "table_caption": [ + "Table 5: Experimental results on the Overlapped-CIFAR-100 dataset with 20 tasks. All results are the mean accuracies over 5 clients, averaged over 3 individual trials. " + ], + "table_footnote": [], + "table_body": "
Overlapped-CIFAR-100 with 20 tasks
MethodsAccuracyM SizeC2S/S2C Cost
FedProx29.76 ± 0.390.061GB1.22/1.22 GB
FedProx-EWC27.80 ± 0.580.061 GB1.22 / 1.22 GB
FedProx-APD43.80 ±0.760.093 GB1.22 / 1.22 GB
FedWeIT46.78 ±0.1470.092 GB0.3771.07 GB
", + "bbox": [ + 455, + 724, + 836, + 809 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "rameters through the communication with the central server, the model gets higher performance while maintaining smaller network capacity since the model with a frequent communication efficiently updates the model parameters as transferring the inter-client knowledge. However, it requires much heavier communication costs than the model with sparser communication. For example, the model trained for 1 epochs at each round may need to about 16.9 times larger entire communication cost than the model trained for 20 epochs at each round. Hence, there is a trade-off between model performance of federated continual learning and communication efficiency, whereas FedWeIT variants consistently outperform (federated) continual learning baselines. ", + "bbox": [ + 173, + 813, + 825, + 924 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/3b657f592fdd90c124b41dc16b9b78e2bc01a6bed1984f8f97607761c7fd63ee.jpg", + "image_caption": [ + "Figure 8: (a) Comparison of adaption for tasks between FedWeIT and APD with 20 clients in federated continual learning scenario (b) Comparison of adaptation for tasks between FedWeIT and APD with 100 clients in federated continual learning scenario. We visualize the last 5 tasks out of 10 tasks per client. Overlapped-CIFAR-100 dataset are used after splitting instances according to the number of clients (20 and 100). " + ], + "image_footnote": [], + "bbox": [ + 181, + 98, + 815, + 268 + ], + "page_idx": 13 + }, + { + "type": "image", + "img_path": "images/32f8172baf1860a819de6a58939b25386f9df87f5382ad5dc1d63dd285ae73e1.jpg", + "image_caption": [ + "Figure 9: Forgetting analysis. Performance change over the increasing number of tasks for all tasks except the last task $1 ^ { s t }$ to $9 ^ { t h }$ ) during federated continual learning on NonIID-50. We observe that our method does not suffer from task forgetting on any tasks. " + ], + "image_footnote": [], + "bbox": [ + 232, + 335, + 753, + 588 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "C.2 ABLATION STUDY FOR MODEL COMPONENTS ", + "text_level": 1, + "bbox": [ + 174, + 661, + 529, + 674 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "We perform an ablation study to analyze the role of each component of our FedWeIT. We compare the performance of four different variations of our model. w/o B communication describes the model that does not transfer the base parameter $\\mathbf { B }$ and only communicates task-adaptive ones. w/o A communication is the model that does not communicate task-adaptive parameters. w/o A is the model which trains the model only with sparse transmission of local base parameter, and w/o m is the model without the sparse vector mask. ", + "bbox": [ + 173, + 688, + 826, + 771 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "As shown in Table 6, without communicating $\\mathbf { B }$ or A, the model yields significantly lower performance compared to the full model since they do not benefit from inter-client knowledge transfer. The model w/o A obtains very low performance due to catastrophic forgetting, and the model w/o sparse mask m achieves lower accuracy with larger capacity and cost, which demonstrates the importance of performing selective transmission. ", + "bbox": [ + 174, + 772, + 455, + 922 + ], + "page_idx": 13 + }, + { + "type": "table", + "img_path": "images/dde7bc84717e0ccafe6d5cb9d96d09fc42b13558f05641fca703f5826d9dc7c2.jpg", + "table_caption": [ + "Table 6: Ablation studies to analyze the effectiveness of parameter decomposition on WeIT. All experiments performed on NonIID-50 dataset. " + ], + "table_footnote": [], + "table_body": "
NonIID-50
MethodsAcc.M SizeC2S/S2C Cost
FedWeIT w/o B comm.84.11% 77.88%0.078 GB 0.070GB0.37/1.07 GB 0.0170.01 GB
w/o A comm.79.21%0.079 GB0.37 /1.04 GB
w/o A w/0 m65.66% 78.71%0.061 GB 0.087 GB0.37 / 1.04 GB 1.23 / 1.25 GB
", + "bbox": [ + 467, + 821, + 820, + 917 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "D DETAILED ALGORITHM FOR FEDWEIT ", + "text_level": 1, + "bbox": [ + 174, + 102, + 534, + 118 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Algorithm 2 Algorithm for FedWeIT ", + "text_level": 1, + "bbox": [ + 174, + 141, + 419, + 156 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "input Dataset {D(1:t)c }Cc=1 , and Global Parameter $\\theta _ { G }$ \noutput $\\{ \\mathbf { B } _ { c } , \\mathbf { m } _ { c } ^ { ( 1 : t ) }$ , , α(1:c ), A(1:t)c }Cc=1 \n1: Initialize $\\mathbf { B } _ { c }$ to $\\theta _ { G }$ for all $c \\in \\mathcal { C } \\equiv \\{ 1 , . . . , C \\}$ \n2: for task $t = 1 , 2 , \\dots$ do \n3: for round $r = 1 , 2 , . . . , R$ do \n4: Select communicable clients ${ \\mathcal { C } } ^ { ( r ) } \\subseteq { \\mathcal { C } }$ \n5: if $r = 1$ then \n6: A(t−1,R) c∈C(r) and $\\hat { \\mathbf { B } } _ { c \\in \\mathcal { C } ^ { ( r ) } } ^ { ( t , r ) }$ are transmitted from $\\mathcal { C } ^ { ( r ) }$ to the central server \n7: Set a new knowledge base $k b ^ { ( t - 1 ) } = \\{ \\mathbf { A } _ { j } ^ { ( t - 1 , R ) } \\} _ { j \\in \\mathcal { C } ^ { ( 1 ) } }$ \n9: 8: el $\\hat { \\mathbf { B } } _ { c \\in \\mathcal { C } ^ { ( r ) } } ^ { ( t , r ) }$ are transmitted from $\\mathcal { C } ^ { ( r ) }$ to the central server \n10: end if \n11: Update 1|C(r)| Pc∈C(r) Bˆ (t,r)c \n12: Distribute $\\theta _ { G } ^ { ( r ) }$ and $k b ^ { ( t - 1 ) }$ to client $c \\in \\mathcal { C } ^ { ( r ) }$ if $c _ { c }$ meets $k b ^ { ( t - 1 ) }$ first, otherwise distribute only $\\theta _ { G } ^ { ( r ) }$ \n13: Minimize Eq. (2) for solving each local CL problems \n14: end for \n15: end for ", + "bbox": [ + 176, + 160, + 823, + 404 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "E FEDWEIT FOR ASYNCHRONOUS FEDERATED CONTINUAL LEARNING ", + "text_level": 1, + "bbox": [ + 171, + 435, + 785, + 453 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Algorithm 3 Algorithm for Asynchronous FedWeIT ", + "text_level": 1, + "bbox": [ + 173, + 476, + 517, + 491 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "input Dataset {D(1:t)c }Cc=1 , and Global Parameter θG \noutput $\\{ \\mathbf { B } _ { c } , \\mathbf { m } _ { c } ^ { ( 1 : t ) }$ , $\\pmb { \\alpha } _ { c } ^ { ( 1 : t ) }$ , ${ \\bf A } _ { c } ^ { ( 1 : t ) } \\} _ { c = 1 } ^ { C }$ \n1: Initialize $\\mathbf { B } _ { c }$ to $\\theta _ { G }$ for all $c \\in \\mathcal { C } \\equiv \\{ 1 , . . . , C \\}$ \n2: the knowledge base $k b \\gets \\{ \\}$ \n3: for round $r = 1 , 2 , \\ldots$ do \n4: if all clients finished the training then \n5: break \n6: else \n7: Select communicable clients ${ \\mathcal { C } } ^ { ( r ) } \\subseteq { \\mathcal { C } }$ \n8: for $c \\in \\mathcal { C } ^ { ( r ) }$ do \n9: if new task $t ^ { \\prime }$ is arrived at the client $c _ { c }$ then \n10: Update the knowledge base $k b \\gets k b \\cup \\{ { \\bf A } _ { c } ^ { ( t ^ { \\prime } - 1 ) } \\}$ at the central server \n11: end if \n12: $\\widehat { \\mathbf { B } } _ { c } ^ { ( r ) }$ are transmitted from the client $c _ { c }$ to the central server \n13: 14: end forUpdate $\\begin{array} { r } { \\pmb { \\theta } _ { G } ^ { ( r ) } \\frac { 1 } { | \\mathcal { C } ^ { ( r ) } | } \\sum _ { c \\in \\mathcal { C } ^ { ( r ) } } \\widehat { \\mathbf { B } } _ { c } ^ { ( r ) } } \\end{array}$ \n15: if a client $c _ { c \\in { \\mathcal { C } } ^ { ( r ) } }$ still learn then \n16: Distribute $\\theta _ { G } ^ { ( r ) }$ and $k b ^ { \\prime } \\subseteq k b$ to the client $c _ { c }$ if new task is arrived, otherwise distribute $\\theta _ { G } ^ { ( r ) }$ \n17: Minimize Eq. (2) for solving local CL problems at the client $c _ { c }$ \n18: end if \n19: end if \n20: end for ", + "bbox": [ + 174, + 493, + 790, + 794 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "We now consider FedWeIT under the asynchronous federated continual learning scenario, where there is no synchronization across clients for each task. This is a more realistic scenario since each task may require different training rounds to converge during federated continual learning. Here, asynchronous implies that each task requires different training costs (i.e., time, epochs, or rounds) for training. Under the asynchronous federated learning scenario, FedWeIT transfers any available task-adaptive parameters from the knowledge base $( k b ^ { \\prime } )$ to each client. We provide the detailed algorithm in Algorithm 3. In Table 7 and Figure 10, we plot the average test accuracy over all tasks during synchronous / asynchronous federated continual learning. As shown in Figure 10, different tasks across clients at the same timestep require the same number of training rounds, receiving new tasks and task-adaptive parameters from the knowledge base simultaneously with the synchronous FedWeIT. On the other hand, with asynchronous FedWeIT, each task requires different training rounds and receives new tasks and task-adaptive parameters in an asynchronous manner. The results in Table 7 shows that the performance of asynchronous FedWeIT is almost similar to that of the synchronous FedWeIT. ", + "bbox": [ + 173, + 827, + 596, + 924 + ], + "page_idx": 14 + }, + { + "type": "table", + "img_path": "images/742154939b78f1dc10530f785d31beb380a9e1201da9649e069d9ad8a7dbb35b.jpg", + "table_caption": [ + "Table 7: Averaged performance of FedWeIT with synchronous and asynchronous federated continual learning scenario. " + ], + "table_footnote": [], + "table_body": "
NonIID-50
FedWeITAccuracy (%)
Synchronous84.11 ± 0.27
Asynchronous84.40 ± 0.41
", + "bbox": [ + 609, + 866, + 831, + 924 + ], + "page_idx": 14 + }, + { + "type": "image", + "img_path": "images/345bee7f94e9da58f53b79209b11767056060b036018900f29baf9c0068f0802.jpg", + "image_caption": [ + "Figure 10: FedWeIT with asynchronous federated continual learning on Non-iid 50 dataset. We measure the test accuracy of all tasks per client. 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The", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 528, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 540 + ], + "score": 1.0, + "content": "problem has been tackled by various prior work (Kirkpatrick et al., 2017; Lee et al., 2017; Shin", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "et al., 2017; Riemer et al., 2019). 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Motivated by our intuition on", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "learning from indirect experience, we tackle the problem of Federated Continual Learning (FCL)", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "where we perform continual learning with multiple clients trained on private task sequences, which", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "communicate their task-specific parameters via a global server. 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To resolve these issues, we propose a novel federated continual learning", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 142, + 288, + 470, + 298 + ], + "spans": [ + { + "bbox": [ + 142, + 288, + 470, + 298 + ], + "score": 1.0, + "content": "framework, Federated Weighted Inter-client Transfer (FedWeIT), which decom-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 298, + 469, + 310 + ], + "spans": [ + { + "bbox": [ + 141, + 298, + 469, + 310 + ], + "score": 1.0, + "content": "poses the network weights into global federated parameters and sparse task-specific", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 309, + 470, + 321 + ], + "spans": [ + { + "bbox": [ + 141, + 309, + 470, + 321 + ], + "score": 1.0, + "content": "parameters, and each client receives selective knowledge from other clients by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 320, + 471, + 333 + ], + "spans": [ + { + "bbox": [ + 141, + 320, + 471, + 333 + ], + "score": 1.0, + "content": "taking a weighted combination of their task-specific parameters. FedWeIT mini-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 330, + 470, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 330, + 470, + 344 + ], + "score": 1.0, + "content": "mizes interference between incompatible tasks, and also allows positive knowledge", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 341, + 469, + 354 + ], + "spans": [ + { + "bbox": [ + 141, + 341, + 469, + 354 + ], + "score": 1.0, + "content": "transfer across clients during learning. We validate our FedWeIT against existing", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 352, + 470, + 365 + ], + "spans": [ + { + "bbox": [ + 141, + 352, + 470, + 365 + ], + "score": 1.0, + "content": "federated learning and continual learning methods under varying degrees of task", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 363, + 469, + 377 + ], + "spans": [ + { + "bbox": [ + 141, + 363, + 469, + 377 + ], + "score": 1.0, + "content": "similarity across clients, and our model significantly outperforms them with a large", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 375, + 292, + 386 + ], + "spans": [ + { + "bbox": [ + 141, + 375, + 292, + 386 + ], + "score": 1.0, + "content": "reduction in the communication cost.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 12.5, + "bbox_fs": [ + 141, + 209, + 471, + 386 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 405, + 206, + 417 + ], + "lines": [ + { + "bbox": [ + 105, + 404, + 208, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 208, + 421 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 429, + 505, + 561 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "Continual learning (Thrun, 1995; Kumar & Daume III, 2012; Ruvolo & Eaton, 2013; Kirkpatrick", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "score": 1.0, + "content": "et al., 2017; Schwarz et al., 2018) describes a learning scenario where a model continuously trains", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 451, + 504, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 504, + 464 + ], + "score": 1.0, + "content": "on a sequence of tasks; it is inspired by the human learning process, as a person learns to perform", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 463, + 504, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 504, + 474 + ], + "score": 1.0, + "content": "numerous tasks with large diversity over his/her lifespan, making use of the past knowledge to learn", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "about new tasks without forgetting previously learned ones. Continual learning is a long-studied topic", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "since having such an ability leads to the potential of building a general artificial intelligence. However,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 496, + 504, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 504, + 507 + ], + "score": 1.0, + "content": "there are crucial challenges in implementing it with conventional models such as deep neural networks", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "(DNNs), such as catastrophic forgetting, which describes the problem where parameters or semantic", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 517, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 529 + ], + "score": 1.0, + "content": "representations learned for the past tasks drift to the direction of new tasks during training. The", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 528, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 540 + ], + "score": 1.0, + "content": "problem has been tackled by various prior work (Kirkpatrick et al., 2017; Lee et al., 2017; Shin", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "et al., 2017; Riemer et al., 2019). More recent works tackle other issues, such as scalability or", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 550, + 415, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 415, + 562 + ], + "score": 1.0, + "content": "order-robustness (Schwarz et al., 2018; Hung et al., 2019; Yoon et al., 2020).", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 429, + 506, + 562 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 567, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "score": 1.0, + "content": "However, all of these models are fundamentally limited in that the models can only learn from its direct", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "experience - they only learn from the sequence of the tasks they have trained on. Contrarily, humans", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 588, + 506, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 602 + ], + "score": 1.0, + "content": "can learn from indirect experience from others, through different means (e.g. verbal communications,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 600, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 505, + 612 + ], + "score": 1.0, + "content": "books, or various media). Then wouldn’t it be beneficial to implement such an ability to a continual", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 610, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 505, + 623 + ], + "score": 1.0, + "content": "learning framework, such that multiple models learning on different machines can learn from the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "score": 1.0, + "content": "knowledge of the tasks that have been already experienced by other clients? One problem that arises", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "score": 1.0, + "content": "here, is that due to data privacy on individual clients and exorbitant communication cost, it may", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "not be possible to communicate data directly between the clients or between the server and clients.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 653, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 506, + 668 + ], + "score": 1.0, + "content": "Federated learning (McMahan et al., 2016; Li et al., 2018; Yurochkin et al., 2019) is a learning", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "paradigm that tackles this issue by communicating the parameters instead of the raw data itself.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "We may have a server that receives the parameters locally trained on multiple clients, aggregates", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "it into a single model parameter, and sends it back to the clients. Motivated by our intuition on", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "learning from indirect experience, we tackle the problem of Federated Continual Learning (FCL)", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "where we perform continual learning with multiple clients trained on private task sequences, which", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "communicate their task-specific parameters via a global server. Figure 1 (a) depicts an example", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 252, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 506, + 265 + ], + "score": 1.0, + "content": "scenario of FCL. Suppose that we are building a network of hospitals, each of which has a disease", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 264, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 506, + 277 + ], + "score": 1.0, + "content": "diagnosis model which continuously learns to perform diagnosis given CT scans, for new types of", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "diseases. Then, under our framework, any diagnosis model which has learned about a new type of", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "score": 1.0, + "content": "disease (e.g. COVID-19) will transmit the task-specific parameters to the global server, which will", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "redistribute them to other hospitals for the local models to utilize. This allows all participants to", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 306, + 416, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 416, + 321 + ], + "score": 1.0, + "content": "benefit from the new task knowledge without compromising the data privacy.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 567, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 72, + 487, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 110, + 72, + 487, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 110, + 72, + 487, + 183 + ], + "spans": [ + { + "bbox": [ + 110, + 72, + 487, + 183 + ], + "score": 0.972, + "type": "image", + "image_path": "6998a6802da248658c2a2e9155a1bc0fe3e656e424795ecf911b7107c7f66236.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 110, + 72, + 487, + 109.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 110, + 109.0, + 487, + 146.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 110, + 146.0, + 487, + 183.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 189, + 505, + 240 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 189, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 506, + 201 + ], + "score": 1.0, + "content": "Figure 1: (a): Concept. A continual learner at a hospital which learns on sequence of disease prediction tasks", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 199, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 211 + ], + "score": 1.0, + "content": "may want to utilize relevant task parameters from other hospitals. FCL allows such inter-client knowledge", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "score": 1.0, + "content": "transfer via the communication of task-decomposed parameters. (b): Challenge of FCL. Interference from", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 219, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 506, + 231 + ], + "score": 1.0, + "content": "other clients, resulting from sharing irrelevant knowledge, may hinder an optimal training of target clients (Red)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 229, + 426, + 240 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 426, + 240 + ], + "score": 1.0, + "content": "while relevant knowledge from other clients will be beneficial for their learning (Green).", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 253, + 505, + 319 + ], + "lines": [ + { + "bbox": [ + 105, + 252, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 506, + 265 + ], + "score": 1.0, + "content": "scenario of FCL. Suppose that we are building a network of hospitals, each of which has a disease", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 264, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 506, + 277 + ], + "score": 1.0, + "content": "diagnosis model which continuously learns to perform diagnosis given CT scans, for new types of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "diseases. Then, under our framework, any diagnosis model which has learned about a new type of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "score": 1.0, + "content": "disease (e.g. COVID-19) will transmit the task-specific parameters to the global server, which will", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "redistribute them to other hospitals for the local models to utilize. This allows all participants to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 306, + 416, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 416, + 321 + ], + "score": 1.0, + "content": "benefit from the new task knowledge without compromising the data privacy.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "Yet, the problem of federated continual learning also brings new challenges. First, there is not only the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "score": 1.0, + "content": "catastrophic forgetting from continual learning, but also the threat of potential interference from", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "score": 1.0, + "content": "other clients. Figure 1 (b) describes this challenge with the results of a simple experiment. Here, we", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "train a model for MNIST digit recognition while communicating the parameters from another client", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "trained on a different dataset. When the knowledge transferred from the other client is relevant to the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 393 + ], + "score": 1.0, + "content": "target task (SVHN), the model starts with high accuracy, converge faster and reach higher accuracy", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "(green line), whereas the model underperforms the base model if the transferred knowledge is from a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 505, + 414 + ], + "score": 1.0, + "content": "task highly different from the target task (CIFAR-10, red line). Thus, we need to selective utilize", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "knowledge from other clients to minimize the inter-client interference and maximize inter-client", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "knowledge transfer. Another problem with the federated learning is efficient communication, as", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 435, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 506, + 447 + ], + "score": 1.0, + "content": "communication cost could become excessively large when utilizing the knowledge of the other clients,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "score": 1.0, + "content": "since the communication cost could be the main bottleneck in practical scenarios when working with", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 456, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 456, + 468 + ], + "score": 1.0, + "content": "edge devices. Thus we want the knowledge to be represented as compactly as possible.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 473, + 505, + 648 + ], + "lines": [ + { + "bbox": [ + 106, + 473, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 506, + 485 + ], + "score": 1.0, + "content": "To tackle these challenges, we propose a novel framework for federated continual learning, Federated", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 484, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 506, + 496 + ], + "score": 1.0, + "content": "Weighted Inter-client Transfer (FedWeIT), which decomposes the local model parameters into a dense", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "base parameter and sparse task-adaptive parameters. FedWeIT reduces the interference between", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "different tasks since the base parameters will encode task-generic knowledge, while the task-specific", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "score": 1.0, + "content": "knowledge will be encoded into the task-adaptive parameters. When we utilize the generic knowledge,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 528, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 540 + ], + "score": 1.0, + "content": "we also want the client to selectively utilize task-specific knowledge obtained at other clients. 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A continual learner at a hospital which learns on sequence of disease prediction tasks", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 199, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 211 + ], + "score": 1.0, + "content": "may want to utilize relevant task parameters from other hospitals. FCL allows such inter-client knowledge", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 505, + 221 + ], + "score": 1.0, + "content": "transfer via the communication of task-decomposed parameters. (b): Challenge of FCL. Interference from", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 219, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 506, + 231 + ], + "score": 1.0, + "content": "other clients, resulting from sharing irrelevant knowledge, may hinder an optimal training of target clients (Red)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 229, + 426, + 240 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 426, + 240 + ], + "score": 1.0, + "content": "while relevant knowledge from other clients will be beneficial for their learning (Green).", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 253, + 505, + 319 + ], + "lines": [], + "index": 10.5, + "bbox_fs": [ + 105, + 252, + 506, + 321 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 467 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "Yet, the problem of federated continual learning also brings new challenges. First, there is not only the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "score": 1.0, + "content": "catastrophic forgetting from continual learning, but also the threat of potential interference from", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 506, + 360 + ], + "score": 1.0, + "content": "other clients. Figure 1 (b) describes this challenge with the results of a simple experiment. Here, we", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "train a model for MNIST digit recognition while communicating the parameters from another client", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "trained on a different dataset. 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Thus, we need to selective utilize", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "knowledge from other clients to minimize the inter-client interference and maximize inter-client", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "knowledge transfer. Another problem with the federated learning is efficient communication, as", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 435, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 506, + 447 + ], + "score": 1.0, + "content": "communication cost could become excessively large when utilizing the knowledge of the other clients,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 457 + ], + "score": 1.0, + "content": "since the communication cost could be the main bottleneck in practical scenarios when working with", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 456, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 456, + 468 + ], + "score": 1.0, + "content": "edge devices. Thus we want the knowledge to be represented as compactly as possible.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 324, + 506, + 468 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 473, + 505, + 648 + ], + "lines": [ + { + "bbox": [ + 106, + 473, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 506, + 485 + ], + "score": 1.0, + "content": "To tackle these challenges, we propose a novel framework for federated continual learning, Federated", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 484, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 506, + 496 + ], + "score": 1.0, + "content": "Weighted Inter-client Transfer (FedWeIT), which decomposes the local model parameters into a dense", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "base parameter and sparse task-adaptive parameters. 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To this", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 539, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 505, + 550 + ], + "score": 1.0, + "content": "end, we allow each model to take a weighted combination of the task-adaptive parameters broadcast", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 550, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 561 + ], + "score": 1.0, + "content": "from the server, such that it can select task-specific knowledge helpful for the task at hand. 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The results show that our model obtains", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "significantly superior performance over all baselines, adapts faster to new tasks, with largely reduced", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 638, + 401, + 649 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 401, + 649 + ], + "score": 1.0, + "content": "communication cost. The main contributions of this paper are as follows:", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 473, + 506, + 649 + ] + }, + { + "type": "text", + "bbox": [ + 115, + 658, + 506, + 729 + ], + "lines": [ + { + "bbox": [ + 118, + 658, + 506, + 671 + ], + "spans": [ + { + "bbox": [ + 118, + 658, + 506, + 671 + ], + "score": 1.0, + "content": "• We introduce a new problem of Federated Continual Learning (FCL), where multiple mod-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 128, + 669, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 128, + 669, + 505, + 681 + ], + "score": 1.0, + "content": "els continuously learn on distributed clients, which poses new challenges such as prevention of", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 127, + 681, + 368, + 693 + ], + "spans": [ + { + "bbox": [ + 127, + 681, + 368, + 693 + ], + "score": 1.0, + "content": "inter-client interference and inter-client knowledge transfer.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 126, + 695, + 506, + 707 + ], + "spans": [ + { + "bbox": [ + 126, + 695, + 506, + 707 + ], + "score": 1.0, + "content": "We propose a novel and communication-efficient framework for federated continual learn-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 127, + 706, + 505, + 718 + ], + "spans": [ + { + "bbox": [ + 127, + 706, + 505, + 718 + ], + "score": 1.0, + "content": "ing, which allows each client to adaptively update the federated parameter and selectively utilize", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 127, + 717, + 436, + 730 + ], + "spans": [ + { + "bbox": [ + 127, + 717, + 436, + 730 + ], + "score": 1.0, + "content": "the past knowledge from other clients, by communicating sparse parameters.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45.5, + "bbox_fs": [ + 118, + 658, + 506, + 730 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 211, + 93 + ], + "lines": [ + { + "bbox": [ + 104, + 79, + 213, + 96 + ], + "spans": [ + { + "bbox": [ + 104, + 79, + 213, + 96 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 104, + 506, + 280 + ], + "lines": [ + { + "bbox": [ + 106, + 104, + 506, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 506, + 116 + ], + "score": 1.0, + "content": "Continual learning While continual learning (Kumar & Daume III, 2012; Ruvolo & Eaton, 2013)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 115, + 506, + 126 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 506, + 126 + ], + "score": 1.0, + "content": "is a long-studied topic with a vast literature, we only discuss recent relevant works. Regularization-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 126, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 138 + ], + "score": 1.0, + "content": "based: EWC (Kirkpatrick et al., 2017) leverages Fisher Information Matrix to restrict the change of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 506, + 149 + ], + "score": 1.0, + "content": "the model parameters such that the model finds solution that is good for both previous and the current", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 147, + 506, + 160 + ], + "spans": [ + { + "bbox": [ + 106, + 147, + 506, + 160 + ], + "score": 1.0, + "content": "task, and IMM (Lee et al., 2017) proposes to learn the posterior distribution for multiple tasks as a", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 158, + 506, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 171 + ], + "score": 1.0, + "content": "mixture of Gaussians. Architecture-based: DEN (Yoon et al., 2018) tackles this issue by expanding", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "score": 1.0, + "content": "the networks size that are necessary via iterative neuron/filter pruning and splitting, and RCL (Xu &", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 181, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 505, + 193 + ], + "score": 1.0, + "content": "Zhu, 2018) tackles the same problem using reinforcement learning. APD (Yoon et al., 2020) additively", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "score": 1.0, + "content": "decomposes the parameters into shared and task-specific parameters to minimize the increase in the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 506, + 215 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 506, + 215 + ], + "score": 1.0, + "content": "network complexity. Coreset-based: GEM variants (Lopez-Paz & Ranzato, 2017; Chaudhry et al.,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "2019) minimize the loss on both of actual dataset and stored episodic memory. FRCL (Titsias et al.,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "2020) memorizes approximated posteriors of previous tasks with sophisticatedly constructed inducing", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 236, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 505, + 248 + ], + "score": 1.0, + "content": "points. To the best of our knowledge, none of the existing approaches considered the communicability", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 246, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 505, + 259 + ], + "score": 1.0, + "content": "for continual learning of deep neural networks, which we tackle. CoLLA (Rostami et al., 2018) aims", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 258, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 269 + ], + "score": 1.0, + "content": "at solving multi-agent lifelong learning with sparse dictionary learning, but it is not applicable to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 268, + 290, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 290, + 282 + ], + "score": 1.0, + "content": "federated learning or continual deep learning.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 285, + 505, + 472 + ], + "lines": [ + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "score": 1.0, + "content": "Federated learning Federated learning is a distributed learning framework under differential", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "score": 1.0, + "content": "privacy, which aims to learn a global model on a server while aggregating the parameters learned", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "at the clients on their private data. FedAvg (McMahan et al., 2016) aggregates the model trained", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 318, + 506, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 330 + ], + "score": 1.0, + "content": "across multiple clients by computing a weighted average of them based on the number of data points", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "score": 1.0, + "content": "trained. FedProx (Li et al., 2018) trains the local models with a proximal term which restricts their", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 339, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 505, + 352 + ], + "score": 1.0, + "content": "updates to be close to the global model. FedCurv (Shoham et al., 2019) aims to minimize the model", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "disparity across clients during federated learning by adopting a modified version of EWC. Recent", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 361, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 374 + ], + "score": 1.0, + "content": "works Yurochkin et al. (2019); Wang et al. (2020) introduce well-designed aggregation policies", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "score": 1.0, + "content": "by leveraging Bayesian non-parametric methods. A crucial challenge of federated learning is the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 381, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 506, + 397 + ], + "score": 1.0, + "content": "reduction of communication cost. TWAFL (Chen et al., 2019) tackles this problem by performing", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "score": 1.0, + "content": "layer-wise parameter aggregation, where shallow layers are aggregated at every step, but deep layers", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 405, + 506, + 418 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 506, + 418 + ], + "score": 1.0, + "content": "are aggregated in the last few steps of a loop. Karimireddy et al. (2020) suggests an algorithm for rapid", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "convergence, which minimizes the interference among discrepant tasks at clients by sacrificing the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 427, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 439 + ], + "score": 1.0, + "content": "local optimality. This is an opposite direction from personalized federated learning methods (Fallah", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 438, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 506, + 451 + ], + "score": 1.0, + "content": "et al., 2020; Lange et al., 2020; Deng et al., 2020) which put more emphasis on the performance of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 450, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 461 + ], + "score": 1.0, + "content": "local models. FCL is a parallel research direction to both, and to the best of our knowledge, ours is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 461, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 506, + 472 + ], + "score": 1.0, + "content": "the first work that considers task-incremental learning of clients under federated learning framework.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 108, + 492, + 395, + 505 + ], + "lines": [ + { + "bbox": [ + 105, + 491, + 397, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 397, + 506 + ], + "score": 1.0, + "content": "3 FEDERATED CONTINUAL LEARNING WITH FEDWEIT", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 505, + 614 + ], + "lines": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "Motivated by the human learning process from indirect experiences, we introduce a novel continual", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 527, + 506, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 539 + ], + "score": 1.0, + "content": "learning under federated learning setting, which we refer to as Federated Continual Learning (FCL).", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 537, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 505, + 549 + ], + "score": 1.0, + "content": "FCL assumes that multiple clients are trained on a sequence of tasks from private data stream, while", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "communicating the learned parameters with a global server. We first formally define the problem in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "Section 3.1, and then propose naive solutions that straightforwardly combine the existing federated", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "learning and continual learning methods in Section 3.2. Then, following Section 3.3 and 3.4, we", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "score": 1.0, + "content": "discuss about two novel challenges that are introduced by federated continual learning, and propose a", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 591, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 505, + 605 + ], + "score": 1.0, + "content": "novel framework, Federated Weighted Inter-client Transfer (FedWeIT) which can effectively handle", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 604, + 418, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 418, + 615 + ], + "score": 1.0, + "content": "the two problems while also reducing the client-to-sever communication cost.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39 + }, + { + "type": "title", + "bbox": [ + 107, + 627, + 227, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 628, + 228, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 228, + 640 + ], + "score": 1.0, + "content": "3.1 PROBLEM DEFINITION", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 645, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 101, + 645, + 502, + 679 + ], + "spans": [ + { + "bbox": [ + 101, + 645, + 141, + 679 + ], + "score": 1.0, + "content": "In the stof tasks", + "type": "text" + }, + { + "bbox": [ + 142, + 657, + 232, + 671 + ], + "score": 0.94, + "content": "\\{ \\mathcal { T } ^ { ( 1 ) } , \\mathcal { T } ^ { ( 2 ) } , . . . , \\mathcal { T } ^ { ( T ) } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 645, + 261, + 679 + ], + "score": 1.0, + "content": "ng (on a where", + "type": "text" + }, + { + "bbox": [ + 261, + 657, + 280, + 669 + ], + "score": 0.91, + "content": "\\mathcal { T } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 645, + 374, + 679 + ], + "score": 1.0, + "content": "le machine), the model i is a labeled dataset of", + "type": "text" + }, + { + "bbox": [ + 374, + 657, + 387, + 668 + ], + "score": 0.88, + "content": "t ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 645, + 411, + 679 + ], + "score": 1.0, + "content": "tivelytask,", + "type": "text" + }, + { + "bbox": [ + 411, + 656, + 502, + 671 + ], + "score": 0.93, + "content": "\\mathcal { T } ^ { ( t ) } = \\{ \\mathbf { x } _ { i } ^ { ( t ) } , \\mathbf { y } _ { i } ^ { ( \\bar { t } ) } \\} _ { i = 1 } ^ { N _ { t } }", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 102, + 668, + 509, + 690 + ], + "spans": [ + { + "bbox": [ + 102, + 668, + 178, + 690 + ], + "score": 1.0, + "content": "which consists of", + "type": "text" + }, + { + "bbox": [ + 178, + 673, + 191, + 684 + ], + "score": 0.88, + "content": "N _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 668, + 263, + 690 + ], + "score": 1.0, + "content": "pairs of instances", + "type": "text" + }, + { + "bbox": [ + 264, + 670, + 280, + 685 + ], + "score": 0.91, + "content": "\\mathbf { x } _ { i } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 668, + 404, + 690 + ], + "score": 1.0, + "content": "and their corresponding labels", + "type": "text" + }, + { + "bbox": [ + 405, + 670, + 420, + 685 + ], + "score": 0.91, + "content": "{ \\bf y } _ { i } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 668, + 509, + 690 + ], + "score": 1.0, + "content": ". 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Regularization-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 126, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 138 + ], + "score": 1.0, + "content": "based: EWC (Kirkpatrick et al., 2017) leverages Fisher Information Matrix to restrict the change of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 506, + 149 + ], + "score": 1.0, + "content": "the model parameters such that the model finds solution that is good for both previous and the current", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 147, + 506, + 160 + ], + "spans": [ + { + "bbox": [ + 106, + 147, + 506, + 160 + ], + "score": 1.0, + "content": "task, and IMM (Lee et al., 2017) proposes to learn the posterior distribution for multiple tasks as a", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 158, + 506, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 506, + 171 + ], + "score": 1.0, + "content": "mixture of Gaussians. Architecture-based: DEN (Yoon et al., 2018) tackles this issue by expanding", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "score": 1.0, + "content": "the networks size that are necessary via iterative neuron/filter pruning and splitting, and RCL (Xu &", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 181, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 505, + 193 + ], + "score": 1.0, + "content": "Zhu, 2018) tackles the same problem using reinforcement learning. APD (Yoon et al., 2020) additively", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 204 + ], + "score": 1.0, + "content": "decomposes the parameters into shared and task-specific parameters to minimize the increase in the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 506, + 215 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 506, + 215 + ], + "score": 1.0, + "content": "network complexity. Coreset-based: GEM variants (Lopez-Paz & Ranzato, 2017; Chaudhry et al.,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "2019) minimize the loss on both of actual dataset and stored episodic memory. FRCL (Titsias et al.,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "2020) memorizes approximated posteriors of previous tasks with sophisticatedly constructed inducing", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 236, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 505, + 248 + ], + "score": 1.0, + "content": "points. To the best of our knowledge, none of the existing approaches considered the communicability", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 246, + 505, + 259 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 505, + 259 + ], + "score": 1.0, + "content": "for continual learning of deep neural networks, which we tackle. 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FedAvg (McMahan et al., 2016) aggregates the model trained", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 318, + 506, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 330 + ], + "score": 1.0, + "content": "across multiple clients by computing a weighted average of them based on the number of data points", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "score": 1.0, + "content": "trained. FedProx (Li et al., 2018) trains the local models with a proximal term which restricts their", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 339, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 505, + 352 + ], + "score": 1.0, + "content": "updates to be close to the global model. FedCurv (Shoham et al., 2019) aims to minimize the model", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "disparity across clients during federated learning by adopting a modified version of EWC. Recent", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 361, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 374 + ], + "score": 1.0, + "content": "works Yurochkin et al. (2019); Wang et al. (2020) introduce well-designed aggregation policies", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 385 + ], + "score": 1.0, + "content": "by leveraging Bayesian non-parametric methods. A crucial challenge of federated learning is the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 381, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 506, + 397 + ], + "score": 1.0, + "content": "reduction of communication cost. TWAFL (Chen et al., 2019) tackles this problem by performing", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "score": 1.0, + "content": "layer-wise parameter aggregation, where shallow layers are aggregated at every step, but deep layers", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 405, + 506, + 418 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 506, + 418 + ], + "score": 1.0, + "content": "are aggregated in the last few steps of a loop. Karimireddy et al. (2020) suggests an algorithm for rapid", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "convergence, which minimizes the interference among discrepant tasks at clients by sacrificing the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 427, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 439 + ], + "score": 1.0, + "content": "local optimality. This is an opposite direction from personalized federated learning methods (Fallah", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 438, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 506, + 451 + ], + "score": 1.0, + "content": "et al., 2020; Lange et al., 2020; Deng et al., 2020) which put more emphasis on the performance of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 450, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 461 + ], + "score": 1.0, + "content": "local models. FCL is a parallel research direction to both, and to the best of our knowledge, ours is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 461, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 506, + 472 + ], + "score": 1.0, + "content": "the first work that considers task-incremental learning of clients under federated learning framework.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 284, + 506, + 472 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 492, + 395, + 505 + ], + "lines": [ + { + "bbox": [ + 105, + 491, + 397, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 397, + 506 + ], + "score": 1.0, + "content": "3 FEDERATED CONTINUAL LEARNING WITH FEDWEIT", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 505, + 614 + ], + "lines": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 106, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "Motivated by the human learning process from indirect experiences, we introduce a novel continual", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 527, + 506, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 539 + ], + "score": 1.0, + "content": "learning under federated learning setting, which we refer to as Federated Continual Learning (FCL).", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 537, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 505, + 549 + ], + "score": 1.0, + "content": "FCL assumes that multiple clients are trained on a sequence of tasks from private data stream, while", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "communicating the learned parameters with a global server. We first formally define the problem in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "Section 3.1, and then propose naive solutions that straightforwardly combine the existing federated", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "learning and continual learning methods in Section 3.2. Then, following Section 3.3 and 3.4, we", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 506, + 594 + ], + "score": 1.0, + "content": "discuss about two novel challenges that are introduced by federated continual learning, and propose a", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 591, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 505, + 605 + ], + "score": 1.0, + "content": "novel framework, Federated Weighted Inter-client Transfer (FedWeIT) which can effectively handle", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 604, + 418, + 615 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 418, + 615 + ], + "score": 1.0, + "content": "the two problems while also reducing the client-to-sever communication cost.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 515, + 506, + 615 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 627, + 227, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 628, + 228, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 228, + 640 + ], + "score": 1.0, + "content": "3.1 PROBLEM DEFINITION", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 645, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 101, + 645, + 502, + 679 + ], + "spans": [ + { + "bbox": [ + 101, + 645, + 141, + 679 + ], + "score": 1.0, + "content": "In the stof tasks", + "type": "text" + }, + { + "bbox": [ + 142, + 657, + 232, + 671 + ], + "score": 0.94, + "content": "\\{ \\mathcal { T } ^ { ( 1 ) } , \\mathcal { T } ^ { ( 2 ) } , . . . , \\mathcal { T } ^ { ( T ) } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 645, + 261, + 679 + ], + "score": 1.0, + "content": "ng (on a where", + "type": "text" + }, + { + "bbox": [ + 261, + 657, + 280, + 669 + ], + "score": 0.91, + "content": "\\mathcal { T } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 645, + 374, + 679 + ], + "score": 1.0, + "content": "le machine), the model i is a labeled dataset of", + "type": "text" + }, + { + "bbox": [ + 374, + 657, + 387, + 668 + ], + "score": 0.88, + "content": "t ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 645, + 411, + 679 + ], + "score": 1.0, + "content": "tivelytask,", + "type": "text" + }, + { + "bbox": [ + 411, + 656, + 502, + 671 + ], + "score": 0.93, + "content": "\\mathcal { T } ^ { ( t ) } = \\{ \\mathbf { x } _ { i } ^ { ( t ) } , \\mathbf { y } _ { i } ^ { ( \\bar { t } ) } \\} _ { i = 1 } ^ { N _ { t } }", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 102, + 668, + 509, + 690 + ], + "spans": [ + { + "bbox": [ + 102, + 668, + 178, + 690 + ], + "score": 1.0, + "content": "which consists of", + "type": "text" + }, + { + "bbox": [ + 178, + 673, + 191, + 684 + ], + "score": 0.88, + "content": "N _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 668, + 263, + 690 + ], + "score": 1.0, + "content": "pairs of instances", + "type": "text" + }, + { + "bbox": [ + 264, + 670, + 280, + 685 + ], + "score": 0.91, + "content": "\\mathbf { x } _ { i } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 668, + 404, + 690 + ], + "score": 1.0, + "content": "and their corresponding labels", + "type": "text" + }, + { + "bbox": [ + 405, + 670, + 420, + 685 + ], + "score": 0.91, + "content": "{ \\bf y } _ { i } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 668, + 509, + 690 + ], + "score": 1.0, + "content": ". Assuming the most", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 684, + 505, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 505, + 696 + ], + "score": 1.0, + "content": "realistic situation, we consider the case where the task sequence is a task stream with an unknown", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 694, + 506, + 709 + ], + "spans": [ + { + "bbox": [ + 105, + 694, + 285, + 709 + ], + "score": 1.0, + "content": "arriving order, such that the model can access", + "type": "text" + }, + { + "bbox": [ + 285, + 694, + 304, + 706 + ], + "score": 0.9, + "content": "\\mathcal { T } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 694, + 436, + 709 + ], + "score": 1.0, + "content": "only at the training period of task", + "type": "text" + }, + { + "bbox": [ + 437, + 696, + 442, + 705 + ], + "score": 0.69, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 694, + 506, + 709 + ], + "score": 1.0, + "content": "which becomes", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 705, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 705, + 228, + 721 + ], + "score": 1.0, + "content": "inaccessible afterwards. Given", + "type": "text" + }, + { + "bbox": [ + 229, + 707, + 247, + 718 + ], + "score": 0.9, + "content": "\\mathcal { T } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 705, + 479, + 721 + ], + "score": 1.0, + "content": "and the model learned so far, the learning objective at task", + "type": "text" + }, + { + "bbox": [ + 479, + 709, + 484, + 718 + ], + "score": 0.79, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 705, + 506, + 721 + ], + "score": 1.0, + "content": "is as", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 104, + 717, + 497, + 734 + ], + "spans": [ + { + "bbox": [ + 104, + 717, + 142, + 734 + ], + "score": 1.0, + "content": "follows:", + "type": "text" + }, + { + "bbox": [ + 142, + 720, + 192, + 733 + ], + "score": 0.25, + "content": "\\mathrm { m i n i m i z e } _ { \\theta ^ { ( t } }", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 717, + 196, + 734 + ], + "score": 1.0, + "content": ")", + "type": "text" + }, + { + "bbox": [ + 197, + 719, + 280, + 732 + ], + "score": 0.89, + "content": "\\mathscr { L } ( \\pmb { \\theta } ^ { ( t ) } ; \\pmb { \\theta } ^ { ( t - 1 ) } , \\tau ^ { ( t ) } )", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 717, + 311, + 734 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 312, + 719, + 327, + 730 + ], + "score": 0.89, + "content": "{ \\pmb \\theta } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 717, + 486, + 734 + ], + "score": 1.0, + "content": "is a set of the model parameters at task", + "type": "text" + }, + { + "bbox": [ + 486, + 721, + 491, + 730 + ], + "score": 0.76, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 717, + 497, + 734 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 47.5, + "bbox_fs": [ + 101, + 645, + 509, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 506, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "We now extend the conventional continual learning to the federated learning setting with multiple", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 348, + 107 + ], + "score": 1.0, + "content": "clients and a global server. 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Now", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 229, + 145 + ], + "score": 1.0, + "content": "the goal is to effectively train", + "type": "text" + }, + { + "bbox": [ + 230, + 132, + 239, + 142 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 131, + 506, + 145 + ], + "score": 1.0, + "content": "continual learning models on their own private task streams, via", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 142, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 106, + 142, + 506, + 155 + ], + "score": 1.0, + "content": "communicating the model parameters with the global server, which aggregates the parameters sent", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 153, + 308, + 165 + ], + "spans": [ + { + "bbox": [ + 106, + 153, + 308, + 165 + ], + "score": 1.0, + "content": "from each client, and redistributes them to clients.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 106, + 175, + 308, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 174, + 309, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 309, + 188 + ], + "score": 1.0, + "content": "3.2 COMMUNICABLE CONTINUAL LEARNING", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 192, + 505, + 361 + ], + "lines": [ + { + "bbox": [ + 105, + 191, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 206 + ], + "score": 1.0, + "content": "In conventional federated learning settings, the learning is done with multiple rounds of local learning", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 203, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 365, + 216 + ], + "score": 1.0, + "content": "and parameter aggregation. 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In the local parameter transmission step, for a randomly selected subset of clients", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 236, + 504, + 250 + ], + "spans": [ + { + "bbox": [ + 104, + 236, + 142, + 250 + ], + "score": 1.0, + "content": "at round", + "type": "text" + }, + { + "bbox": [ + 143, + 240, + 149, + 248 + ], + "score": 0.4, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 236, + 151, + 250 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 152, + 236, + 244, + 250 + ], + "score": 0.89, + "content": "\\mathcal { C } ^ { ( r ) } \\subseteq \\{ c _ { 1 } , c _ { 2 } , . . . , c _ { C } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 236, + 294, + 250 + ], + "score": 1.0, + "content": ", each client", + "type": "text" + }, + { + "bbox": [ + 294, + 240, + 304, + 249 + ], + "score": 0.86, + "content": "c _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 236, + 412, + 250 + ], + "score": 1.0, + "content": "sends updated parameters", + "type": "text" + }, + { + "bbox": [ + 412, + 236, + 430, + 248 + ], + "score": 0.9, + "content": "\\pmb \\theta ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 236, + 504, + 250 + ], + "score": 1.0, + "content": "to the server. The", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "score": 1.0, + "content": "server-clients transmission is not done at every client because some of the clients may be temporarily", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 102, + 258, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 102, + 258, + 344, + 279 + ], + "score": 1.0, + "content": "disconnected. Then the server aggregates the parameters", + "type": "text" + }, + { + "bbox": [ + 344, + 259, + 362, + 273 + ], + "score": 0.94, + "content": "\\pmb { \\theta } _ { c } ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 258, + 505, + 279 + ], + "score": 1.0, + "content": "sent from the clients into a single", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 272, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 104, + 272, + 506, + 285 + ], + "score": 1.0, + "content": "parameter. The most popular frameworks for this aggregation are FedAvg (McMahan et al., 2016)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "and FedProx (Li et al., 2018). However, naive federated continual learning with these two algorithms", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "on local sequences of tasks may result in catastrophic forgetting. One simple solution is to use a", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 306, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 505, + 318 + ], + "score": 1.0, + "content": "regularization-based, such as Elastic Weight Consolidation (EWC) (Kirkpatrick et al., 2017), which", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "allows the model to obtain a solution that is optimal for both the previous and the current tasks. There", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 327, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 506, + 340 + ], + "score": 1.0, + "content": "exist other advanced solutions (Rusu et al., 2016; Nguyen et al., 2018; Chaudhry et al., 2019) that", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 338, + 506, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 506, + 351 + ], + "score": 1.0, + "content": "successfully prevents catastrophic forgetting. However, the prevention of catastrophic forgetting at", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 348, + 369, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 369, + 363 + ], + "score": 1.0, + "content": "the client level is an orthogonal problem from federated learning.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 366, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "Thus we focus on challenges that newly arise in this federated continual learning setting. In the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 376, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 390 + ], + "score": 1.0, + "content": "federated continual learning framework, the aggregation of the parameters into a global parameter", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 387, + 508, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 120, + 402 + ], + "score": 0.88, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 387, + 375, + 405 + ], + "score": 1.0, + "content": "allows inter-client knowledge transfer across clients, since a task", + "type": "text" + }, + { + "bbox": [ + 375, + 388, + 394, + 403 + ], + "score": 0.93, + "content": "\\mathcal { T } _ { i } ^ { ( q ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 387, + 460, + 405 + ], + "score": 1.0, + "content": "learned at client", + "type": "text" + }, + { + "bbox": [ + 460, + 392, + 469, + 402 + ], + "score": 0.84, + "content": "c _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 387, + 508, + 405 + ], + "score": 1.0, + "content": "at round", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 399, + 508, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 113, + 417 + ], + "score": 0.68, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 399, + 230, + 421 + ], + "score": 1.0, + "content": "may be similar or related to", + "type": "text" + }, + { + "bbox": [ + 231, + 402, + 250, + 419 + ], + "score": 0.92, + "content": "\\mathcal { T } _ { j } ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 399, + 320, + 421 + ], + "score": 1.0, + "content": "learned at client", + "type": "text" + }, + { + "bbox": [ + 320, + 407, + 330, + 417 + ], + "score": 0.86, + "content": "c _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 399, + 368, + 421 + ], + "score": 1.0, + "content": "at round", + "type": "text" + }, + { + "bbox": [ + 368, + 407, + 374, + 415 + ], + "score": 0.65, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 399, + 508, + 421 + ], + "score": 1.0, + "content": ". Yet, using a single aggregated", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 416, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 149, + 430 + ], + "score": 1.0, + "content": "parameter", + "type": "text" + }, + { + "bbox": [ + 149, + 417, + 163, + 428 + ], + "score": 0.87, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 416, + 505, + 430 + ], + "score": 1.0, + "content": "may be suboptimal in achieving this goal since knowledge from irrelevant tasks may", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "score": 1.0, + "content": "not to be useful or even hinder the training at each client by altering its parameters into incorrect", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "score": 1.0, + "content": "directions, which we describe as inter-client interference. Another problem that is also practically", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "score": 1.0, + "content": "important, is the communication-efficiency. Both the parameter transmission from the client to the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 461, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 505, + 473 + ], + "score": 1.0, + "content": "server, and server to client will incur large communication cost, which will be problematic for the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 473, + 477, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 477, + 485 + ], + "score": 1.0, + "content": "continual learning setting, since the clients may train on possibly unlimited streams of tasks.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 107, + 493, + 346, + 504 + ], + "lines": [ + { + "bbox": [ + 105, + 492, + 347, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 347, + 506 + ], + "score": 1.0, + "content": "3.3 FEDERATED WEIGHTED INTER-CLIENT TRANSFER", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "How can we then maximize the knowledge transfer between clients while minimizing the inter-client", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 522, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 506, + 533 + ], + "score": 1.0, + "content": "interference, and communication cost? We now describe our model, Federated Weighted Inter-client", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 533, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 506, + 544 + ], + "score": 1.0, + "content": "Transfer (FedWeIT), which can resolve the these two problems that arise with a naive combination of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 543, + 372, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 372, + 555 + ], + "score": 1.0, + "content": "continual learning approaches with federated learning framework.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5 + }, + { + "type": "text", + "bbox": [ + 106, + 559, + 505, + 615 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "score": 1.0, + "content": "The main cause of the problems, as briefly alluded to earlier, is that the knowledge of all tasks learned", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 338, + 583 + ], + "score": 1.0, + "content": "at multiple clients is stored into a single set of parameters", + "type": "text" + }, + { + "bbox": [ + 339, + 571, + 352, + 582 + ], + "score": 0.88, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 570, + 505, + 583 + ], + "score": 1.0, + "content": ". However, for the knowledge transfer", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "to be effective, each client should selectively utilize only the knowledge of the relevant tasks that is", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "trained at other clients. This selective transfer is also the key to minimize the inter-client interference", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 603, + 478, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 478, + 618 + ], + "score": 1.0, + "content": "as well as it will disregard the knowledge of irrelevant tasks that may interfere with learning.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 106, + 620, + 505, + 678 + ], + "lines": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "We tackle this problem by decomposing the parameters, into three different types of the parameters", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 261, + 644 + ], + "score": 1.0, + "content": "with different roles: global parameters", + "type": "text" + }, + { + "bbox": [ + 262, + 632, + 281, + 643 + ], + "score": 0.88, + "content": "( \\pmb \\theta _ { G } )", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "that capture the global and generic knowledge across all", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 225, + 655 + ], + "score": 1.0, + "content": "clients, local base parameters", + "type": "text" + }, + { + "bbox": [ + 226, + 643, + 239, + 654 + ], + "score": 0.46, + "content": "\\mathbf { \\delta } ( \\mathbf { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 643, + 505, + 655 + ], + "score": 1.0, + "content": "which capture generic knowledge for each client, and task-adaptive", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "score": 1.0, + "content": "parameters (A) for each specific task per client, motivated by Yoon et al. (2020). A set of the model", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 664, + 437, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 153, + 680 + ], + "score": 1.0, + "content": "parameters", + "type": "text" + }, + { + "bbox": [ + 153, + 665, + 169, + 678 + ], + "score": 0.92, + "content": "\\pmb { \\theta } _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 664, + 203, + 680 + ], + "score": 1.0, + "content": "for task", + "type": "text" + }, + { + "bbox": [ + 204, + 668, + 209, + 676 + ], + "score": 0.77, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 664, + 318, + 680 + ], + "score": 1.0, + "content": "at continual learning client", + "type": "text" + }, + { + "bbox": [ + 319, + 668, + 328, + 677 + ], + "score": 0.84, + "content": "c _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 664, + 437, + 680 + ], + "score": 1.0, + "content": "is then defined as follows:", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45 + }, + { + "type": "interline_equation", + "bbox": [ + 208, + 683, + 402, + 713 + ], + "lines": [ + { + "bbox": [ + 208, + 683, + 402, + 713 + ], + "spans": [ + { + "bbox": [ + 208, + 683, + 402, + 713 + ], + "score": 0.93, + "content": "\\pmb { \\theta } _ { c } ^ { ( t ) } = \\mathbf { B } _ { c } ^ { ( t ) } \\odot \\mathbf { m } _ { c } ^ { ( t ) } + \\mathbf { A } _ { c } ^ { ( t ) } + \\sum _ { i \\in \\mathcal { C } _ { \\backslash c } } \\sum _ { j < | t | } \\alpha _ { i , j } ^ { ( t ) } \\mathbf { A } _ { i } ^ { ( j ) }", + "type": "interline_equation", + "image_path": "e9fa79e8d9e76fe428194db35faadc7881639a065831ccd0d94f3c86bd92fce6.jpg" + } + ] + } + ], + "index": 48.5, + "virtual_lines": [ + { + "bbox": [ + 208, + 683, + 402, + 698.0 + ], + "spans": [], + "index": 48 + }, + { + "bbox": [ + 208, + 698.0, + 402, + 713.0 + ], + "spans": [], + "index": 49 + } + ] + }, + { + "type": "text", + "bbox": [ + 109, + 719, + 503, + 733 + ], + "lines": [ + { + "bbox": [ + 108, + 716, + 506, + 735 + ], + "spans": [ + { + "bbox": [ + 108, + 716, + 136, + 735 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 136, + 718, + 218, + 733 + ], + "score": 0.93, + "content": "\\mathbf { B } _ { c } ^ { ( t ) } \\in \\{ \\mathbb { R } ^ { I _ { l } \\times O _ { l } } \\} _ { l = 1 } ^ { L }", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 716, + 349, + 735 + ], + "score": 1.0, + "content": "is the set of base parameters for", + "type": "text" + }, + { + "bbox": [ + 349, + 720, + 362, + 730 + ], + "score": 0.9, + "content": "c ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 716, + 506, + 735 + ], + "score": 1.0, + "content": "client shared across all tasks in the", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 50 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 307, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 8 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 506, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "We now extend the conventional continual learning to the federated learning setting with multiple", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 348, + 107 + ], + "score": 1.0, + "content": "clients and a global server. Let us assume that we have", + "type": "text" + }, + { + "bbox": [ + 348, + 94, + 358, + 104 + ], + "score": 0.79, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 92, + 482, + 107 + ], + "score": 1.0, + "content": "clients, where at each client", + "type": "text" + }, + { + "bbox": [ + 482, + 95, + 505, + 105 + ], + "score": 0.86, + "content": "c _ { c } \\in", + "type": "inline_equation" + } + ], + "index": 1 + }, + { + "bbox": [ + 107, + 102, + 508, + 122 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 160, + 119 + ], + "score": 0.92, + "content": "\\{ c _ { 1 } , \\ldots , c _ { C } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 102, + 394, + 122 + ], + "score": 1.0, + "content": "trains a model on a privately accessible sequence of tasks", + "type": "text" + }, + { + "bbox": [ + 394, + 104, + 503, + 119 + ], + "score": 0.92, + "content": "\\{ \\mathcal { T } _ { c } ^ { ( 1 ) } , \\mathcal { T } _ { c } ^ { ( 2 ) } , . . . , \\mathcal { T } _ { c } ^ { ( t ) } \\} \\subseteq \\mathcal { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 102, + 508, + 122 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 118, + 506, + 133 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 324, + 133 + ], + "score": 1.0, + "content": "Please note that there is no relation among the tasks", + "type": "text" + }, + { + "bbox": [ + 325, + 118, + 343, + 133 + ], + "score": 0.92, + "content": "\\mathcal { T } _ { 1 : c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 120, + 411, + 133 + ], + "score": 1.0, + "content": "received at step", + "type": "text" + }, + { + "bbox": [ + 412, + 122, + 417, + 131 + ], + "score": 0.72, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 120, + 506, + 133 + ], + "score": 1.0, + "content": ", across clients. Now", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 229, + 145 + ], + "score": 1.0, + "content": "the goal is to effectively train", + "type": "text" + }, + { + "bbox": [ + 230, + 132, + 239, + 142 + ], + "score": 0.8, + "content": "C", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 131, + 506, + 145 + ], + "score": 1.0, + "content": "continual learning models on their own private task streams, via", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 142, + 506, + 155 + ], + "spans": [ + { + "bbox": [ + 106, + 142, + 506, + 155 + ], + "score": 1.0, + "content": "communicating the model parameters with the global server, which aggregates the parameters sent", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 153, + 308, + 165 + ], + "spans": [ + { + "bbox": [ + 106, + 153, + 308, + 165 + ], + "score": 1.0, + "content": "from each client, and redistributes them to clients.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 82, + 508, + 165 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 175, + 308, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 174, + 309, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 309, + 188 + ], + "score": 1.0, + "content": "3.2 COMMUNICABLE CONTINUAL LEARNING", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 192, + 505, + 361 + ], + "lines": [ + { + "bbox": [ + 105, + 191, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 206 + ], + "score": 1.0, + "content": "In conventional federated learning settings, the learning is done with multiple rounds of local learning", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 203, + 504, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 365, + 216 + ], + "score": 1.0, + "content": "and parameter aggregation. At each round of communication", + "type": "text" + }, + { + "bbox": [ + 366, + 206, + 371, + 213 + ], + "score": 0.69, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 203, + 424, + 216 + ], + "score": 1.0, + "content": ", each client", + "type": "text" + }, + { + "bbox": [ + 424, + 205, + 434, + 214 + ], + "score": 0.86, + "content": "c _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 203, + 497, + 216 + ], + "score": 1.0, + "content": "and the server", + "type": "text" + }, + { + "bbox": [ + 498, + 205, + 504, + 213 + ], + "score": 0.55, + "content": "s", + "type": "inline_equation" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 213, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 506, + 228 + ], + "score": 1.0, + "content": "perform the following two procedures: local parameter transmission and parameter aggregation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 115, + 235 + ], + "score": 0.3, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 225, + 505, + 238 + ], + "score": 1.0, + "content": "broadcasting. In the local parameter transmission step, for a randomly selected subset of clients", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 236, + 504, + 250 + ], + "spans": [ + { + "bbox": [ + 104, + 236, + 142, + 250 + ], + "score": 1.0, + "content": "at round", + "type": "text" + }, + { + "bbox": [ + 143, + 240, + 149, + 248 + ], + "score": 0.4, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 236, + 151, + 250 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 152, + 236, + 244, + 250 + ], + "score": 0.89, + "content": "\\mathcal { C } ^ { ( r ) } \\subseteq \\{ c _ { 1 } , c _ { 2 } , . . . , c _ { C } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 236, + 294, + 250 + ], + "score": 1.0, + "content": ", each client", + "type": "text" + }, + { + "bbox": [ + 294, + 240, + 304, + 249 + ], + "score": 0.86, + "content": "c _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 236, + 412, + 250 + ], + "score": 1.0, + "content": "sends updated parameters", + "type": "text" + }, + { + "bbox": [ + 412, + 236, + 430, + 248 + ], + "score": 0.9, + "content": "\\pmb \\theta ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 236, + 504, + 250 + ], + "score": 1.0, + "content": "to the server. The", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 505, + 262 + ], + "score": 1.0, + "content": "server-clients transmission is not done at every client because some of the clients may be temporarily", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 102, + 258, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 102, + 258, + 344, + 279 + ], + "score": 1.0, + "content": "disconnected. Then the server aggregates the parameters", + "type": "text" + }, + { + "bbox": [ + 344, + 259, + 362, + 273 + ], + "score": 0.94, + "content": "\\pmb { \\theta } _ { c } ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 258, + 505, + 279 + ], + "score": 1.0, + "content": "sent from the clients into a single", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 272, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 104, + 272, + 506, + 285 + ], + "score": 1.0, + "content": "parameter. The most popular frameworks for this aggregation are FedAvg (McMahan et al., 2016)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "and FedProx (Li et al., 2018). However, naive federated continual learning with these two algorithms", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "on local sequences of tasks may result in catastrophic forgetting. One simple solution is to use a", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 306, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 505, + 318 + ], + "score": 1.0, + "content": "regularization-based, such as Elastic Weight Consolidation (EWC) (Kirkpatrick et al., 2017), which", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "allows the model to obtain a solution that is optimal for both the previous and the current tasks. There", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 327, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 506, + 340 + ], + "score": 1.0, + "content": "exist other advanced solutions (Rusu et al., 2016; Nguyen et al., 2018; Chaudhry et al., 2019) that", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 338, + 506, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 506, + 351 + ], + "score": 1.0, + "content": "successfully prevents catastrophic forgetting. However, the prevention of catastrophic forgetting at", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 348, + 369, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 369, + 363 + ], + "score": 1.0, + "content": "the client level is an orthogonal problem from federated learning.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 15, + "bbox_fs": [ + 102, + 191, + 506, + 363 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 366, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "Thus we focus on challenges that newly arise in this federated continual learning setting. In the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 376, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 390 + ], + "score": 1.0, + "content": "federated continual learning framework, the aggregation of the parameters into a global parameter", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 387, + 508, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 120, + 402 + ], + "score": 0.88, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 387, + 375, + 405 + ], + "score": 1.0, + "content": "allows inter-client knowledge transfer across clients, since a task", + "type": "text" + }, + { + "bbox": [ + 375, + 388, + 394, + 403 + ], + "score": 0.93, + "content": "\\mathcal { T } _ { i } ^ { ( q ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 387, + 460, + 405 + ], + "score": 1.0, + "content": "learned at client", + "type": "text" + }, + { + "bbox": [ + 460, + 392, + 469, + 402 + ], + "score": 0.84, + "content": "c _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 387, + 508, + 405 + ], + "score": 1.0, + "content": "at round", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 399, + 508, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 113, + 417 + ], + "score": 0.68, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 113, + 399, + 230, + 421 + ], + "score": 1.0, + "content": "may be similar or related to", + "type": "text" + }, + { + "bbox": [ + 231, + 402, + 250, + 419 + ], + "score": 0.92, + "content": "\\mathcal { T } _ { j } ^ { ( r ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 399, + 320, + 421 + ], + "score": 1.0, + "content": "learned at client", + "type": "text" + }, + { + "bbox": [ + 320, + 407, + 330, + 417 + ], + "score": 0.86, + "content": "c _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 399, + 368, + 421 + ], + "score": 1.0, + "content": "at round", + "type": "text" + }, + { + "bbox": [ + 368, + 407, + 374, + 415 + ], + "score": 0.65, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 399, + 508, + 421 + ], + "score": 1.0, + "content": ". Yet, using a single aggregated", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 416, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 149, + 430 + ], + "score": 1.0, + "content": "parameter", + "type": "text" + }, + { + "bbox": [ + 149, + 417, + 163, + 428 + ], + "score": 0.87, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 416, + 505, + 430 + ], + "score": 1.0, + "content": "may be suboptimal in achieving this goal since knowledge from irrelevant tasks may", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 441 + ], + "score": 1.0, + "content": "not to be useful or even hinder the training at each client by altering its parameters into incorrect", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "score": 1.0, + "content": "directions, which we describe as inter-client interference. Another problem that is also practically", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "score": 1.0, + "content": "important, is the communication-efficiency. Both the parameter transmission from the client to the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 461, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 505, + 473 + ], + "score": 1.0, + "content": "server, and server to client will incur large communication cost, which will be problematic for the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 473, + 477, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 477, + 485 + ], + "score": 1.0, + "content": "continual learning setting, since the clients may train on possibly unlimited streams of tasks.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 366, + 508, + 485 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 493, + 346, + 504 + ], + "lines": [ + { + "bbox": [ + 105, + 492, + 347, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 347, + 506 + ], + "score": 1.0, + "content": "3.3 FEDERATED WEIGHTED INTER-CLIENT TRANSFER", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "How can we then maximize the knowledge transfer between clients while minimizing the inter-client", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 522, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 506, + 533 + ], + "score": 1.0, + "content": "interference, and communication cost? We now describe our model, Federated Weighted Inter-client", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 533, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 506, + 544 + ], + "score": 1.0, + "content": "Transfer (FedWeIT), which can resolve the these two problems that arise with a naive combination of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 543, + 372, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 372, + 555 + ], + "score": 1.0, + "content": "continual learning approaches with federated learning framework.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 510, + 506, + 555 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 559, + 505, + 615 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "score": 1.0, + "content": "The main cause of the problems, as briefly alluded to earlier, is that the knowledge of all tasks learned", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 338, + 583 + ], + "score": 1.0, + "content": "at multiple clients is stored into a single set of parameters", + "type": "text" + }, + { + "bbox": [ + 339, + 571, + 352, + 582 + ], + "score": 0.88, + "content": "\\theta _ { G }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 570, + 505, + 583 + ], + "score": 1.0, + "content": ". However, for the knowledge transfer", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "to be effective, each client should selectively utilize only the knowledge of the relevant tasks that is", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "trained at other clients. This selective transfer is also the key to minimize the inter-client interference", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 603, + 478, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 478, + 618 + ], + "score": 1.0, + "content": "as well as it will disregard the knowledge of irrelevant tasks that may interfere with learning.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 560, + 505, + 618 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 620, + 505, + 678 + ], + "lines": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "We tackle this problem by decomposing the parameters, into three different types of the parameters", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 261, + 644 + ], + "score": 1.0, + "content": "with different roles: global parameters", + "type": "text" + }, + { + "bbox": [ + 262, + 632, + 281, + 643 + ], + "score": 0.88, + "content": "( \\pmb \\theta _ { G } )", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "that capture the global and generic knowledge across all", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 225, + 655 + ], + "score": 1.0, + "content": "clients, local base parameters", + "type": "text" + }, + { + "bbox": [ + 226, + 643, + 239, + 654 + ], + "score": 0.46, + "content": "\\mathbf { \\delta } ( \\mathbf { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 643, + 505, + 655 + ], + "score": 1.0, + "content": "which capture generic knowledge for each client, and task-adaptive", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 666 + ], + "score": 1.0, + "content": "parameters (A) for each specific task per client, motivated by Yoon et al. 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(a) A client sends sparsified federated parameter", + "type": "text" + }, + { + "bbox": [ + 407, + 203, + 446, + 216 + ], + "score": 0.92, + "content": "\\mathbf { B } _ { c } \\odot \\mathbf { m } _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 204, + 506, + 218 + ], + "score": 1.0, + "content": ". After that, the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 216, + 505, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 227 + ], + "score": 1.0, + "content": "server redistributes aggregated parameters to the clients. 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In Figure 2 (a), we initialize", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 102, + 319, + 509, + 343 + ], + "spans": [ + { + "bbox": [ + 102, + 319, + 170, + 343 + ], + "score": 1.0, + "content": "it at each round", + "type": "text" + }, + { + "bbox": [ + 170, + 326, + 175, + 335 + ], + "score": 0.73, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 319, + 391, + 343 + ], + "score": 1.0, + "content": "with the global parameter from the previous iteration,", + "type": "text" + }, + { + "bbox": [ + 391, + 323, + 417, + 338 + ], + "score": 0.93, + "content": "\\theta _ { G } ^ { ( t - 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 418, + 319, + 509, + 343 + ], + "score": 1.0, + "content": "which aggregates the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 337, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 337, + 288, + 352 + ], + "score": 1.0, + "content": "parameters sent from the client. 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Thus we only transmit the task-adaptive parameter of the previous task", + "type": "text" + }, + { + "bbox": [ + 446, + 498, + 474, + 509 + ], + "score": 0.87, + "content": "( t - 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 497, + 505, + 509 + ], + "score": 1.0, + "content": ", which", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 509, + 327, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 327, + 521 + ], + "score": 1.0, + "content": "we empirically find to achieve good results in practice.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 108, + 530, + 496, + 544 + ], + "lines": [ + { + "bbox": [ + 104, + 528, + 500, + 547 + ], + "spans": [ + { + "bbox": [ + 104, + 528, + 310, + 547 + ], + "score": 1.0, + "content": "Training. 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Here,", + "type": "text" + }, + { + "bbox": [ + 271, + 627, + 364, + 641 + ], + "score": 0.92, + "content": "\\Delta \\mathbf { B } _ { c } ^ { ( t ) } = \\mathbf { B } _ { c } ^ { ( t ) } - \\mathbf { B } _ { c } ^ { ( t - 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 626, + 506, + 641 + ], + "score": 1.0, + "content": "is the difference between the base", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 640, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 104, + 640, + 309, + 655 + ], + "score": 1.0, + "content": "parameter at the current and previous timestep, and", + "type": "text" + }, + { + "bbox": [ + 309, + 641, + 335, + 654 + ], + "score": 0.91, + "content": "\\Delta \\mathbf { A } _ { c } ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 640, + 506, + 655 + ], + "score": 1.0, + "content": "is the difference between the task-adaptive", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 652, + 506, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 179, + 666 + ], + "score": 1.0, + "content": "parameter for task", + "type": "text" + }, + { + "bbox": [ + 179, + 654, + 184, + 663 + ], + "score": 0.7, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 652, + 506, + 666 + ], + "score": 1.0, + "content": "at the current and previous timestep. 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(a) A client sends sparsified federated parameter", + "type": "text" + }, + { + "bbox": [ + 407, + 203, + 446, + 216 + ], + "score": 0.92, + "content": "\\mathbf { B } _ { c } \\odot \\mathbf { m } _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 204, + 506, + 218 + ], + "score": 1.0, + "content": ". After that, the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 216, + 505, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 227 + ], + "score": 1.0, + "content": "server redistributes aggregated parameters to the clients. 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In Figure 2 (a), we initialize", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 102, + 319, + 509, + 343 + ], + "spans": [ + { + "bbox": [ + 102, + 319, + 170, + 343 + ], + "score": 1.0, + "content": "it at each round", + "type": "text" + }, + { + "bbox": [ + 170, + 326, + 175, + 335 + ], + "score": 0.73, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 319, + 391, + 343 + ], + "score": 1.0, + "content": "with the global parameter from the previous iteration,", + "type": "text" + }, + { + "bbox": [ + 391, + 323, + 417, + 338 + ], + "score": 0.93, + "content": "\\theta _ { G } ^ { ( t - 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 418, + 319, + 509, + 343 + ], + "score": 1.0, + "content": "which aggregates the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 337, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 337, + 288, + 352 + ], + "score": 1.0, + "content": "parameters sent from the client. This allows", + "type": "text" + }, + { + "bbox": [ + 288, + 337, + 306, + 351 + ], + "score": 0.91, + "content": "\\mathbf { B } _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 337, + 506, + 352 + ], + "score": 1.0, + "content": "to also benefit from the global knowledge about", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 101, + 345, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 101, + 345, + 224, + 372 + ], + "score": 1.0, + "content": "all the tasks. 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This sparse parameter selection helps minimize inter-client interference, and also allows for", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 388, + 506, + 404 + ], + "spans": [ + { + "bbox": [ + 104, + 388, + 402, + 404 + ], + "score": 1.0, + "content": "efficient communication. The second term is the task-adaptive parameters", + "type": "text" + }, + { + "bbox": [ + 402, + 389, + 420, + 402 + ], + "score": 0.91, + "content": "\\mathbf { A } _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 388, + 506, + 404 + ], + "score": 1.0, + "content": ". 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The final term describes", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 427, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 505, + 438 + ], + "score": 1.0, + "content": "weighted inter-client knowledge transfer. We have a set of parameters that are transmitted from the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "server, which contain all task-adaptive parameters from all the clients. To selectively utilizes these", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 448, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 387, + 464 + ], + "score": 1.0, + "content": "indirect experiences from other clients, we further allocate attention", + "type": "text" + }, + { + "bbox": [ + 388, + 448, + 406, + 462 + ], + "score": 0.92, + "content": "\\alpha _ { c } ^ { ( t ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 449, + 506, + 464 + ], + "score": 1.0, + "content": "on these parameters, to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "take a weighted combination of them. By learning this attention, each client can select only the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 472, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 104, + 472, + 436, + 489 + ], + "score": 1.0, + "content": "relevant task-adaptive parameters that help learn the given task. 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After generating and", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 570, + 470, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 470, + 582 + ], + "score": 1.0, + "content": "processing tasks, we randomly distribute them to multiple clients as illustrated in Figure 3.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 459, + 506, + 582 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 595, + 505, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "Experimental setup We use a modified version of LeNet (LeCun et al., 1998) for the experiments", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 606, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 505, + 618 + ], + "score": 1.0, + "content": "with both Overlapped-CIFAR-100 and NonIID-50 dataset. Further, we use ResNet-18 He et al. (2016)", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 617, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 630 + ], + "score": 1.0, + "content": "with NonIID-50 dataset. We followed other experimental setups from Serrà et al. (2018) and Yoon", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "score": 1.0, + "content": "et al. (2020). For detailed descriptions of the task configuration and hyperparameters used, please see", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 639, + 464, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 464, + 653 + ], + "score": 1.0, + "content": "Section B in appendix. Also, for more ablation studies, please see Section C in appendix.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49, + "bbox_fs": [ + 105, + 595, + 505, + 653 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 666, + 506, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 665, + 507, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 507, + 678 + ], + "score": 1.0, + "content": "Baselines and our model 1) STL: Single Task Learning at each arriving task. 2) Local-EWC: In-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "dividual continual learning with EWC (Kirkpatrick et al., 2017) per client. 3) Local-APD: Individual", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "continual learning with APD (Yoon et al., 2020) per client. 4) FedProx: FCL using FedProx (Li", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "et al., 2018) algorithm. 5) Scaffold: FCL using Scaffold (Karimireddy et al., 2020) algorithm. 6)", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "score": 1.0, + "content": "FedCurv: FCL using FedCurv (Shoham et al., 2019) algorithm. 7) FedProx-[model]: FCL, that is", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 720, + 452, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 452, + 733 + ], + "score": 1.0, + "content": "trained using FedProx algorithm with [model]. 8) FedWeIT: Our FedWeIT algorithm.", + "type": "text" + } + ], + "index": 57 + } + ], + "index": 54.5, + "bbox_fs": [ + 105, + 665, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 124, + 509, + 225 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 93, + 504, + 123 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 92, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 431, + 105 + ], + "score": 1.0, + "content": "Table 1: Averaged Per-task performance on both dataset during FCL with 5 clients (fraction", + "type": "text" + }, + { + "bbox": [ + 432, + 94, + 449, + 103 + ], + "score": 0.56, + "content": "\\scriptstyle 1 = 1 . 0", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 92, + 505, + 105 + ], + "score": 1.0, + "content": "). We measured", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 103, + 505, + 114 + ], + "spans": [ + { + "bbox": [ + 106, + 103, + 505, + 114 + ], + "score": 1.0, + "content": "task accuracy and model size after completing all learning phases over 3 individual trials. We also measured", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 113, + 297, + 124 + ], + "spans": [ + { + "bbox": [ + 106, + 113, + 297, + 124 + ], + "score": 1.0, + "content": "C2S/S2C communication cost for training each task.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 106, + 124, + 509, + 225 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 124, + 509, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 124, + 509, + 225 + ], + "score": 0.857, + "html": "
NonIID-50Dataset (F=1.0, R=20)Overlapped CIFAR-100 (F=1.0,R=20)
MethodsAccuracyModel SizeC2S/S2C CostAccuracyModel SizeC2S/S2C Cost
STL85.78 ±0.170.610GBN/A57.15 ±0.070.610 GBN/A
Local-EWC74.30±0.080.061GB- -N/A44.26±0.430.061GBN7A
Local-APD81.42 ± 0.720.090 GBN/A50.82 ± 0.330.073 GBN/A
FedProx63.691.750.061GB1.22/1.22GB33.83±0.480.061GB1.22/1.22GB
Scaffold30.84 ± 1.410.061 GB2.44 /2.44 GB22.80 ±0.470.061 GB2.44/2.44 GB
FedCurv72.39 ±0.320.061GB1.22/1.22 GB40.36 ±0.440.061GB1.22/1.22 GB
FedProx-EWC68.18 ± 0.580.061 GB1.22/1.22 GB41.91 ± 0.470.061 GB1.22/1.22 GB
FedProx-APD81.20 ± 1.240.079 GB1.22/1.22 GB52.20 ± 0.410.075 GB1.22/1.22 GB
FedWeIT84.11 ± 0.270.078 GB0.37/1.07 GB55.16 ± 0.190.075 GB0.37/1.07 GB
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100 clients (F=0.05,R=20,1,000 tasks in total)
MethodsAccuracyModel SizeC2S/S2C Cost
STL32.96 ±0.2312.20 GBN/A
Local-APD37.50 ±0.174.01GBN/A
FedProx24.11 ±0.441.22 GB1.2271.22 GB
FedCurv29.11 ± 0.201.22 GB1.22 /1.22 GB
FedCurv-EWC29.72 ± 0.201.22 GB1.22 /1.22 GB
FedWeIT39.58 ± 0.274.03 GB0.38 /1.10 GB
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Table 1 shows the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "score": 1.0, + "content": "final average per-task performance after the completion of (federated) continual learning on both", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "datasets. We observe that FedProx-based federated continual learning (FCL) approaches degenerate", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "score": 1.0, + "content": "the performance of continual learning (CL) methods over the same methods without federated", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 453, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 505, + 466 + ], + "score": 1.0, + "content": "learning. This is because the aggregation of all client parameters that are learned on irrelevant tasks", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 463, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 104, + 463, + 506, + 477 + ], + "score": 1.0, + "content": "results in severe interference in the learning for each task, which leads to catastrophic forgetting and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 475, + 504, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 504, + 486 + ], + "score": 1.0, + "content": "suboptimal task adaptation. Scaffold achieves poor performance on FCL, as its regularization on the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "score": 1.0, + "content": "local gradients is harmful for FCL, where all clients learn from a different task sequences. While", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "FedCurv reduces inter-task disparity in parameters, it cannot minimize inter-task interference, which", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "results it to underperform single-machine CL methods. On the other hand, FedWeIT significantly", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 518, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 531 + ], + "score": 1.0, + "content": "outperforms both single-machine CL baselines and naive FCL baselines on both datasets. Even", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 226, + 542 + ], + "score": 1.0, + "content": "with larger number of clients", + "type": "text" + }, + { + "bbox": [ + 226, + 530, + 264, + 540 + ], + "score": 0.87, + "content": "C = 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "), FedWeIT consistently outperforms all baselines (Figure 4).", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "This improvement largely owes to FedWeIT’s ability to selectively utilize the knowledge from", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 552, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 506, + 564 + ], + "score": 1.0, + "content": "other clients to rapidly adapt to the target task, and obtain better final performance (Figure 4 Left).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 344, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 562, + 345, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 345, + 574 + ], + "score": 1.0, + "content": "The fast adaptation to new task is another clear advantage of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 573, + 344, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 344, + 584 + ], + "score": 1.0, + "content": "inter-client knowledge transfer. To further demonstrate the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 583, + 345, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 583, + 345, + 597 + ], + "score": 1.0, + "content": "practicality of our method with larger networks, we experi-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 595, + 344, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 344, + 607 + ], + "score": 1.0, + "content": "ment on Non-IID dtaset with ResNet-18 (Table 2), on which", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 606, + 345, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 345, + 618 + ], + "score": 1.0, + "content": "FedWeIT still significantly outperforms the strongest base-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 617, + 345, + 629 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 345, + 629 + ], + "score": 1.0, + "content": "line (FedProx-APD) while using fewer parameters. Also,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 627, + 345, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 300, + 641 + ], + "score": 1.0, + "content": "our model is not sensitive to the hyperparameters", + "type": "text" + }, + { + "bbox": [ + 300, + 628, + 312, + 639 + ], + "score": 0.87, + "content": "\\lambda _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 627, + 329, + 641 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 330, + 628, + 341, + 639 + ], + "score": 0.85, + "content": "\\lambda _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 627, + 345, + 641 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 313, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 313, + 651 + ], + "score": 1.0, + "content": "if they are within reasonable scales (Figure 6 Left).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 35.5 + }, + { + "type": "table", + "bbox": [ + 351, + 592, + 503, + 649 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 351, + 571, + 504, + 591 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 350, + 570, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 350, + 570, + 505, + 582 + ], + "score": 1.0, + "content": "Table 2: FCL results on NonIID-50", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 351, + 581, + 439, + 591 + ], + "spans": [ + { + "bbox": [ + 351, + 581, + 439, + 591 + ], + "score": 1.0, + "content": "dataset with ResNet-18.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.0 + }, + { + "type": "table_body", + "bbox": [ + 351, + 592, + 503, + 649 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 351, + 592, + 503, + 649 + ], + "spans": [ + { + "bbox": [ + 351, + 592, + 503, + 649 + ], + "score": 0.973, + "html": "
ResNet-18
MethodsAcc.M Size
Local-APDFedProx-APDFedWeIT92.44 %92.89%94.86 %1.86 GB2.05GB1.84 GB
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NonIID-50Dataset (F=1.0, R=20)Overlapped CIFAR-100 (F=1.0,R=20)
MethodsAccuracyModel SizeC2S/S2C CostAccuracyModel SizeC2S/S2C Cost
STL85.78 ±0.170.610GBN/A57.15 ±0.070.610 GBN/A
Local-EWC74.30±0.080.061GB- -N/A44.26±0.430.061GBN7A
Local-APD81.42 ± 0.720.090 GBN/A50.82 ± 0.330.073 GBN/A
FedProx63.691.750.061GB1.22/1.22GB33.83±0.480.061GB1.22/1.22GB
Scaffold30.84 ± 1.410.061 GB2.44 /2.44 GB22.80 ±0.470.061 GB2.44/2.44 GB
FedCurv72.39 ±0.320.061GB1.22/1.22 GB40.36 ±0.440.061GB1.22/1.22 GB
FedProx-EWC68.18 ± 0.580.061 GB1.22/1.22 GB41.91 ± 0.470.061 GB1.22/1.22 GB
FedProx-APD81.20 ± 1.240.079 GB1.22/1.22 GB52.20 ± 0.410.075 GB1.22/1.22 GB
FedWeIT84.11 ± 0.270.078 GB0.37/1.07 GB55.16 ± 0.190.075 GB0.37/1.07 GB
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100 clients (F=0.05,R=20,1,000 tasks in total)
MethodsAccuracyModel SizeC2S/S2C Cost
STL32.96 ±0.2312.20 GBN/A
Local-APD37.50 ±0.174.01GBN/A
FedProx24.11 ±0.441.22 GB1.2271.22 GB
FedCurv29.11 ± 0.201.22 GB1.22 /1.22 GB
FedCurv-EWC29.72 ± 0.201.22 GB1.22 /1.22 GB
FedWeIT39.58 ± 0.274.03 GB0.38 /1.10 GB
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Table 1 shows the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "score": 1.0, + "content": "final average per-task performance after the completion of (federated) continual learning on both", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "datasets. 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While", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "FedCurv reduces inter-task disparity in parameters, it cannot minimize inter-task interference, which", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "results it to underperform single-machine CL methods. On the other hand, FedWeIT significantly", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 518, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 531 + ], + "score": 1.0, + "content": "outperforms both single-machine CL baselines and naive FCL baselines on both datasets. Even", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 226, + 542 + ], + "score": 1.0, + "content": "with larger number of clients", + "type": "text" + }, + { + "bbox": [ + 226, + 530, + 264, + 540 + ], + "score": 0.87, + "content": "C = 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "), FedWeIT consistently outperforms all baselines (Figure 4).", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "This improvement largely owes to FedWeIT’s ability to selectively utilize the knowledge from", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 552, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 506, + 564 + ], + "score": 1.0, + "content": "other clients to rapidly adapt to the target task, and obtain better final performance (Figure 4 Left).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 21.5, + "bbox_fs": [ + 104, + 387, + 506, + 564 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 344, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 562, + 345, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 345, + 574 + ], + "score": 1.0, + "content": "The fast adaptation to new task is another clear advantage of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 573, + 344, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 344, + 584 + ], + "score": 1.0, + "content": "inter-client knowledge transfer. To further demonstrate the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 583, + 345, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 583, + 345, + 597 + ], + "score": 1.0, + "content": "practicality of our method with larger networks, we experi-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 595, + 344, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 344, + 607 + ], + "score": 1.0, + "content": "ment on Non-IID dtaset with ResNet-18 (Table 2), on which", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 606, + 345, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 345, + 618 + ], + "score": 1.0, + "content": "FedWeIT still significantly outperforms the strongest base-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 617, + 345, + 629 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 345, + 629 + ], + "score": 1.0, + "content": "line (FedProx-APD) while using fewer parameters. Also,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 627, + 345, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 300, + 641 + ], + "score": 1.0, + "content": "our model is not sensitive to the hyperparameters", + "type": "text" + }, + { + "bbox": [ + 300, + 628, + 312, + 639 + ], + "score": 0.87, + "content": "\\lambda _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 627, + 329, + 641 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 330, + 628, + 341, + 639 + ], + "score": 0.85, + "content": "\\lambda _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 627, + 345, + 641 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 313, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 313, + 651 + ], + "score": 1.0, + "content": "if they are within reasonable scales (Figure 6 Left).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 35.5, + "bbox_fs": [ + 104, + 562, + 345, + 651 + ] + }, + { + "type": "table", + "bbox": [ + 351, + 592, + 503, + 649 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 351, + 571, + 504, + 591 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 350, + 570, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 350, + 570, + 505, + 582 + ], + "score": 1.0, + "content": "Table 2: FCL results on NonIID-50", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 351, + 581, + 439, + 591 + ], + "spans": [ + { + "bbox": [ + 351, + 581, + 439, + 591 + ], + "score": 1.0, + "content": "dataset with ResNet-18.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.0 + }, + { + "type": "table_body", + "bbox": [ + 351, + 592, + 503, + 649 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 351, + 592, + 503, + 649 + ], + "spans": [ + { + "bbox": [ + 351, + 592, + 503, + 649 + ], + "score": 0.973, + "html": "
ResNet-18
MethodsAcc.M Size
Local-APDFedProx-APDFedWeIT92.44 %92.89%94.86 %1.86 GB2.05GB1.84 GB
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We observe that FedWeIT obtains much", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "higher accuracy while utilizing less number of parameters compared to FedProx-APD. This efficiency", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "mainly comes from the reuse of task-adaptive parameters from other clients, which is not possible", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "score": 1.0, + "content": "with single-machine CL methods or naive FCL methods. We also examine the communication cost", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "(the size of non-zero parameters transmitted) of each method. Table 1 reports both the client-to-server", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 720, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 484, + 732 + ], + "score": 1.0, + "content": "(C2S) / server-to-client (S2C) communication cost at training each task. FedWeIT, uses only", + "type": "text" + }, + { + "bbox": [ + 485, + 720, + 505, + 731 + ], + "score": 0.88, + "content": "3 0 \\%", + "type": "inline_equation" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 326, + 506, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 123, + 341 + ], + "score": 1.0, + "content": "and", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 124, + 328, + 138, + 339 + ], + "score": 0.87, + "content": "3 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 139, + 327, + 212, + 341 + ], + "score": 1.0, + "content": "of parameters for", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 212, + 326, + 221, + 339 + ], + "score": 0.61, + "content": "\\widehat { \\mathbf B }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 221, + 327, + 506, + 341 + ], + "score": 1.0, + "content": "and A of the dense models respectively. We observe that FedWeIT is", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 340, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 505, + 352 + ], + "score": 1.0, + "content": "significantly more communication-efficient than FCL baselines although it broadcasts task-adaptive", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 350, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 506, + 363 + ], + "score": 1.0, + "content": "parameters, due to high sparsity of the parameters. Figure 5 (a) shows the accuracy as a function of", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 360, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 282, + 375 + ], + "score": 1.0, + "content": "C2S cost according to a transmission of top-", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 283, + 361, + 298, + 372 + ], + "score": 0.89, + "content": "\\kappa \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 298, + 360, + 505, + 375 + ], + "score": 1.0, + "content": "informative parameters. Since FedWeIT selectively", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "score": 1.0, + "content": "utilizes task-specific parameters learned from other clients, it results in superior performance over", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 383, + 410, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 410, + 396 + ], + "score": 1.0, + "content": "APD-baselines especially with sparse communication of model parameters.", + "type": "text", + "cross_page": true + } + ], + "index": 17 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 655, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 83, + 488, + 170 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 118, + 83, + 488, + 170 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 118, + 83, + 488, + 170 + ], + "spans": [ + { + "bbox": [ + 118, + 83, + 488, + 170 + ], + "score": 0.95, + "type": "image", + "image_path": "42b7c39389253e8c6b14218f62c8e3c835b18e61b7312d3849dc060008c81811.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 118, + 83, + 488, + 112.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 118, + 112.0, + 488, + 141.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 118, + 141.0, + 488, + 170.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 173, + 504, + 204 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 172, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 172, + 506, + 185 + ], + "score": 1.0, + "content": "Figure 5: (a) Accuracy over C2S cost. We report the relative communication cost to the original network. All", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 183, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 194 + ], + "score": 1.0, + "content": "results are averaged over the 5 clients. (b) Inter-client transfer for NonIID-50. We compare the scale of the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 193, + 503, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 193, + 503, + 204 + ], + "score": 1.0, + "content": "attentions at first FC layer which gives the weights on transferred task-adaptive parameters from other clients.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 108, + 207, + 489, + 284 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 207, + 489, + 284 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 207, + 489, + 284 + ], + "spans": [ + { + "bbox": [ + 108, + 207, + 489, + 284 + ], + "score": 0.951, + "type": "image", + "image_path": "b48b317b40e852b5ce1c0fd7677219d4191234672dc950bc7d939cfbf41b0cf8.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 108, + 207, + 489, + 232.66666666666666 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 108, + 232.66666666666666, + 489, + 258.3333333333333 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 108, + 258.3333333333333, + 489, + 284.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 286, + 504, + 318 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 286, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 506, + 297 + ], + "score": 1.0, + "content": "Figure 6: Left: Performance of FedWeIT with different scale of hyperparameters on Non-iid 50. Middle:", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 312, + 309 + ], + "score": 1.0, + "content": "Performance comparison about current task adaptation at", + "type": "text" + }, + { + "bbox": [ + 312, + 296, + 326, + 307 + ], + "score": 0.88, + "content": "6 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 295, + 342, + 309 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 342, + 296, + 356, + 307 + ], + "score": 0.88, + "content": "8 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 295, + 506, + 309 + ], + "score": 1.0, + "content": "tasks during federated continual learning", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 307, + 384, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 384, + 318 + ], + "score": 1.0, + "content": "on NonIID-50. Right: Forgetting measure using Backward Transfer (BWT).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 327, + 505, + 394 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 506, + 341 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 123, + 341 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 124, + 328, + 138, + 339 + ], + "score": 0.87, + "content": "3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 327, + 212, + 341 + ], + "score": 1.0, + "content": "of parameters for", + "type": "text" + }, + { + "bbox": [ + 212, + 326, + 221, + 339 + ], + "score": 0.61, + "content": "\\widehat { \\mathbf B }", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 327, + 506, + 341 + ], + "score": 1.0, + "content": "and A of the dense models respectively. We observe that FedWeIT is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 340, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 505, + 352 + ], + "score": 1.0, + "content": "significantly more communication-efficient than FCL baselines although it broadcasts task-adaptive", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 350, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 506, + 363 + ], + "score": 1.0, + "content": "parameters, due to high sparsity of the parameters. Figure 5 (a) shows the accuracy as a function of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 360, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 282, + 375 + ], + "score": 1.0, + "content": "C2S cost according to a transmission of top-", + "type": "text" + }, + { + "bbox": [ + 283, + 361, + 298, + 372 + ], + "score": 0.89, + "content": "\\kappa \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 360, + 505, + 375 + ], + "score": 1.0, + "content": "informative parameters. Since FedWeIT selectively", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 385 + ], + "score": 1.0, + "content": "utilizes task-specific parameters learned from other clients, it results in superior performance over", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 383, + 410, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 410, + 396 + ], + "score": 1.0, + "content": "APD-baselines especially with sparse communication of model parameters.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 401, + 505, + 532 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 414 + ], + "score": 1.0, + "content": "Catastrophic forgetting Further, we examine how the performance of the past tasks change during", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "continual learning, to see the severity of catastrophic forgetting with each method. Figure 6 Left", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 420, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 104, + 420, + 349, + 436 + ], + "score": 1.0, + "content": "shows the performance of FedWeIT and FCL baselines on the", + "type": "text" + }, + { + "bbox": [ + 350, + 422, + 364, + 433 + ], + "score": 0.88, + "content": "6 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 420, + 381, + 436 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 381, + 422, + 396, + 433 + ], + "score": 0.88, + "content": "8 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 420, + 506, + 436 + ], + "score": 1.0, + "content": "tasks, at the end of training", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 432, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 104, + 432, + 506, + 448 + ], + "score": 1.0, + "content": "for later tasks. We observe that naive FCL baselines suffer from more severe catastrophic forgetting", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 443, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 104, + 443, + 505, + 458 + ], + "score": 1.0, + "content": "than local continual learning with EWC because of the inter-client interference, where the knowledge", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "of irrelevant tasks from other clients overwrites the knowledge of the past tasks. Contrarily, our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 467, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 506, + 479 + ], + "score": 1.0, + "content": "model shows no sign of catastrophic forgetting. This is mainly due to the selective utilization of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "the prior knowledge learned from other clients through the global/task-adaptive parameters, which", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "score": 1.0, + "content": "allows it to effectively alleviate inter-client interference. FedProx-APD also does not suffer from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 500, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 512 + ], + "score": 1.0, + "content": "catastrophic forgetting, but they yield inferior performance due to ineffective knowledge transfer. We", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 510, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 524 + ], + "score": 1.0, + "content": "also report Backward Transfer (BWT), which is a measure on catastrophic forgetting for all models", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 521, + 457, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 457, + 534 + ], + "score": 1.0, + "content": "(more positive the better). We provide the details of BWT in the Section B in appendix.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 539, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 504, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 400, + 551 + ], + "score": 1.0, + "content": "Weighted inter-client knowledge transfer By analyzing the attention", + "type": "text" + }, + { + "bbox": [ + 400, + 541, + 409, + 549 + ], + "score": 0.71, + "content": "_ \\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 539, + 504, + 551 + ], + "score": 1.0, + "content": "in Eq. (1), we examine", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 550, + 504, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 504, + 561 + ], + "score": 1.0, + "content": "which task parameters from other clients each client selected. Figure 5 (b), shows example of the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 265, + 573 + ], + "score": 1.0, + "content": "attention weights that are learned for the", + "type": "text" + }, + { + "bbox": [ + 265, + 560, + 280, + 571 + ], + "score": 0.88, + "content": "0 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 560, + 357, + 573 + ], + "score": 1.0, + "content": "split of MNIST and", + "type": "text" + }, + { + "bbox": [ + 358, + 560, + 377, + 571 + ], + "score": 0.89, + "content": "1 0 ^ { \\hat { t h } }", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 560, + 505, + 573 + ], + "score": 1.0, + "content": "split of CIFAR-100. We observe", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "that large attentions are allocated to the task parameters from the same dataset (CIFAR-100 utilizes", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "parameters from CIFAR-100 tasks with disjoint classes), or from a similar dataset (MNIST utilizes", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 593, + 506, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 606 + ], + "score": 1.0, + "content": "parameters from Traffic Sign and SVHN). This shows that FedWeIT effectively selects beneficial", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "parameters to maximize inter-client knowledge transfer. This is an impressive result since it does not", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 616, + 312, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 312, + 627 + ], + "score": 1.0, + "content": "know which datasets the parameters are trained on.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5 + }, + { + "type": "title", + "bbox": [ + 108, + 642, + 195, + 655 + ], + "lines": [ + { + "bbox": [ + 105, + 641, + 197, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 197, + 658 + ], + "score": 1.0, + "content": "5 CONCLUSION", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We tackled a novel problem of federated continual learning, whose goal is to continuously learn local", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "models at each client while allowing it to utilize indirect experience (task knowledge) from other", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "score": 1.0, + "content": "clients. This poses new challenges such as inter-client knowledge transfer and prevention of inter-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "client interference between irrelevant tasks. To tackle these challenges, we additively decomposed", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 709, + 507, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 507, + 722 + ], + "score": 1.0, + "content": "the model parameters at each client into the global parameters that are shared across all clients,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "and sparse local task-adaptive parameters that are specific to each task. Further, we allowed each", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 306, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 83, + 488, + 170 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 118, + 83, + 488, + 170 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 118, + 83, + 488, + 170 + ], + "spans": [ + { + "bbox": [ + 118, + 83, + 488, + 170 + ], + "score": 0.95, + "type": "image", + "image_path": "42b7c39389253e8c6b14218f62c8e3c835b18e61b7312d3849dc060008c81811.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 118, + 83, + 488, + 112.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 118, + 112.0, + 488, + 141.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 118, + 141.0, + 488, + 170.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 173, + 504, + 204 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 172, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 172, + 506, + 185 + ], + "score": 1.0, + "content": "Figure 5: (a) Accuracy over C2S cost. We report the relative communication cost to the original network. All", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 183, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 505, + 194 + ], + "score": 1.0, + "content": "results are averaged over the 5 clients. (b) Inter-client transfer for NonIID-50. We compare the scale of the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 193, + 503, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 193, + 503, + 204 + ], + "score": 1.0, + "content": "attentions at first FC layer which gives the weights on transferred task-adaptive parameters from other clients.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 108, + 207, + 489, + 284 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 207, + 489, + 284 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 207, + 489, + 284 + ], + "spans": [ + { + "bbox": [ + 108, + 207, + 489, + 284 + ], + "score": 0.951, + "type": "image", + "image_path": "b48b317b40e852b5ce1c0fd7677219d4191234672dc950bc7d939cfbf41b0cf8.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 108, + 207, + 489, + 232.66666666666666 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 108, + 232.66666666666666, + 489, + 258.3333333333333 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 108, + 258.3333333333333, + 489, + 284.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 286, + 504, + 318 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 286, + 506, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 506, + 297 + ], + "score": 1.0, + "content": "Figure 6: Left: Performance of FedWeIT with different scale of hyperparameters on Non-iid 50. Middle:", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 312, + 309 + ], + "score": 1.0, + "content": "Performance comparison about current task adaptation at", + "type": "text" + }, + { + "bbox": [ + 312, + 296, + 326, + 307 + ], + "score": 0.88, + "content": "6 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 295, + 342, + 309 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 342, + 296, + 356, + 307 + ], + "score": 0.88, + "content": "8 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 295, + 506, + 309 + ], + "score": 1.0, + "content": "tasks during federated continual learning", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 307, + 384, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 384, + 318 + ], + "score": 1.0, + "content": "on NonIID-50. Right: Forgetting measure using Backward Transfer (BWT).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 327, + 505, + 394 + ], + "lines": [], + "index": 14.5, + "bbox_fs": [ + 105, + 326, + 506, + 396 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 401, + 505, + 532 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 414 + ], + "score": 1.0, + "content": "Catastrophic forgetting Further, we examine how the performance of the past tasks change during", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "continual learning, to see the severity of catastrophic forgetting with each method. Figure 6 Left", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 420, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 104, + 420, + 349, + 436 + ], + "score": 1.0, + "content": "shows the performance of FedWeIT and FCL baselines on the", + "type": "text" + }, + { + "bbox": [ + 350, + 422, + 364, + 433 + ], + "score": 0.88, + "content": "6 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 420, + 381, + 436 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 381, + 422, + 396, + 433 + ], + "score": 0.88, + "content": "8 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 420, + 506, + 436 + ], + "score": 1.0, + "content": "tasks, at the end of training", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 432, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 104, + 432, + 506, + 448 + ], + "score": 1.0, + "content": "for later tasks. We observe that naive FCL baselines suffer from more severe catastrophic forgetting", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 443, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 104, + 443, + 505, + 458 + ], + "score": 1.0, + "content": "than local continual learning with EWC because of the inter-client interference, where the knowledge", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 468 + ], + "score": 1.0, + "content": "of irrelevant tasks from other clients overwrites the knowledge of the past tasks. Contrarily, our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 467, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 506, + 479 + ], + "score": 1.0, + "content": "model shows no sign of catastrophic forgetting. This is mainly due to the selective utilization of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "the prior knowledge learned from other clients through the global/task-adaptive parameters, which", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 501 + ], + "score": 1.0, + "content": "allows it to effectively alleviate inter-client interference. FedProx-APD also does not suffer from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 500, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 512 + ], + "score": 1.0, + "content": "catastrophic forgetting, but they yield inferior performance due to ineffective knowledge transfer. We", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 510, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 524 + ], + "score": 1.0, + "content": "also report Backward Transfer (BWT), which is a measure on catastrophic forgetting for all models", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 521, + 457, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 457, + 534 + ], + "score": 1.0, + "content": "(more positive the better). We provide the details of BWT in the Section B in appendix.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 23.5, + "bbox_fs": [ + 104, + 400, + 506, + 534 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 539, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 539, + 504, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 539, + 400, + 551 + ], + "score": 1.0, + "content": "Weighted inter-client knowledge transfer By analyzing the attention", + "type": "text" + }, + { + "bbox": [ + 400, + 541, + 409, + 549 + ], + "score": 0.71, + "content": "_ \\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 539, + 504, + 551 + ], + "score": 1.0, + "content": "in Eq. (1), we examine", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 550, + 504, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 504, + 561 + ], + "score": 1.0, + "content": "which task parameters from other clients each client selected. Figure 5 (b), shows example of the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 265, + 573 + ], + "score": 1.0, + "content": "attention weights that are learned for the", + "type": "text" + }, + { + "bbox": [ + 265, + 560, + 280, + 571 + ], + "score": 0.88, + "content": "0 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 560, + 357, + 573 + ], + "score": 1.0, + "content": "split of MNIST and", + "type": "text" + }, + { + "bbox": [ + 358, + 560, + 377, + 571 + ], + "score": 0.89, + "content": "1 0 ^ { \\hat { t h } }", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 560, + 505, + 573 + ], + "score": 1.0, + "content": "split of CIFAR-100. 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This shows that FedWeIT effectively selects beneficial", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 617 + ], + "score": 1.0, + "content": "parameters to maximize inter-client knowledge transfer. This is an impressive result since it does not", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 616, + 312, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 312, + 627 + ], + "score": 1.0, + "content": "know which datasets the parameters are trained on.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 539, + 506, + 627 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 642, + 195, + 655 + ], + "lines": [ + { + "bbox": [ + 105, + 641, + 197, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 197, + 658 + ], + "score": 1.0, + "content": "5 CONCLUSION", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We tackled a novel problem of federated continual learning, whose goal is to continuously learn local", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "models at each client while allowing it to utilize indirect experience (task knowledge) from other", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "score": 1.0, + "content": "clients. 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Further, we allowed each", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "model to selectively update the global task-shared parameters and selectively utilize the task-adaptive", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 107 + ], + "score": 1.0, + "content": "parameters from other clients. The experimental validation of our model under various task similarity", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 117 + ], + "score": 1.0, + "content": "across clients, against existing federated learning and continual learning baselines shows that our", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "model obtains significantly outperforms baselines with reduced communication cost. 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The experimental validation of our model under various task similarity", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 117 + ], + "score": 1.0, + "content": "across clients, against existing federated learning and continual learning baselines shows that our", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "model obtains significantly outperforms baselines with reduced communication cost. 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NonIID-50
Dataset#Classes#Tasks#Classes (Task)#Train Set#Valid Set#Test Set
CIFAR-100Face Scrub10015536,75010,5005,250
10016513,8593,9591,979
Traffic SignsSVHNMNIST4395 (3)32,1709,1914,595
102561,81017,6608,830
102542,70012,2006,100
CIFAR-10Not MNIST102536,75010,5005,250
102511,3393,2391,619
Fashion MNIST102542,70012,2006,100
Total29350248278,07839,72379,449
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Overlapped-CIFAR-100
MethodsAccuracyModel SizeC2S/S2C CostEpochs /Round
FedWeIT55.16 ± 0.190.075 GB0.37/1.07 GB1
FedWeIT55.18 ± 0.080.077GB0.19/0.53GB2
FedWeIT53.73 ± 0.440.083 GB0.08/0.22 GB5
FedWeIT53.22 ±0.140.088 GB0.02 /0.07 GB20
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Overlapped-CIFAR-100 with 20 tasks
MethodsAccuracyM SizeC2S/S2C Cost
FedProx29.76 ± 0.390.061GB1.22/1.22 GB
FedProx-EWC27.80 ± 0.580.061 GB1.22 / 1.22 GB
FedProx-APD43.80 ±0.760.093 GB1.22 / 1.22 GB
FedWeIT46.78 ±0.1470.092 GB0.3771.07 GB
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NonIID-50
Dataset#Classes#Tasks#Classes (Task)#Train Set#Valid Set#Test Set
CIFAR-100Face Scrub10015536,75010,5005,250
10016513,8593,9591,979
Traffic SignsSVHNMNIST4395 (3)32,1709,1914,595
102561,81017,6608,830
102542,70012,2006,100
CIFAR-10Not MNIST102536,75010,5005,250
102511,3393,2391,619
Fashion MNIST102542,70012,2006,100
Total29350248278,07839,72379,449
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Overlapped-CIFAR-100
MethodsAccuracyModel SizeC2S/S2C CostEpochs /Round
FedWeIT55.16 ± 0.190.075 GB0.37/1.07 GB1
FedWeIT55.18 ± 0.080.077GB0.19/0.53GB2
FedWeIT53.73 ± 0.440.083 GB0.08/0.22 GB5
FedWeIT53.22 ±0.140.088 GB0.02 /0.07 GB20
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Red arrows at each point describes the standard deviation of the performance.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5 + } + ], + "index": 12.0 + }, + { + "type": "title", + "bbox": [ + 107, + 453, + 329, + 466 + ], + "lines": [ + { + "bbox": [ + 106, + 452, + 330, + 468 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 330, + 468 + ], + "score": 1.0, + "content": "C ADDITIONAL EXPERIMENTAL RESULTS", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 481, + 504, + 503 + ], + "lines": [ + { + "bbox": [ + 105, + 480, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 505, + 495 + ], + "score": 1.0, + "content": "We further include a quantitative analysis about the communication round frequency and additional", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 492, + 306, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 306, + 504 + ], + "score": 1.0, + "content": "experimental results across the number of clients.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 480, + 505, + 504 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 522, + 333, + 533 + ], + "lines": [ + { + "bbox": [ + 105, + 520, + 335, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 335, + 536 + ], + "score": 1.0, + "content": "C.1 EFFECT OF THE COMMUNICATION FREQUENCY", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 272, + 644 + ], + "lines": [ + { + "bbox": [ + 106, + 545, + 272, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 272, + 557 + ], + "score": 1.0, + "content": "We provide an analysis on the effect of", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 555, + 273, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 273, + 569 + ], + "score": 1.0, + "content": "the communication frequency by compar-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 567, + 273, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 273, + 579 + ], + "score": 1.0, + "content": "ing the performance of the model, mea-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 579, + 272, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 579, + 272, + 590 + ], + "score": 1.0, + "content": "sured by the number of training epochs", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 590, + 272, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 590, + 272, + 600 + ], + "score": 1.0, + "content": "per communication round. 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Figure 7 shows", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 621, + 274, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 274, + 633 + ], + "score": 1.0, + "content": "the performance of our FedWeIT variants.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 632, + 273, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 273, + 645 + ], + "score": 1.0, + "content": "As clients frequently update the model pa-", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 545, + 274, + 645 + ] + }, + { + "type": "table", + "bbox": [ + 279, + 574, + 512, + 641 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 278, + 543, + 505, + 573 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 279, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 279, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "Table 5: Experimental results on the Overlapped-CIFAR-100", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 279, + 552, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 279, + 552, + 506, + 564 + ], + "score": 1.0, + "content": "dataset with 20 tasks. All results are the mean accuracies over", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 279, + 563, + 433, + 574 + ], + "spans": [ + { + "bbox": [ + 279, + 563, + 433, + 574 + ], + "score": 1.0, + "content": "5 clients, averaged over 3 individual trials.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31 + }, + { + "type": "table_body", + "bbox": [ + 279, + 574, + 512, + 641 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 279, + 574, + 512, + 641 + ], + "spans": [ + { + "bbox": [ + 279, + 574, + 512, + 641 + ], + "score": 0.972, + "html": "
Overlapped-CIFAR-100 with 20 tasks
MethodsAccuracyM SizeC2S/S2C Cost
FedProx29.76 ± 0.390.061GB1.22/1.22 GB
FedProx-EWC27.80 ± 0.580.061 GB1.22 / 1.22 GB
FedProx-APD43.80 ±0.760.093 GB1.22 / 1.22 GB
FedWeIT46.78 ±0.1470.092 GB0.3771.07 GB
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However, it requires much", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 505, + 689 + ], + "score": 1.0, + "content": "heavier communication costs than the model with sparser communication. For example, the model", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 504, + 699 + ], + "score": 1.0, + "content": "trained for 1 epochs at each round may need to about 16.9 times larger entire communication cost than", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "the model trained for 20 epochs at each round. 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Performance change over the increasing number of tasks for all tasks except the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 141, + 498 + ], + "score": 1.0, + "content": "last task", + "type": "text" + }, + { + "bbox": [ + 141, + 487, + 154, + 497 + ], + "score": 0.83, + "content": "1 ^ { s t }", + "type": "inline_equation" + }, + { + "bbox": [ + 154, + 486, + 164, + 498 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 164, + 486, + 177, + 497 + ], + "score": 0.85, + "content": "9 ^ { t h }", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 486, + 505, + 498 + ], + "score": 1.0, + "content": ") during federated continual learning on NonIID-50. We observe that our method does not", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 496, + 252, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 252, + 509 + ], + "score": 1.0, + "content": "suffer from task forgetting on any tasks.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "title", + "bbox": [ + 107, + 524, + 324, + 534 + ], + "lines": [ + { + "bbox": [ + 106, + 523, + 325, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 523, + 325, + 536 + ], + "score": 1.0, + "content": "C.2 ABLATION STUDY FOR MODEL COMPONENTS", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 545, + 506, + 611 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 506, + 556 + ], + "score": 1.0, + "content": "We perform an ablation study to analyze the role of each component of our FedWeIT. We", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 556, + 507, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 507, + 568 + ], + "score": 1.0, + "content": "compare the performance of four different variations of our model. w/o B communica-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 567, + 507, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 406, + 579 + ], + "score": 1.0, + "content": "tion describes the model that does not transfer the base parameter", + "type": "text" + }, + { + "bbox": [ + 406, + 567, + 415, + 577 + ], + "score": 0.27, + "content": "\\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 416, + 567, + 507, + 579 + ], + "score": 1.0, + "content": "and only communi-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "score": 1.0, + "content": "cates task-adaptive ones. w/o A communication is the model that does not communicate", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 588, + 507, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 507, + 601 + ], + "score": 1.0, + "content": "task-adaptive parameters. w/o A is the model which trains the model only with sparse trans-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 600, + 506, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 612 + ], + "score": 1.0, + "content": "mission of local base parameter, and w/o m is the model without the sparse vector mask.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 107, + 612, + 279, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 610, + 280, + 622 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 280, + 622 + ], + "score": 1.0, + "content": "As shown in Table 6, without communi-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 622, + 280, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 135, + 633 + ], + "score": 1.0, + "content": "cating", + "type": "text" + }, + { + "bbox": [ + 135, + 622, + 144, + 632 + ], + "score": 0.26, + "content": "\\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 622, + 280, + 633 + ], + "score": 1.0, + "content": "or A, the model yields signifi-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 633, + 279, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 279, + 645 + ], + "score": 1.0, + "content": "cantly lower performance compared to the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 643, + 280, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 280, + 655 + ], + "score": 1.0, + "content": "full model since they do not benefit from", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 655, + 279, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 279, + 667 + ], + "score": 1.0, + "content": "inter-client knowledge transfer. The model", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 666, + 279, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 279, + 677 + ], + "score": 1.0, + "content": "w/o A obtains very low performance due", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 677, + 280, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 280, + 689 + ], + "score": 1.0, + "content": "to catastrophic forgetting, and the model", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 688, + 281, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 281, + 700 + ], + "score": 1.0, + "content": "w/o sparse mask m achieves lower accu-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 699, + 280, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 280, + 711 + ], + "score": 1.0, + "content": "racy with larger capacity and cost, which", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 709, + 279, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 279, + 722 + ], + "score": 1.0, + "content": "demonstrates the importance of performing", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 720, + 199, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 199, + 732 + ], + "score": 1.0, + "content": "selective transmission.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 25 + }, + { + "type": "table", + "bbox": [ + 286, + 651, + 502, + 727 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 286, + 619, + 505, + 650 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 285, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 285, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "Table 6: Ablation studies to analyze the effectiveness of pa-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 285, + 630, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 285, + 630, + 505, + 641 + ], + "score": 1.0, + "content": "rameter decomposition on WeIT. All experiments performed", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 286, + 640, + 369, + 650 + ], + "spans": [ + { + "bbox": [ + 286, + 640, + 369, + 650 + ], + "score": 1.0, + "content": "on NonIID-50 dataset.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "table_body", + "bbox": [ + 286, + 651, + 502, + 727 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 286, + 651, + 502, + 727 + ], + "spans": [ + { + "bbox": [ + 286, + 651, + 502, + 727 + ], + "score": 0.981, + "html": "
NonIID-50
MethodsAcc.M SizeC2S/S2C Cost
FedWeIT w/o B comm.84.11% 77.88%0.078 GB 0.070GB0.37/1.07 GB 0.0170.01 GB
w/o A comm.79.21%0.079 GB0.37 /1.04 GB
w/o A w/0 m65.66% 78.71%0.061 GB 0.087 GB0.37 / 1.04 GB 1.23 / 1.25 GB
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NonIID-50
MethodsAcc.M SizeC2S/S2C Cost
FedWeIT w/o B comm.84.11% 77.88%0.078 GB 0.070GB0.37/1.07 GB 0.0170.01 GB
w/o A comm.79.21%0.079 GB0.37 /1.04 GB
w/o A w/0 m65.66% 78.71%0.061 GB 0.087 GB0.37 / 1.04 GB 1.23 / 1.25 GB
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NonIID-50
FedWeITAccuracy (%)
Synchronous84.11 ± 0.27
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We provide the detailed algorithm in Algorithm 3. In Table 7 and Figure 10, we", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 281, + 505, + 294 + ], + "score": 1.0, + "content": "plot the average test accuracy over all tasks during synchronous / asynchronous federated continual", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 292, + 506, + 305 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 506, + 305 + ], + "score": 1.0, + "content": "learning. As shown in Figure 10, different tasks across clients at the same timestep require the same", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "score": 1.0, + "content": "number of training rounds, receiving new tasks and task-adaptive parameters from the knowledge", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 315, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 315, + 506, + 326 + ], + "score": 1.0, + "content": "base simultaneously with the synchronous FedWeIT. 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The results in Table 7 shows that the performance of asynchronous FedWeIT", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 348, + 322, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 322, + 359 + ], + "score": 1.0, + "content": "is almost similar to that of the synchronous FedWeIT.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9 + } + ], + "page_idx": 15, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 306, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 113, + 86, + 500, + 208 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 113, + 86, + 500, + 208 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 113, + 86, + 500, + 208 + ], + "spans": [ + { + "bbox": [ + 113, + 86, + 500, + 208 + ], + "score": 0.949, + "type": "image", + "image_path": "345bee7f94e9da58f53b79209b11767056060b036018900f29baf9c0068f0802.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 113, + 86, + 500, + 126.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 113, + 126.66666666666666, + 500, + 167.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 113, + 167.33333333333331, + 500, + 207.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 229, + 504, + 250 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "Figure 10: FedWeIT with asynchronous federated continual learning on Non-iid 50 dataset. 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Algorithm1Federated Weighted Inter-client Transfer
input Dataset {D(1:t)yC }=1,and Global Parameter 0G output {Bc, m(1:t), (1:t) A1:t αc
c=1 1: InitializeBc to 0g for all c ∈C= {1,., C}
2:for task t = 1,2,...do 3: for round r=1,2,..,R do
4: (t,r) and A(t-1,R) of client Cc to server
B Compute0 (t,r) 5:
j Σcec and {A(e-1,R)}jec to client c
6: Distribute 0() 7: Minimize Eq.(2) for solving each local CL problems
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ResNet-18
MethodsAcc.M Size
Local-APDFedProx-APDFedWeIT92.44 %92.89%94.86 %1.86 GB2.05GB1.84 GB
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NonIID-50Dataset (F=1.0, R=20)Overlapped CIFAR-100 (F=1.0,R=20)
MethodsAccuracyModel SizeC2S/S2C CostAccuracyModel SizeC2S/S2C Cost
STL85.78 ±0.170.610GBN/A57.15 ±0.070.610 GBN/A
Local-EWC74.30±0.080.061GB- -N/A44.26±0.430.061GBN7A
Local-APD81.42 ± 0.720.090 GBN/A50.82 ± 0.330.073 GBN/A
FedProx63.691.750.061GB1.22/1.22GB33.83±0.480.061GB1.22/1.22GB
Scaffold30.84 ± 1.410.061 GB2.44 /2.44 GB22.80 ±0.470.061 GB2.44/2.44 GB
FedCurv72.39 ±0.320.061GB1.22/1.22 GB40.36 ±0.440.061GB1.22/1.22 GB
FedProx-EWC68.18 ± 0.580.061 GB1.22/1.22 GB41.91 ± 0.470.061 GB1.22/1.22 GB
FedProx-APD81.20 ± 1.240.079 GB1.22/1.22 GB52.20 ± 0.410.075 GB1.22/1.22 GB
FedWeIT84.11 ± 0.270.078 GB0.37/1.07 GB55.16 ± 0.190.075 GB0.37/1.07 GB
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100 clients (F=0.05,R=20,1,000 tasks in total)
MethodsAccuracyModel SizeC2S/S2C Cost
STL32.96 ±0.2312.20 GBN/A
Local-APD37.50 ±0.174.01GBN/A
FedProx24.11 ±0.441.22 GB1.2271.22 GB
FedCurv29.11 ± 0.201.22 GB1.22 /1.22 GB
FedCurv-EWC29.72 ± 0.201.22 GB1.22 /1.22 GB
FedWeIT39.58 ± 0.274.03 GB0.38 /1.10 GB
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FC1800N/A1×1×800
FC2500N/A1×1× 500
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NonIID-50
Dataset#Classes#Tasks#Classes (Task)#Train Set#Valid Set#Test Set
CIFAR-100Face Scrub10015536,75010,5005,250
10016513,8593,9591,979
Traffic SignsSVHNMNIST4395 (3)32,1709,1914,595
102561,81017,6608,830
102542,70012,2006,100
CIFAR-10Not MNIST102536,75010,5005,250
102511,3393,2391,619
Fashion MNIST102542,70012,2006,100
Total29350248278,07839,72379,449
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Overlapped-CIFAR-100 with 20 tasks
MethodsAccuracyM SizeC2S/S2C Cost
FedProx29.76 ± 0.390.061GB1.22/1.22 GB
FedProx-EWC27.80 ± 0.580.061 GB1.22 / 1.22 GB
FedProx-APD43.80 ±0.760.093 GB1.22 / 1.22 GB
FedWeIT46.78 ±0.1470.092 GB0.3771.07 GB
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Overlapped-CIFAR-100
MethodsAccuracyModel SizeC2S/S2C CostEpochs /Round
FedWeIT55.16 ± 0.190.075 GB0.37/1.07 GB1
FedWeIT55.18 ± 0.080.077GB0.19/0.53GB2
FedWeIT53.73 ± 0.440.083 GB0.08/0.22 GB5
FedWeIT53.22 ±0.140.088 GB0.02 /0.07 GB20
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NonIID-50
MethodsAcc.M SizeC2S/S2C Cost
FedWeIT w/o B comm.84.11% 77.88%0.078 GB 0.070GB0.37/1.07 GB 0.0170.01 GB
w/o A comm.79.21%0.079 GB0.37 /1.04 GB
w/o A w/0 m65.66% 78.71%0.061 GB 0.087 GB0.37 / 1.04 GB 1.23 / 1.25 GB
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NonIID-50
FedWeITAccuracy (%)
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2200 + } + } +] \ No newline at end of file diff --git a/parse/train/Syx7A3NFvH/Syx7A3NFvH.md b/parse/train/Syx7A3NFvH/Syx7A3NFvH.md new file mode 100644 index 0000000000000000000000000000000000000000..8eb671e10e94a0a15251bdd094447c5b24bf8001 --- /dev/null +++ b/parse/train/Syx7A3NFvH/Syx7A3NFvH.md @@ -0,0 +1,393 @@ +# MULTI-AGENT REINFORCEMENT LEARNING FOR NETWORKED SYSTEM CONTROL + +Tianshu Chu +Uhana Inc. +Palo Alto, CA 94304, USA +cts198859@hotmail.com +Sandeep Chinchali & Sachin Katti +Stanford University +Stanford, CA 94305, USA +{csandeep,skatti}@stanford.edu + +# ABSTRACT + +This paper considers multi-agent reinforcement learning (MARL) in networked system control. Specifically, each agent learns a decentralized control policy based on local observations and messages from connected neighbors. We formulate such a networked MARL (NMARL) problem as a spatiotemporal Markov decision process and introduce a spatial discount factor to stabilize the training of each local agent. Further, we propose a new differentiable communication protocol, called NeurComm, to reduce information loss and non-stationarity in NMARL. Based on experiments in realistic NMARL scenarios of adaptive traffic signal control and cooperative adaptive cruise control, an appropriate spatial discount factor effectively enhances the learning curves of non-communicative MARL algorithms, while NeurComm outperforms existing communication protocols in both learning efficiency and control performance. + +# 1 INTRODUCTION + +Reinforcement learning (RL), formulated as a Markov decision process (MDP), is a promising data-driven approach for learning adaptive control policies (Sutton & Barto, 1998). Recent advances in deep neural networks (DNNs) further enhance its learning capacity on complex tasks. Successful algorithms include deep Q-network (DQN) (Mnih et al., 2015), deep deterministic policy gradient (DDPG) (Lillicrap et al., 2015), and advantage actor critic (A2C) (Mnih et al., 2016). However, RL is not scalable in many real-world control problems. This scalability issue is addressed in multi-agent RL (MARL), where each agent learns its individual policy from only local observations. However, MARL introduces new challenges in model training and execution, due to non-stationarity and partial observability in a decentralized MDP from the viewpoint of each agent. To address these challenges, various learning methods and communication protocols are proposed to stabilize training and improve observability. + +This paper considers networked MARL (NMARL) in the context of networked system control (NSC), where agents are connected via a communication network for a cooperative control objective. Each agent performs decentralized control based on its local observations and messages from connected neighbors. NSC is extensively studied and widely applied. Examples include connected vehicle control (Jin & Orosz, 2014), traffic signal control (Chu et al., 2019), distributed sensing (Xu et al., 2018), and networked storage operation (Qin et al., 2016). We expect an increasing trend of NMARL based controllers in the near future, after the development of advanced communication technologies such as 5G and Internet-of-Things. + +Recent works studied decentralized NMARL under assumptions of global observations and local rewards (Zhang et al., 2018; Qu et al., 2019), which are reasonable in multi-agent gaming but not suitable in NSC. First, the control infrastructures are distributed in a wide region, so collecting global observations in execution increases communication delay and failure rate, and hurts the robustness. Second, online learning is not common due to safety and efficiency concerns. Rather, each model is trained offline and tested extensively before field deployment. In online execution, the model only runs forward propagation, and its performance is constantly monitored for triggering re-training. To reflect these practical constraints in NSC, we assume 1) each agent is connected to a limited number of neighbors and communication is restricted to its neighborhood, and 2) training is offline and global information is available in rollout training minibatches, despite a decentralized training process. + +The contributions of this paper are three-fold. First, we formulate NMARL under the aforementioned NSC assumptions as a decentralized spatiotemporal MDP, and introduce a spatial discount factor to stabilize training, especially for non-communicative algorithms. Second, we propose a new neural communication protocol, called NeurComm, to adaptively share information on both system states and agent behaviors. Third, we design and simulate realistic NMARL environments to evaluate and compare our approaches against recent MARL baselines. + +# 2 RELATED WORK + +MARL works can be classified into four groups based on their communication methods. The first group is non-communicative and focuses on stabilizing training with advanced value estimation methods. In MADDPG, each action-value is estimated by a centralized critic based on global observations and actions (or inferred actions) (Lowe et al., 2017). COMA extends the same idea to A2C and estimates each advantage using a centralized critic and a counterfactual baseline (Foerster et al., 2018). In Dec-HDRQN (Omidshafiei et al., 2017) and PS-TRPO (Gupta et al., 2017), the centralized critic takes local observations, but the parameters are shared globally. In the NMARL work of Zhang et al. (2018), the critic is fully decentralized but each takes global observations and performs consensus updates. In this paper, we empirically confirm that a spatial discount factor helps stabilize the training of non-communicative algorithms under neighborhood observation. + +The second group considers heuristic communication protocols or direct information sharing. Foerster et al. (2017) shows performance gains with directly-shared low dimensional policy fingerprints from other agents. Similarly, mean field MARL takes the average of neighbor policies for informed action-value estimation (Yang et al., 2018). The major disadvantage of this group is that, unlike NeurComm, the communication is not explicitly designed for performance optimization, which may cause inefficient and redundant communications in execution. + +The third group proposes learnable communication protocols. In DIAL, the message is generated together with action-value estimation by each DQN agent, then it is encoded and summed with other input signals at the receiver side (Foerster et al., 2016). CommNet is a more general communication protocol, but it calculates the mean of all messages instead of encoding them (Sukhbaatar et al., 2016). Both works, especially CommNet, incur an information loss due to aggregation on input signals. Another collection of works focuses on communications in strategy games. In BiCNet (Peng et al., 2017), a bi-directional RNN is used to enable flat communication among agents, while in MasterSlave (Kong et al., 2017), two-way message passing is utilized in a hierarchical RNN architecture of master and slave agents. In contrast to existing protocols, NeurComm 1) encodes and concatenates signals, instead of aggregating them, to minimize information loss, and 2) includes policy fingerprints in communication to reduce non-stationarity. + +The fourth group focuses on communication attentions to selectively send messages. ATOC (Jiang & Lu, 2018) learns a soft attention which allocates a communication probability to each other agent, while IC3Net (Singh et al., 2018) learns a hard binary attention which decides communicating or not. These works are especially useful when each agent has to prioritize the communication targets. NMARL is less likely the case since the communication range is restricted to small neighborhoods. + +# 3 SPATIOTEMPORAL RL + +This section formulates the NMARL problem as a decentralized spatiotemporal MDP, and introduces the spatial discount factor to reduce its learning difficulty. To simplify the notation, we assume the true system state is observable, and use “state” and “observation” interchangeably. This does not affect the validity of proposed methods in practice. To save space, all proofs are deferred to A. + +# 3.1 NETWORKED MARL + +The networked system is represented by a graph $G ( \nu , \mathcal { E } )$ where $i \in \mathcal V$ is each agent and $i j \in \mathcal { E }$ is each communication link. The corresponding MDP is characterized as $( G , \{ S _ { i } , A _ { i } \} _ { i \in \mathcal { V } } , p , r )$ where $s _ { i }$ and $A _ { i }$ are the local state space and action space of agent $i$ . Let $\boldsymbol { S } : = \times _ { i \in \mathcal { V } } \boldsymbol { S } _ { i }$ and $\mathcal { A } : = \times _ { i \in \mathcal { V } } \mathcal { A } _ { i }$ be the global state space and action space, MDP transitions follow a stationary probability distribution $p : \mathcal { S } \times \mathcal { A } \times \mathcal { S } [ 0 , 1 ]$ , and global step rewards be denoted by $r : S \times \mathcal { A } \mathbb { R }$ . In a multi-agent nt at $i$ follime ws a decentralized policy . The MDP objective is to $\pi _ { i } : S _ { i } \times \mathcal { A } _ { i } [ 0 , 1 ]$ te onis $a _ { i , t } \sim \pi _ { i } ( \cdot | s _ { i , t } )$ $t$ $\mathbb { E } [ R _ { 0 } ^ { \pi } ]$ $\begin{array} { r } { R _ { t } ^ { \pi } = \sum _ { \tau = t } ^ { T } \gamma ^ { \tau - t } r _ { \tau } } \end{array}$ the long-term global return with discount factor . Here the expectation is taken over the global policy $\pi : \mathcal { S } \times \mathcal { A } [ 0 , 1 ]$ , the initial distribution $s _ { t } \sim \rho$ , and the transition $s _ { \tau + 1 } \sim p ( \cdot | s _ { \tau } , a _ { \tau } )$ , regarding the step reward $\dot { r _ { \tau } } = \dot { r } ( s _ { \tau } , a _ { \tau } )$ , $\forall \tau < T$ , and the terminal reward $r _ { T } = r _ { T } ( s _ { T } ) ^ { 2 }$ . The same system can be formulated as a centralized MDP. Defining $V ^ { \pi } ( s ) = \mathbb { E } [ R _ { t } ^ { \pi } | s _ { t } = s ]$ as the state-value function and $Q ^ { \pi } ( s , a ) = \mathbb { E } [ R _ { t } ^ { \pi } | s _ { t } = s , a _ { t } = a ]$ as the action-value function, we have $\begin{array} { r } { \mathbb { E } [ R _ { 0 } ^ { \pi } ] = \sum _ { s \in \cal S } \rho ( s ) V ^ { \pi } ( s ) } \end{array}$ $\begin{array} { r } { V ^ { \pi } ( s ) = \sum _ { a \in \mathcal { A } } \pi ( a | s ) Q ^ { \pi } ( s , a ) , } \end{array}$ , and the advantage function $A ^ { \pi } ( s , a ) = Q ^ { \pi } ( s , a ) - \mathbf { \bar { \psi } } V ^ { \pi } ( s )$ . + +MARL provides a scalable solution for controlling networked systems, but it introduces partial observability and non-stationarity in decentralized MDP of each agent, leading to inefficient and unstable learning performance. To see this, note $s _ { i , t } \in S _ { i } \subseteq S$ does not provide sufficient information for $\pi _ { i }$ . Even assuming $s _ { i , t } = s _ { t }$ , the transition $\begin{array} { r } { p _ { i } ( s _ { i , t + 1 } \vert s _ { i , t } , a _ { i , t } ) = \sum _ { a _ { - i , t } \in A _ { - i } } \pi _ { - i } ( a _ { - i , t } \vert s _ { t } ) \ . } \end{array}$ · $p ( s _ { t + 1 } | s _ { t } , a _ { i , t } , a _ { - i , t } )$ is non-stationary if the behavior policies of other agents $\pi _ { - i } : = \{ \pi _ { j } \} _ { j \in \mathcal { V } \backslash \{ i \} }$ are evolving over time. In this paper, we enforce practical constraints and only allow local observations and neighborhood communications, which makes MARL even more challenging. + +Definition 3.1 (Networked Multi-agent MDP with Neighborhood Communication). In a networked cooperative multi-agent MDP $( G , \{ S _ { i } , A _ { i } \} _ { i \in \mathcal { V } } , \{ \mathcal { M } _ { i j } \} _ { i j \in \mathcal { E } } , p , \{ r _ { i } \} _ { i \in \mathcal { V } } )$ with the message space $\mathcal { M }$ , the global reward is defined as $\begin{array} { r } { r = \frac { 1 } { | \mathcal { V } | } \sum _ { i \in \mathcal { V } } r _ { i } } \end{array}$ . All local rewards are shared globally, whereas the communication is limited to neighborhoods, that is, each agent $i$ observes $\tilde { s } _ { i , t } : = s _ { i , t } \cup m _ { \mathcal { N } _ { i } i , t }$ . Here $\mathcal { N } _ { i } : = \{ j \in \mathcal { V } | j i \in \mathcal { E } \}$ , $m _ { \mathcal { N } _ { i } i , t } : = \{ m _ { j i , t } \} _ { j \in \mathcal { N } _ { i } }$ , and each message $m _ { j i , t } \in \mathcal { M } _ { j i }$ is derived from all the available information at that neighbor. + +# 3.2 SPATIOTEMPORAL RL + +Definition 3.2 (Spatiotemporal MDP). We assume local transitions are independent of other agents given the neighboring agents, that is, + +$$ +p _ { i } ( s _ { i , t + 1 } | s _ { \mathcal { V } _ { i } , t } , a _ { i , t } ) = \sum _ { a _ { \mathcal { N } _ { i } , t } \in A _ { \mathcal { N } _ { i } } } \prod _ { j \in \mathcal { N } _ { i } } \pi _ { j } ( a _ { j , t } | \tilde { s } _ { j , t } ) \cdot p ( s _ { i , t + 1 } | s _ { \mathcal { V } _ { i } , t } , a _ { i , t } , a _ { \mathcal { N } _ { i } , t } ) , +$$ + +where $\mathcal { V } _ { i } : = \mathcal { N } _ { i } \cup \{ i \}$ is the closed neighborhood, and $p$ is abused to denote any stationary transition. Then from the viewpoint of each agent $i$ , Definition 3.1 is equivalent to a decentralized spatiotemporal MDP, characterized as $( S _ { i } , \mathcal { A } _ { i } , \{ \mathcal { M } _ { j i } \} _ { j \in \mathcal { N } _ { i } } , p _ { i } , \{ r _ { i } \} _ { i \in \mathcal { V } } )$ , by optimizing the discounted return + +$$ +R _ { i , t } ^ { \pi } = \sum _ { \tau = t } ^ { T } \gamma ^ { \tau - t } \left( \sum _ { j \in \mathcal { V } } \alpha ^ { d _ { i j } } r _ { j , t } \right) , +$$ + +where $0 \leq \alpha \leq 1$ is the spatial discount factor, and $d _ { i j }$ is distance between agents $i$ and $j$ + +The major assumption in Definition 3.2 is that the Markovian property holds both temporally and spatially, so that the next local state depends on the neighborhood states and policies only. This assumption is valid in most networked control systems such as traffic and wireless networks, as well as the power grid, where the impact of each agent is spread over the entire system via controlled flows, or chained local transitions. Note in NSC, each agent is connected to a limited number of neighbors (the degree of $G$ is low). So spatiotemporal MDP is decentralized during model execution, and it naturally extends properties of MDP. To reduce the learning difficulty of spatiotemporal MDP, a spatiotemporally discounted return is introduced in Eq. (2) to scale down reward signals further away (which are more difficult to fit using local information). When $\alpha 0$ , each agent performs local greedy control; when $\alpha 1$ , each agent performs global coordination and $R _ { i , t } ^ { \pi } = R _ { t } ^ { \pi } , \forall i \in \mathcal { V }$ . Further, we have $Q _ { i } ^ { \pi } ( s , a ) = Q _ { i } ^ { \pi } ( s , a \nu _ { i } ) = \mathbb { E } [ R _ { i , t } ^ { \pi } | s _ { t } = s , a \nu _ { i } , t = a \nu _ { i } ]$ and $\begin{array} { r } { V _ { i } ^ { \pi } ( s , a _ { - i } ) = V _ { i } ^ { \pi } ( s , a _ { \mathcal { N } _ { i } } ) = \sum _ { a _ { i } \in \mathcal { A } _ { i } } \pi _ { i } ( a _ { i } | \tilde { s } _ { i } ) Q _ { i } ^ { \pi } ( s , a _ { \mathcal { V } _ { i } } ) } \end{array}$ , since the immediate local reward of each agent is only affected by controls within its closed neighborhood. + +Now we assume each agent is A2C, with parametric models $\pi _ { \theta _ { i } } ( \tilde { s } _ { i } )$ and $V _ { \omega _ { i } } ( \tilde { s } _ { i } , a _ { \mathcal { N } _ { i } } )$ for fitting the optimal policy $\pi _ { i } ^ { * }$ and value function $V ^ { \pi _ { i } }$ . Note if $\tilde { s } _ { i }$ is able to provide global information through icascaded neighborhood communications, both $\pi _ { \theta _ { i } }$ and $V _ { \omega _ { i } }$ are able to fit return $R _ { i , t } ^ { \pi }$ . Also, global and future information, such as $R _ { i , \tau } ^ { \pi }$ and $\boldsymbol { a } _ { \mathcal { N } _ { i } , \tau }$ , are always available from each rollout minibatch in offline training. In contrast, only local information $\tilde { s } _ { i , t }$ is allowed in online execution of policy $\pi _ { \boldsymbol { \theta } _ { i } }$ . + +Proposition 3.1 (Spatiotemporal RL with A2C). Let $\{ \pi _ { \boldsymbol { \theta } _ { i } } \} _ { i \in \mathcal { V } }$ and $\{ V _ { \omega _ { i } } \} _ { i \in \mathcal { V } }$ be the decentralized actor-critics, and $\{ ( s _ { i , \tau } , m _ { \mathcal { N } _ { i } i , \tau } , a _ { i , \tau } , r _ { i , \tau } ) \} _ { i \in \mathcal { V } , \tau \in \mathcal { B } }$ be the on-policy minibatch from spatiotemporal MDPs under stationary policies $\{ \pi _ { \boldsymbol { \theta } _ { i } } \} _ { i \in \mathcal { V } }$ . Then each actor and critic are updated by losses + +$$ +\begin{array} { r l } & { \mathcal { L } ( \boldsymbol { \theta } _ { i } ) = \displaystyle \frac { 1 } { | \mathcal { B } | } \sum _ { \tau \in \mathcal { B } } \left( - \log \pi _ { \boldsymbol { \theta } _ { i } } ( a _ { i , \tau } | \tilde { s } _ { i , \tau } ) \hat { A } _ { i , \tau } ^ { \pi } + \beta \sum _ { a _ { i } \in A _ { i } } \pi _ { \boldsymbol { \theta } _ { i } } ( a _ { i } | \tilde { s } _ { i , \tau } ) \log \pi _ { \boldsymbol { \theta } _ { i } } ( a _ { i } | \tilde { s } _ { i , \tau } ) \right) , } \\ & { \mathcal { L } ( \omega _ { i } ) = \displaystyle \frac { 1 } { | \mathcal { B } | } \sum _ { \tau \in \mathcal { B } } \left( \hat { R } _ { i , \tau } ^ { \pi } - V _ { \omega _ { i } } ( \tilde { s } _ { i , \tau } , a _ { N _ { i } , \tau } ) \right) ^ { 2 } , } \end{array} +$$ + +where $\hat { A } _ { i , \tau } ^ { \pi } = \hat { R } _ { i , \tau } ^ { \pi } - v _ { i , \tau }$ is the estimated advantage, $\begin{array} { r } { \hat { R } _ { i , \tau } ^ { \pi } = \sum _ { \tau ^ { \prime } = \tau } ^ { \tau _ { B } - 1 } \gamma ^ { \tau ^ { \prime } - \tau } \left( \sum _ { j \in \mathcal { V } } \alpha ^ { d _ { i j } } r _ { j , \tau ^ { \prime } } \right) + } \end{array}$ $\gamma ^ { \tau _ { B } - \tau } v _ { i , \tau _ { B } }$ is the sampled action-value, $v _ { i , \tau } = V _ { \omega _ { i } ^ { - } } ( \tilde { s } _ { i , \tau } , a _ { \mathcal { N } _ { i } , \tau } )$ is the estimated state-value, and $\beta$ is the coefficient of the entropy loss. + +# 4 SPATIOTEMPORAL RL WITH NEURAL COMMUNICATION + +For efficient and adaptive information sharing, we propose a new communication protocol called NeurComm. To simplify the notation, we assume all messages sent from agent $i$ are identical, i.e., $m _ { i j } = m _ { i } , \forall j \in \mathcal { N } _ { i }$ . Then + +$$ +h _ { i , t } = g _ { \nu _ { i } } ( h _ { i , t - 1 } , e _ { \lambda _ { i } ^ { s } } ( s \nu _ { i , t } ) , e _ { \lambda _ { i } ^ { p } } ( \pi _ { \mathcal { N } _ { i } , t - 1 } ) , e _ { \lambda _ { i } ^ { h } } ( h _ { \mathcal { N } _ { i } , t - 1 } ) ) , +$$ + +where $h _ { i , t }$ is the hidden state (or the belief ) of each agent and $e _ { \lambda _ { i } }$ and $g _ { \nu _ { i } }$ are differentiable message encoding and extracting functions 3. To avoid dilution of state and policy information (the former is for improving observability while the later is for reducing non-stationarity), state and policy are explicitly included in the message besides agent belief, i.e., $m _ { i , t } = s _ { i , t } \cup \pi _ { i , t - 1 } \cup h _ { i , t - 1 }$ , or $\tilde { s } _ { i , t } : = s { \nu } _ { i , t } \cup \pi _ { \mathcal { N } _ { i } , t - 1 } \cup h _ { \mathcal { N } _ { i } , t - 1 }$ as in Eq. (5). Note the communication phase is prior-decision, so only $h _ { i , t - 1 }$ $h _ { i , t } ^ { ( k ) } = g _ { \nu _ { i } ^ { ( k ) } } ( h _ { i , t } ^ { ( k - 1 ) } , e _ { \lambda _ { i } ^ { s } } ( s \nu _ { i } , t ) , e _ { \lambda _ { i } ^ { p } } ( \pi _ { \mathcal { N } _ { i } , t - 1 } ) , e _ { \lambda _ { i } ^ { h } } ( h _ { \mathcal { N } _ { i } , t } ^ { ( k - 1 ) } ) )$ and $\pi _ { i , t - 1 }$ are available. This protocol can be easily extended for multi-pass communication: , where $h _ { i , t } ^ { ( 0 ) } = h _ { i , t - 1 }$ , and $k$ denotes each of the communication passes. The communication attentions can be integrated either at the sender as $\mu _ { i , t } ( m _ { i , t } )$ , or at the receiver as $\mu _ { i , t } ( m _ { \mathcal { N } _ { i } , t } )$ . Replacing the input $( \tilde { s } _ { i , t } )$ of Eq. (3)(4) with the belief $( h _ { i , t } )$ , the actor and critic become $\pi _ { \boldsymbol { \theta } _ { i } } ( \cdot | h _ { i , t } )$ and $V _ { \omega _ { i } } \left( h _ { i , t } , a _ { \mathcal { N } _ { i } , t } \right)$ , and the frozen estimations are $\pi _ { i , t }$ and $v _ { i , t }$ , respectively. + +Proposition 4.1 (Neighborhood Neural Communication). In spatiotemporal RL with neighborhood NeurComm, each agent utilizes the delayed global information to learn its belief, and it learns the message to optimize the control performance of all other agents. + +NeurComm enabled MARL can be represented using a single meta-DNN since all agents are connected by differentiable communication links, and $\tilde { s } _ { i }$ are the intermediate outputs after communication layers. Fig. 1a illustrates the forward propagations inside each individual agent and Fig. 1b shows the broader multi-step spatiotemporal propagations. Note the gradient propagation of this meta-DNN is decentralized based on each local loss signal. As time advances, the involved parameters in each propagation expand spatially in the meta-DNN, due to the cascaded neighborhood communication. To see this mathematically, $\pi _ { \theta _ { i , t } } ( \cdot | h _ { i , t } ) = \pi _ { \tilde { \theta } _ { i , t } } ( \cdot | s \nu _ { i , t } , \pi _ { \mathcal { N } _ { i } , t - 1 } )$ , with $\tilde { \theta } _ { i , t } = \{ \lambda _ { i } , \nu _ { i } , \theta _ { i } \}$ ; while $\pi _ { \boldsymbol { \theta } _ { i , t + 1 } } ( \cdot \vert h _ { i , t + 1 } ) = \pi _ { \tilde { \theta } _ { i , t + 1 } } ( \cdot \vert s _ { \mathcal { V } _ { i } , t + 1 } , \pi _ { \mathcal { N } _ { i } , t } , \{ s _ { \mathcal { N } _ { j } , t } , \pi _ { \mathcal { N } _ { j } , t - 1 } \} _ { j \in \mathcal { N } _ { i } } )$ , with $\widetilde { \boldsymbol { \theta } } _ { i , t + 1 } = \{ \lambda _ { j } , \nu _ { j } \} _ { j \in { \mathcal { N } } _ { i } } \cup \{ \lambda _ { i } , \nu _ { i } , \theta _ { i } \}$ . In other words, $\{ \lambda _ { i } , \nu _ { i } \}$ will be updated for improving actors $\pi _ { \boldsymbol { \theta } _ { j } }$ $ . , \forall j \in \nu$ , as soon as they are included in $\widetilde { \theta } _ { j }$ ; meanwhile, $r _ { i }$ will be included in $R _ { j } ^ { \pi }$ . In contrast, the policy is fully decentralized in execution, as $g _ { \nu _ { i } }$ depends on $\tilde { s } _ { i }$ only. + +![](images/29c3dbc71fbdb357ff97a54520ba7973e9fe90df4dd323232c8beb5fc8697693.jpg) +Figure 1: Forward propagations of NeurComm enabled MARL, illustrated in a queueing system. (a) Single-step forward propagations inside agent $i$ . Different colored boxes and arrows show different outputs and functions, respectively. Solid and dashed arrows indicate actor and critic propagations, respectively. (b) Multi-step forward propagations for updating the belief of agent $i$ . + +NeurComm is general enough and has connections to other communication protocols. CommNet performs a more lossy aggregation since the received messages are averaged before encoding, and all encoded inputs are summed up (Sukhbaatar et al., 2016). In DIAL, each DQN agent encodes the received messages instead of averaging them, but still it sums all encoded inputs (Foerster et al., 2016). Also, both CommNet and DIAL do not have policy fingerprints included in messages. + +# 5 NUMERICAL EXPERIMENTS + +# 5.1 ENVIRONMENT SETUP + +There are several benchmark MARL environments such as cooperative navigation and predator-prey, but few of them represent NSC. Here we design two NSC environments: adaptive traffic signal control (ATSC) and cooperative adaptive cruise control (CACC). Both ATSC and CACC are extensively studied in intelligent transportation systems, and they hold assumptions of a spatiotemporal MDP. + +# 5.1.1 ADAPTIVE TRAFFIC SIGNAL CONTROL + +The objective of ATSC is to adaptively adjust signal phases to minimize traffic congestion based on real-time road-traffic measurements. Here we implement two ATSC scenarios: a $5 \times 5$ synthetic traffic grid and a real-world 28-intersection traffic network from Monaco city, using standard microscopic traffic simulator SUMO (Krajzewicz et al., 2012). + +General settings. For both scenarios, each episode simulates the peak-hour traffic, and a 5s control interval is applied to prevent traffic light from too frequent switches, based on RL control latency and driver response delay. Thus, one MDP step corresponds to 5s simulation and the horizon is 720 steps. Further, a 2s yellow time is inserted before switching to red light for safety purposes. In ATSC, the real-time traffic flow, that is, the total number of approaching vehicles along each incoming lane, is measured by near-intersection induction-loop detectors (ILDs) (shown as the blue areas of example intersections in Fig. 2). The cost of each agent is the sum of queue lengths along all incoming lanes. + +Scenario settings. Fig. 2a illustrates the traffic grid formed by two-lane arterial streets with speed limit $2 0 \mathrm { m / s }$ and one-lane avenues with speed limit $1 1 \mathrm { m / s }$ . We simulate the peak-hour traffic dynamics through four collections of time-variant traffic flows, with both loading and recovering phases. At beginning, three major flows $F _ { 1 }$ are generated with origin-destination (O-D) pairs $x _ { 1 0 } – x _ { 4 }$ , $x _ { 1 1 } - x _ { 5 }$ , and $x _ { 1 2 } { - } x _ { 6 }$ , meanwhile three minor flows $f _ { 1 }$ are generated with O-D pairs $x _ { 1 } – x _ { 7 }$ , $x _ { 2 } \mathrm { - } x _ { 8 }$ , and $x _ { 3 } – x _ { 9 }$ + +After 15 minutes, $F _ { 1 }$ and $f _ { 1 }$ start to decay, while their opposite flows $F _ { 2 }$ and $f _ { 2 }$ start to dominate, as shown in Fig. 2b. Note the flows define the high-level demand only, the particular route of each vehicle is randomly generated. The grid is homogeneous and all agents have the same action space, which is a set of five pre-defined signal phases. Fig. 2c illustrates the Monaco traffic network, with controlled intersections in blue. NMARL in this scenario is more challenging since the network is heterogeneous with a variety of observation and action spaces. Four traffic flow collections are generated to simulate the peak-hour traffic, and each flow is a multiple of a “unit” flow of 325veh/hr, with randomly sampled O-D pairs inside rectangle areas in Fig. 2c. $F _ { 1 }$ and $F _ { 2 }$ are simulated during the first $4 0 \mathrm { { m i n } }$ , as $[ 1 , 2 , 4 , 4 , 4 , 4 , 2 , 1 ]$ unit flows with $5 \mathrm { { m i n } }$ intervals; $F _ { 3 }$ and $F _ { 4 }$ are generated in the same way, but with a delay of $1 5 \mathrm { { m i n } }$ . See code for more details. + +![](images/86ef284ef38198e0908abd3bf88ef2db19af879e4cb915eddb76fad3701f8e07.jpg) +Figure 2: ATSC scenarios for NMARL. (a) Synthetic traffic grid, with major and minor traffic flows shown in solid and dotted arrows. (b) Simulated time-variant traffic flows within the traffic grid. (c) Monaco traffic network, with traffic flow collections shown in colored arrows. + +# 5.1.2 COOPERATIVE ADAPTIVE CRUISE CONTROL + +The objective of CACC is to adaptively coordinate a platoon of vehicles to minimize the car-following headway and speed perturbations based on real-time vehicle-to-vehicle communication. Here we implement two CACC scenarios: “Catch-up” and “Slow-down”, with physical vehicle dynamics. + +General settings. For both CACC tasks, we simulate a string of 8 vehicles for 60s, with a 0.1s control interval. Each vehicle observes and shares its headway $_ \mathrm { h }$ , velocity $\mathrm { v }$ , and acceleration a to neighbors within two steps. The safety constraints are: $\mathrm { ~ h ~ } \geq 1 { \mathrm { m } }$ , $\mathrm { { v } \leq 3 0 m / s }$ , $| \mathrm { a } | \le 2 . 5 \mathrm { m / s ^ { 2 } }$ . Safe RL is relevant here, but itself is a big topic and out of the scope of this paper. So we adopt a simple heuristic optimal velocity model (OVM) (Bando et al., 1995) to perform longitudinal vehicle control under above constraints, whose behavior is affected by hyper-parameters: headway gain $\alpha ^ { \circ }$ , relative velocity gain $\beta ^ { \circ }$ , stop headway $\mathrm { h _ { s t } } = 5 \mathrm { m }$ and full-speed headway $\mathrm { h } _ { \mathrm { g o } } = 3 5 \mathrm { m }$ . Usually $( \alpha ^ { \circ } , \beta ^ { \circ } )$ represent the human driver behavior, here we train NMARL to recommend appropriate $( \alpha ^ { \circ } , \beta ^ { \circ } )$ for each OVM controller, selected from four levels $\left\{ ( 0 , 0 ) , ( 0 . 5 , 0 ) , ( 0 , 0 . 5 ) , ( 0 . 5 , 0 . 5 ) \right\}$ . Assuming the target headway and velocity profile are $\mathrm { h } ^ { \ast } = 2 0 \mathrm { m }$ and $\nabla _ { t } ^ { * }$ , respectively, the cost of each agent is $( \mathrm { h } _ { i , t } ^ { } - \mathrm { h } ^ { \ast } ) ^ { 2 } + ( \mathrm { v } _ { i , t } - \mathrm { v } _ { t } ^ { \ast } ) ^ { 2 } + 0 . 1 \mathrm { u } _ { i , t } ^ { 2 }$ . Whenever a collision happens $( \mathrm { h } _ { i , t } < \mathrm { 1 m } )$ , a large penalty of 1000 is assigned to each agent and the state becomes absorbing. An additional cost $5 ( 2 \mathrm { n } _ { \mathrm { s t } } - \mathrm { n } _ { i , t } ) _ { + } ^ { 2 }$ is provided in training for potential collisions. + +Scenario settings. Since exploring a collision-free CACC strategy itself is challenging for onpolicy RL, we consider simple scenarios. In Catch-up scenario, $\mathrm { v } _ { i , 0 } = \mathrm { v } _ { t } ^ { \ast } = 1 5 \mathrm { m } / \mathrm { s }$ and $\mathrm { h } _ { i , 0 } = \mathrm { h } ^ { * }$ , $\forall i \ne 1$ , whereas $\mathtt { h } _ { 1 , 0 } = a \cdot \mathrm { h } ^ { * }$ , with $a \in U [ 3 , 4 ]$ . In Slow-down scenario, $\mathrm { v } _ { i , 0 } = \mathrm { v } _ { 0 } ^ { \ast } = { b } { \cdot } 1 5 \mathrm { m } / \mathrm { s }$ , $b \in U [ 1 . 5 , 2 . 5 ]$ , and $\mathrm { h } _ { i , 0 } = \mathrm { h } ^ { * }$ , $\forall i$ , whereas $\nabla _ { t } ^ { * }$ linearly decreases to $1 5 \mathrm { m / s }$ during the first 30s and then stays at constant. + +# 5.2 ALGORITHM SETUP + +For fair comparison, all MARL approaches are applied to A2C agents with learning methods in Eq. (3)(4), and only neighborhood observation and communication are allowed. IA2C performs independent learning, which is an A2C implementation of MADDPG (Lowe et al., 2017) as the critic takes neighboring actions (see Eq. (4)). ConseNet (Zhang et al., 2018) has the additional consensus update to overwrite parameters of each critic as the mean of those of all critics inside the closed neighborhood. FPrint (Foerster et al., 2017) includes neighbor policies. DIAL (Foerster et al., 2016) and CommNet (Sukhbaatar et al., 2016) are described in Section 4. IA2C, ConseNet, and FPrint are non-communicative policies since they utilize only neighborhood information. In contrast, DIAL, CommNet, and NeurComm are communicative policies. Note communicative policies require more messages to be transferred and so higher communication bandwidth. In particular, the local message sizes are $O ( | s _ { i } | + | \pi _ { i } | + | h _ { i } | )$ for DIAL and NeurComm, $O ( | s _ { i } | + | h _ { i } | )$ for CommNet, $O ( | s _ { i } | + | \pi _ { i } | )$ for FPrint, and $O ( | s _ { i } | )$ for IA2C and ConseNet. The implementation details are in C.1. + +All algorithms use the same DNN hidden layers: one fully-connected layer for message encoding $e _ { \lambda }$ and one LSTM layer for message extracting $g _ { \nu }$ . All hidden layers have 64 units. The encoding layer implicitly learns normalization across different input signal types. We train each model over 1M steps, with $\gamma = 0 . 9 9$ , actor learning rate $5 \times 1 0 ^ { - 4 }$ , and critic learning rate $2 . 5 \times 1 0 ^ { - 4 }$ . Also, each training episode has a different seed for generalization purposes. In ATSC, $\beta = 0 . 0 1$ , $| B | = 1 2 0$ , while in CACC, $\beta = 0 . 0 5$ , $| B | = 6 0$ , to encourage the exploration of collision-free policies. Each training takes about 30 hours on a 32GB memory, Intel Xeon CPU machine. + +# 5.3 ABLATION STUDY + +We perform ablation study in proposed scenarios, which are sorted as ATSC Monaco $>$ ATSC Grid $> { \mathrm { C A C C } }$ Slow-down $>$ CACC Catch-up by task difficulty. ATSC is more challenging than CACC due to larger scale $> = 2 5$ vs 8), more complex dynamics (stochastic traffic flow vs deterministic vehicle dynamics), and longer control interval (5s vs 0.1s). ATSC Monaco $>$ ATSC Grid due to more heterogenous network, while CACC Slow-down $> { \mathrm { C A C C } }$ Catch-up due to more frequently changing leading vehicle profile. To visualize the learning performance, we plot the learning curve, that is, average episode return $\begin{array} { r } { \begin{array} { r } { ( \bar { R } = \frac { 1 } { T } \sum _ { t = 0 } ^ { T - 1 } \sum _ { i \in \mathcal { V } } r _ { i , t } ) } \end{array} } \end{array}$ vs training step. For better visualization, all learning curves are smoothened using moving average with a window size of 100 episodes. + +First, we investigate the impact of spatial discount factor, by comparing the learning curves among $\alpha \in \{ 0 . 8 , 0 . 9 , 1 \}$ for IA2C and CommNet. Fig. 3 reveals a few interesting facts. First, $\alpha _ { \mathrm { C o m m N e t } } ^ { * }$ is always higher than $\alpha _ { \mathrm { I A 2 C } } ^ { * }$ . Indeed, $\alpha _ { \mathrm { C o m m N e t } } ^ { * } = 1$ in almost all scenarios (except for ATSC Monaco). This is because communicative policies perform delayed global information sharing, whereas noncommunicative policies utilize neighborhood information only, causing difficulty to fit the global return. Second, learning performance becomes much more sensitive to $\alpha$ when the task is more difficult. Specifically, all $\alpha$ values lead to similar learning curves in CACC Catch-up, whereas appropriate $\alpha$ values help IA2C converge to much better policies more steadily in other scenarios. Third, $\alpha ^ { * }$ is high enough: $\alpha _ { \mathrm { I A 2 C } } ^ { * } = 0 . 9$ except for CACC Slow-down where $\alpha _ { \mathrm { I A 2 C } } ^ { * } = 0 . 8$ . This is because the discounted problem must be similar enough to the original problem in execution. + +Next, we investigate the impact of NeurComm under $\alpha = 1$ . We start with a baseline which is similar to existing differentiable protocols, i.e., $h _ { i , t } = \mathtt { L S T M } \left( h _ { i , t - 1 } , \mathtt { r e l u } ( s \nu _ { i } , t ) + \mathtt { r e l u } ( m _ { \mathcal { N } _ { i } , t } ) \right)$ . We then evaluate two intermediate protocols “Concat Only” and “FPrint Only”, in which encoded inputs are concatenated and neighbor policies are included, respectively. Finally we evaluate their combination NeurComm. As shown in Fig. 3, all protocols have similar learning curves in easy CACC Catch-up scenario. Otherwise, both “Concat” and “FPrint” are able to enhance the baseline learning curves in certain scenarios and their affects are additive in NeurComm. + +# 5.4 TRAINING RESULTS + +Fig. 4 compares the learning curves of all MARL algorithms, after tuned $\alpha ^ { * } \in \{ 0 . 6 , 0 . 8 , 0 . 9 , 0 . 9 5 , 1 \}$ As expected, $\alpha ^ { * }$ for non-communicative policies are lower than those for communicative policies. + +Table 1: Best spatial discount factors $\alpha ^ { * }$ across NMARL scenarios. + +
Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid1.01.01.00.90.950.9
ATSC Monaco1.00.90.90.90.90.9
CACC Catch-up1.01.01.01.01.01.0
CACC Slow-down1.01.01.00.80.90.8
+ +![](images/6c2100444c8e4ea85b1ca1e4698b9d60935c0640eec806518ad0aa48064c4ef9.jpg) +Figure 3: Sensitivity and ablation study of spatial discount factor (top) and NeurComm (bottom). The best learning curves are in bold. + +![](images/a49927f565d3416c65c615f9e2a002481594ecf566bcdd48da18c15efad67f91.jpg) +Figure 4: Training performance comparison after tuned spatial discount factors. + +Tab. 1 summarizes $\alpha ^ { * }$ of controllers across different NMARL scenarios. For challenging scenarios like ATSC Monaco, lower $\alpha$ is preferred by almost all policies (except NeurComm). This demonstrates that $\alpha$ is an effective way to enhance MARL performance in general, especially for challenging tasks like ATSC Monaco. From another view point, $\alpha$ serves as an informative indicator on problem difficulty and algorithm coordination level. Based on Fig. 4, NeurComm is at least competitive in CACC scenarios, and it clearly outperforms other policies on both sample efficiency and learning stability in more challenging ATSC scenarios. Note in CACC a big penalty is assigned whenever a collision happens, so the standard deviation of episode returns is high. + +# 5.5 EXECUTION RESULTS + +We freeze and evaluate trained MARL policies in another 50 episodes, and summarize the results in Tab. 2. In CACC scenarios, $\alpha$ enhanced FPrint policy achieves the best execution performance. Note NeurComm still outperforms other communicative algorithms, so this result implies that delayed information sharing may not be helpful in easy but real-time and safety-critical CACC tasks. In contrast, NeurComm achieves the best execution performance for ATSC tasks. We also evaluate the execution performance of ATSC and CACC using domain-specific metrics in Tab. 3 and Tab. 4, respectively. The results are consistent with the reward-defined ones in Tab. 2. + +Further, we investigate the performance of top policies in ATSC scenarios. For each ATSC scenario, we select the top two non-communicative and communicative policies and visualize their impact on network traffic by plotting the time series of network averaged queue length and intersection delay in Fig. 5. Note the line and shade show the mean and standard deviation of each metric across execution runs, respectively. Based on Fig. 5a, NeurComm achieves the most sustainable traffic control in ATSC Grid, so that the congested grid starts recovering immediately after the loading phase ends at 3000s. During the same unloading phase, CommNet prevents the queues from further increasing while non-communicative policies are failed to do so. Also, FPrint is less robust than IA2C as it introduces a sudden congestion jump at 1000s. Similarly, NeurComm achieves the lowest saturation rate in ATSC Monaco (Fig. 5b). + +Table 2: Execution performance comparison over trained MARL policies. Best values are in bold. + +
Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid-136.1-165.1-214.4-160.2-155.9-187.5
ATSC Monaco-226.3-263.0-339.4-369.7-359.4-528.9
CACC Catch-up-94.6-95.6-246.4-261.7-57.8-419.7
CACC Slow-down-934.7-950.8-1112-2209-697.9-1038
+ +![](images/7a001631792b12bc25593af36f82b39c8470ff98f192111f802169e74d226f6b.jpg) +Figure 5: Execution performance comparison among top policies in ATSC scenarios, measured as average queue length and average intersection delay over time. + +Intersection delay is another key metric in ATSC. Based on Fig. 5c, communicative policies are able to reduce intersection delay as well in ATSC Grid, though it is not explicitly included in the objective and so is not optimized by non-communicative policies. In contrast, communicative policies have fast increase on intersection delay in ATSC Monaco. This implies that communicative algorithms are able to capture the spatiotemporal traffic pattern in homogeneous networks whereas they still have the risk of overfitting on queue reduction in realistic and heterogenous networks. For example, they block the short source edges on purpose to reduce on-road vehicles by paying a small cost of queue length. + +Finally, we investigate the robustness (string stability) of top policies in CACC scenarios. In particular, we plot the time series of headway and velocity for the first and the last vehicles in the platoon. The profile of the first vehicle indicates how adaptively the controller pursues $\mathrm { ~ h ~ } ^ { * }$ and $\boldsymbol { \tau } ^ { * }$ , while that of the last vehicle indicates how stable the controlled platoon is. Based on Tab. 1 and Tab. 4, the top communicative and non-communicative controllers are NeurComm and FPrint. + +Fig. 6 shows the corresponding headway and velocity profiles for the selected controllers. Interestingly, MARL controllers are able to achieve steady state $\boldsymbol { \tau } ^ { * }$ and $\mathrm { h ^ { * } }$ for the first vehicle of platoon, whereas they still have difficulty to eliminate the perturbation through the platoon. This may be because of the heuristic low-level controller as well as the delayed information sharing. + +![](images/7ff08398439d1963fe5c9490267a1bb0be0276ac701c7c7e0dcea9361682a818.jpg) +Figure 6: Headway and velocity profiles of the first and last vehicles of the platoon, controlled by top communicative and non-communicative policies in execution. + +# 6 CONCLUSIONS + +We have formulated the spatiotemporal MDP for decentralized NSC under neighborhood communication. Further, we have introduced the spatial discount factor to enhance non-communicative MARL algorithms, and proposed a neural communication protocol NeurComm to design adaptive and efficient communicative MARL algorithms. We hope this paper provides a rethink on developing scalable and robust MARL controllers for NSC, by following practical engineering assumptions and combining appropriate learning and communication methods rather than reusing existing MARL algorithms. One future direction is improving the recurrent units to naturally control spatiotemporal information flows within the meta-DNN in a decentralized way. + +# ACKNOWLEDGMENTS + +We would like to thank Marco Pavone and Alexander Anemogiannis for valuable discussions and insightful comments. + +# REFERENCES + +Masako Bando, Katsuya Hasebe, Akihiro Nakayama, Akihiro Shibata, and Yuki Sugiyama. Dynamical model of traffic congestion and numerical simulation. Physical review E, 51(2):1035, 1995. + +Tianshu Chu, Jie Wang, Lara Codecà, and Zhaojian Li. Multi-agent deep reinforcement learning for large-scale traffic signal control. 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Fully decentralized multiagent reinforcement learning with networked agents. arXiv preprint arXiv:1802.08757, 2018. + +APPENDIX + +# A PROOFS + +# A.1 PROOF OF PROPOSITION 3.1 + +Proof. The proof follows the learning method in A2C Mnih et al. (2016), which shows that + +$$ +\begin{array} { l } { \displaystyle \mathcal { L } ( \theta ) = \frac { 1 } { | \mathcal { B } | } \sum _ { \tau \in \mathcal { B } } \left( - \log \pi _ { \theta } ( a _ { \tau } | s _ { \tau } ) \hat { A } _ { \tau } ^ { \pi } + \beta \sum _ { a \in \mathcal { A } } \pi _ { \theta } ( a | s _ { \tau } ) \log \pi _ { \theta } ( a | s _ { \tau } ) \right) , } \\ { \displaystyle \mathcal { L } ( \omega ) = \frac { 1 } { | \mathcal { B } | } \sum _ { \tau \in \mathcal { B } } \left( \hat { R } _ { \tau } ^ { \pi } - V _ { \omega } ( s _ { \tau } ) \right) ^ { 2 } , } \end{array} +$$ + +where minib $\hat { A } _ { \tau } ^ { \pi } = \hat { R } _ { \tau } ^ { \pi } - v _ { \tau }$ , $\begin{array} { r } { \hat { R } _ { \tau } ^ { \pi } = \sum _ { \tau ^ { \prime } = \tau } ^ { \tau _ { B } - 1 } \gamma ^ { \tau ^ { \prime } - \tau } r _ { \tau ^ { \prime } } + \gamma ^ { \tau _ { B } - \tau } v _ { \tau _ { B } } } \end{array}$ , and $v _ { \tau } = V _ { \omega ^ { - } } ( s _ { \tau } )$ , based on on-policy $\{ ( s _ { \tau } , a _ { \tau } , r _ { \tau } ) \} _ { \tau \in { \mathcal B } }$ + +Now we consider spatiotemporal MDP, which has transition in Eq. (1), optimizes return in Eq. (2), and collects experience $( s _ { i , t } , m _ { N _ { i } i , t } , a _ { i , t } , \tilde { r } _ { i , t } )$ , where $\begin{array} { r } { \tilde { r } _ { i , t } = \sum _ { j \in \mathcal { V } } \alpha ^ { d _ { i j } } r _ { j , t } ^ { - } } \end{array}$ . In Theorem 3.1 of Zhang et al. (2018), the decentralized actor and critic are $\tilde { \pi } _ { \boldsymbol { \theta } _ { i } } ( s )$ and $\tilde { V } _ { \omega _ { i } } ( s , a _ { - i } )$ , for fitting $\pi _ { i } ^ { * } ( \cdot | s )$ and $\begin{array} { r } { \sum _ { a _ { i } \in \mathcal { A } _ { i } } \pi _ { i } ( a _ { i } \vert s ) Q ^ { \pi _ { i } } ( s , a ) } \end{array}$ under global observations, respectively. Now assuming the observations and communications are restricted to each neighborhood as in Definition 3.1, then the actor and critic become $\pi _ { \theta _ { i } } ( \tilde { s } _ { i } ) \approx \tilde { \pi } _ { \theta _ { i } } ( s )$ and $V _ { \omega _ { i } } ( \tilde { s } _ { i } , a _ { \mathcal { N } _ { i } } ) \approx \tilde { V } _ { \omega _ { i } } ( s , a _ { - i } )$ , with the best observability. + +Hence, replacing $\pi _ { \boldsymbol { \theta } } ( a | \boldsymbol { s } )$ , $V _ { \omega } ( s )$ , $r$ by $\pi _ { \theta _ { i } } ( a _ { i } | \tilde { s } _ { i } )$ , $V _ { \omega _ { i } } ( \tilde { s } _ { i } , a _ { \mathcal { N } _ { i } } )$ , and $\tilde { r } _ { i }$ , respectively, we establish Eq. (3)(4) from Eq. (6)(7), which concludes the proof. □ + +Note partial observability and non-stationarity are present in $\pi _ { \theta _ { i } } ( a _ { i } | \tilde { s } _ { i } )$ and $V _ { \omega _ { i } } \left( \tilde { s } _ { i } , a _ { \mathcal { N } _ { i } } \right)$ . Fortunately, communication improves the observability. Based on Definition 3.1, any information that agent $j$ knows at time $t$ can be included in $m _ { j i , t }$ . We assume $s _ { j , t } \cup \{ m _ { k j , t - 1 } \} _ { k \in \mathcal { N } _ { j } } \subset m _ { j i , t } .$ . Then + +$$ +\begin{array} { r l } & { \widetilde { s } _ { i , t } \supset s _ { i , t } \cup \big \{ s _ { j , t } \cup \big \{ m _ { k j , t - 1 } \big \} _ { k \in \mathcal { N } _ { j } } \big \} _ { j \in \mathcal { N } _ { i } } } \\ & { \qquad \supset \big \{ s _ { j , t } \big \} _ { j \in \mathcal { V } _ { i } } \cup \big \{ s _ { j , t - 1 } \cup \big \{ m _ { k j , t - 2 } \big \} _ { k \in \mathcal { N } _ { j } } \big \} _ { j \in \mathcal { V } | d _ { i j } = 2 } } \\ & { \qquad \supset \big \{ s _ { j , t } \big \} _ { j \in \mathcal { V } _ { i } } \cup \big \{ s _ { j , t - 1 } \big \} _ { j \in \mathcal { V } | d _ { i j } = 2 } \cup \big \{ s _ { j , t - 2 } \cup \big \{ m _ { k j , t - 3 } \big \} _ { k \in \mathcal { N } _ { j } } \big \} _ { j \in \mathcal { V } | d _ { i j } = 3 } } \\ & { \qquad \supset \dots } \\ & { \qquad \supset s _ { i , t } \cup \big \{ s _ { j , t + 1 - d _ { i j } } \big \} _ { j \in \mathcal { V } \backslash \{ i \} } . } \end{array} +$$ + +Thus, $\tilde { s } _ { i , t }$ includes the delayed global observations. On the other hand, Eq. (1)(2) mitigate the non-stationarity. To see this mathematically, + +$$ +\begin{array} { l } { { \mathbb { E } _ { \pi _ { i } , p } } [ \tilde { r } _ { i , t } | s _ { t } , a _ { t } ] = { \mathbb { E } _ { \pi _ { i } , p _ { i } } } [ r _ { i , t } | s \nu _ { i } , t , a _ { \mathcal { N } _ { i } , t } ] + \alpha \displaystyle \sum _ { j \in \mathcal { N } _ { i } } { \mathbb { E } _ { \pi _ { i } , p _ { j } } } [ r _ { j , t } | s \nu _ { j } , t , a \nu _ { j } \backslash \{ i \} , t ] } \\ { ~ + \displaystyle \sum _ { d = 2 } ^ { d _ { \operatorname* { m a x } } } \left( \alpha ^ { d } \sum _ { j \in \{ \mathcal { V } | d _ { i j } = d \} } { \mathbb { E } _ { p _ { j } } } [ r _ { j , t } | s \nu _ { j } , t , a \nu _ { j } , t ] \right) , \qquad } \end{array} +$$ + +where the further away reward signals are discounted more. Note if communication is allowed, each agent will have delayed global observations, and the non-stationarity mainly comes from limited information of future actions. + +# A.2 PROOF OF PROPOSITION 4.1 + +This proposition contains two statements regarding neural communication based global information sharing in forward and backward propagations. We establish each of them separately. + +Lemma A.1 (Spatial Information Propagation). In NeurComm, the delayed global information is utilized to estimate each hidden state, that is, + +$$ +h _ { i , t } \supset s _ { i , 0 : t } \cup \left\{ s _ { j , 0 : t + 1 - d _ { i j } } , \pi _ { j , 0 : t - d _ { i j } } \right\} _ { j \in \mathcal { V } \backslash \{ i \} } , +$$ + +where $x \supset y$ if information $y$ is utilized to estimate $x$ , and $x _ { 0 : t } : = \{ x _ { 0 } , x _ { 1 } , \ldots , x _ { t } \}$ + +Proof. Based on the definition of NeurComm protocol (Eq. (5)), $m _ { i , t } \supset h _ { i , t - 1 }$ , and $h _ { i , t } \supset h _ { i , t - 1 } \cup$ $s _ { \mathcal { V } _ { i } , t } \cup \pi _ { \mathcal { N } _ { i } , t - 1 } \cup m _ { \mathcal { N } _ { i } , t }$ . Hence, + +$$ +\begin{array} { r l } & { h _ { i , t } \supset s _ { i , t } \cup \big \{ s _ { j , t } , \pi _ { j , t - 1 } \big \} _ { j \in \mathcal { N } _ { i } } \cup \big \{ h _ { j , t - 1 } \big \} _ { j \in \mathcal { V } _ { i } } } \\ & { \qquad \supset s _ { i , t } \cup \big \{ s _ { j , t } , \pi _ { j , t - 1 } \big \} _ { j \in \mathcal { N } _ { i } } \cup \big \{ s _ { j , t - 1 } \cup \big \{ s _ { k , t - 1 } , \pi _ { k , t - 2 } \big \} _ { k \in \mathcal { N } _ { j } } \cup \big \{ h _ { k , t - 2 } \big \} _ { k \in \mathcal { V } _ { j } } \big \} _ { j \in \mathcal { V } _ { i } } } \\ & { \qquad = s _ { i , t - 1 : t } \cup \big \{ s _ { j , t - 1 : t } , \pi _ { j , t - 2 : t - 1 } \big \} _ { j \in \mathcal { N } _ { i } } \cup \big \{ s _ { j , t - 1 } , \pi _ { j , t - 2 } \big \} _ { j \in \{ \mathcal { V } | d _ { i , j } = 2 \} } } \\ & { \qquad \cup \big \{ h _ { j , t - 2 } \big \} _ { j \in \{ \mathcal { V } | d _ { i , j } \leq 2 \} } } \\ & { \qquad \supset \big . s . . } \\ & { \qquad \cup \big \{ s _ { j , 0 : t } , \pi _ { j , t - 2 : t - 1 } \big \} _ { j \in \mathcal { N } _ { i } } \cup \big \{ s _ { j , 0 : t - 1 } , \pi _ { j , 0 : t - 2 } \big \} _ { j \in \{ \mathcal { V } | d _ { i , j } = 2 \} } } \\ & { \qquad \cup \big \{ s _ { j , 0 : t + 1 } - \mathcal { U } _ { \mathrm { m a x } } , \pi _ { j , 0 : t - d _ { \mathrm { m a x } } } \big \} _ { j \in \{ \mathcal { V } | d _ { i , j } = d _ { \mathrm { m a x } } \} } , } \end{array} +$$ + +which concludes the proof. + +Lemma A.2 (Spatial Gradient Propagation). In NeurComm, each message is learned to optimize the performance of other agents, that is, $\{ \nu _ { i } , \lambda _ { i } \}$ receive almost all gradients from $\bar { \mathcal { L } } ( \theta _ { j } ) , \bar { \mathcal { L } } ( \omega _ { j } )$ , $\forall j \in \{ \mathcal { V } | j \neq i \}$ . + +Proof. If we rewrite the required information for a given hidden state $h _ { i , t }$ using intermediate messages instead of inputs, the result of Lemma A.1 becomes + +$$ +\begin{array} { r l } & { h _ { i , t } \supset \{ m _ { j , t } \} _ { j \in { \cal N } _ { i } } \supset \{ h _ { j , t - 1 } \} _ { j \in { \cal N } _ { i } } } \\ & { \qquad \supset \{ m _ { j , t - 1 } \} _ { j \in \{ { \mathcal V } \mid d _ { i j } = 2 \} } \supset \ . . . } \\ & { \qquad \supset \{ m _ { j , t + 1 - d } \} _ { j \in \{ { \mathcal V } \mid d _ { i j } = d \} } \supset . . . } \end{array} +$$ + +Hence, $m _ { i , \tau }$ is included in the meta-DNN of agent $j$ at time $\tau + d _ { i j } - 1$ . In other words, $\{ \nu _ { i } , \lambda _ { i } \}$ receive gradients from $\mathcal { L } ( \theta _ { j } ) , \mathcal { L } ( \omega _ { j } ) , \forall j \in \{ \mathcal { V } | j \neq i \}$ , except for the first $d _ { i j } - 1$ experience samples. Assuming $d _ { \operatorname* { m a x } } \ll | B | , \{ \nu _ { i } , \lambda _ { i } \}$ receive almost all gradients from loss signals of all other agents, which concludes the proof. □ + +# B ALGORITHMS + +Algo. 1 presents the algorithm of model training in a synchronous way, following descriptions in Section 3 and 4. Four iterations are performed at each step: the first iteration (lines 3-5) updates and sends messages; the second iteration (lines 6-10) updates hidden state, policy, and action; the third iteration (lines 11-14) updates value estimation and executes action; the fourth iteration (lines 22-26) performs gradient updates on actor, critic, and neural communication. On the other hand, Algo. 2 presents the algorithm of decentralized model execution in an asynchronous way. It runs as a job that repeatedly measures traffic, sends message, receives messages, and performs control. + +# Algorithm 1: Multi-agent A2C with NeurComm (Training) + +Parameter : $\alpha$ , $\beta , \gamma , T , | B |$ , $\eta _ { \omega } , \eta _ { \theta }$ . +Result: $\{ \lambda _ { i } , \nu _ { i } , \omega _ { i } , \theta _ { i } \} _ { i \in \mathcal { V } }$ . +1 initialize s0, $\pi _ { - 1 }$ , $h _ { - 1 }$ , $t \gets 0$ , $k 0$ , $B \emptyset$ ; +2 repeat +3 for $i \in \nu$ do +4 send $m _ { i , t } = f _ { \lambda _ { i } } ( h _ { i , t - 1 } )$ ; +5 end +6 for $i \in \nu$ do +7 observe $\tilde { s } _ { i , t } = s { \nu } _ { i , t } \cup { \pi } _ { N _ { i } , t - 1 } \cup m _ { \ N _ { i } , t }$ ; +8 update $h _ { i , t } \gets g _ { \nu _ { i } } ( h _ { i , t - 1 } , \tilde { s } _ { i , t } ) .$ , $\pi _ { i , t } \pi _ { \theta _ { i } } ( \cdot | h _ { i , t } )$ ; +9 update $a _ { i , t } \sim \pi _ { i , t }$ ; +10 end +11 for $i \in \nu$ do +12 update $v _ { i , t } \gets V _ { \omega _ { i } } ( h _ { i , t } , a _ { \mathcal { N } _ { i } , t } )$ ; +13 execute $a _ { i , t }$ ; +14 end +15 simulate $\{ s _ { i , t + 1 } , r _ { i , t } \} _ { i \in \mathcal { V } }$ ; +16 update $\boldsymbol { B } \gets \boldsymbol { B } \cup \{ \left( s _ { i , t } , \pi _ { i , t - 1 } , a _ { i , t } , r _ { i , t } , v _ { i , t } \right) \} _ { i \in \mathcal { V } }$ ; +17 update $t \gets t + 1$ , $k \gets k + 1$ ; +18 if $t = T$ then +19 initialize $s _ { 0 } , \pi _ { - 1 } , h _ { - 1 } , t 0$ ; +20 end +21 if $k = | \boldsymbol { B } |$ then +22 for $i \in \mathcal V$ do +23 update $\hat { R } _ { \tau } ^ { \pi _ { i } } , \hat { A } _ { \tau } ^ { \pi _ { i } } , \forall \tau \in B$ , based on Proposition 3.1; +24 update $\{ \lambda _ { j } , \nu _ { j } \} _ { j \in \mathcal { V } } \cup \{ \omega _ { i } \}$ , based on $\eta _ { w } \nabla \mathcal { L } ( w _ { i } )$ ; +25 update $\{ \lambda _ { j } , \nu _ { j } \} _ { j \in \mathcal { V } } \cup \{ \theta _ { i } \} _ { \mathrm { { } } }$ , based on $\eta _ { \boldsymbol { \theta } } \nabla \mathcal { L } ( \boldsymbol { \theta } _ { i } )$ ; +26 end +27 initialize $\boldsymbol { B } \gets \emptyset , \boldsymbol { k } \gets \mathrm { 0 }$ ; +28 end +29 until Stop condition is reached; + +# Algorithm 2: Multi-agent A2C with NeurComm (Execution) + +Parameter : $\{ \lambda _ { i } , \nu _ { i } , \omega _ { i } , \theta _ { i } \} _ { i \in \mathcal { V } }$ , ∆tcomm, ∆tcontrol. +1 for $i \in \nu$ do +2 initialize $h _ { i } \gets 0$ , $\pi _ { i } \gets 0$ , $\{ s _ { j } , \pi _ { j } , m _ { j } \} _ { j \in \mathcal { N } _ { i } } \gets 0$ ; +3 repeat +4 observe $s _ { i }$ ; +5 update $m _ { i } \gets f _ { \lambda _ { i } } ( h _ { i } )$ ; +6 send $s _ { i } , \pi _ { i } , m _ { i }$ ; +7 for $j \in \mathcal N$ do +8 receive and update $s _ { j } , \pi _ { j } , m _ { j }$ within $\Delta t _ { c o m m }$ ; +9 end +10 update $\tilde { s } _ { i } \gets s _ { \mathcal { V } _ { i } } \cup \pi _ { \mathcal { N } _ { i } } \cup m _ { \mathcal { N } _ { i } }$ ; +11 update $h _ { i } \gets g _ { \nu _ { i } } ( h _ { i } , \tilde { s } _ { i } )$ , $\pi _ { i } \pi _ { \theta _ { i } } ( \cdot | h _ { i } )$ ; +12 execute $a _ { i } \sim \pi _ { i }$ ; +13 sleep $\Delta t _ { c o n t r o l }$ ; +14 until Stop condition is reached; + +15 end + +# C EXPERIMENT DETAILS + +# C.1 ALGORITHM SETUP + +Detailed algorithm implementations are listed below, in term of Eq. (5). IA2C: $\begin{array} { r l } { h _ { i , t } } & { { } = } \end{array}$ $\mathtt { L S T M } ( h _ { i , t - 1 } , \mathtt { r e l u } ( s \nu _ { i , t } ) )$ . ConseNet: same as IA2C but with consensus critic update. FPrint: $\begin{array} { r l r } { h _ { i , t } } & { = } & { \mathtt { L S T M } \mathtt { ( } h _ { i , t - 1 } , \mathtt { c o n c a t ( r e l u ( } s \nu _ { i } , t ) , \mathtt { r e l u ( } \pi _ { \mathcal { N } _ { i } , t - 1 } ) \mathtt { ) } \mathtt { ) } } \end{array}$ . NeurComm: $h _ { i , t } \ = \ \tt L S T M ( h _ { i , t - 1 }$ , concat $\left( \boldsymbol { \mathrm { r e l u } } ( s \nu _ { i } , t ) \right)$ , $\mathtt { r e l u } ( \pi _ { \mathcal { N } _ { i } , t - 1 } )$ , $\mathsf { r e l u } ( h _ { \mathcal { N } _ { i } , t - 1 } ) ) ,$ . DIAL: $h _ { i , t } ~ =$ LSTM(hi,t−1, $\mathtt { r e l u } ( s _ { \mathcal { V } _ { i } , t } ) \ + \ \mathtt { r e l u } ( \mathtt { r e l u } ( h _ { i , t - 1 } ) ) \ + \ \mathtt { o n e }$ hot(ai,t−1)). CommNet: $\begin{array} { r l } { h _ { i , t } } & { { } = } \end{array}$ $\mathtt { L S T M } ( h _ { i , t - 1 }$ , $\mathsf { t a n h } ( s _ { \mathcal { V } _ { i } , t } ) + \mathtt { l i n e a r } ( \mathtt { m e a n } ( h _ { \mathcal { N } _ { i } , t - 1 } ) ) )$ ). For ConseNet, we only do consensus update on the LSTM layer, since the input and output layer sizes may not be fixed across agents. Also, the actor and critic are $\pi _ { i , t } = { \tt s o f t m a x } ( h _ { i , t } )$ , and $v _ { i , t } = \mathrm { 1 i n e a r } ( \mathsf { c o n c a t } ( h _ { i , t } , \mathsf { o n e h o t } ( a _ { \mathcal { N } _ { i } , t } ) ) )$ + +# C.2 EXPERIMENTS IN ATSC ENVIRONMENT + +# C.2.1 ACTION SPACE + +Fig. 7 illustrates the action space of five phases for each intersection in the ATSC Grid scenario. The ATSC Monaco scenario has complex and heterogeneous action spaces, please see the code for more details. To summarize, there are 11 two-phase intersections, 3 three-phase intersections, 10 four-phase intersections, 1 five-phase intersection, and 3 six-phase intersections. + +# C.2.2 SUMMARY OF EXECUTION PERFORMANCE + +Table 3 summarizes the key metrics in ATSC. The spatial average is taken at each second, and then the temporal average is calculated for all metrics (except for trip delay, which is directly aggregated over all trips). NeurComm outperforms all baselines on minimizing queue length and intersection delay. Interestingly, even though IA2C is good at optimizing the given objective of queue length, it performs poorly on optimizing intersection and trip delays. + +# C.2.3 VISUALIZATION OF EXECUTION PERFORMANCE + +Fig. 8 and Fig. 9 show screenshots of traffic distributions in the grid at different simulation steps for each MARL controller. The visualization is based on one execution episode with random seed 2000. Clearly, communicative MARL controllers have better performance on reducing the intersection delay. NeurComm and CommNet have the best overall performance. + +![](images/5f50f419fc5de41ee4fe64e1b39a09764d2f84d8b02175d549124fcc27bc36b0.jpg) +Figure 7: Possible signal phases at each intersection. + +Table 3: Performance of MARL controllers in ATSC environments: synthetic traffic grid (top) and Monaco traffic network (bottom). Best values are in bold. + +
Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
avg queue length [veh] avg intersection delay [s/veh] avg vehicle speed [m/s]1.16 68 2.281.442.361.631.622.04
111145376415366
1.821.780.260.230.29
trip delay [s] avg queue length [veh] avg intersection delay [s/veh]293 1.27 221.1455194920671949321
1.561.881.931.872.74
236.5231.3147.4174.8187.3
avg vehicle speed [m/s] trip delay [s]0.550.610.942.361.261.03
569847506295428
540
+ +# C.3 EXPERIMENTS IN CACC ENVIRONMENTS + +# C.3.1 SUMMARY OF EXECUTION PERFORMANCE + +Table 4 summarizes the key metrics in CACC. The best headway and velocity averages are closest ones to $\mathrm { h } ^ { * } = 2 0 \mathrm { m }$ , and $\mathrm { v ^ { * } } = 1 5 \mathrm { m / s }$ . Note the averages are only computed from safe execution episodes, and we use another metric “collision number” to count the number of episodes where an collision happens within the horizon. Ideally, “collision-free” is the top priority. However, safe RL is not the focus of this paper so trained MARL controllers cannot achieve this goal in the experiments of CACC. + +Table 4: Performance of MARL controllers in CACC environments: catch-up (above) and slow-down (below). Best values are in bold. + +
Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
avg vehicle headway [m] std vehicle headway [m]20.4520.47 1.1821.99 0.2022.02 0.1920.44 1.0321.45
avg vehicle velocity [m/s]1.200
15.3315.3315.0715.0715.3315.00
std vehicle velocity [m/s]0.900.870.160.180.750
collision number avg vehicle headway [m]0 15.8400000
std vehicle headway [m]2.1016.2414.42118.2111.60
13.432.161.7012.400.49
avg vehicle velocity [m/s]13.8212.28115.478.59
std vehicle velocity [m/s]2.772.882.4913.371.19
collision number13121650823
+ +![](images/c422f0265bdd104c373babd00f707f3a4ba43097921ba20ff7ef562fd74bb6c7.jpg) +Figure 8: Screenshots of traffic distribution in the grid. Each row is a non-communicative MARL controller and each column is a simulation step. The traffic condition along each lane is visualized as a line segment, with the color indicating the queue length or congestion level (grey: $0 \%$ traffic, green: $2 5 \%$ traffic, yellow: $50 \%$ traffic, orange: $70 \%$ traffic, red: $90 \%$ traffic, intermediate traffic condition is shown as the interpolated color), while the thickness indicating the intersection delay (the thicker the longer waiting time at intersection). + +![](images/05864f63cf1a20871cfb9b93eb0fb8693eb045a828b30024c49544f91919cc57.jpg) +Figure 9: Screenshots of traffic distribution in the grid. 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Further, we propose a new differentiable communication protocol, called", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "spans": [ + { + "bbox": [ + 141, + 302, + 470, + 314 + ], + "score": 1.0, + "content": "NeurComm, to reduce information loss and non-stationarity in NMARL. Based", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 313, + 470, + 325 + ], + "spans": [ + { + "bbox": [ + 141, + 313, + 470, + 325 + ], + "score": 1.0, + "content": "on experiments in realistic NMARL scenarios of adaptive traffic signal control", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 324, + 470, + 337 + ], + "spans": [ + { + "bbox": [ + 141, + 324, + 470, + 337 + ], + "score": 1.0, + "content": "and cooperative adaptive cruise control, an appropriate spatial discount factor", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 335, + 470, + 347 + ], + "spans": [ + { + "bbox": [ + 141, + 335, + 470, + 347 + ], + "score": 1.0, + "content": "effectively enhances the learning curves of non-communicative MARL algorithms,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "spans": [ + { + "bbox": [ + 141, + 345, + 470, + 359 + ], + "score": 1.0, + "content": "while NeurComm outperforms existing communication protocols in both learning", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 357, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 142, + 357, + 286, + 369 + ], + "score": 1.0, + "content": "efficiency and control performance.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 16.5, + "bbox_fs": [ + 141, + 237, + 470, + 369 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 396, + 206, + 408 + ], + "lines": [ + { + "bbox": [ + 105, + 395, + 208, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 208, + 412 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 424, + 505, + 544 + ], + "lines": [ + { + "bbox": [ + 105, + 422, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 505, + 438 + ], + "score": 1.0, + "content": "Reinforcement learning (RL), formulated as a Markov decision process (MDP), is a promising", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "data-driven approach for learning adaptive control policies (Sutton & Barto, 1998). Recent advances", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "in deep neural networks (DNNs) further enhance its learning capacity on complex tasks. Successful", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 457, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 469 + ], + "score": 1.0, + "content": "algorithms include deep Q-network (DQN) (Mnih et al., 2015), deep deterministic policy gradient", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "(DDPG) (Lillicrap et al., 2015), and advantage actor critic (A2C) (Mnih et al., 2016). However, RL is", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 479, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 491 + ], + "score": 1.0, + "content": "not scalable in many real-world control problems. This scalability issue is addressed in multi-agent", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "RL (MARL), where each agent learns its individual policy from only local observations. However,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "MARL introduces new challenges in model training and execution, due to non-stationarity and partial", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 510, + 506, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 525 + ], + "score": 1.0, + "content": "observability in a decentralized MDP from the viewpoint of each agent. 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First, the control infrastructures are distributed in a wide region, so collecting global", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "observations in execution increases communication delay and failure rate, and hurts the robustness.", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "Second, online learning is not common due to safety and efficiency concerns. Rather, each model is", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "trained offline and tested extensively before field deployment. In online execution, the model only", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "runs forward propagation, and its performance is constantly monitored for triggering re-training. To", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "reflect these practical constraints in NSC, we assume 1) each agent is connected to a limited number", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "of neighbors and communication is restricted to its neighborhood, and 2) training is offline and global", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 490, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 490, + 106 + ], + "score": 1.0, + "content": "information is available in rollout training minibatches, despite a decentralized training process.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 46.5, + "bbox_fs": [ + 105, + 644, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "of neighbors and communication is restricted to its neighborhood, and 2) training is offline and global", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 490, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 490, + 106 + ], + "score": 1.0, + "content": "information is available in rollout training minibatches, despite a decentralized training process.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 110, + 505, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "The contributions of this paper are three-fold. First, we formulate NMARL under the aforementioned", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "score": 1.0, + "content": "NSC assumptions as a decentralized spatiotemporal MDP, and introduce a spatial discount factor to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "stabilize training, especially for non-communicative algorithms. Second, we propose a new neural", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "communication protocol, called NeurComm, to adaptively share information on both system states", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "score": 1.0, + "content": "and agent behaviors. Third, we design and simulate realistic NMARL environments to evaluate and", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 339, + 177 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 339, + 177 + ], + "score": 1.0, + "content": "compare our approaches against recent MARL baselines.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4.5 + }, + { + "type": "title", + "bbox": [ + 108, + 200, + 210, + 213 + ], + "lines": [ + { + "bbox": [ + 104, + 199, + 213, + 216 + ], + "spans": [ + { + "bbox": [ + 104, + 199, + 213, + 216 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 230, + 505, + 341 + ], + "lines": [ + { + "bbox": [ + 105, + 231, + 506, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 243 + ], + "score": 1.0, + "content": "MARL works can be classified into four groups based on their communication methods. The first", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "group is non-communicative and focuses on stabilizing training with advanced value estimation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "score": 1.0, + "content": "methods. In MADDPG, each action-value is estimated by a centralized critic based on global", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "observations and actions (or inferred actions) (Lowe et al., 2017). COMA extends the same idea to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "A2C and estimates each advantage using a centralized critic and a counterfactual baseline (Foerster", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "score": 1.0, + "content": "et al., 2018). In Dec-HDRQN (Omidshafiei et al., 2017) and PS-TRPO (Gupta et al., 2017), the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 296, + 507, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 507, + 309 + ], + "score": 1.0, + "content": "centralized critic takes local observations, but the parameters are shared globally. In the NMARL", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "score": 1.0, + "content": "work of Zhang et al. (2018), the critic is fully decentralized but each takes global observations and", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 505, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 505, + 332 + ], + "score": 1.0, + "content": "performs consensus updates. In this paper, we empirically confirm that a spatial discount factor helps", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 330, + 462, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 462, + 342 + ], + "score": 1.0, + "content": "stabilize the training of non-communicative algorithms under neighborhood observation.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 346, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 106, + 347, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 505, + 358 + ], + "score": 1.0, + "content": "The second group considers heuristic communication protocols or direct information sharing. Foerster", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "score": 1.0, + "content": "et al. (2017) shows performance gains with directly-shared low dimensional policy fingerprints from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "other agents. Similarly, mean field MARL takes the average of neighbor policies for informed", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "action-value estimation (Yang et al., 2018). The major disadvantage of this group is that, unlike", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 388, + 506, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 404 + ], + "score": 1.0, + "content": "NeurComm, the communication is not explicitly designed for performance optimization, which may", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 401, + 354, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 354, + 413 + ], + "score": 1.0, + "content": "cause inefficient and redundant communications in execution.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 418, + 506, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 506, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 431 + ], + "score": 1.0, + "content": "The third group proposes learnable communication protocols. In DIAL, the message is generated", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "together with action-value estimation by each DQN agent, then it is encoded and summed with other", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "input signals at the receiver side (Foerster et al., 2016). CommNet is a more general communication", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 451, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 104, + 451, + 506, + 464 + ], + "score": 1.0, + "content": "protocol, but it calculates the mean of all messages instead of encoding them (Sukhbaatar et al., 2016).", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "score": 1.0, + "content": "Both works, especially CommNet, incur an information loss due to aggregation on input signals.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "Another collection of works focuses on communications in strategy games. In BiCNet (Peng et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 483, + 507, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 507, + 497 + ], + "score": 1.0, + "content": "2017), a bi-directional RNN is used to enable flat communication among agents, while in Master-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "Slave (Kong et al., 2017), two-way message passing is utilized in a hierarchical RNN architecture of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "master and slave agents. In contrast to existing protocols, NeurComm 1) encodes and concatenates", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "score": 1.0, + "content": "signals, instead of aggregating them, to minimize information loss, and 2) includes policy fingerprints", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 527, + 288, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 288, + 541 + ], + "score": 1.0, + "content": "in communication to reduce non-stationarity.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "score": 1.0, + "content": "The fourth group focuses on communication attentions to selectively send messages. ATOC (Jiang &", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "score": 1.0, + "content": "Lu, 2018) learns a soft attention which allocates a communication probability to each other agent,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 565, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 506, + 580 + ], + "score": 1.0, + "content": "while IC3Net (Singh et al., 2018) learns a hard binary attention which decides communicating or", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 577, + 507, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 507, + 591 + ], + "score": 1.0, + "content": "not. These works are especially useful when each agent has to prioritize the communication targets.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "score": 1.0, + "content": "NMARL is less likely the case since the communication range is restricted to small neighborhoods.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38 + }, + { + "type": "title", + "bbox": [ + 108, + 624, + 237, + 637 + ], + "lines": [ + { + "bbox": [ + 105, + 623, + 240, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 240, + 639 + ], + "score": 1.0, + "content": "3 SPATIOTEMPORAL RL", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 698 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "This section formulates the NMARL problem as a decentralized spatiotemporal MDP, and introduces", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "the spatial discount factor to reduce its learning difficulty. To simplify the notation, we assume the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "score": 1.0, + "content": "true system state is observable, and use “state” and “observation” interchangeably. This does not", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 687, + 485, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 485, + 699 + ], + "score": 1.0, + "content": "affect the validity of proposed methods in practice. To save space, all proofs are deferred to A.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 119, + 722, + 398, + 732 + ], + "lines": [ + { + "bbox": [ + 119, + 720, + 399, + 733 + ], + "spans": [ + { + "bbox": [ + 119, + 720, + 399, + 733 + ], + "score": 1.0, + "content": "1Code link: https://github.com/cts198859/deeprl_network.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 82, + 504, + 105 + ], + "lines": [], + "index": 0.5, + "bbox_fs": [ + 106, + 82, + 505, + 106 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 110, + 505, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "The contributions of this paper are three-fold. First, we formulate NMARL under the aforementioned", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "score": 1.0, + "content": "NSC assumptions as a decentralized spatiotemporal MDP, and introduce a spatial discount factor to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "stabilize training, especially for non-communicative algorithms. Second, we propose a new neural", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "communication protocol, called NeurComm, to adaptively share information on both system states", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 166 + ], + "score": 1.0, + "content": "and agent behaviors. Third, we design and simulate realistic NMARL environments to evaluate and", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 339, + 177 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 339, + 177 + ], + "score": 1.0, + "content": "compare our approaches against recent MARL baselines.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4.5, + "bbox_fs": [ + 105, + 110, + 506, + 177 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 200, + 210, + 213 + ], + "lines": [ + { + "bbox": [ + 104, + 199, + 213, + 216 + ], + "spans": [ + { + "bbox": [ + 104, + 199, + 213, + 216 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 230, + 505, + 341 + ], + "lines": [ + { + "bbox": [ + 105, + 231, + 506, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 243 + ], + "score": 1.0, + "content": "MARL works can be classified into four groups based on their communication methods. The first", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 506, + 255 + ], + "score": 1.0, + "content": "group is non-communicative and focuses on stabilizing training with advanced value estimation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "score": 1.0, + "content": "methods. In MADDPG, each action-value is estimated by a centralized critic based on global", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "observations and actions (or inferred actions) (Lowe et al., 2017). COMA extends the same idea to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 506, + 288 + ], + "score": 1.0, + "content": "A2C and estimates each advantage using a centralized critic and a counterfactual baseline (Foerster", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "score": 1.0, + "content": "et al., 2018). In Dec-HDRQN (Omidshafiei et al., 2017) and PS-TRPO (Gupta et al., 2017), the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 296, + 507, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 507, + 309 + ], + "score": 1.0, + "content": "centralized critic takes local observations, but the parameters are shared globally. 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In this paper, we empirically confirm that a spatial discount factor helps", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 330, + 462, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 462, + 342 + ], + "score": 1.0, + "content": "stabilize the training of non-communicative algorithms under neighborhood observation.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 231, + 507, + 342 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 346, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 106, + 347, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 505, + 358 + ], + "score": 1.0, + "content": "The second group considers heuristic communication protocols or direct information sharing. Foerster", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "score": 1.0, + "content": "et al. (2017) shows performance gains with directly-shared low dimensional policy fingerprints from", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "other agents. Similarly, mean field MARL takes the average of neighbor policies for informed", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "action-value estimation (Yang et al., 2018). The major disadvantage of this group is that, unlike", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 388, + 506, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 404 + ], + "score": 1.0, + "content": "NeurComm, the communication is not explicitly designed for performance optimization, which may", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 401, + 354, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 354, + 413 + ], + "score": 1.0, + "content": "cause inefficient and redundant communications in execution.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 347, + 506, + 413 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 418, + 506, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 506, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 431 + ], + "score": 1.0, + "content": "The third group proposes learnable communication protocols. In DIAL, the message is generated", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "together with action-value estimation by each DQN agent, then it is encoded and summed with other", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "input signals at the receiver side (Foerster et al., 2016). CommNet is a more general communication", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 451, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 104, + 451, + 506, + 464 + ], + "score": 1.0, + "content": "protocol, but it calculates the mean of all messages instead of encoding them (Sukhbaatar et al., 2016).", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 506, + 475 + ], + "score": 1.0, + "content": "Both works, especially CommNet, incur an information loss due to aggregation on input signals.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "Another collection of works focuses on communications in strategy games. In BiCNet (Peng et al.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 483, + 507, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 507, + 497 + ], + "score": 1.0, + "content": "2017), a bi-directional RNN is used to enable flat communication among agents, while in Master-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 495, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 508 + ], + "score": 1.0, + "content": "Slave (Kong et al., 2017), two-way message passing is utilized in a hierarchical RNN architecture of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "master and slave agents. In contrast to existing protocols, NeurComm 1) encodes and concatenates", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "score": 1.0, + "content": "signals, instead of aggregating them, to minimize information loss, and 2) includes policy fingerprints", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 527, + 288, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 288, + 541 + ], + "score": 1.0, + "content": "in communication to reduce non-stationarity.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30, + "bbox_fs": [ + 104, + 417, + 507, + 541 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "score": 1.0, + "content": "The fourth group focuses on communication attentions to selectively send messages. ATOC (Jiang &", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "score": 1.0, + "content": "Lu, 2018) learns a soft attention which allocates a communication probability to each other agent,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 565, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 506, + 580 + ], + "score": 1.0, + "content": "while IC3Net (Singh et al., 2018) learns a hard binary attention which decides communicating or", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 577, + 507, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 507, + 591 + ], + "score": 1.0, + "content": "not. These works are especially useful when each agent has to prioritize the communication targets.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 602 + ], + "score": 1.0, + "content": "NMARL is less likely the case since the communication range is restricted to small neighborhoods.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 544, + 507, + 602 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 624, + 237, + 637 + ], + "lines": [ + { + "bbox": [ + 105, + 623, + 240, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 240, + 639 + ], + "score": 1.0, + "content": "3 SPATIOTEMPORAL RL", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 698 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "This section formulates the NMARL problem as a decentralized spatiotemporal MDP, and introduces", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "the spatial discount factor to reduce its learning difficulty. To simplify the notation, we assume the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "score": 1.0, + "content": "true system state is observable, and use “state” and “observation” interchangeably. This does not", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 687, + 485, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 485, + 699 + ], + "score": 1.0, + "content": "affect the validity of proposed methods in practice. To save space, all proofs are deferred to A.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 654, + 506, + 699 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 221, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 223, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 223, + 96 + ], + "score": 1.0, + "content": "3.1 NETWORKED MARL", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 102, + 505, + 251 + ], + "lines": [ + { + "bbox": [ + 104, + 102, + 506, + 116 + ], + "spans": [ + { + "bbox": [ + 104, + 102, + 305, + 116 + ], + "score": 1.0, + "content": "The networked system is represented by a graph", + "type": "text" + }, + { + "bbox": [ + 306, + 103, + 339, + 115 + ], + "score": 0.94, + "content": "G ( \\nu , \\mathcal { E } )", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 102, + 368, + 116 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 368, + 104, + 393, + 113 + ], + "score": 0.9, + "content": "i \\in \\mathcal V", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 102, + 466, + 116 + ], + "score": 1.0, + "content": "is each agent and", + "type": "text" + }, + { + "bbox": [ + 466, + 103, + 494, + 114 + ], + "score": 0.91, + "content": "i j \\in \\mathcal { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 102, + 506, + 116 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 104, + 113, + 388, + 127 + ], + "score": 1.0, + "content": "each communication link. The corresponding MDP is characterized as", + "type": "text" + }, + { + "bbox": [ + 389, + 114, + 477, + 126 + ], + "score": 0.91, + "content": "( G , \\{ S _ { i } , A _ { i } \\} _ { i \\in \\mathcal { V } } , p , r )", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "where", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 124, + 504, + 137 + ], + "spans": [ + { + "bbox": [ + 106, + 125, + 117, + 136 + ], + "score": 0.87, + "content": "s _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 124, + 135, + 137 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 135, + 126, + 147, + 136 + ], + "score": 0.89, + "content": "A _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 124, + 347, + 137 + ], + "score": 1.0, + "content": "are the local state space and action space of agent", + "type": "text" + }, + { + "bbox": [ + 347, + 126, + 352, + 135 + ], + "score": 0.62, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 124, + 372, + 137 + ], + "score": 1.0, + "content": ". Let", + "type": "text" + }, + { + "bbox": [ + 372, + 126, + 427, + 136 + ], + "score": 0.91, + "content": "\\boldsymbol { S } : = \\times _ { i \\in \\mathcal { V } } \\boldsymbol { S } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 124, + 445, + 137 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 446, + 126, + 504, + 136 + ], + "score": 0.92, + "content": "\\mathcal { A } : = \\times _ { i \\in \\mathcal { V } } \\mathcal { A } _ { i }", + "type": "inline_equation" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 505, + 148 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 505, + 148 + ], + "score": 1.0, + "content": "be the global state space and action space, MDP transitions follow a stationary probability distribution", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 146, + 506, + 159 + ], + "spans": [ + { + "bbox": [ + 106, + 147, + 204, + 159 + ], + "score": 0.9, + "content": "p : \\mathcal { S } \\times \\mathcal { A } \\times \\mathcal { S } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 146, + 367, + 159 + ], + "score": 1.0, + "content": ", and global step rewards be denoted by", + "type": "text" + }, + { + "bbox": [ + 367, + 147, + 433, + 157 + ], + "score": 0.92, + "content": "r : S \\times \\mathcal { A } \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 146, + 506, + 159 + ], + "score": 1.0, + "content": ". 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The MDP objective is to", + "type": "text" + }, + { + "bbox": [ + 313, + 158, + 405, + 169 + ], + "score": 0.91, + "content": "\\pi _ { i } : S _ { i } \\times \\mathcal { A } _ { i } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 157, + 411, + 192 + ], + "score": 1.0, + "content": "te", + "type": "text" + }, + { + "bbox": [ + 494, + 157, + 507, + 192 + ], + "score": 1.0, + "content": "onis", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 169, + 494, + 183 + ], + "spans": [ + { + "bbox": [ + 107, + 171, + 171, + 183 + ], + "score": 0.92, + "content": "a _ { i , t } \\sim \\pi _ { i } ( \\cdot | s _ { i , t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 172, + 207, + 181 + ], + "score": 0.6, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 171, + 380, + 183 + ], + "score": 0.91, + "content": "\\mathbb { E } [ R _ { 0 } ^ { \\pi } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 169, + 494, + 183 + ], + "score": 0.93, + "content": "\\begin{array} { r } { R _ { t } ^ { \\pi } = \\sum _ { \\tau = t } ^ { T } \\gamma ^ { \\tau - t } r _ { \\tau } } \\end{array}", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 293, + 196 + ], + "score": 1.0, + "content": "the long-term global return with discount factor", + "type": "text" + }, + { + "bbox": [ + 300, + 180, + 506, + 196 + ], + "score": 1.0, + "content": ". Here the expectation is taken over the global policy", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 192, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 107, + 193, + 182, + 205 + ], + "score": 0.9, + "content": "\\pi : \\mathcal { S } \\times \\mathcal { A } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 192, + 271, + 207 + ], + "score": 1.0, + "content": ", the initial distribution", + "type": "text" + }, + { + "bbox": [ + 271, + 195, + 298, + 204 + ], + "score": 0.89, + "content": "s _ { t } \\sim \\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 192, + 371, + 207 + ], + "score": 1.0, + "content": ", and the transition", + "type": "text" + }, + { + "bbox": [ + 372, + 193, + 448, + 205 + ], + "score": 0.9, + "content": "s _ { \\tau + 1 } \\sim p ( \\cdot | s _ { \\tau } , a _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 192, + 506, + 207 + ], + "score": 1.0, + "content": ", regarding the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 203, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 104, + 203, + 155, + 217 + ], + "score": 1.0, + "content": "step reward", + "type": "text" + }, + { + "bbox": [ + 155, + 204, + 215, + 216 + ], + "score": 0.87, + "content": "\\dot { r _ { \\tau } } = \\dot { r } ( s _ { \\tau } , a _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 203, + 218, + 217 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 219, + 204, + 252, + 215 + ], + "score": 0.78, + "content": "\\forall \\tau < T", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 203, + 352, + 217 + ], + "score": 1.0, + "content": ", and the terminal reward", + "type": "text" + }, + { + "bbox": [ + 352, + 204, + 412, + 216 + ], + "score": 0.88, + "content": "r _ { T } = r _ { T } ( s _ { T } ) ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 203, + 506, + 217 + ], + "score": 1.0, + "content": ". The same system can", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 506, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 287, + 229 + ], + "score": 1.0, + "content": "be formulated as a centralized MDP. Defining", + "type": "text" + }, + { + "bbox": [ + 288, + 215, + 382, + 227 + ], + "score": 0.92, + "content": "V ^ { \\pi } ( s ) = \\mathbb { E } [ R _ { t } ^ { \\pi } | s _ { t } = s ]", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 214, + 506, + 229 + ], + "score": 1.0, + "content": "as the state-value function and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 107, + 224, + 502, + 241 + ], + "spans": [ + { + "bbox": [ + 107, + 226, + 242, + 237 + ], + "score": 0.89, + "content": "Q ^ { \\pi } ( s , a ) = \\mathbb { E } [ R _ { t } ^ { \\pi } | s _ { t } = s , a _ { t } = a ]", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 224, + 392, + 241 + ], + "score": 1.0, + "content": "as the action-value function, we have", + "type": "text" + }, + { + "bbox": [ + 392, + 226, + 502, + 239 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\mathbb { E } [ R _ { 0 } ^ { \\pi } ] = \\sum _ { s \\in \\cal S } \\rho ( s ) V ^ { \\pi } ( s ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 235, + 480, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 239, + 251 + ], + "score": 0.9, + "content": "\\begin{array} { r } { V ^ { \\pi } ( s ) = \\sum _ { a \\in \\mathcal { A } } \\pi ( a | s ) Q ^ { \\pi } ( s , a ) , } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 235, + 353, + 253 + ], + "score": 1.0, + "content": ", and the advantage function", + "type": "text" + }, + { + "bbox": [ + 353, + 238, + 475, + 250 + ], + "score": 0.91, + "content": "A ^ { \\pi } ( s , a ) = Q ^ { \\pi } ( s , a ) - \\mathbf { \\bar { \\psi } } V ^ { \\pi } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 235, + 480, + 253 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 254, + 505, + 335 + ], + "lines": [ + { + "bbox": [ + 106, + 255, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 266 + ], + "score": 1.0, + "content": "MARL provides a scalable solution for controlling networked systems, but it introduces partial", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 278 + ], + "score": 1.0, + "content": "observability and non-stationarity in decentralized MDP of each agent, leading to inefficient and", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 295, + 290 + ], + "score": 1.0, + "content": "unstable learning performance. To see this, note", + "type": "text" + }, + { + "bbox": [ + 295, + 277, + 351, + 288 + ], + "score": 0.9, + "content": "s _ { i , t } \\in S _ { i } \\subseteq S", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 276, + 505, + 290 + ], + "score": 1.0, + "content": "does not provide sufficient information", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 285, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 104, + 285, + 121, + 304 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 289, + 131, + 299 + ], + "score": 0.84, + "content": "\\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 285, + 203, + 304 + ], + "score": 1.0, + "content": ". Even assuming", + "type": "text" + }, + { + "bbox": [ + 203, + 289, + 241, + 300 + ], + "score": 0.9, + "content": "s _ { i , t } = s _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 285, + 302, + 304 + ], + "score": 1.0, + "content": ", the transition", + "type": "text" + }, + { + "bbox": [ + 303, + 288, + 502, + 302 + ], + "score": 0.9, + "content": "\\begin{array} { r } { p _ { i } ( s _ { i , t + 1 } \\vert s _ { i , t } , a _ { i , t } ) = \\sum _ { a _ { - i , t } \\in A _ { - i } } \\pi _ { - i } ( a _ { - i , t } \\vert s _ { t } ) \\ . } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 285, + 506, + 304 + ], + "score": 1.0, + "content": "·", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 503, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 192, + 313 + ], + "score": 0.92, + "content": "p ( s _ { t + 1 } | s _ { t } , a _ { i , t } , a _ { - i , t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 298, + 421, + 317 + ], + "score": 1.0, + "content": "is non-stationary if the behavior policies of other agents", + "type": "text" + }, + { + "bbox": [ + 421, + 301, + 503, + 314 + ], + "score": 0.88, + "content": "\\pi _ { - i } : = \\{ \\pi _ { j } \\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} }", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "score": 1.0, + "content": "are evolving over time. In this paper, we enforce practical constraints and only allow local observations", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 322, + 434, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 434, + 337 + ], + "score": 1.0, + "content": "and neighborhood communications, which makes MARL even more challenging.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 337, + 505, + 408 + ], + "lines": [ + { + "bbox": [ + 106, + 337, + 506, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 506, + 350 + ], + "score": 1.0, + "content": "Definition 3.1 (Networked Multi-agent MDP with Neighborhood Communication). 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All local rewards are shared globally, whereas the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 373, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 373, + 354, + 388 + ], + "score": 1.0, + "content": "communication is limited to neighborhoods, that is, each agent", + "type": "text" + }, + { + "bbox": [ + 354, + 375, + 360, + 384 + ], + "score": 0.74, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 373, + 397, + 388 + ], + "score": 1.0, + "content": "observes", + "type": "text" + }, + { + "bbox": [ + 397, + 374, + 479, + 386 + ], + "score": 0.91, + "content": "\\tilde { s } _ { i , t } : = s _ { i , t } \\cup m _ { \\mathcal { N } _ { i } i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 373, + 505, + 388 + ], + "score": 1.0, + "content": ". 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We assume local transitions are independent of other agents", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 452, + 256, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 256, + 465 + ], + "score": 1.0, + "content": "given the neighboring agents, that is,", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28.5 + }, + { + "type": "interline_equation", + "bbox": [ + 146, + 468, + 464, + 497 + ], + "lines": [ + { + "bbox": [ + 146, + 468, + 464, + 497 + ], + "spans": [ + { + "bbox": [ + 146, + 468, + 464, + 497 + ], + "score": 0.92, + "content": "p _ { i } ( s _ { i , t + 1 } | s _ { \\mathcal { V } _ { i } , t } , a _ { i , t } ) = \\sum _ { a _ { \\mathcal { N } _ { i } , t } \\in A _ { \\mathcal { N } _ { i } } } \\prod _ { j \\in \\mathcal { N } _ { i } } \\pi _ { j } ( a _ { j , t } | \\tilde { s } _ { j , t } ) \\cdot p ( s _ { i , t + 1 } | s _ { \\mathcal { V } _ { i } , t } , a _ { i , t } , a _ { \\mathcal { N } _ { i } , t } ) ,", + "type": "interline_equation", + "image_path": "35ee4be3fd5d6a6c05c2d725b764bd04bb8d20592d6df72015a123a34a9bce3f.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 146, + 468, + 464, + 477.6666666666667 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 146, + 477.6666666666667, + 464, + 487.33333333333337 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 146, + 487.33333333333337, + 464, + 497.00000000000006 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 502, + 505, + 537 + ], + "lines": [ + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 133, + 515 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 502, + 195, + 515 + ], + "score": 0.93, + "content": "\\mathcal { V } _ { i } : = \\mathcal { N } _ { i } \\cup \\{ i \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 501, + 323, + 515 + ], + "score": 1.0, + "content": "is the closed neighborhood, and", + "type": "text" + }, + { + "bbox": [ + 323, + 505, + 329, + 514 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 501, + 506, + 515 + ], + "score": 1.0, + "content": "is abused to denote any stationary transition.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 513, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 513, + 258, + 526 + ], + "score": 1.0, + "content": "Then from the viewpoint of each agent", + "type": "text" + }, + { + "bbox": [ + 259, + 515, + 263, + 523 + ], + "score": 0.78, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 513, + 505, + 526 + ], + "score": 1.0, + "content": ", Definition 3.1 is equivalent to a decentralized spatiotemporal", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 524, + 483, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 199, + 538 + ], + "score": 1.0, + "content": "MDP, characterized as", + "type": "text" + }, + { + "bbox": [ + 199, + 524, + 334, + 537 + ], + "score": 0.91, + "content": "( S _ { i } , \\mathcal { A } _ { i } , \\{ \\mathcal { M } _ { j i } \\} _ { j \\in \\mathcal { N } _ { i } } , p _ { i } , \\{ r _ { i } \\} _ { i \\in \\mathcal { V } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 524, + 483, + 538 + ], + "score": 1.0, + "content": ", by optimizing the discounted return", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + }, + { + "type": "interline_equation", + "bbox": [ + 236, + 541, + 374, + 581 + ], + "lines": [ + { + "bbox": [ + 236, + 541, + 374, + 581 + ], + "spans": [ + { + "bbox": [ + 236, + 541, + 374, + 581 + ], + "score": 0.95, + "content": "R _ { i , t } ^ { \\pi } = \\sum _ { \\tau = t } ^ { T } \\gamma ^ { \\tau - t } \\left( \\sum _ { j \\in \\mathcal { V } } \\alpha ^ { d _ { i j } } r _ { j , t } \\right) ,", + "type": "interline_equation", + "image_path": "7190edde23aebeb65a830915fc36ac5d858d5e73114fb496628d0e77c5d49de4.jpg" + } + ] + } + ], + "index": 36.5, + "virtual_lines": [ + { + "bbox": [ + 236, + 541, + 374, + 561.0 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 236, + 561.0, + 374, + 581.0 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 584, + 465, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 462, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 133, + 599 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 585, + 177, + 596 + ], + "score": 0.91, + "content": "0 \\leq \\alpha \\leq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 582, + 311, + 599 + ], + "score": 1.0, + "content": "is the spatial discount factor, and", + "type": "text" + }, + { + "bbox": [ + 312, + 585, + 325, + 597 + ], + "score": 0.91, + "content": "d _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 582, + 434, + 599 + ], + "score": 1.0, + "content": "is distance between agents", + "type": "text" + }, + { + "bbox": [ + 434, + 586, + 439, + 595 + ], + "score": 0.76, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 582, + 457, + 599 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 457, + 586, + 462, + 596 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 106, + 604, + 506, + 705 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "score": 1.0, + "content": "The major assumption in Definition 3.2 is that the Markovian property holds both temporally", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 616, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 629 + ], + "score": 1.0, + "content": "and spatially, so that the next local state depends on the neighborhood states and policies only.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "score": 1.0, + "content": "This assumption is valid in most networked control systems such as traffic and wireless networks,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "as well as the power grid, where the impact of each agent is spread over the entire system via", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 649, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 662 + ], + "score": 1.0, + "content": "controlled flows, or chained local transitions. 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Let", + "type": "text" + }, + { + "bbox": [ + 372, + 126, + 427, + 136 + ], + "score": 0.91, + "content": "\\boldsymbol { S } : = \\times _ { i \\in \\mathcal { V } } \\boldsymbol { S } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 124, + 445, + 137 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 446, + 126, + 504, + 136 + ], + "score": 0.92, + "content": "\\mathcal { A } : = \\times _ { i \\in \\mathcal { V } } \\mathcal { A } _ { i }", + "type": "inline_equation" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 505, + 148 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 505, + 148 + ], + "score": 1.0, + "content": "be the global state space and action space, MDP transitions follow a stationary probability distribution", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 146, + 506, + 159 + ], + "spans": [ + { + "bbox": [ + 106, + 147, + 204, + 159 + ], + "score": 0.9, + "content": "p : \\mathcal { S } \\times \\mathcal { A } \\times \\mathcal { S } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 146, + 367, + 159 + ], + "score": 1.0, + "content": ", and global step rewards be denoted by", + "type": "text" + }, + { + "bbox": [ + 367, + 147, + 433, + 157 + ], + "score": 0.92, + "content": "r : S \\times \\mathcal { A } \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 146, + 506, + 159 + ], + "score": 1.0, + "content": ". 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The MDP objective is to", + "type": "text" + }, + { + "bbox": [ + 313, + 158, + 405, + 169 + ], + "score": 0.91, + "content": "\\pi _ { i } : S _ { i } \\times \\mathcal { A } _ { i } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 157, + 411, + 192 + ], + "score": 1.0, + "content": "te", + "type": "text" + }, + { + "bbox": [ + 494, + 157, + 507, + 192 + ], + "score": 1.0, + "content": "onis", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 169, + 494, + 183 + ], + "spans": [ + { + "bbox": [ + 107, + 171, + 171, + 183 + ], + "score": 0.92, + "content": "a _ { i , t } \\sim \\pi _ { i } ( \\cdot | s _ { i , t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 172, + 207, + 181 + ], + "score": 0.6, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 171, + 380, + 183 + ], + "score": 0.91, + "content": "\\mathbb { E } [ R _ { 0 } ^ { \\pi } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 169, + 494, + 183 + ], + "score": 0.93, + "content": "\\begin{array} { r } { R _ { t } ^ { \\pi } = \\sum _ { \\tau = t } ^ { T } \\gamma ^ { \\tau - t } r _ { \\tau } } \\end{array}", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 293, + 196 + ], + "score": 1.0, + "content": "the long-term global return with discount factor", + "type": "text" + }, + { + "bbox": [ + 300, + 180, + 506, + 196 + ], + "score": 1.0, + "content": ". Here the expectation is taken over the global policy", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 107, + 192, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 107, + 193, + 182, + 205 + ], + "score": 0.9, + "content": "\\pi : \\mathcal { S } \\times \\mathcal { A } [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 192, + 271, + 207 + ], + "score": 1.0, + "content": ", the initial distribution", + "type": "text" + }, + { + "bbox": [ + 271, + 195, + 298, + 204 + ], + "score": 0.89, + "content": "s _ { t } \\sim \\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 192, + 371, + 207 + ], + "score": 1.0, + "content": ", and the transition", + "type": "text" + }, + { + "bbox": [ + 372, + 193, + 448, + 205 + ], + "score": 0.9, + "content": "s _ { \\tau + 1 } \\sim p ( \\cdot | s _ { \\tau } , a _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 192, + 506, + 207 + ], + "score": 1.0, + "content": ", regarding the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 104, + 203, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 104, + 203, + 155, + 217 + ], + "score": 1.0, + "content": "step reward", + "type": "text" + }, + { + "bbox": [ + 155, + 204, + 215, + 216 + ], + "score": 0.87, + "content": "\\dot { r _ { \\tau } } = \\dot { r } ( s _ { \\tau } , a _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 203, + 218, + 217 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 219, + 204, + 252, + 215 + ], + "score": 0.78, + "content": "\\forall \\tau < T", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 203, + 352, + 217 + ], + "score": 1.0, + "content": ", and the terminal reward", + "type": "text" + }, + { + "bbox": [ + 352, + 204, + 412, + 216 + ], + "score": 0.88, + "content": "r _ { T } = r _ { T } ( s _ { T } ) ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 203, + 506, + 217 + ], + "score": 1.0, + "content": ". The same system can", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 506, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 287, + 229 + ], + "score": 1.0, + "content": "be formulated as a centralized MDP. Defining", + "type": "text" + }, + { + "bbox": [ + 288, + 215, + 382, + 227 + ], + "score": 0.92, + "content": "V ^ { \\pi } ( s ) = \\mathbb { E } [ R _ { t } ^ { \\pi } | s _ { t } = s ]", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 214, + 506, + 229 + ], + "score": 1.0, + "content": "as the state-value function and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 107, + 224, + 502, + 241 + ], + "spans": [ + { + "bbox": [ + 107, + 226, + 242, + 237 + ], + "score": 0.89, + "content": "Q ^ { \\pi } ( s , a ) = \\mathbb { E } [ R _ { t } ^ { \\pi } | s _ { t } = s , a _ { t } = a ]", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 224, + 392, + 241 + ], + "score": 1.0, + "content": "as the action-value function, we have", + "type": "text" + }, + { + "bbox": [ + 392, + 226, + 502, + 239 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\mathbb { E } [ R _ { 0 } ^ { \\pi } ] = \\sum _ { s \\in \\cal S } \\rho ( s ) V ^ { \\pi } ( s ) } \\end{array}", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 235, + 480, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 239, + 251 + ], + "score": 0.9, + "content": "\\begin{array} { r } { V ^ { \\pi } ( s ) = \\sum _ { a \\in \\mathcal { A } } \\pi ( a | s ) Q ^ { \\pi } ( s , a ) , } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 235, + 353, + 253 + ], + "score": 1.0, + "content": ", and the advantage function", + "type": "text" + }, + { + "bbox": [ + 353, + 238, + 475, + 250 + ], + "score": 0.91, + "content": "A ^ { \\pi } ( s , a ) = Q ^ { \\pi } ( s , a ) - \\mathbf { \\bar { \\psi } } V ^ { \\pi } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 235, + 480, + 253 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 7, + "bbox_fs": [ + 104, + 102, + 507, + 253 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 254, + 505, + 335 + ], + "lines": [ + { + "bbox": [ + 106, + 255, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 505, + 266 + ], + "score": 1.0, + "content": "MARL provides a scalable solution for controlling networked systems, but it introduces partial", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 278 + ], + "score": 1.0, + "content": "observability and non-stationarity in decentralized MDP of each agent, leading to inefficient and", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 295, + 290 + ], + "score": 1.0, + "content": "unstable learning performance. To see this, note", + "type": "text" + }, + { + "bbox": [ + 295, + 277, + 351, + 288 + ], + "score": 0.9, + "content": "s _ { i , t } \\in S _ { i } \\subseteq S", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 276, + 505, + 290 + ], + "score": 1.0, + "content": "does not provide sufficient information", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 285, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 104, + 285, + 121, + 304 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 289, + 131, + 299 + ], + "score": 0.84, + "content": "\\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 285, + 203, + 304 + ], + "score": 1.0, + "content": ". Even assuming", + "type": "text" + }, + { + "bbox": [ + 203, + 289, + 241, + 300 + ], + "score": 0.9, + "content": "s _ { i , t } = s _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 285, + 302, + 304 + ], + "score": 1.0, + "content": ", the transition", + "type": "text" + }, + { + "bbox": [ + 303, + 288, + 502, + 302 + ], + "score": 0.9, + "content": "\\begin{array} { r } { p _ { i } ( s _ { i , t + 1 } \\vert s _ { i , t } , a _ { i , t } ) = \\sum _ { a _ { - i , t } \\in A _ { - i } } \\pi _ { - i } ( a _ { - i , t } \\vert s _ { t } ) \\ . } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 285, + 506, + 304 + ], + "score": 1.0, + "content": "·", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 503, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 192, + 313 + ], + "score": 0.92, + "content": "p ( s _ { t + 1 } | s _ { t } , a _ { i , t } , a _ { - i , t } )", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 298, + 421, + 317 + ], + "score": 1.0, + "content": "is non-stationary if the behavior policies of other agents", + "type": "text" + }, + { + "bbox": [ + 421, + 301, + 503, + 314 + ], + "score": 0.88, + "content": "\\pi _ { - i } : = \\{ \\pi _ { j } \\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} }", + "type": "inline_equation" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "score": 1.0, + "content": "are evolving over time. 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t } \\left( \\sum _ { j \\in \\mathcal { V } } \\alpha ^ { d _ { i j } } r _ { j , t } \\right) ,", + "type": "interline_equation", + "image_path": "7190edde23aebeb65a830915fc36ac5d858d5e73114fb496628d0e77c5d49de4.jpg" + } + ] + } + ], + "index": 36.5, + "virtual_lines": [ + { + "bbox": [ + 236, + 541, + 374, + 561.0 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 236, + 561.0, + 374, + 581.0 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 584, + 465, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 462, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 133, + 599 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 585, + 177, + 596 + ], + "score": 0.91, + "content": "0 \\leq \\alpha \\leq 1", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 582, + 311, + 599 + ], + "score": 1.0, + "content": "is the spatial discount factor, and", + "type": "text" + }, + { + "bbox": [ + 312, + 585, + 325, + 597 + ], + "score": 0.91, + "content": "d _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 582, + 434, + 599 + ], + "score": 1.0, + "content": "is distance between agents", + "type": "text" + }, + { + "bbox": [ + 434, + 586, + 439, + 595 + ], + "score": 0.76, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 582, + 457, + 599 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 457, + 586, + 462, + 596 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + } + ], + "index": 38 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 582, + 462, + 599 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 604, + 506, + 705 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "score": 1.0, + "content": "The major assumption in Definition 3.2 is that the Markovian property holds both temporally", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 616, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 629 + ], + "score": 1.0, + "content": "and spatially, so that the next local state depends on the neighborhood states and policies only.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 506, + 640 + ], + "score": 1.0, + "content": "This assumption is valid in most networked control systems such as traffic and wireless networks,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "as well as the power grid, where the impact of each agent is spread over the entire system via", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 649, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 662 + ], + "score": 1.0, + "content": "controlled flows, or chained local transitions. 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To reduce the learning difficulty of", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 104, + 682, + 506, + 695 + ], + "spans": [ + { + "bbox": [ + 104, + 682, + 506, + 695 + ], + "score": 1.0, + "content": "spatiotemporal MDP, a spatiotemporally discounted return is introduced in Eq. (2) to scale down", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 694, + 507, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 694, + 474, + 705 + ], + "score": 1.0, + "content": "reward signals further away (which are more difficult to fit using local information). When", + "type": "text" + }, + { + "bbox": [ + 474, + 694, + 502, + 703 + ], + "score": 0.88, + "content": "\\alpha 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 694, + 507, + 705 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 304, + 95 + ], + "score": 1.0, + "content": "each agent performs local greedy control; when", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 304, + 83, + 333, + 92 + ], + "score": 0.89, + "content": "\\alpha 1", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 334, + 82, + 505, + 95 + ], + "score": 1.0, + "content": ", each agent performs global coordination", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 91, + 503, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 91, + 124, + 108 + ], + "score": 1.0, + "content": "and", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 124, + 93, + 203, + 106 + ], + "score": 0.9, + "content": "R _ { i , t } ^ { \\pi } = R _ { t } ^ { \\pi } , \\forall i \\in \\mathcal { V }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 204, + 91, + 280, + 108 + ], + "score": 1.0, + "content": ". 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To simplify the notation, we assume all messages sent from agent", + "type": "text" + }, + { + "bbox": [ + 428, + 398, + 433, + 406 + ], + "score": 0.78, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 395, + 507, + 410 + ], + "score": 1.0, + "content": "are identical, i.e.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 408, + 215, + 420 + ], + "spans": [ + { + "bbox": [ + 107, + 408, + 187, + 420 + ], + "score": 0.87, + "content": "m _ { i j } = m _ { i } , \\forall j \\in \\mathcal { N } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 408, + 215, + 420 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "interline_equation", + "bbox": [ + 186, + 424, + 424, + 439 + ], + "lines": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "spans": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "score": 0.9, + "content": "h _ { i , t } = g _ { \\nu _ { i } } ( h _ { i , t - 1 } , e _ { \\lambda _ { i } ^ { s } } ( s \\nu _ { i , t } ) , e _ { \\lambda _ { i } ^ { p } } ( \\pi _ { \\mathcal { N } _ { i } , t - 1 } ) , e _ { \\lambda _ { i } ^ { h } } ( h _ { \\mathcal { N } _ { i } , t - 1 } ) ) ,", + "type": "interline_equation", + "image_path": "c92c9ae28dd48cda13d06c9b78c15aa65c01825f96a2c71852032322f90b2e72.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 443, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 105, + 442, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 132, + 457 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 444, + 148, + 456 + ], + "score": 0.91, + "content": "h _ { i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 442, + 352, + 457 + ], + "score": 1.0, + "content": "is the hidden state (or the belief ) of each agent and", + "type": "text" + }, + { + "bbox": [ + 352, + 445, + 366, + 456 + ], + "score": 0.88, + "content": "e _ { \\lambda _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 442, + 384, + 457 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 384, + 445, + 398, + 456 + ], + "score": 0.87, + "content": "g _ { \\nu _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 442, + 506, + 457 + ], + "score": 1.0, + "content": "are differentiable message", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "encoding and extracting functions 3. To avoid dilution of state and policy information (the former", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "is for improving observability while the later is for reducing non-stationarity), state and policy", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 476, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 104, + 476, + 370, + 492 + ], + "score": 1.0, + "content": "are explicitly included in the message besides agent belief, i.e.,", + "type": "text" + }, + { + "bbox": [ + 370, + 478, + 489, + 490 + ], + "score": 0.89, + "content": "m _ { i , t } = s _ { i , t } \\cup \\pi _ { i , t - 1 } \\cup h _ { i , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 476, + 506, + 492 + ], + "score": 1.0, + "content": ", or", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 488, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 233, + 501 + ], + "score": 0.9, + "content": "\\tilde { s } _ { i , t } : = s { \\nu } _ { i , t } \\cup \\pi _ { \\mathcal { N } _ { i } , t - 1 } \\cup h _ { \\mathcal { N } _ { i } , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 488, + 506, + 502 + ], + "score": 1.0, + "content": "as in Eq. 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Then each actor and critic are updated by losses", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 191, + 506, + 227 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 133, + 230, + 477, + 296 + ], + "lines": [ + { + "bbox": [ + 133, + 230, + 477, + 296 + ], + "spans": [ + { + "bbox": [ + 133, + 230, + 477, + 296 + ], + "score": 0.92, + "content": "\\begin{array} { r l } & { \\mathcal { L } ( \\boldsymbol { \\theta } _ { i } ) = \\displaystyle \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( - \\log \\pi _ { \\boldsymbol { \\theta } _ { i } } ( a _ { i , \\tau } | \\tilde { s } _ { i , \\tau } ) \\hat { A } _ { i , \\tau } ^ { \\pi } + \\beta \\sum _ { a _ { i } \\in A _ { i } } \\pi _ { \\boldsymbol { \\theta } _ { i } } ( a _ { i } | \\tilde { s } _ { i , \\tau } ) \\log \\pi _ { \\boldsymbol { \\theta } _ { i } } ( a _ { i } | \\tilde { s } _ { i , \\tau } ) \\right) , } \\\\ & { \\mathcal { L } ( \\omega _ { i } ) = \\displaystyle \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( \\hat { R } _ { i , \\tau } ^ { \\pi } - V _ { \\omega _ { i } } ( \\tilde { s } _ { i , \\tau } , a _ { N _ { i } , \\tau } ) \\right) ^ { 2 } , } \\end{array}", + "type": "interline_equation", + "image_path": "9683218aa918e47361b4034caa7a87f4210ff355cffbead19fef5946195aa196.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 133, + 230, + 477, + 252.0 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 133, + 252.0, + 477, + 274.0 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 133, + 274.0, + 477, + 296.0 + ], + "spans": [], + "index": 14 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 506, + 345 + ], + "lines": [ + { + "bbox": [ + 103, + 298, + 508, + 322 + ], + "spans": [ + { + "bbox": [ + 103, + 298, + 134, + 322 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 303, + 213, + 318 + ], + "score": 0.94, + "content": "\\hat { A } _ { i , \\tau } ^ { \\pi } = \\hat { R } _ { i , \\tau } ^ { \\pi } - v _ { i , \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 214, + 298, + 329, + 322 + ], + "score": 1.0, + "content": "is the estimated advantage,", + "type": "text" + }, + { + "bbox": [ + 330, + 301, + 508, + 321 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\hat { R } _ { i , \\tau } ^ { \\pi } = \\sum _ { \\tau ^ { \\prime } = \\tau } ^ { \\tau _ { B } - 1 } \\gamma ^ { \\tau ^ { \\prime } - \\tau } \\left( \\sum _ { j \\in \\mathcal { V } } \\alpha ^ { d _ { i j } } r _ { j , \\tau ^ { \\prime } } \\right) + } \\end{array}", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 317, + 504, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 152, + 333 + ], + "score": 0.92, + "content": "\\gamma ^ { \\tau _ { B } - \\tau } v _ { i , \\tau _ { B } }", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 317, + 268, + 335 + ], + "score": 1.0, + "content": "is the sampled action-value,", + "type": "text" + }, + { + "bbox": [ + 269, + 320, + 365, + 335 + ], + "score": 0.94, + "content": "v _ { i , \\tau } = V _ { \\omega _ { i } ^ { - } } ( \\tilde { s } _ { i , \\tau } , a _ { \\mathcal { N } _ { i } , \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 317, + 496, + 335 + ], + "score": 1.0, + "content": "is the estimated state-value, and", + "type": "text" + }, + { + "bbox": [ + 497, + 321, + 504, + 332 + ], + "score": 0.81, + "content": "\\beta", + "type": "inline_equation" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 333, + 253, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 253, + 346 + ], + "score": 1.0, + "content": "is the coefficient of the entropy loss.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16, + "bbox_fs": [ + 103, + 298, + 508, + 346 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 360, + 410, + 374 + ], + "lines": [ + { + "bbox": [ + 105, + 359, + 412, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 412, + 376 + ], + "score": 1.0, + "content": "4 SPATIOTEMPORAL RL WITH NEURAL COMMUNICATION", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 385, + 506, + 419 + ], + "lines": [ + { + "bbox": [ + 105, + 384, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 506, + 399 + ], + "score": 1.0, + "content": "For efficient and adaptive information sharing, we propose a new communication protocol called", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 395, + 507, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 428, + 410 + ], + "score": 1.0, + "content": "NeurComm. To simplify the notation, we assume all messages sent from agent", + "type": "text" + }, + { + "bbox": [ + 428, + 398, + 433, + 406 + ], + "score": 0.78, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 395, + 507, + 410 + ], + "score": 1.0, + "content": "are identical, i.e.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 408, + 215, + 420 + ], + "spans": [ + { + "bbox": [ + 107, + 408, + 187, + 420 + ], + "score": 0.87, + "content": "m _ { i j } = m _ { i } , \\forall j \\in \\mathcal { N } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 408, + 215, + 420 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 384, + 507, + 420 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 186, + 424, + 424, + 439 + ], + "lines": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "spans": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "score": 0.9, + "content": "h _ { i , t } = g _ { \\nu _ { i } } ( h _ { i , t - 1 } , e _ { \\lambda _ { i } ^ { s } } ( s \\nu _ { i , t } ) , e _ { \\lambda _ { i } ^ { p } } ( \\pi _ { \\mathcal { N } _ { i } , t - 1 } ) , e _ { \\lambda _ { i } ^ { h } } ( h _ { \\mathcal { N } _ { i } , t - 1 } ) ) ,", + "type": "interline_equation", + "image_path": "c92c9ae28dd48cda13d06c9b78c15aa65c01825f96a2c71852032322f90b2e72.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 186, + 424, + 424, + 439 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 443, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 105, + 442, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 132, + 457 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 444, + 148, + 456 + ], + "score": 0.91, + "content": "h _ { i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 442, + 352, + 457 + ], + "score": 1.0, + "content": "is the hidden state (or the belief ) of each agent and", + "type": "text" + }, + { + "bbox": [ + 352, + 445, + 366, + 456 + ], + "score": 0.88, + "content": "e _ { \\lambda _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 442, + 384, + 457 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 384, + 445, + 398, + 456 + ], + "score": 0.87, + "content": "g _ { \\nu _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 442, + 506, + 457 + ], + "score": 1.0, + "content": "are differentiable message", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 469 + ], + "score": 1.0, + "content": "encoding and extracting functions 3. To avoid dilution of state and policy information (the former", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "is for improving observability while the later is for reducing non-stationarity), state and policy", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 476, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 104, + 476, + 370, + 492 + ], + "score": 1.0, + "content": "are explicitly included in the message besides agent belief, i.e.,", + "type": "text" + }, + { + "bbox": [ + 370, + 478, + 489, + 490 + ], + "score": 0.89, + "content": "m _ { i , t } = s _ { i , t } \\cup \\pi _ { i , t - 1 } \\cup h _ { i , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 476, + 506, + 492 + ], + "score": 1.0, + "content": ", or", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 488, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 107, + 489, + 233, + 501 + ], + "score": 0.9, + "content": "\\tilde { s } _ { i , t } : = s { \\nu } _ { i , t } \\cup \\pi _ { \\mathcal { N } _ { i } , t - 1 } \\cup h _ { \\mathcal { N } _ { i } , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 488, + 506, + 502 + ], + "score": 1.0, + "content": "as in Eq. 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In spatiotemporal RL with neighborhood", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 586, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 505, + 599 + ], + "score": 1.0, + "content": "NeurComm, each agent utilizes the delayed global information to learn its belief, and it learns the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 598, + 365, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 365, + 610 + ], + "score": 1.0, + "content": "message to optimize the control performance of all other agents.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 574, + 506, + 610 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 617, + 506, + 714 + ], + "lines": [ + { + "bbox": [ + 106, + 617, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 506, + 630 + ], + "score": 1.0, + "content": "NeurComm enabled MARL can be represented using a single meta-DNN since all agents are", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 629, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 331, + 642 + ], + "score": 1.0, + "content": "connected by differentiable communication links, and", + "type": "text" + }, + { + "bbox": [ + 332, + 630, + 341, + 640 + ], + "score": 0.86, + "content": "\\tilde { s } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 629, + 506, + 642 + ], + "score": 1.0, + "content": "are the intermediate outputs after com-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 640, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 653 + ], + "score": 1.0, + "content": "munication layers. Fig. 1a illustrates the forward propagations inside each individual agent and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "Fig. 1b shows the broader multi-step spatiotemporal propagations. Note the gradient propagation", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 661, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 506, + 674 + ], + "score": 1.0, + "content": "of this meta-DNN is decentralized based on each local loss signal. As time advances, the involved", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 672, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 104, + 672, + 506, + 685 + ], + "score": 1.0, + "content": "parameters in each propagation expand spatially in the meta-DNN, due to the cascaded neigh-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 104, + 682, + 506, + 699 + ], + "spans": [ + { + "bbox": [ + 104, + 682, + 330, + 699 + ], + "score": 1.0, + "content": "borhood communication. 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(a)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 304, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 292, + 318 + ], + "score": 1.0, + "content": "Single-step forward propagations inside agent", + "type": "text" + }, + { + "bbox": [ + 293, + 306, + 297, + 315 + ], + "score": 0.32, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 304, + 506, + 318 + ], + "score": 1.0, + "content": ". Different colored boxes and arrows show different", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 316, + 507, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 507, + 329 + ], + "score": 1.0, + "content": "outputs and functions, respectively. Solid and dashed arrows indicate actor and critic propagations,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 327, + 440, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 431, + 340 + ], + "score": 1.0, + "content": "respectively. (b) Multi-step forward propagations for updating the belief of agent", + "type": "text" + }, + { + "bbox": [ + 431, + 328, + 436, + 337 + ], + "score": 0.59, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 327, + 440, + 340 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + } + ], + "index": 5.75 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "score": 1.0, + "content": "NeurComm is general enough and has connections to other communication protocols. CommNet", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "performs a more lossy aggregation since the received messages are averaged before encoding, and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 386 + ], + "score": 1.0, + "content": "all encoded inputs are summed up (Sukhbaatar et al., 2016). In DIAL, each DQN agent encodes", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "score": 1.0, + "content": "the received messages instead of averaging them, but still it sums all encoded inputs (Foerster et al.,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 393, + 481, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 481, + 408 + ], + "score": 1.0, + "content": "2016). Also, both CommNet and DIAL do not have policy fingerprints included in messages.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 108, + 422, + 267, + 435 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 268, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 268, + 437 + ], + "score": 1.0, + "content": "5 NUMERICAL EXPERIMENTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 447, + 227, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 228, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 228, + 460 + ], + "score": 1.0, + "content": "5.1 ENVIRONMENT SETUP", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 505, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 467, + 507, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 507, + 482 + ], + "score": 1.0, + "content": "There are several benchmark MARL environments such as cooperative navigation and predator-prey,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "score": 1.0, + "content": "but few of them represent NSC. Here we design two NSC environments: adaptive traffic signal control", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "(ATSC) and cooperative adaptive cruise control (CACC). Both ATSC and CACC are extensively", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 502, + 499, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 499, + 513 + ], + "score": 1.0, + "content": "studied in intelligent transportation systems, and they hold assumptions of a spatiotemporal MDP.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 107, + 524, + 304, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 524, + 305, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 305, + 537 + ], + "score": 1.0, + "content": "5.1.1 ADAPTIVE TRAFFIC SIGNAL CONTROL", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "The objective of ATSC is to adaptively adjust signal phases to minimize traffic congestion based on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 555, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 420, + 567 + ], + "score": 1.0, + "content": "real-time road-traffic measurements. Here we implement two ATSC scenarios: a", + "type": "text" + }, + { + "bbox": [ + 421, + 556, + 441, + 566 + ], + "score": 0.89, + "content": "5 \\times 5", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 555, + 505, + 567 + ], + "score": 1.0, + "content": "synthetic traffic", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "grid and a real-world 28-intersection traffic network from Monaco city, using standard microscopic", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 577, + 307, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 307, + 589 + ], + "score": 1.0, + "content": "traffic simulator SUMO (Krajzewicz et al., 2012).", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 106, + 594, + 505, + 672 + ], + "lines": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "General settings. For both scenarios, each episode simulates the peak-hour traffic, and a 5s control", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "interval is applied to prevent traffic light from too frequent switches, based on RL control latency and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "score": 1.0, + "content": "driver response delay. Thus, one MDP step corresponds to 5s simulation and the horizon is 720 steps.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "Further, a 2s yellow time is inserted before switching to red light for safety purposes. In ATSC, the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "real-time traffic flow, that is, the total number of approaching vehicles along each incoming lane, is", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "measured by near-intersection induction-loop detectors (ILDs) (shown as the blue areas of example", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 659, + 507, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 507, + 673 + ], + "score": 1.0, + "content": "intersections in Fig. 2). The cost of each agent is the sum of queue lengths along all incoming lanes.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "Scenario settings. Fig. 2a illustrates the traffic grid formed by two-lane arterial streets with speed", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 686, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 686, + 127, + 700 + ], + "score": 1.0, + "content": "limit", + "type": "text" + }, + { + "bbox": [ + 127, + 688, + 153, + 698 + ], + "score": 0.77, + "content": "2 0 \\mathrm { m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 686, + 304, + 700 + ], + "score": 1.0, + "content": "and one-lane avenues with speed limit", + "type": "text" + }, + { + "bbox": [ + 304, + 688, + 329, + 698 + ], + "score": 0.76, + "content": "1 1 \\mathrm { m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 686, + 505, + 700 + ], + "score": 1.0, + "content": ". We simulate the peak-hour traffic dynamics", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "through four collections of time-variant traffic flows, with both loading and recovering phases. At", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 707, + 507, + 725 + ], + "spans": [ + { + "bbox": [ + 104, + 707, + 225, + 725 + ], + "score": 1.0, + "content": "beginning, three major flows", + "type": "text" + }, + { + "bbox": [ + 225, + 710, + 237, + 721 + ], + "score": 0.88, + "content": "F _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 707, + 441, + 725 + ], + "score": 1.0, + "content": "are generated with origin-destination (O-D) pairs", + "type": "text" + }, + { + "bbox": [ + 441, + 712, + 470, + 721 + ], + "score": 0.85, + "content": "x _ { 1 0 } – x _ { 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 707, + 473, + 725 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 474, + 712, + 502, + 721 + ], + "score": 0.83, + "content": "x _ { 1 1 } - x _ { 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 707, + 507, + 725 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 502, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 123, + 734 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 123, + 722, + 152, + 732 + ], + "score": 0.89, + "content": "x _ { 1 2 } { - } x _ { 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 720, + 274, + 734 + ], + "score": 1.0, + "content": ", meanwhile three minor flows", + "type": "text" + }, + { + "bbox": [ + 275, + 721, + 285, + 732 + ], + "score": 0.88, + "content": "f _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 720, + 403, + 734 + ], + "score": 1.0, + "content": "are generated with O-D pairs", + "type": "text" + }, + { + "bbox": [ + 404, + 722, + 429, + 732 + ], + "score": 0.85, + "content": "x _ { 1 } – x _ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 720, + 432, + 734 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 433, + 722, + 457, + 732 + ], + "score": 0.84, + "content": "x _ { 2 } \\mathrm { - } x _ { 8 }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 720, + 478, + 734 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 478, + 722, + 502, + 732 + ], + "score": 0.9, + "content": "x _ { 3 } – x _ { 9 }", + "type": "inline_equation" + } + ], + "index": 37 + } + ], + "index": 35 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 81, + 506, + 118 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 106, + 81, + 506, + 120 + ], + "lines_deleted": true + }, + { + "type": "image", + "bbox": [ + 137, + 129, + 475, + 284 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 137, + 129, + 475, + 284 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 137, + 129, + 475, + 284 + ], + "spans": [ + { + "bbox": [ + 137, + 129, + 475, + 284 + ], + "score": 0.953, + "type": "image", + "image_path": "29c3dbc71fbdb357ff97a54520ba7973e9fe90df4dd323232c8beb5fc8697693.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 137, + 129, + 475, + 180.66666666666666 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 137, + 180.66666666666666, + 475, + 232.33333333333331 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 137, + 232.33333333333331, + 475, + 284.0 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 294, + 506, + 339 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 506, + 307 + ], + "score": 1.0, + "content": "Figure 1: Forward propagations of NeurComm enabled MARL, illustrated in a queueing system. (a)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 304, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 292, + 318 + ], + "score": 1.0, + "content": "Single-step forward propagations inside agent", + "type": "text" + }, + { + "bbox": [ + 293, + 306, + 297, + 315 + ], + "score": 0.32, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 304, + 506, + 318 + ], + "score": 1.0, + "content": ". Different colored boxes and arrows show different", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 316, + 507, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 507, + 329 + ], + "score": 1.0, + "content": "outputs and functions, respectively. Solid and dashed arrows indicate actor and critic propagations,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 327, + 440, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 431, + 340 + ], + "score": 1.0, + "content": "respectively. (b) Multi-step forward propagations for updating the belief of agent", + "type": "text" + }, + { + "bbox": [ + 431, + 328, + 436, + 337 + ], + "score": 0.59, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 327, + 440, + 340 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7.5 + } + ], + "index": 5.75 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "score": 1.0, + "content": "NeurComm is general enough and has connections to other communication protocols. CommNet", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "performs a more lossy aggregation since the received messages are averaged before encoding, and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 506, + 386 + ], + "score": 1.0, + "content": "all encoded inputs are summed up (Sukhbaatar et al., 2016). In DIAL, each DQN agent encodes", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "score": 1.0, + "content": "the received messages instead of averaging them, but still it sums all encoded inputs (Foerster et al.,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 393, + 481, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 481, + 408 + ], + "score": 1.0, + "content": "2016). Also, both CommNet and DIAL do not have policy fingerprints included in messages.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 351, + 506, + 408 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 422, + 267, + 435 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 268, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 268, + 437 + ], + "score": 1.0, + "content": "5 NUMERICAL EXPERIMENTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 447, + 227, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 228, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 228, + 460 + ], + "score": 1.0, + "content": "5.1 ENVIRONMENT SETUP", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 505, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 467, + 507, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 507, + 482 + ], + "score": 1.0, + "content": "There are several benchmark MARL environments such as cooperative navigation and predator-prey,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "score": 1.0, + "content": "but few of them represent NSC. Here we design two NSC environments: adaptive traffic signal control", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "(ATSC) and cooperative adaptive cruise control (CACC). Both ATSC and CACC are extensively", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 502, + 499, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 499, + 513 + ], + "score": 1.0, + "content": "studied in intelligent transportation systems, and they hold assumptions of a spatiotemporal MDP.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 467, + 507, + 513 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 524, + 304, + 536 + ], + "lines": [ + { + "bbox": [ + 106, + 524, + 305, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 305, + 537 + ], + "score": 1.0, + "content": "5.1.1 ADAPTIVE TRAFFIC SIGNAL CONTROL", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 544, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "The objective of ATSC is to adaptively adjust signal phases to minimize traffic congestion based on", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 555, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 420, + 567 + ], + "score": 1.0, + "content": "real-time road-traffic measurements. Here we implement two ATSC scenarios: a", + "type": "text" + }, + { + "bbox": [ + 421, + 556, + 441, + 566 + ], + "score": 0.89, + "content": "5 \\times 5", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 555, + 505, + 567 + ], + "score": 1.0, + "content": "synthetic traffic", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "grid and a real-world 28-intersection traffic network from Monaco city, using standard microscopic", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 577, + 307, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 307, + 589 + ], + "score": 1.0, + "content": "traffic simulator SUMO (Krajzewicz et al., 2012).", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 545, + 505, + 589 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 594, + 505, + 672 + ], + "lines": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "General settings. For both scenarios, each episode simulates the peak-hour traffic, and a 5s control", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "interval is applied to prevent traffic light from too frequent switches, based on RL control latency and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 630 + ], + "score": 1.0, + "content": "driver response delay. Thus, one MDP step corresponds to 5s simulation and the horizon is 720 steps.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "Further, a 2s yellow time is inserted before switching to red light for safety purposes. In ATSC, the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "real-time traffic flow, that is, the total number of approaching vehicles along each incoming lane, is", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "measured by near-intersection induction-loop detectors (ILDs) (shown as the blue areas of example", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 659, + 507, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 507, + 673 + ], + "score": 1.0, + "content": "intersections in Fig. 2). The cost of each agent is the sum of queue lengths along all incoming lanes.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 594, + 507, + 673 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "Scenario settings. Fig. 2a illustrates the traffic grid formed by two-lane arterial streets with speed", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 686, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 686, + 127, + 700 + ], + "score": 1.0, + "content": "limit", + "type": "text" + }, + { + "bbox": [ + 127, + 688, + 153, + 698 + ], + "score": 0.77, + "content": "2 0 \\mathrm { m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 686, + 304, + 700 + ], + "score": 1.0, + "content": "and one-lane avenues with speed limit", + "type": "text" + }, + { + "bbox": [ + 304, + 688, + 329, + 698 + ], + "score": 0.76, + "content": "1 1 \\mathrm { m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 686, + 505, + 700 + ], + "score": 1.0, + "content": ". We simulate the peak-hour traffic dynamics", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "through four collections of time-variant traffic flows, with both loading and recovering phases. At", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 707, + 507, + 725 + ], + "spans": [ + { + "bbox": [ + 104, + 707, + 225, + 725 + ], + "score": 1.0, + "content": "beginning, three major flows", + "type": "text" + }, + { + "bbox": [ + 225, + 710, + 237, + 721 + ], + "score": 0.88, + "content": "F _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 707, + 441, + 725 + ], + "score": 1.0, + "content": "are generated with origin-destination (O-D) pairs", + "type": "text" + }, + { + "bbox": [ + 441, + 712, + 470, + 721 + ], + "score": 0.85, + "content": "x _ { 1 0 } – x _ { 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 707, + 473, + 725 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 474, + 712, + 502, + 721 + ], + "score": 0.83, + "content": "x _ { 1 1 } - x _ { 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 707, + 507, + 725 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 502, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 123, + 734 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 123, + 722, + 152, + 732 + ], + "score": 0.89, + "content": "x _ { 1 2 } { - } x _ { 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 720, + 274, + 734 + ], + "score": 1.0, + "content": ", meanwhile three minor flows", + "type": "text" + }, + { + "bbox": [ + 275, + 721, + 285, + 732 + ], + "score": 0.88, + "content": "f _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 720, + 403, + 734 + ], + "score": 1.0, + "content": "are generated with O-D pairs", + "type": "text" + }, + { + "bbox": [ + 404, + 722, + 429, + 732 + ], + "score": 0.85, + "content": "x _ { 1 } – x _ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 720, + 432, + 734 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 433, + 722, + 457, + 732 + ], + "score": 0.84, + "content": "x _ { 2 } \\mathrm { - } x _ { 8 }", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 720, + 478, + 734 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 478, + 722, + 502, + 732 + ], + "score": 0.9, + "content": "x _ { 3 } – x _ { 9 }", + "type": "inline_equation" + } + ], + "index": 37 + } + ], + "index": 35, + "bbox_fs": [ + 104, + 677, + 507, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 506, + 192 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 180, + 95 + ], + "score": 1.0, + "content": "After 15 minutes,", + "type": "text" + }, + { + "bbox": [ + 180, + 83, + 192, + 93 + ], + "score": 0.87, + "content": "F _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 81, + 211, + 95 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 211, + 83, + 222, + 94 + ], + "score": 0.88, + "content": "f _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 81, + 390, + 95 + ], + "score": 1.0, + "content": "start to decay, while their opposite flows", + "type": "text" + }, + { + "bbox": [ + 390, + 83, + 402, + 93 + ], + "score": 0.89, + "content": "F _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 81, + 420, + 95 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 421, + 83, + 431, + 94 + ], + "score": 0.88, + "content": "f _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 432, + 81, + 506, + 95 + ], + "score": 1.0, + "content": "start to dominate,", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 506, + 106 + ], + "score": 1.0, + "content": "as shown in Fig. 2b. Note the flows define the high-level demand only, the particular route of each", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "vehicle is randomly generated. The grid is homogeneous and all agents have the same action space,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "which is a set of five pre-defined signal phases. Fig. 2c illustrates the Monaco traffic network, with", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "controlled intersections in blue. NMARL in this scenario is more challenging since the network", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "is heterogeneous with a variety of observation and action spaces. Four traffic flow collections are", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 148, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 104, + 148, + 506, + 161 + ], + "score": 1.0, + "content": "generated to simulate the peak-hour traffic, and each flow is a multiple of a “unit” flow of 325veh/hr,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 158, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 104, + 158, + 376, + 173 + ], + "score": 1.0, + "content": "with randomly sampled O-D pairs inside rectangle areas in Fig. 2c.", + "type": "text" + }, + { + "bbox": [ + 377, + 159, + 389, + 170 + ], + "score": 0.86, + "content": "F _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 158, + 407, + 173 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 407, + 159, + 419, + 170 + ], + "score": 0.9, + "content": "F _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 158, + 506, + 173 + ], + "score": 1.0, + "content": "are simulated during", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 170, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 138, + 183 + ], + "score": 1.0, + "content": "the first", + "type": "text" + }, + { + "bbox": [ + 139, + 171, + 165, + 181 + ], + "score": 0.34, + "content": "4 0 \\mathrm { { m i n } }", + "type": "inline_equation" + }, + { + "bbox": [ + 166, + 170, + 180, + 183 + ], + "score": 1.0, + "content": ", as", + "type": "text" + }, + { + "bbox": [ + 180, + 171, + 257, + 182 + ], + "score": 0.73, + "content": "[ 1 , 2 , 4 , 4 , 4 , 4 , 2 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 170, + 320, + 183 + ], + "score": 1.0, + "content": "unit flows with", + "type": "text" + }, + { + "bbox": [ + 320, + 171, + 342, + 181 + ], + "score": 0.26, + "content": "5 \\mathrm { { m i n } }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 170, + 381, + 183 + ], + "score": 1.0, + "content": "intervals;", + "type": "text" + }, + { + "bbox": [ + 382, + 171, + 394, + 181 + ], + "score": 0.88, + "content": "F _ { 3 }", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 170, + 411, + 183 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 412, + 171, + 424, + 181 + ], + "score": 0.88, + "content": "F _ { 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 170, + 506, + 183 + ], + "score": 1.0, + "content": "are generated in the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 365, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 227, + 193 + ], + "score": 1.0, + "content": "same way, but with a delay of", + "type": "text" + }, + { + "bbox": [ + 228, + 182, + 254, + 192 + ], + "score": 0.45, + "content": "1 5 \\mathrm { { m i n } }", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 181, + 365, + 193 + ], + "score": 1.0, + "content": ". See code for more details.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 4.5 + }, + { + "type": "image", + "bbox": [ + 141, + 204, + 473, + 325 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 141, + 204, + 473, + 325 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 141, + 204, + 473, + 325 + ], + "spans": [ + { + "bbox": [ + 141, + 204, + 473, + 325 + ], + "score": 0.963, + "type": "image", + "image_path": "86ef284ef38198e0908abd3bf88ef2db19af879e4cb915eddb76fad3701f8e07.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 141, + 204, + 473, + 244.33333333333334 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 141, + 244.33333333333334, + 473, + 284.6666666666667 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 141, + 284.6666666666667, + 473, + 325.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 334, + 505, + 367 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "Figure 2: ATSC scenarios for NMARL. (a) Synthetic traffic grid, with major and minor traffic flows", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 345, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 505, + 357 + ], + "score": 1.0, + "content": "shown in solid and dotted arrows. (b) Simulated time-variant traffic flows within the traffic grid. (c)", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 355, + 420, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 420, + 368 + ], + "score": 1.0, + "content": "Monaco traffic network, with traffic flow collections shown in colored arrows.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 107, + 388, + 328, + 399 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 329, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 329, + 401 + ], + "score": 1.0, + "content": "5.1.2 COOPERATIVE ADAPTIVE CRUISE CONTROL", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 108, + 407, + 504, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 506, + 421 + ], + "score": 1.0, + "content": "The objective of CACC is to adaptively coordinate a platoon of vehicles to minimize the car-following", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "headway and speed perturbations based on real-time vehicle-to-vehicle communication. Here we", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 429, + 495, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 495, + 443 + ], + "score": 1.0, + "content": "implement two CACC scenarios: “Catch-up” and “Slow-down”, with physical vehicle dynamics.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 446, + 505, + 591 + ], + "lines": [ + { + "bbox": [ + 106, + 446, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 458 + ], + "score": 1.0, + "content": "General settings. For both CACC tasks, we simulate a string of 8 vehicles for 60s, with a 0.1s", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 457, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 360, + 470 + ], + "score": 1.0, + "content": "control interval. Each vehicle observes and shares its headway", + "type": "text" + }, + { + "bbox": [ + 361, + 459, + 368, + 468 + ], + "score": 0.38, + "content": "_ \\mathrm { h }", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 457, + 407, + 470 + ], + "score": 1.0, + "content": ", velocity", + "type": "text" + }, + { + "bbox": [ + 407, + 460, + 414, + 468 + ], + "score": 0.58, + "content": "\\mathrm { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 457, + 506, + 470 + ], + "score": 1.0, + "content": ", and acceleration a to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 468, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 332, + 480 + ], + "score": 1.0, + "content": "neighbors within two steps. The safety constraints are:", + "type": "text" + }, + { + "bbox": [ + 333, + 469, + 367, + 479 + ], + "score": 0.68, + "content": "\\mathrm { ~ h ~ } \\geq 1 { \\mathrm { m } }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 468, + 371, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 371, + 469, + 417, + 480 + ], + "score": 0.7, + "content": "\\mathrm { { v } \\leq 3 0 m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 468, + 421, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 421, + 468, + 479, + 480 + ], + "score": 0.89, + "content": "| \\mathrm { a } | \\le 2 . 5 \\mathrm { m / s ^ { 2 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 468, + 505, + 480 + ], + "score": 1.0, + "content": ". Safe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "RL is relevant here, but itself is a big topic and out of the scope of this paper. So we adopt a simple", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "score": 1.0, + "content": "heuristic optimal velocity model (OVM) (Bando et al., 1995) to perform longitudinal vehicle control", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 457, + 514 + ], + "score": 1.0, + "content": "under above constraints, whose behavior is affected by hyper-parameters: headway gain", + "type": "text" + }, + { + "bbox": [ + 457, + 502, + 469, + 512 + ], + "score": 0.87, + "content": "\\alpha ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 501, + 505, + 514 + ], + "score": 1.0, + "content": ", relative", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 511, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 162, + 526 + ], + "score": 1.0, + "content": "velocity gain", + "type": "text" + }, + { + "bbox": [ + 163, + 513, + 174, + 524 + ], + "score": 0.88, + "content": "\\beta ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 511, + 237, + 526 + ], + "score": 1.0, + "content": ", stop headway", + "type": "text" + }, + { + "bbox": [ + 238, + 513, + 279, + 523 + ], + "score": 0.91, + "content": "\\mathrm { h _ { s t } } = 5 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 511, + 380, + 526 + ], + "score": 1.0, + "content": "and full-speed headway", + "type": "text" + }, + { + "bbox": [ + 381, + 513, + 429, + 524 + ], + "score": 0.91, + "content": "\\mathrm { h } _ { \\mathrm { g o } } = 3 5 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 511, + 470, + 526 + ], + "score": 1.0, + "content": ". Usually", + "type": "text" + }, + { + "bbox": [ + 470, + 512, + 505, + 524 + ], + "score": 0.92, + "content": "( \\alpha ^ { \\circ } , \\beta ^ { \\circ } )", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 522, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 104, + 522, + 455, + 536 + ], + "score": 1.0, + "content": "represent the human driver behavior, here we train NMARL to recommend appropriate", + "type": "text" + }, + { + "bbox": [ + 455, + 524, + 489, + 535 + ], + "score": 0.92, + "content": "( \\alpha ^ { \\circ } , \\beta ^ { \\circ } )", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 522, + 506, + 536 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 534, + 506, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 298, + 547 + ], + "score": 1.0, + "content": "each OVM controller, selected from four levels", + "type": "text" + }, + { + "bbox": [ + 299, + 534, + 442, + 546 + ], + "score": 0.77, + "content": "\\left\\{ ( 0 , 0 ) , ( 0 . 5 , 0 ) , ( 0 , 0 . 5 ) , ( 0 . 5 , 0 . 5 ) \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 534, + 506, + 547 + ], + "score": 1.0, + "content": ". Assuming the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 545, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 269, + 558 + ], + "score": 1.0, + "content": "target headway and velocity profile are", + "type": "text" + }, + { + "bbox": [ + 269, + 546, + 315, + 556 + ], + "score": 0.91, + "content": "\\mathrm { h } ^ { \\ast } = 2 0 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 545, + 333, + 558 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 333, + 546, + 345, + 557 + ], + "score": 0.89, + "content": "\\nabla _ { t } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 545, + 506, + 558 + ], + "score": 1.0, + "content": ", respectively, the cost of each agent is", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 554, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 258, + 569 + ], + "score": 0.9, + "content": "( \\mathrm { h } _ { i , t } ^ { } - \\mathrm { h } ^ { \\ast } ) ^ { 2 } + ( \\mathrm { v } _ { i , t } - \\mathrm { v } _ { t } ^ { \\ast } ) ^ { 2 } + 0 . 1 \\mathrm { u } _ { i , t } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 554, + 383, + 570 + ], + "score": 1.0, + "content": ". Whenever a collision happens", + "type": "text" + }, + { + "bbox": [ + 383, + 557, + 430, + 568 + ], + "score": 0.9, + "content": "( \\mathrm { h } _ { i , t } < \\mathrm { 1 m } )", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 554, + 506, + 570 + ], + "score": 1.0, + "content": ", a large penalty of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 568, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 432, + 583 + ], + "score": 1.0, + "content": "1000 is assigned to each agent and the state becomes absorbing. An additional cost", + "type": "text" + }, + { + "bbox": [ + 433, + 568, + 495, + 582 + ], + "score": 0.93, + "content": "5 ( 2 \\mathrm { n } _ { \\mathrm { s t } } - \\mathrm { n } _ { i , t } ) _ { + } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 568, + 506, + 583 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 579, + 283, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 283, + 594 + ], + "score": 1.0, + "content": "provided in training for potential collisions.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 597, + 506, + 653 + ], + "lines": [ + { + "bbox": [ + 106, + 597, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 506, + 609 + ], + "score": 1.0, + "content": "Scenario settings. Since exploring a collision-free CACC strategy itself is challenging for on-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 607, + 507, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 367, + 621 + ], + "score": 1.0, + "content": "policy RL, we consider simple scenarios. In Catch-up scenario,", + "type": "text" + }, + { + "bbox": [ + 367, + 608, + 443, + 620 + ], + "score": 0.91, + "content": "\\mathrm { v } _ { i , 0 } = \\mathrm { v } _ { t } ^ { \\ast } = 1 5 \\mathrm { m } / \\mathrm { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 607, + 461, + 621 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 462, + 609, + 502, + 620 + ], + "score": 0.9, + "content": "\\mathrm { h } _ { i , 0 } = \\mathrm { h } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 607, + 507, + 621 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 617, + 507, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 136, + 630 + ], + "score": 0.9, + "content": "\\forall i \\ne 1", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 617, + 177, + 633 + ], + "score": 1.0, + "content": ", whereas", + "type": "text" + }, + { + "bbox": [ + 177, + 619, + 234, + 631 + ], + "score": 0.9, + "content": "\\mathtt { h } _ { 1 , 0 } = a \\cdot \\mathrm { h } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 617, + 259, + 633 + ], + "score": 1.0, + "content": ", with", + "type": "text" + }, + { + "bbox": [ + 259, + 619, + 307, + 631 + ], + "score": 0.91, + "content": "a \\in U [ 3 , 4 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 308, + 617, + 413, + 633 + ], + "score": 1.0, + "content": ". 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(3)(4), and only neighborhood observation and communication are allowed. IA2C performs", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "independent learning, which is an A2C implementation of MADDPG (Lowe et al., 2017) as the critic", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "takes neighboring actions (see Eq. (4)). 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Note the flows define the high-level demand only, the particular route of each", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "vehicle is randomly generated. The grid is homogeneous and all agents have the same action space,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "which is a set of five pre-defined signal phases. Fig. 2c illustrates the Monaco traffic network, with", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "controlled intersections in blue. 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(a) Synthetic traffic grid, with major and minor traffic flows", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 345, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 505, + 357 + ], + "score": 1.0, + "content": "shown in solid and dotted arrows. (b) Simulated time-variant traffic flows within the traffic grid. (c)", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 355, + 420, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 420, + 368 + ], + "score": 1.0, + "content": "Monaco traffic network, with traffic flow collections shown in colored arrows.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 107, + 388, + 328, + 399 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 329, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 329, + 401 + ], + "score": 1.0, + "content": "5.1.2 COOPERATIVE ADAPTIVE CRUISE CONTROL", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 108, + 407, + 504, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 506, + 421 + ], + "score": 1.0, + "content": "The objective of CACC is to adaptively coordinate a platoon of vehicles to minimize the car-following", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "headway and speed perturbations based on real-time vehicle-to-vehicle communication. Here we", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 429, + 495, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 495, + 443 + ], + "score": 1.0, + "content": "implement two CACC scenarios: “Catch-up” and “Slow-down”, with physical vehicle dynamics.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 106, + 406, + 506, + 443 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 446, + 505, + 591 + ], + "lines": [ + { + "bbox": [ + 106, + 446, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 505, + 458 + ], + "score": 1.0, + "content": "General settings. For both CACC tasks, we simulate a string of 8 vehicles for 60s, with a 0.1s", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 457, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 360, + 470 + ], + "score": 1.0, + "content": "control interval. 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The safety constraints are:", + "type": "text" + }, + { + "bbox": [ + 333, + 469, + 367, + 479 + ], + "score": 0.68, + "content": "\\mathrm { ~ h ~ } \\geq 1 { \\mathrm { m } }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 468, + 371, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 371, + 469, + 417, + 480 + ], + "score": 0.7, + "content": "\\mathrm { { v } \\leq 3 0 m / s }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 468, + 421, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 421, + 468, + 479, + 480 + ], + "score": 0.89, + "content": "| \\mathrm { a } | \\le 2 . 5 \\mathrm { m / s ^ { 2 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 468, + 505, + 480 + ], + "score": 1.0, + "content": ". Safe", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "RL is relevant here, but itself is a big topic and out of the scope of this paper. 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In ATSC,", + "type": "text" + }, + { + "bbox": [ + 416, + 220, + 455, + 231 + ], + "score": 0.86, + "content": "\\beta = 0 . 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 220, + 460, + 232 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 460, + 220, + 502, + 232 + ], + "score": 0.9, + "content": "| B | = 1 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 220, + 506, + 232 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 174, + 244 + ], + "score": 1.0, + "content": "while in CACC,", + "type": "text" + }, + { + "bbox": [ + 174, + 231, + 213, + 242 + ], + "score": 0.89, + "content": "\\beta = 0 . 0 5", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 230, + 217, + 244 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 217, + 231, + 254, + 243 + ], + "score": 0.9, + "content": "| B | = 6 0", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 230, + 506, + 244 + ], + "score": 1.0, + "content": ", to encourage the exploration of collision-free policies. Each", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 413, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 413, + 254 + ], + "score": 1.0, + "content": "training takes about 30 hours on a 32GB memory, Intel Xeon CPU machine.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 107, + 267, + 209, + 278 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 210, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 210, + 280 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDY", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 287, + 506, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 448, + 300 + ], + "score": 1.0, + "content": "We perform ablation study in proposed scenarios, which are sorted as ATSC Monaco", + "type": "text" + }, + { + "bbox": [ + 448, + 289, + 457, + 298 + ], + "score": 0.76, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "ATSC Grid", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 143, + 309 + ], + "score": 0.4, + "content": "> { \\mathrm { C A C C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 298, + 192, + 312 + ], + "score": 1.0, + "content": "Slow-down", + "type": "text" + }, + { + "bbox": [ + 192, + 300, + 201, + 308 + ], + "score": 0.71, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 298, + 506, + 312 + ], + "score": 1.0, + "content": "CACC Catch-up by task difficulty. ATSC is more challenging than CACC", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 310, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 187, + 322 + ], + "score": 1.0, + "content": "due to larger scale", + "type": "text" + }, + { + "bbox": [ + 188, + 310, + 212, + 320 + ], + "score": 0.83, + "content": "> = 2 5", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 310, + 505, + 322 + ], + "score": 1.0, + "content": "vs 8), more complex dynamics (stochastic traffic flow vs deterministic", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 417, + 333 + ], + "score": 1.0, + "content": "vehicle dynamics), and longer control interval (5s vs 0.1s). ATSC Monaco", + "type": "text" + }, + { + "bbox": [ + 417, + 321, + 427, + 331 + ], + "score": 0.74, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "ATSC Grid due to", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 332, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 329, + 344 + ], + "score": 1.0, + "content": "more heterogenous network, while CACC Slow-down", + "type": "text" + }, + { + "bbox": [ + 330, + 332, + 368, + 343 + ], + "score": 0.38, + "content": "> { \\mathrm { C A C C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 332, + 505, + 344 + ], + "score": 1.0, + "content": "Catch-up due to more frequently", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "score": 1.0, + "content": "changing leading vehicle profile. To visualize the learning performance, we plot the learning curve,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 101, + 348, + 511, + 374 + ], + "spans": [ + { + "bbox": [ + 101, + 348, + 231, + 374 + ], + "score": 1.0, + "content": "that is, average episode return", + "type": "text" + }, + { + "bbox": [ + 232, + 353, + 338, + 369 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\begin{array} { r } { ( \\bar { R } = \\frac { 1 } { T } \\sum _ { t = 0 } ^ { T - 1 } \\sum _ { i \\in \\mathcal { V } } r _ { i , t } ) } \\end{array} } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 348, + 511, + 374 + ], + "score": 1.0, + "content": "vs training step. For better visualization,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 366, + 485, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 485, + 380 + ], + "score": 1.0, + "content": "all learning curves are smoothened using moving average with a window size of 100 episodes.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 106, + 383, + 505, + 494 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 507, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 507, + 398 + ], + "score": 1.0, + "content": "First, we investigate the impact of spatial discount factor, by comparing the learning curves among", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 107, + 391, + 507, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 394, + 176, + 406 + ], + "score": 0.93, + "content": "\\alpha \\in \\{ 0 . 8 , 0 . 9 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 391, + 457, + 410 + ], + "score": 1.0, + "content": "for IA2C and CommNet. Fig. 3 reveals a few interesting facts. First,", + "type": "text" + }, + { + "bbox": [ + 457, + 395, + 495, + 407 + ], + "score": 0.92, + "content": "\\alpha _ { \\mathrm { C o m m N e t } } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 391, + 507, + 410 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 404, + 508, + 421 + ], + "spans": [ + { + "bbox": [ + 104, + 404, + 184, + 421 + ], + "score": 1.0, + "content": "always higher than", + "type": "text" + }, + { + "bbox": [ + 185, + 406, + 208, + 417 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 208, + 404, + 244, + 421 + ], + "score": 1.0, + "content": ". Indeed,", + "type": "text" + }, + { + "bbox": [ + 245, + 406, + 300, + 417 + ], + "score": 0.92, + "content": "\\alpha _ { \\mathrm { C o m m N e t } } ^ { * } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 404, + 508, + 421 + ], + "score": 1.0, + "content": "in almost all scenarios (except for ATSC Monaco).", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "score": 1.0, + "content": "This is because communicative policies perform delayed global information sharing, whereas non-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "score": 1.0, + "content": "communicative policies utilize neighborhood information only, causing difficulty to fit the global", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 439, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 402, + 450 + ], + "score": 1.0, + "content": "return. Second, learning performance becomes much more sensitive to", + "type": "text" + }, + { + "bbox": [ + 402, + 440, + 410, + 448 + ], + "score": 0.75, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 439, + 505, + 450 + ], + "score": 1.0, + "content": "when the task is more", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 214, + 462 + ], + "score": 1.0, + "content": "difficult. Specifically, all", + "type": "text" + }, + { + "bbox": [ + 214, + 451, + 222, + 459 + ], + "score": 0.78, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 448, + 506, + 462 + ], + "score": 1.0, + "content": "values lead to similar learning curves in CACC Catch-up, whereas", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 460, + 507, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 155, + 473 + ], + "score": 1.0, + "content": "appropriate", + "type": "text" + }, + { + "bbox": [ + 155, + 462, + 163, + 470 + ], + "score": 0.79, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 460, + 507, + 473 + ], + "score": 1.0, + "content": "values help IA2C converge to much better policies more steadily in other scenarios.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 470, + 507, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 134, + 487 + ], + "score": 1.0, + "content": "Third,", + "type": "text" + }, + { + "bbox": [ + 134, + 471, + 146, + 481 + ], + "score": 0.87, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 470, + 215, + 487 + ], + "score": 1.0, + "content": "is high enough:", + "type": "text" + }, + { + "bbox": [ + 215, + 471, + 266, + 483 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * } = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 470, + 418, + 487 + ], + "score": 1.0, + "content": "except for CACC Slow-down where", + "type": "text" + }, + { + "bbox": [ + 419, + 471, + 469, + 483 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * } = 0 . 8", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 470, + 507, + 487 + ], + "score": 1.0, + "content": ". This is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 482, + 480, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 480, + 495 + ], + "score": 1.0, + "content": "because the discounted problem must be similar enough to the original problem in execution.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 498, + 505, + 576 + ], + "lines": [ + { + "bbox": [ + 106, + 498, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 329, + 511 + ], + "score": 1.0, + "content": "Next, we investigate the impact of NeurComm under", + "type": "text" + }, + { + "bbox": [ + 330, + 500, + 358, + 509 + ], + "score": 0.89, + "content": "\\alpha = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 498, + 505, + 511 + ], + "score": 1.0, + "content": ". We start with a baseline which is", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 294, + 523 + ], + "score": 1.0, + "content": "similar to existing differentiable protocols, i.e.,", + "type": "text" + }, + { + "bbox": [ + 295, + 510, + 502, + 522 + ], + "score": 0.84, + "content": "h _ { i , t } = \\mathtt { L S T M } \\left( h _ { i , t - 1 } , \\mathtt { r e l u } ( s \\nu _ { i } , t ) + \\mathtt { r e l u } ( m _ { \\mathcal { N } _ { i } , t } ) \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 509, + 506, + 523 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "We then evaluate two intermediate protocols “Concat Only” and “FPrint Only”, in which encoded", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 532, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 505, + 544 + ], + "score": 1.0, + "content": "inputs are concatenated and neighbor policies are included, respectively. Finally we evaluate their", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "score": 1.0, + "content": "combination NeurComm. As shown in Fig. 3, all protocols have similar learning curves in easy", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "CACC Catch-up scenario. Otherwise, both “Concat” and “FPrint” are able to enhance the baseline", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 565, + 426, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 426, + 576 + ], + "score": 1.0, + "content": "learning curves in certain scenarios and their affects are additive in NeurComm.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 37 + }, + { + "type": "title", + "bbox": [ + 108, + 589, + 216, + 601 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 218, + 602 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 218, + 602 + ], + "score": 1.0, + "content": "5.4 TRAINING RESULTS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 504, + 633 + ], + "lines": [ + { + "bbox": [ + 105, + 609, + 503, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 390, + 624 + ], + "score": 1.0, + "content": "Fig. 4 compares the learning curves of all MARL algorithms, after tuned", + "type": "text" + }, + { + "bbox": [ + 390, + 610, + 503, + 623 + ], + "score": 0.91, + "content": "\\alpha ^ { * } \\in \\{ 0 . 6 , 0 . 8 , 0 . 9 , 0 . 9 5 , 1 \\}", + "type": "inline_equation" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 620, + 507, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 161, + 635 + ], + "score": 1.0, + "content": "As expected,", + "type": "text" + }, + { + "bbox": [ + 161, + 622, + 173, + 632 + ], + "score": 0.86, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 620, + 507, + 635 + ], + "score": 1.0, + "content": "for non-communicative policies are lower than those for communicative policies.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + }, + { + "type": "table", + "bbox": [ + 126, + 671, + 485, + 730 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 168, + 651, + 440, + 663 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 170, + 651, + 441, + 664 + ], + "spans": [ + { + "bbox": [ + 170, + 651, + 320, + 664 + ], + "score": 1.0, + "content": "Table 1: Best spatial discount factors", + "type": "text" + }, + { + "bbox": [ + 320, + 652, + 332, + 661 + ], + "score": 0.87, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 651, + 441, + 664 + ], + "score": 1.0, + "content": "across NMARL scenarios.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "table_body", + "bbox": [ + 126, + 671, + 485, + 730 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 671, + 485, + 730 + ], + "spans": [ + { + "bbox": [ + 126, + 671, + 485, + 730 + ], + "score": 0.981, + "html": "
Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid1.01.01.00.90.950.9
ATSC Monaco1.00.90.90.90.90.9
CACC Catch-up1.01.01.01.01.01.0
CACC Slow-down1.01.01.00.80.90.8
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All hidden layers have 64 units. The encoding layer", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "score": 1.0, + "content": "implicitly learns normalization across different input signal types. We train each model over 1M", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 208, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 152, + 222 + ], + "score": 1.0, + "content": "steps, with", + "type": "text" + }, + { + "bbox": [ + 152, + 209, + 190, + 221 + ], + "score": 0.9, + "content": "\\gamma = 0 . 9 9", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 208, + 271, + 222 + ], + "score": 1.0, + "content": ", actor learning rate", + "type": "text" + }, + { + "bbox": [ + 271, + 208, + 309, + 220 + ], + "score": 0.91, + "content": "5 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 208, + 408, + 222 + ], + "score": 1.0, + "content": ", and critic learning rate", + "type": "text" + }, + { + "bbox": [ + 408, + 209, + 455, + 219 + ], + "score": 0.91, + "content": "2 . 5 \\times 1 0 ^ { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 208, + 506, + 222 + ], + "score": 1.0, + "content": ". Also, each", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 415, + 232 + ], + "score": 1.0, + "content": "training episode has a different seed for generalization purposes. In ATSC,", + "type": "text" + }, + { + "bbox": [ + 416, + 220, + 455, + 231 + ], + "score": 0.86, + "content": "\\beta = 0 . 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 220, + 460, + 232 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 460, + 220, + 502, + 232 + ], + "score": 0.9, + "content": "| B | = 1 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 220, + 506, + 232 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 174, + 244 + ], + "score": 1.0, + "content": "while in CACC,", + "type": "text" + }, + { + "bbox": [ + 174, + 231, + 213, + 242 + ], + "score": 0.89, + "content": "\\beta = 0 . 0 5", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 230, + 217, + 244 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 217, + 231, + 254, + 243 + ], + "score": 0.9, + "content": "| B | = 6 0", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 230, + 506, + 244 + ], + "score": 1.0, + "content": ", to encourage the exploration of collision-free policies. Each", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 413, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 413, + 254 + ], + "score": 1.0, + "content": "training takes about 30 hours on a 32GB memory, Intel Xeon CPU machine.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11, + "bbox_fs": [ + 104, + 173, + 506, + 254 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 267, + 209, + 278 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 210, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 210, + 280 + ], + "score": 1.0, + "content": "5.3 ABLATION STUDY", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 287, + 506, + 378 + ], + "lines": [ + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 448, + 300 + ], + "score": 1.0, + "content": "We perform ablation study in proposed scenarios, which are sorted as ATSC Monaco", + "type": "text" + }, + { + "bbox": [ + 448, + 289, + 457, + 298 + ], + "score": 0.76, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "ATSC Grid", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 506, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 143, + 309 + ], + "score": 0.4, + "content": "> { \\mathrm { C A C C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 298, + 192, + 312 + ], + "score": 1.0, + "content": "Slow-down", + "type": "text" + }, + { + "bbox": [ + 192, + 300, + 201, + 308 + ], + "score": 0.71, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 298, + 506, + 312 + ], + "score": 1.0, + "content": "CACC Catch-up by task difficulty. ATSC is more challenging than CACC", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 310, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 310, + 187, + 322 + ], + "score": 1.0, + "content": "due to larger scale", + "type": "text" + }, + { + "bbox": [ + 188, + 310, + 212, + 320 + ], + "score": 0.83, + "content": "> = 2 5", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 310, + 505, + 322 + ], + "score": 1.0, + "content": "vs 8), more complex dynamics (stochastic traffic flow vs deterministic", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 417, + 333 + ], + "score": 1.0, + "content": "vehicle dynamics), and longer control interval (5s vs 0.1s). ATSC Monaco", + "type": "text" + }, + { + "bbox": [ + 417, + 321, + 427, + 331 + ], + "score": 0.74, + "content": ">", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "ATSC Grid due to", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 332, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 329, + 344 + ], + "score": 1.0, + "content": "more heterogenous network, while CACC Slow-down", + "type": "text" + }, + { + "bbox": [ + 330, + 332, + 368, + 343 + ], + "score": 0.38, + "content": "> { \\mathrm { C A C C } }", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 332, + 505, + 344 + ], + "score": 1.0, + "content": "Catch-up due to more frequently", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "score": 1.0, + "content": "changing leading vehicle profile. To visualize the learning performance, we plot the learning curve,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 101, + 348, + 511, + 374 + ], + "spans": [ + { + "bbox": [ + 101, + 348, + 231, + 374 + ], + "score": 1.0, + "content": "that is, average episode return", + "type": "text" + }, + { + "bbox": [ + 232, + 353, + 338, + 369 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\begin{array} { r } { ( \\bar { R } = \\frac { 1 } { T } \\sum _ { t = 0 } ^ { T - 1 } \\sum _ { i \\in \\mathcal { V } } r _ { i , t } ) } \\end{array} } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 348, + 511, + 374 + ], + "score": 1.0, + "content": "vs training step. For better visualization,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 366, + 485, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 485, + 380 + ], + "score": 1.0, + "content": "all learning curves are smoothened using moving average with a window size of 100 episodes.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5, + "bbox_fs": [ + 101, + 288, + 511, + 380 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 383, + 505, + 494 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 507, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 507, + 398 + ], + "score": 1.0, + "content": "First, we investigate the impact of spatial discount factor, by comparing the learning curves among", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 107, + 391, + 507, + 410 + ], + "spans": [ + { + "bbox": [ + 107, + 394, + 176, + 406 + ], + "score": 0.93, + "content": "\\alpha \\in \\{ 0 . 8 , 0 . 9 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 391, + 457, + 410 + ], + "score": 1.0, + "content": "for IA2C and CommNet. Fig. 3 reveals a few interesting facts. First,", + "type": "text" + }, + { + "bbox": [ + 457, + 395, + 495, + 407 + ], + "score": 0.92, + "content": "\\alpha _ { \\mathrm { C o m m N e t } } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 391, + 507, + 410 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 404, + 508, + 421 + ], + "spans": [ + { + "bbox": [ + 104, + 404, + 184, + 421 + ], + "score": 1.0, + "content": "always higher than", + "type": "text" + }, + { + "bbox": [ + 185, + 406, + 208, + 417 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 208, + 404, + 244, + 421 + ], + "score": 1.0, + "content": ". Indeed,", + "type": "text" + }, + { + "bbox": [ + 245, + 406, + 300, + 417 + ], + "score": 0.92, + "content": "\\alpha _ { \\mathrm { C o m m N e t } } ^ { * } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 404, + 508, + 421 + ], + "score": 1.0, + "content": "in almost all scenarios (except for ATSC Monaco).", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 429 + ], + "score": 1.0, + "content": "This is because communicative policies perform delayed global information sharing, whereas non-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "score": 1.0, + "content": "communicative policies utilize neighborhood information only, causing difficulty to fit the global", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 439, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 402, + 450 + ], + "score": 1.0, + "content": "return. Second, learning performance becomes much more sensitive to", + "type": "text" + }, + { + "bbox": [ + 402, + 440, + 410, + 448 + ], + "score": 0.75, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 439, + 505, + 450 + ], + "score": 1.0, + "content": "when the task is more", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 214, + 462 + ], + "score": 1.0, + "content": "difficult. Specifically, all", + "type": "text" + }, + { + "bbox": [ + 214, + 451, + 222, + 459 + ], + "score": 0.78, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 448, + 506, + 462 + ], + "score": 1.0, + "content": "values lead to similar learning curves in CACC Catch-up, whereas", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 460, + 507, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 155, + 473 + ], + "score": 1.0, + "content": "appropriate", + "type": "text" + }, + { + "bbox": [ + 155, + 462, + 163, + 470 + ], + "score": 0.79, + "content": "\\alpha", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 460, + 507, + 473 + ], + "score": 1.0, + "content": "values help IA2C converge to much better policies more steadily in other scenarios.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 470, + 507, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 470, + 134, + 487 + ], + "score": 1.0, + "content": "Third,", + "type": "text" + }, + { + "bbox": [ + 134, + 471, + 146, + 481 + ], + "score": 0.87, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 470, + 215, + 487 + ], + "score": 1.0, + "content": "is high enough:", + "type": "text" + }, + { + "bbox": [ + 215, + 471, + 266, + 483 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * } = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 470, + 418, + 487 + ], + "score": 1.0, + "content": "except for CACC Slow-down where", + "type": "text" + }, + { + "bbox": [ + 419, + 471, + 469, + 483 + ], + "score": 0.91, + "content": "\\alpha _ { \\mathrm { I A 2 C } } ^ { * } = 0 . 8", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 470, + 507, + 487 + ], + "score": 1.0, + "content": ". This is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 482, + 480, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 480, + 495 + ], + "score": 1.0, + "content": "because the discounted problem must be similar enough to the original problem in execution.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 28.5, + "bbox_fs": [ + 104, + 381, + 508, + 495 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 498, + 505, + 576 + ], + "lines": [ + { + "bbox": [ + 106, + 498, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 329, + 511 + ], + "score": 1.0, + "content": "Next, we investigate the impact of NeurComm under", + "type": "text" + }, + { + "bbox": [ + 330, + 500, + 358, + 509 + ], + "score": 0.89, + "content": "\\alpha = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 498, + 505, + 511 + ], + "score": 1.0, + "content": ". We start with a baseline which is", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 509, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 294, + 523 + ], + "score": 1.0, + "content": "similar to existing differentiable protocols, i.e.,", + "type": "text" + }, + { + "bbox": [ + 295, + 510, + 502, + 522 + ], + "score": 0.84, + "content": "h _ { i , t } = \\mathtt { L S T M } \\left( h _ { i , t - 1 } , \\mathtt { r e l u } ( s \\nu _ { i } , t ) + \\mathtt { r e l u } ( m _ { \\mathcal { N } _ { i } , t } ) \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 509, + 506, + 523 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "We then evaluate two intermediate protocols “Concat Only” and “FPrint Only”, in which encoded", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 532, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 505, + 544 + ], + "score": 1.0, + "content": "inputs are concatenated and neighbor policies are included, respectively. Finally we evaluate their", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "score": 1.0, + "content": "combination NeurComm. As shown in Fig. 3, all protocols have similar learning curves in easy", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "CACC Catch-up scenario. Otherwise, both “Concat” and “FPrint” are able to enhance the baseline", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 565, + 426, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 426, + 576 + ], + "score": 1.0, + "content": "learning curves in certain scenarios and their affects are additive in NeurComm.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 498, + 506, + 576 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 589, + 216, + 601 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 218, + 602 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 218, + 602 + ], + "score": 1.0, + "content": "5.4 TRAINING RESULTS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 504, + 633 + ], + "lines": [ + { + "bbox": [ + 105, + 609, + 503, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 390, + 624 + ], + "score": 1.0, + "content": "Fig. 4 compares the learning curves of all MARL algorithms, after tuned", + "type": "text" + }, + { + "bbox": [ + 390, + 610, + 503, + 623 + ], + "score": 0.91, + "content": "\\alpha ^ { * } \\in \\{ 0 . 6 , 0 . 8 , 0 . 9 , 0 . 9 5 , 1 \\}", + "type": "inline_equation" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 620, + 507, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 161, + 635 + ], + "score": 1.0, + "content": "As expected,", + "type": "text" + }, + { + "bbox": [ + 161, + 622, + 173, + 632 + ], + "score": 0.86, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 620, + 507, + 635 + ], + "score": 1.0, + "content": "for non-communicative policies are lower than those for communicative policies.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 609, + 507, + 635 + ] + }, + { + "type": "table", + "bbox": [ + 126, + 671, + 485, + 730 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 168, + 651, + 440, + 663 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 170, + 651, + 441, + 664 + ], + "spans": [ + { + "bbox": [ + 170, + 651, + 320, + 664 + ], + "score": 1.0, + "content": "Table 1: Best spatial discount factors", + "type": "text" + }, + { + "bbox": [ + 320, + 652, + 332, + 661 + ], + "score": 0.87, + "content": "\\alpha ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 651, + 441, + 664 + ], + "score": 1.0, + "content": "across NMARL scenarios.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "table_body", + "bbox": [ + 126, + 671, + 485, + 730 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 671, + 485, + 730 + ], + "spans": [ + { + "bbox": [ + 126, + 671, + 485, + 730 + ], + "score": 0.981, + "html": "
Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid1.01.01.00.90.950.9
ATSC Monaco1.00.90.90.90.90.9
CACC Catch-up1.01.01.01.01.01.0
CACC Slow-down1.01.01.00.80.90.8
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The results are consistent with the reward-defined ones in Tab. 2.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 561, + 507, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 656 + ], + "score": 1.0, + "content": "Further, we investigate the performance of top policies in ATSC scenarios. For each ATSC scenario,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "we select the top two non-communicative and communicative policies and visualize their impact on", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "network traffic by plotting the time series of network averaged queue length and intersection delay in", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "Fig. 5. Note the line and shade show the mean and standard deviation of each metric across execution", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "runs, respectively. Based on Fig. 5a, NeurComm achieves the most sustainable traffic control in", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "ATSC Grid, so that the congested grid starts recovering immediately after the loading phase ends", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "at 3000s. During the same unloading phase, CommNet prevents the queues from further increasing", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 721, + 506, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 506, + 732 + ], + "score": 1.0, + "content": "while non-communicative policies are failed to do so. Also, FPrint is less robust than IA2C as it", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 349, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 505, + 362 + ], + "score": 1.0, + "content": "introduces a sudden congestion jump at 1000s. 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Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid-136.1-165.1-214.4-160.2-155.9-187.5
ATSC Monaco-226.3-263.0-339.4-369.7-359.4-528.9
CACC Catch-up-94.6-95.6-246.4-261.7-57.8-419.7
CACC Slow-down-934.7-950.8-1112-2209-697.9-1038
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Similarly, NeurComm achieves the lowest saturation", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 360, + 236, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 236, + 373 + ], + "score": 1.0, + "content": "rate in ATSC Monaco (Fig. 5b).", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 106, + 376, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 106, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "Intersection delay is another key metric in ATSC. Based on Fig. 5c, communicative policies are able", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "to reduce intersection delay as well in ATSC Grid, though it is not explicitly included in the objective", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "and so is not optimized by non-communicative policies. In contrast, communicative policies have fast", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 410, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 505, + 423 + ], + "score": 1.0, + "content": "increase on intersection delay in ATSC Monaco. This implies that communicative algorithms are able", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "score": 1.0, + "content": "to capture the spatiotemporal traffic pattern in homogeneous networks whereas they still have the risk", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "of overfitting on queue reduction in realistic and heterogenous networks. For example, they block the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 443, + 495, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 495, + 456 + ], + "score": 1.0, + "content": "short source edges on purpose to reduce on-road vehicles by paying a small cost of queue length.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 460, + 505, + 515 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 506, + 472 + ], + "score": 1.0, + "content": "Finally, we investigate the robustness (string stability) of top policies in CACC scenarios. In particular,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "we plot the time series of headway and velocity for the first and the last vehicles in the platoon. The", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 482, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 405, + 494 + ], + "score": 1.0, + "content": "profile of the first vehicle indicates how adaptively the controller pursues", + "type": "text" + }, + { + "bbox": [ + 405, + 482, + 417, + 492 + ], + "score": 0.84, + "content": "\\mathrm { ~ h ~ } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 482, + 435, + 494 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 435, + 482, + 447, + 492 + ], + "score": 0.8, + "content": "\\boldsymbol { \\tau } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 482, + 506, + 494 + ], + "score": 1.0, + "content": ", while that of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 491, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 506 + ], + "score": 1.0, + "content": "the last vehicle indicates how stable the controlled platoon is. Based on Tab. 1 and Tab. 4, the top", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 504, + 425, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 425, + 516 + ], + "score": 1.0, + "content": "communicative and non-communicative controllers are NeurComm and FPrint.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 505, + 565 + ], + "lines": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "score": 1.0, + "content": "Fig. 6 shows the corresponding headway and velocity profiles for the selected controllers. Interest-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 531, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 336, + 544 + ], + "score": 1.0, + "content": "ingly, MARL controllers are able to achieve steady state", + "type": "text" + }, + { + "bbox": [ + 337, + 532, + 349, + 542 + ], + "score": 0.82, + "content": "\\boldsymbol { \\tau } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 531, + 367, + 544 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 367, + 532, + 379, + 542 + ], + "score": 0.85, + "content": "\\mathrm { h ^ { * } }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 531, + 506, + 544 + ], + "score": 1.0, + "content": "for the first vehicle of platoon,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 543, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 505, + 555 + ], + "score": 1.0, + "content": "whereas they still have difficulty to eliminate the perturbation through the platoon. 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Scenario NameNeurCommCommNetDIALIA2CFPrintConseNet
ATSC Grid-136.1-165.1-214.4-160.2-155.9-187.5
ATSC Monaco-226.3-263.0-339.4-369.7-359.4-528.9
CACC Catch-up-94.6-95.6-246.4-261.7-57.8-419.7
CACC Slow-down-934.7-950.8-1112-2209-697.9-1038
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Based on Fig. 5c, communicative policies are able", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "to reduce intersection delay as well in ATSC Grid, though it is not explicitly included in the objective", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "and so is not optimized by non-communicative policies. In contrast, communicative policies have fast", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 410, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 505, + 423 + ], + "score": 1.0, + "content": "increase on intersection delay in ATSC Monaco. This implies that communicative algorithms are able", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 506, + 434 + ], + "score": 1.0, + "content": "to capture the spatiotemporal traffic pattern in homogeneous networks whereas they still have the risk", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "of overfitting on queue reduction in realistic and heterogenous networks. For example, they block the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 443, + 495, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 495, + 456 + ], + "score": 1.0, + "content": "short source edges on purpose to reduce on-road vehicles by paying a small cost of queue length.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 377, + 506, + 456 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 460, + 505, + 515 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 506, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 506, + 472 + ], + "score": 1.0, + "content": "Finally, we investigate the robustness (string stability) of top policies in CACC scenarios. In particular,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "we plot the time series of headway and velocity for the first and the last vehicles in the platoon. The", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 482, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 405, + 494 + ], + "score": 1.0, + "content": "profile of the first vehicle indicates how adaptively the controller pursues", + "type": "text" + }, + { + "bbox": [ + 405, + 482, + 417, + 492 + ], + "score": 0.84, + "content": "\\mathrm { ~ h ~ } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 482, + 435, + 494 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 435, + 482, + 447, + 492 + ], + "score": 0.8, + "content": "\\boldsymbol { \\tau } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 482, + 506, + 494 + ], + "score": 1.0, + "content": ", while that of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 491, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 506 + ], + "score": 1.0, + "content": "the last vehicle indicates how stable the controlled platoon is. Based on Tab. 1 and Tab. 4, the top", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 504, + 425, + 516 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 425, + 516 + ], + "score": 1.0, + "content": "communicative and non-communicative controllers are NeurComm and FPrint.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 459, + 506, + 516 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 505, + 565 + ], + "lines": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "score": 1.0, + "content": "Fig. 6 shows the corresponding headway and velocity profiles for the selected controllers. Interest-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 531, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 336, + 544 + ], + "score": 1.0, + "content": "ingly, MARL controllers are able to achieve steady state", + "type": "text" + }, + { + "bbox": [ + 337, + 532, + 349, + 542 + ], + "score": 0.82, + "content": "\\boldsymbol { \\tau } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 531, + 367, + 544 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 367, + 532, + 379, + 542 + ], + "score": 0.85, + "content": "\\mathrm { h ^ { * } }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 531, + 506, + 544 + ], + "score": 1.0, + "content": "for the first vehicle of platoon,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 543, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 505, + 555 + ], + "score": 1.0, + "content": "whereas they still have difficulty to eliminate the perturbation through the platoon. This may be", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 552, + 457, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 457, + 567 + ], + "score": 1.0, + "content": "because of the heuristic low-level controller as well as the delayed information sharing.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 24.5, + "bbox_fs": [ + 105, + 520, + 506, + 567 + ] + }, + { + "type": "image", + "bbox": [ + 106, + 596, + 504, + 698 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 106, + 596, + 504, + 698 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 596, + 504, + 698 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 504, + 698 + ], + "score": 0.968, + "type": "image", + "image_path": "7ff08398439d1963fe5c9490267a1bb0be0276ac701c7c7e0dcea9361682a818.jpg" + } + ] + } + ], + "index": 28, + "virtual_lines": [ + { + "bbox": [ + 106, + 596, + 504, + 630.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 106, + 630.0, + 504, + 664.0 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 106, + 664.0, + 504, + 698.0 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 104, + 706, + 505, + 729 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 705, + 505, + 720 + ], + "spans": [ + { + "bbox": [ + 105, + 705, + 505, + 720 + ], + "score": 1.0, + "content": "Figure 6: Headway and velocity profiles of the first and last vehicles of the platoon, controlled by top", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 717, + 356, + 730 + ], + "spans": [ + { + "bbox": [ + 105, + 717, + 356, + 730 + ], + "score": 1.0, + "content": "communicative and non-communicative policies in execution.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + } + ], + "index": 29.25 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 201, + 93 + ], + "lines": [ + { + "bbox": [ + 104, + 79, + 203, + 97 + ], + "spans": [ + { + "bbox": [ + 104, + 79, + 203, + 97 + ], + "score": 1.0, + "content": "6 CONCLUSIONS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 194 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 506, + 119 + ], + "score": 1.0, + "content": "We have formulated the spatiotemporal MDP for decentralized NSC under neighborhood commu-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 118, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 505, + 129 + ], + "score": 1.0, + "content": "nication. Further, we have introduced the spatial discount factor to enhance non-communicative", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 127, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 141 + ], + "score": 1.0, + "content": "MARL algorithms, and proposed a neural communication protocol NeurComm to design adaptive", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 505, + 153 + ], + "score": 1.0, + "content": "and efficient communicative MARL algorithms. We hope this paper provides a rethink on developing", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "score": 1.0, + "content": "scalable and robust MARL controllers for NSC, by following practical engineering assumptions and", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "combining appropriate learning and communication methods rather than reusing existing MARL", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 506, + 186 + ], + "score": 1.0, + "content": "algorithms. One future direction is improving the recurrent units to naturally control spatiotemporal", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 363, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 363, + 196 + ], + "score": 1.0, + "content": "information flows within the meta-DNN in a decentralized way.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4.5 + }, + { + "type": "title", + "bbox": [ + 108, + 208, + 200, + 218 + ], + "lines": [ + { + "bbox": [ + 107, + 209, + 200, + 219 + ], + "spans": [ + { + "bbox": [ + 107, + 209, + 200, + 219 + ], + "score": 1.0, + "content": "ACKNOWLEDGMENTS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 108, + 226, + 504, + 249 + ], + "lines": [ + { + "bbox": [ + 106, + 225, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 505, + 239 + ], + "score": 1.0, + "content": "We would like to thank Marco Pavone and Alexander Anemogiannis for valuable discussions and", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 237, + 194, + 250 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 194, + 250 + ], + "score": 1.0, + "content": "insightful comments.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 108, + 266, + 175, + 278 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 176, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 176, + 279 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 285, + 506, + 317 + ], + "lines": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "Masako Bando, Katsuya Hasebe, Akihiro Nakayama, Akihiro Shibata, and Yuki Sugiyama. 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The proof follows the learning method in A2C Mnih et al. (2016), which shows that", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "interline_equation", + "bbox": [ + 158, + 610, + 451, + 675 + ], + "lines": [ + { + "bbox": [ + 158, + 610, + 451, + 675 + ], + "spans": [ + { + "bbox": [ + 158, + 610, + 451, + 675 + ], + "score": 0.95, + "content": "\\begin{array} { l } { \\displaystyle \\mathcal { L } ( \\theta ) = \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( - \\log \\pi _ { \\theta } ( a _ { \\tau } | s _ { \\tau } ) \\hat { A } _ { \\tau } ^ { \\pi } + \\beta \\sum _ { a \\in \\mathcal { A } } \\pi _ { \\theta } ( a | s _ { \\tau } ) \\log \\pi _ { \\theta } ( a | s _ { \\tau } ) \\right) , } \\\\ { \\displaystyle \\mathcal { L } ( \\omega ) = \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( \\hat { R } _ { \\tau } ^ { \\pi } - V _ { \\omega } ( s _ { \\tau } ) \\right) ^ { 2 } , } \\end{array}", + "type": "interline_equation", + "image_path": "3e1bc61f5790b9c8abb522540845c6909b8570915224bbe514e80c8625164c5b.jpg" + } + ] + } + ], + "index": 36, + "virtual_lines": [ + { + "bbox": [ + 158, + 610, + 451, + 631.6666666666666 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 158, + 631.6666666666666, + 451, + 653.3333333333333 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 158, + 653.3333333333333, + 451, + 674.9999999999999 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 680, + 504, + 705 + ], + "lines": [ + { + "bbox": [ + 101, + 673, + 509, + 707 + ], + "spans": [ + { + "bbox": [ + 101, + 673, + 132, + 707 + ], + "score": 1.0, + "content": "where minib", + "type": "text" + }, + { + "bbox": [ + 133, + 680, + 193, + 694 + ], + "score": 0.8, + "content": "\\hat { A } _ { \\tau } ^ { \\pi } = \\hat { R } _ { \\tau } ^ { \\pi } - v _ { \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 673, + 197, + 707 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 197, + 680, + 345, + 694 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\hat { R } _ { \\tau } ^ { \\pi } = \\sum _ { \\tau ^ { \\prime } = \\tau } ^ { \\tau _ { B } - 1 } \\gamma ^ { \\tau ^ { \\prime } - \\tau } r _ { \\tau ^ { \\prime } } + \\gamma ^ { \\tau _ { B } - \\tau } v _ { \\tau _ { B } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 673, + 366, + 707 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 366, + 681, + 425, + 694 + ], + "score": 0.93, + "content": "v _ { \\tau } = V _ { \\omega ^ { - } } ( s _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 673, + 509, + 707 + ], + "score": 1.0, + "content": ", based on on-policy", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 203, + 694, + 274, + 705 + ], + "spans": [ + { + "bbox": [ + 203, + 694, + 274, + 705 + ], + "score": 0.81, + "content": "\\{ ( s _ { \\tau } , a _ { \\tau } , r _ { \\tau } ) \\} _ { \\tau \\in { \\mathcal B } }", + "type": "inline_equation" + } + ], + "index": 39 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 105, + 709, + 506, + 734 + ], + "lines": [ + { + "bbox": [ + 106, + 708, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 708, + 505, + 722 + ], + "score": 1.0, + "content": "Now we consider spatiotemporal MDP, which has transition in Eq. 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The proof follows the learning method in A2C Mnih et al. (2016), which shows that", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 595, + 474, + 609 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 158, + 610, + 451, + 675 + ], + "lines": [ + { + "bbox": [ + 158, + 610, + 451, + 675 + ], + "spans": [ + { + "bbox": [ + 158, + 610, + 451, + 675 + ], + "score": 0.95, + "content": "\\begin{array} { l } { \\displaystyle \\mathcal { L } ( \\theta ) = \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( - \\log \\pi _ { \\theta } ( a _ { \\tau } | s _ { \\tau } ) \\hat { A } _ { \\tau } ^ { \\pi } + \\beta \\sum _ { a \\in \\mathcal { A } } \\pi _ { \\theta } ( a | s _ { \\tau } ) \\log \\pi _ { \\theta } ( a | s _ { \\tau } ) \\right) , } \\\\ { \\displaystyle \\mathcal { L } ( \\omega ) = \\frac { 1 } { | \\mathcal { B } | } \\sum _ { \\tau \\in \\mathcal { B } } \\left( \\hat { R } _ { \\tau } ^ { \\pi } - V _ { \\omega } ( s _ { \\tau } ) \\right) ^ { 2 } , } \\end{array}", + "type": "interline_equation", + "image_path": "3e1bc61f5790b9c8abb522540845c6909b8570915224bbe514e80c8625164c5b.jpg" + } + ] + } + ], + "index": 36, + "virtual_lines": [ + { + "bbox": [ + 158, + 610, + 451, + 631.6666666666666 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 158, + 631.6666666666666, + 451, + 653.3333333333333 + ], + "spans": [], + "index": 36 + }, + { + "bbox": [ + 158, + 653.3333333333333, + 451, + 674.9999999999999 + ], + "spans": [], + "index": 37 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 680, + 504, + 705 + ], + "lines": [ + { + "bbox": [ + 101, + 673, + 509, + 707 + ], + "spans": [ + { + "bbox": [ + 101, + 673, + 132, + 707 + ], + "score": 1.0, + "content": "where minib", + "type": "text" + }, + { + "bbox": [ + 133, + 680, + 193, + 694 + ], + "score": 0.8, + "content": "\\hat { A } _ { \\tau } ^ { \\pi } = \\hat { R } _ { \\tau } ^ { \\pi } - v _ { \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 673, + 197, + 707 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 197, + 680, + 345, + 694 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\hat { R } _ { \\tau } ^ { \\pi } = \\sum _ { \\tau ^ { \\prime } = \\tau } ^ { \\tau _ { B } - 1 } \\gamma ^ { \\tau ^ { \\prime } - \\tau } r _ { \\tau ^ { \\prime } } + \\gamma ^ { \\tau _ { B } - \\tau } v _ { \\tau _ { B } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 673, + 366, + 707 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 366, + 681, + 425, + 694 + ], + "score": 0.93, + "content": "v _ { \\tau } = V _ { \\omega ^ { - } } ( s _ { \\tau } )", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 673, + 509, + 707 + ], + "score": 1.0, + "content": ", based on on-policy", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 203, + 694, + 274, + 705 + ], + "spans": [ + { + "bbox": [ + 203, + 694, + 274, + 705 + ], + "score": 0.81, + "content": "\\{ ( s _ { \\tau } , a _ { \\tau } , r _ { \\tau } ) \\} _ { \\tau \\in { \\mathcal B } }", + "type": "inline_equation" + } + ], + "index": 39 + } + ], + "index": 38.5, + "bbox_fs": [ + 101, + 673, + 509, + 707 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 709, + 506, + 734 + ], + "lines": [ + { + "bbox": [ + 106, + 708, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 708, + 505, + 722 + ], + "score": 1.0, + "content": "Now we consider spatiotemporal MDP, which has transition in Eq. 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Now assuming the observations", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "and communications are restricted to each neighborhood as in Definition 3.1, then the actor and critic", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 451, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 140, + 129 + ], + "score": 1.0, + "content": "become", + "type": "text" + }, + { + "bbox": [ + 140, + 116, + 209, + 129 + ], + "score": 0.93, + "content": "\\pi _ { \\theta _ { i } } ( \\tilde { s } _ { i } ) \\approx \\tilde { \\pi } _ { \\theta _ { i } } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 117, + 227, + 129 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 227, + 115, + 338, + 129 + ], + "score": 0.92, + "content": "V _ { \\omega _ { i } } ( \\tilde { s } _ { i } , a _ { \\mathcal { N } _ { i } } ) \\approx \\tilde { V } _ { \\omega _ { i } } ( s , a _ { - i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 117, + 451, + 129 + ], + "score": 1.0, + "content": ", with the best observability.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 105, + 133, + 505, + 157 + ], + "lines": [ + { + "bbox": [ + 105, + 132, + 506, + 147 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 178, + 147 + ], + "score": 1.0, + "content": "Hence, replacing", + "type": "text" + }, + { + "bbox": [ + 179, + 133, + 210, + 146 + ], + "score": 0.88, + "content": "\\pi _ { \\boldsymbol { \\theta } } ( a | \\boldsymbol { s } )", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 132, + 215, + 147 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 215, + 133, + 240, + 146 + ], + "score": 0.79, + "content": "V _ { \\omega } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 132, + 244, + 147 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 245, + 136, + 251, + 144 + ], + "score": 0.53, + "content": "r", + "type": "inline_equation" + }, + { + "bbox": [ + 251, + 132, + 266, + 147 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 266, + 133, + 307, + 146 + ], + "score": 0.84, + "content": "\\pi _ { \\theta _ { i } } ( a _ { i } | \\tilde { s } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 132, + 311, + 147 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 312, + 133, + 362, + 146 + ], + "score": 0.82, + "content": "V _ { \\omega _ { i } } ( \\tilde { s } _ { i } , a _ { \\mathcal { N } _ { i } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 132, + 384, + 147 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 385, + 134, + 394, + 145 + ], + "score": 0.86, + "content": "\\tilde { r } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 132, + 506, + 147 + ], + "score": 1.0, + "content": ", respectively, we establish", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 144, + 504, + 158 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 325, + 158 + ], + "score": 1.0, + "content": "Eq. (3)(4) from Eq. (6)(7), which concludes the proof.", + "type": "text" + }, + { + "bbox": [ + 495, + 147, + 504, + 154 + ], + "score": 0.997, + "content": "□", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 107, + 168, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 168, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 343, + 182 + ], + "score": 1.0, + "content": "Note partial observability and non-stationarity are present in", + "type": "text" + }, + { + "bbox": [ + 343, + 169, + 384, + 181 + ], + "score": 0.94, + "content": "\\pi _ { \\theta _ { i } } ( a _ { i } | \\tilde { s } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 168, + 402, + 182 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 402, + 169, + 453, + 181 + ], + "score": 0.91, + "content": "V _ { \\omega _ { i } } \\left( \\tilde { s } _ { i } , a _ { \\mathcal { N } _ { i } } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 168, + 506, + 182 + ], + "score": 1.0, + "content": ". Fortunately,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 178, + 504, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 498, + 193 + ], + "score": 1.0, + "content": "communication improves the observability. Based on Definition 3.1, any information that agent", + "type": "text" + }, + { + "bbox": [ + 498, + 181, + 504, + 191 + ], + "score": 0.78, + "content": "j", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 189, + 473, + 205 + ], + "spans": [ + { + "bbox": [ + 104, + 189, + 164, + 205 + ], + "score": 1.0, + "content": "knows at time", + "type": "text" + }, + { + "bbox": [ + 165, + 191, + 169, + 200 + ], + "score": 0.73, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 189, + 246, + 205 + ], + "score": 1.0, + "content": "can be included in", + "type": "text" + }, + { + "bbox": [ + 246, + 191, + 268, + 203 + ], + "score": 0.9, + "content": "m _ { j i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 189, + 320, + 205 + ], + "score": 1.0, + "content": ". We assume", + "type": "text" + }, + { + "bbox": [ + 320, + 190, + 444, + 203 + ], + "score": 0.93, + "content": "s _ { j , t } \\cup \\{ m _ { k j , t - 1 } \\} _ { k \\in \\mathcal { N } _ { j } } \\subset m _ { j i , t } .", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 189, + 473, + 205 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 206, + 462, + 285 + ], + "lines": [ + { + "bbox": [ + 149, + 206, + 462, + 285 + ], + "spans": [ + { + "bbox": [ + 149, + 206, + 462, + 285 + ], + "score": 0.93, + "content": "\\begin{array} { r l } & { \\widetilde { s } _ { i , t } \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } \\cup \\big \\{ m _ { k j , t - 1 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { N } _ { i } } } \\\\ & { \\qquad \\supset \\big \\{ s _ { j , t } \\big \\} _ { j \\in \\mathcal { V } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\cup \\big \\{ m _ { k j , t - 2 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 2 } } \\\\ & { \\qquad \\supset \\big \\{ s _ { j , t } \\big \\} _ { j \\in \\mathcal { V } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 2 } \\cup \\big \\{ s _ { j , t - 2 } \\cup \\big \\{ m _ { k j , t - 3 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 3 } } \\\\ & { \\qquad \\supset \\dots } \\\\ & { \\qquad \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t + 1 - d _ { i j } } \\big \\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} } . } \\end{array}", + "type": "interline_equation", + "image_path": "397de13bd15c4d6e9a79dc00e5a76bd3b9a8b797774c7e035a954993dccb3380.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 149, + 206, + 462, + 232.33333333333334 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 149, + 232.33333333333334, + 462, + 258.6666666666667 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 149, + 258.6666666666667, + 462, + 285.0 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 287, + 505, + 310 + ], + "lines": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 133, + 300 + ], + "score": 1.0, + "content": "Thus,", + "type": "text" + }, + { + "bbox": [ + 133, + 288, + 147, + 299 + ], + "score": 0.89, + "content": "\\tilde { s } _ { i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "includes the delayed global observations. On the other hand, Eq. (1)(2) mitigate the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 298, + 285, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 285, + 311 + ], + "score": 1.0, + "content": "non-stationarity. To see this mathematically,", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5 + }, + { + "type": "interline_equation", + "bbox": [ + 148, + 313, + 463, + 382 + ], + "lines": [ + { + "bbox": [ + 148, + 313, + 463, + 382 + ], + "spans": [ + { + "bbox": [ + 148, + 313, + 463, + 382 + ], + "score": 0.93, + "content": "\\begin{array} { l } { { \\mathbb { E } _ { \\pi _ { i } , p } } [ \\tilde { r } _ { i , t } | s _ { t } , a _ { t } ] = { \\mathbb { E } _ { \\pi _ { i } , p _ { i } } } [ r _ { i , t } | s \\nu _ { i } , t , a _ { \\mathcal { N } _ { i } , t } ] + \\alpha \\displaystyle \\sum _ { j \\in \\mathcal { N } _ { i } } { \\mathbb { E } _ { \\pi _ { i } , p _ { j } } } [ r _ { j , t } | s \\nu _ { j } , t , a \\nu _ { j } \\backslash \\{ i \\} , t ] } \\\\ { ~ + \\displaystyle \\sum _ { d = 2 } ^ { d _ { \\operatorname* { m a x } } } \\left( \\alpha ^ { d } \\sum _ { j \\in \\{ \\mathcal { V } | d _ { i j } = d \\} } { \\mathbb { E } _ { p _ { j } } } [ r _ { j , t } | s \\nu _ { j } , t , a \\nu _ { j } , t ] \\right) , \\qquad } \\end{array}", + "type": "interline_equation", + "image_path": "c1f3fc1c2630ba8801d08b5b09e045505295e76f35472c4e4373cb969c50f767.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 148, + 313, + 463, + 336.0 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 148, + 336.0, + 463, + 359.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 148, + 359.0, + 463, + 382.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 383, + 503, + 417 + ], + "lines": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "score": 1.0, + "content": "where the further away reward signals are discounted more. Note if communication is allowed, each", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 394, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 407 + ], + "score": 1.0, + "content": "agent will have delayed global observations, and the non-stationarity mainly comes from limited", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 405, + 226, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 226, + 417 + ], + "score": 1.0, + "content": "information of future actions.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "title", + "bbox": [ + 108, + 430, + 253, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 430, + 254, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 254, + 443 + ], + "score": 1.0, + "content": "A.2 PROOF OF PROPOSITION 4.1", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 504, + 473 + ], + "lines": [ + { + "bbox": [ + 106, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "This proposition contains two statements regarding neural communication based global information", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 460, + 449, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 449, + 475 + ], + "score": 1.0, + "content": "sharing in forward and backward propagations. We establish each of them separately.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 106, + 475, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 488 + ], + "score": 1.0, + "content": "Lemma A.1 (Spatial Information Propagation). In NeurComm, the delayed global information is", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 487, + 288, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 288, + 500 + ], + "score": 1.0, + "content": "utilized to estimate each hidden state, that is,", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "interline_equation", + "bbox": [ + 207, + 500, + 402, + 518 + ], + "lines": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "spans": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "score": 0.9, + "content": "h _ { i , t } \\supset s _ { i , 0 : t } \\cup \\left\\{ s _ { j , 0 : t + 1 - d _ { i j } } , \\pi _ { j , 0 : t - d _ { i j } } \\right\\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} } ,", + "type": "interline_equation", + "image_path": "1e453c919067a3dcb2e6816bdecded5dc1bc896803be13d0a2f18b3afd68ab9e.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 521, + 441, + 534 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 440, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 133, + 536 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 523, + 158, + 533 + ], + "score": 0.89, + "content": "x \\supset y", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 519, + 217, + 536 + ], + "score": 1.0, + "content": "if information", + "type": "text" + }, + { + "bbox": [ + 218, + 524, + 225, + 533 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 519, + 313, + 536 + ], + "score": 1.0, + "content": "is utilized to estimate", + "type": "text" + }, + { + "bbox": [ + 313, + 524, + 320, + 532 + ], + "score": 0.77, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 519, + 340, + 536 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 341, + 522, + 440, + 534 + ], + "score": 0.91, + "content": "x _ { 0 : t } : = \\{ x _ { 0 } , x _ { 1 } , \\ldots , x _ { t } \\}", + "type": "inline_equation" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 545, + 504, + 568 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 364, + 559 + ], + "score": 1.0, + "content": "Proof. Based on the definition of NeurComm protocol (Eq. (5)),", + "type": "text" + }, + { + "bbox": [ + 365, + 546, + 420, + 558 + ], + "score": 0.93, + "content": "m _ { i , t } \\supset h _ { i , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 544, + 441, + 559 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 442, + 546, + 505, + 558 + ], + "score": 0.94, + "content": "h _ { i , t } \\supset h _ { i , t - 1 } \\cup", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 556, + 240, + 569 + ], + "spans": [ + { + "bbox": [ + 107, + 558, + 205, + 569 + ], + "score": 0.88, + "content": "s _ { \\mathcal { V } _ { i } , t } \\cup \\pi _ { \\mathcal { N } _ { i } , t - 1 } \\cup m _ { \\mathcal { N } _ { i } , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 556, + 240, + 569 + ], + "score": 1.0, + "content": ". Hence,", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5 + }, + { + "type": "interline_equation", + "bbox": [ + 127, + 570, + 483, + 681 + ], + "lines": [ + { + "bbox": [ + 127, + 570, + 483, + 681 + ], + "spans": [ + { + "bbox": [ + 127, + 570, + 483, + 681 + ], + "score": 0.86, + "content": "\\begin{array} { r l } & { h _ { i , t } \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } , \\pi _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ h _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { V } _ { i } } } \\\\ & { \\qquad \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } , \\pi _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\cup \\big \\{ s _ { k , t - 1 } , \\pi _ { k , t - 2 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\cup \\big \\{ h _ { k , t - 2 } \\big \\} _ { k \\in \\mathcal { V } _ { j } } \\big \\} _ { j \\in \\mathcal { V } _ { i } } } \\\\ & { \\qquad = s _ { i , t - 1 : t } \\cup \\big \\{ s _ { j , t - 1 : t } , \\pi _ { j , t - 2 : t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } , \\pi _ { j , t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = 2 \\} } } \\\\ & { \\qquad \\cup \\big \\{ h _ { j , t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } \\leq 2 \\} } } \\\\ & { \\qquad \\supset \\big . s . . } \\\\ & { \\qquad \\cup \\big \\{ s _ { j , 0 : t } , \\pi _ { j , t - 2 : t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , 0 : t - 1 } , \\pi _ { j , 0 : t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = 2 \\} } } \\\\ & { \\qquad \\cup \\big \\{ s _ { j , 0 : t + 1 } - \\mathcal { U } _ { \\mathrm { m a x } } , \\pi _ { j , 0 : t - d _ { \\mathrm { m a x } } } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = d _ { \\mathrm { m a x } } \\} } , } \\end{array}", + "type": "interline_equation", + "image_path": "da3d5ace36b94686a1b3215e1b429eaed4d5acd627d317778bc82d4c09c97acc.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 127, + 570, + 483, + 607.0 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 127, + 607.0, + 483, + 644.0 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 127, + 644.0, + 483, + 681.0 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 681, + 216, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 680, + 216, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 680, + 216, + 693 + ], + "score": 1.0, + "content": "which concludes the proof.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 506, + 733 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "Lemma A.2 (Spatial Gradient Propagation). 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(3)(4) from Eq. (6)(7), which concludes the proof.", + "type": "text" + }, + { + "bbox": [ + 495, + 147, + 504, + 154 + ], + "score": 0.997, + "content": "□", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4.5, + "bbox_fs": [ + 105, + 132, + 506, + 158 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 168, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 168, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 343, + 182 + ], + "score": 1.0, + "content": "Note partial observability and non-stationarity are present in", + "type": "text" + }, + { + "bbox": [ + 343, + 169, + 384, + 181 + ], + "score": 0.94, + "content": "\\pi _ { \\theta _ { i } } ( a _ { i } | \\tilde { s } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 168, + 402, + 182 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 402, + 169, + 453, + 181 + ], + "score": 0.91, + "content": "V _ { \\omega _ { i } } \\left( \\tilde { s } _ { i } , a _ { \\mathcal { N } _ { i } } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 168, + 506, + 182 + ], + "score": 1.0, + "content": ". 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Then", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 104, + 168, + 506, + 205 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 206, + 462, + 285 + ], + "lines": [ + { + "bbox": [ + 149, + 206, + 462, + 285 + ], + "spans": [ + { + "bbox": [ + 149, + 206, + 462, + 285 + ], + "score": 0.93, + "content": "\\begin{array} { r l } & { \\widetilde { s } _ { i , t } \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } \\cup \\big \\{ m _ { k j , t - 1 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { N } _ { i } } } \\\\ & { \\qquad \\supset \\big \\{ s _ { j , t } \\big \\} _ { j \\in \\mathcal { V } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\cup \\big \\{ m _ { k j , t - 2 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 2 } } \\\\ & { \\qquad \\supset \\big \\{ s _ { j , t } \\big \\} _ { j \\in \\mathcal { V } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 2 } \\cup \\big \\{ s _ { j , t - 2 } \\cup \\big \\{ m _ { k j , t - 3 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\big \\} _ { j \\in \\mathcal { V } | d _ { i j } = 3 } } \\\\ & { \\qquad \\supset \\dots } \\\\ & { \\qquad \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t + 1 - d _ { i j } } \\big \\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} } . } \\end{array}", + "type": "interline_equation", + "image_path": "397de13bd15c4d6e9a79dc00e5a76bd3b9a8b797774c7e035a954993dccb3380.jpg" + } + ] + } + ], + "index": 10, + "virtual_lines": [ + { + "bbox": [ + 149, + 206, + 462, + 232.33333333333334 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 149, + 232.33333333333334, + 462, + 258.6666666666667 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 149, + 258.6666666666667, + 462, + 285.0 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 287, + 505, + 310 + ], + "lines": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 133, + 300 + ], + "score": 1.0, + "content": "Thus,", + "type": "text" + }, + { + "bbox": [ + 133, + 288, + 147, + 299 + ], + "score": 0.89, + "content": "\\tilde { s } _ { i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "includes the delayed global observations. On the other hand, Eq. (1)(2) mitigate the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 298, + 285, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 285, + 311 + ], + "score": 1.0, + "content": "non-stationarity. To see this mathematically,", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 287, + 505, + 311 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 148, + 313, + 463, + 382 + ], + "lines": [ + { + "bbox": [ + 148, + 313, + 463, + 382 + ], + "spans": [ + { + "bbox": [ + 148, + 313, + 463, + 382 + ], + "score": 0.93, + "content": "\\begin{array} { l } { { \\mathbb { E } _ { \\pi _ { i } , p } } [ \\tilde { r } _ { i , t } | s _ { t } , a _ { t } ] = { \\mathbb { E } _ { \\pi _ { i } , p _ { i } } } [ r _ { i , t } | s \\nu _ { i } , t , a _ { \\mathcal { N } _ { i } , t } ] + \\alpha \\displaystyle \\sum _ { j \\in \\mathcal { N } _ { i } } { \\mathbb { E } _ { \\pi _ { i } , p _ { j } } } [ r _ { j , t } | s \\nu _ { j } , t , a \\nu _ { j } \\backslash \\{ i \\} , t ] } \\\\ { ~ + \\displaystyle \\sum _ { d = 2 } ^ { d _ { \\operatorname* { m a x } } } \\left( \\alpha ^ { d } \\sum _ { j \\in \\{ \\mathcal { V } | d _ { i j } = d \\} } { \\mathbb { E } _ { p _ { j } } } [ r _ { j , t } | s \\nu _ { j } , t , a \\nu _ { j } , t ] \\right) , \\qquad } \\end{array}", + "type": "interline_equation", + "image_path": "c1f3fc1c2630ba8801d08b5b09e045505295e76f35472c4e4373cb969c50f767.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 148, + 313, + 463, + 336.0 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 148, + 336.0, + 463, + 359.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 148, + 359.0, + 463, + 382.0 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 383, + 503, + 417 + ], + "lines": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 106, + 383, + 505, + 395 + ], + "score": 1.0, + "content": "where the further away reward signals are discounted more. Note if communication is allowed, each", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 394, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 407 + ], + "score": 1.0, + "content": "agent will have delayed global observations, and the non-stationarity mainly comes from limited", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 405, + 226, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 226, + 417 + ], + "score": 1.0, + "content": "information of future actions.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 383, + 506, + 417 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 430, + 253, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 430, + 254, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 254, + 443 + ], + "score": 1.0, + "content": "A.2 PROOF OF PROPOSITION 4.1", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 504, + 473 + ], + "lines": [ + { + "bbox": [ + 106, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "This proposition contains two statements regarding neural communication based global information", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 460, + 449, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 449, + 475 + ], + "score": 1.0, + "content": "sharing in forward and backward propagations. We establish each of them separately.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 450, + 505, + 475 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 475, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 488 + ], + "score": 1.0, + "content": "Lemma A.1 (Spatial Information Propagation). In NeurComm, the delayed global information is", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 487, + 288, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 288, + 500 + ], + "score": 1.0, + "content": "utilized to estimate each hidden state, that is,", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 106, + 475, + 505, + 500 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 207, + 500, + 402, + 518 + ], + "lines": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "spans": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "score": 0.9, + "content": "h _ { i , t } \\supset s _ { i , 0 : t } \\cup \\left\\{ s _ { j , 0 : t + 1 - d _ { i j } } , \\pi _ { j , 0 : t - d _ { i j } } \\right\\} _ { j \\in \\mathcal { V } \\backslash \\{ i \\} } ,", + "type": "interline_equation", + "image_path": "1e453c919067a3dcb2e6816bdecded5dc1bc896803be13d0a2f18b3afd68ab9e.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 207, + 500, + 402, + 518 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 521, + 441, + 534 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 440, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 133, + 536 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 523, + 158, + 533 + ], + "score": 0.89, + "content": "x \\supset y", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 519, + 217, + 536 + ], + "score": 1.0, + "content": "if information", + "type": "text" + }, + { + "bbox": [ + 218, + 524, + 225, + 533 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 519, + 313, + 536 + ], + "score": 1.0, + "content": "is utilized to estimate", + "type": "text" + }, + { + "bbox": [ + 313, + 524, + 320, + 532 + ], + "score": 0.77, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 519, + 340, + 536 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 341, + 522, + 440, + 534 + ], + "score": 0.91, + "content": "x _ { 0 : t } : = \\{ x _ { 0 } , x _ { 1 } , \\ldots , x _ { t } \\}", + "type": "inline_equation" + } + ], + "index": 26 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 519, + 440, + 536 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 545, + 504, + 568 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 364, + 559 + ], + "score": 1.0, + "content": "Proof. Based on the definition of NeurComm protocol (Eq. (5)),", + "type": "text" + }, + { + "bbox": [ + 365, + 546, + 420, + 558 + ], + "score": 0.93, + "content": "m _ { i , t } \\supset h _ { i , t - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 544, + 441, + 559 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 442, + 546, + 505, + 558 + ], + "score": 0.94, + "content": "h _ { i , t } \\supset h _ { i , t - 1 } \\cup", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 556, + 240, + 569 + ], + "spans": [ + { + "bbox": [ + 107, + 558, + 205, + 569 + ], + "score": 0.88, + "content": "s _ { \\mathcal { V } _ { i } , t } \\cup \\pi _ { \\mathcal { N } _ { i } , t - 1 } \\cup m _ { \\mathcal { N } _ { i } , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 556, + 240, + 569 + ], + "score": 1.0, + "content": ". Hence,", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 544, + 505, + 569 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 127, + 570, + 483, + 681 + ], + "lines": [ + { + "bbox": [ + 127, + 570, + 483, + 681 + ], + "spans": [ + { + "bbox": [ + 127, + 570, + 483, + 681 + ], + "score": 0.86, + "content": "\\begin{array} { r l } & { h _ { i , t } \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } , \\pi _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ h _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { V } _ { i } } } \\\\ & { \\qquad \\supset s _ { i , t } \\cup \\big \\{ s _ { j , t } , \\pi _ { j , t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } \\cup \\big \\{ s _ { k , t - 1 } , \\pi _ { k , t - 2 } \\big \\} _ { k \\in \\mathcal { N } _ { j } } \\cup \\big \\{ h _ { k , t - 2 } \\big \\} _ { k \\in \\mathcal { V } _ { j } } \\big \\} _ { j \\in \\mathcal { V } _ { i } } } \\\\ & { \\qquad = s _ { i , t - 1 : t } \\cup \\big \\{ s _ { j , t - 1 : t } , \\pi _ { j , t - 2 : t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , t - 1 } , \\pi _ { j , t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = 2 \\} } } \\\\ & { \\qquad \\cup \\big \\{ h _ { j , t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } \\leq 2 \\} } } \\\\ & { \\qquad \\supset \\big . s . . } \\\\ & { \\qquad \\cup \\big \\{ s _ { j , 0 : t } , \\pi _ { j , t - 2 : t - 1 } \\big \\} _ { j \\in \\mathcal { N } _ { i } } \\cup \\big \\{ s _ { j , 0 : t - 1 } , \\pi _ { j , 0 : t - 2 } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = 2 \\} } } \\\\ & { \\qquad \\cup \\big \\{ s _ { j , 0 : t + 1 } - \\mathcal { U } _ { \\mathrm { m a x } } , \\pi _ { j , 0 : t - d _ { \\mathrm { m a x } } } \\big \\} _ { j \\in \\{ \\mathcal { V } | d _ { i , j } = d _ { \\mathrm { m a x } } \\} } , } \\end{array}", + "type": "interline_equation", + "image_path": "da3d5ace36b94686a1b3215e1b429eaed4d5acd627d317778bc82d4c09c97acc.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 127, + 570, + 483, + 607.0 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 127, + 607.0, + 483, + 644.0 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 127, + 644.0, + 483, + 681.0 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 681, + 216, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 680, + 216, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 680, + 216, + 693 + ], + "score": 1.0, + "content": "which concludes the proof.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32, + "bbox_fs": [ + 106, + 680, + 216, + 693 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 506, + 733 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "Lemma A.2 (Spatial Gradient Propagation). 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If we rewrite the required information for a given hidden state", + "type": "text" + }, + { + "bbox": [ + 375, + 83, + 391, + 95 + ], + "score": 0.9, + "content": "h _ { i , t }", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 81, + 505, + 96 + ], + "score": 1.0, + "content": "using intermediate messages", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 315, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 315, + 106 + ], + "score": 1.0, + "content": "instead of inputs, the result of Lemma A.1 becomes", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "interline_equation", + "bbox": [ + 230, + 112, + 381, + 159 + ], + "lines": [ + { + "bbox": [ + 230, + 112, + 381, + 159 + ], + "spans": [ + { + "bbox": [ + 230, + 112, + 381, + 159 + ], + "score": 0.93, + "content": "\\begin{array} { r l } & { h _ { i , t } \\supset \\{ m _ { j , t } \\} _ { j \\in { \\cal N } _ { i } } \\supset \\{ h _ { j , t - 1 } \\} _ { j \\in { \\cal N } _ { i } } } \\\\ & { \\qquad \\supset \\{ m _ { j , t - 1 } \\} _ { j \\in \\{ { \\mathcal V } \\mid d _ { i j } = 2 \\} } \\supset \\ . . . } \\\\ & { \\qquad \\supset \\{ m _ { j , t + 1 - d } \\} _ { j \\in \\{ { \\mathcal V } \\mid d _ { i j } = d \\} } \\supset . . . } \\end{array}", + "type": "interline_equation", + "image_path": "e7ded2ef5e9bba741a379b7793ab70908028bd556562c1dadbd6046659dae4b4.jpg" + } + ] + } + ], + "index": 2.5, + "virtual_lines": [ + { + "bbox": [ + 230, + 112, + 381, + 135.5 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 230, + 135.5, + 381, + 159.0 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 165, + 506, + 210 + ], + "lines": [ + { + "bbox": [ + 105, + 164, + 504, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 137, + 179 + ], + "score": 1.0, + "content": "Hence,", + "type": "text" + }, + { + "bbox": [ + 138, + 168, + 158, + 178 + ], + "score": 0.85, + "content": "m _ { i , \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 164, + 315, + 179 + ], + "score": 1.0, + "content": "is included in the meta-DNN of agent", + "type": "text" + }, + { + "bbox": [ + 315, + 167, + 321, + 177 + ], + "score": 0.82, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 164, + 352, + 179 + ], + "score": 1.0, + "content": "at time", + "type": "text" + }, + { + "bbox": [ + 353, + 167, + 402, + 178 + ], + "score": 0.92, + "content": "\\tau + d _ { i j } - 1", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 164, + 471, + 179 + ], + "score": 1.0, + "content": ". 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Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
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Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
avg vehicle headway [m] std vehicle headway [m]20.4520.47 1.1821.99 0.2022.02 0.1920.44 1.0321.45
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avg vehicle velocity [m/s]13.8212.28115.478.59
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Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
avg queue length [veh] avg intersection delay [s/veh] avg vehicle speed [m/s]1.16 68 2.281.442.361.631.622.04
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trip delay [s] avg queue length [veh] avg intersection delay [s/veh]293 1.27 221.1455194920671949321
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avg vehicle speed [m/s] trip delay [s]0.550.610.942.361.261.03
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Temporal Average MetricsNeurCommCommNetDIALIA2CFPrintConseNet
avg vehicle headway [m] std vehicle headway [m]20.4520.47 1.1821.99 0.2022.02 0.1920.44 1.0321.45
avg vehicle velocity [m/s]1.200
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std vehicle velocity [m/s]0.900.870.160.180.750
collision number avg vehicle headway [m]0 15.8400000
std vehicle headway [m]2.1016.2414.42118.2111.60
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avg vehicle velocity [m/s]13.8212.28115.478.59
std vehicle velocity [m/s]2.772.882.4913.371.19
collision number13121650823
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Surprisingly, in our experiments we", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 275, + 470, + 289 + ], + "spans": [ + { + "bbox": [ + 141, + 275, + 470, + 289 + ], + "score": 1.0, + "content": "found that, for Prototypical Networks, it is detrimental to use the episodic learn-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 140, + 286, + 470, + 300 + ], + "spans": [ + { + "bbox": [ + 140, + 286, + 470, + 300 + ], + "score": 1.0, + "content": "ing strategy of separating training samples between support and query set, as it is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 297, + 470, + 310 + ], + "spans": [ + { + "bbox": [ + 141, + 297, + 470, + 310 + ], + "score": 1.0, + "content": "a data-inefficient way to exploit training batches. This “non-episodic” version of", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "spans": [ + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "score": 1.0, + "content": "Prototypical Networks, which corresponds to the classic Neighbourhood Compo-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "spans": [ + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "score": 1.0, + "content": "nent Analysis, reliably improves over its episodic counterpart in multiple datasets,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 329, + 470, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 329, + 470, + 344 + ], + "score": 1.0, + "content": "achieving an accuracy that is competitive with the state-of-the-art, despite being", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 342, + 216, + 355 + ], + "spans": [ + { + "bbox": [ + 141, + 342, + 216, + 355 + ], + "score": 1.0, + "content": "extremely simple.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 108, + 371, + 206, + 384 + ], + "lines": [ + { + "bbox": [ + 105, + 370, + 208, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 208, + 387 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 395, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 105, + 395, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 506, + 409 + ], + "score": 1.0, + "content": "The problem of few-shot learning (FSL) – classifying examples from previously unseen classes", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "given only a handful of training data – has considerably grown in popularity within the machine", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "learning community in the last few years. The reason is likely twofold. First, being able to perform", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "well on FSL problems is important for several applications, from learning new characters (Lake", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "score": 1.0, + "content": "et al., 2015) to drug discovery (Altae-Tran et al., 2017). Second, since the aim of researchers in-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 450, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 464 + ], + "score": 1.0, + "content": "terested in meta-learning is to design systems that can quickly learn novel concepts by generalising", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "from previously encountered learning tasks, FSL benchmarks are often adopted as a practical way", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 472, + 304, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 304, + 486 + ], + "score": 1.0, + "content": "to empirically validate meta-learning algorithms.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 489, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "To the best of our knowledge, there is not a widely recognised definition of meta-learning. In", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 500, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 104, + 500, + 506, + 514 + ], + "score": 1.0, + "content": "a recent survey, Hospedales et al. (2020) informally describe it as “the process of improving a", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "score": 1.0, + "content": "learning algorithm over multiple learning episodes”. Several popular papers in the FSL community", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "score": 1.0, + "content": "(e.g. Vinyals et al. (2016); Ravi & Larochelle (2017); Finn et al. (2017); Snell et al. (2017)) have", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "emphasised the importance of organising training into episodes, i.e. learning problems with a limited", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "amount of training and (pseudo-)test examples that resemble the test-time scenario. This popularity", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "has reached such a point that an “episodic” data-loader is often at the core of new FSL algorithms, a", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 566, + 475, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 475, + 579 + ], + "score": 1.0, + "content": "practice facilitated by frameworks such as Deleu et al. (2019) and Grefenstette et al. (2019).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "Despite the considerable strides made in FSL over the past few years, several recent works (e.g. Chen", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "et al. (2019); Wang et al. (2019); Dhillon et al. (2020); Tian et al. (2020)) showed that simple base-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "lines can outperform established meta-learning methods by using embeddings pre-trained with stan-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "score": 1.0, + "content": "dard classification losses. These results have cast a doubt in the FSL community on the usefulness", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "of meta-learning and its pervasive episodes. Inspired by these results, we aim at understanding the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "practical usefulness of episodic learning in arguably the simplest method which makes use of it:", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "Prototypical Networks (Snell et al., 2017). We chose to analyse Prototypical Networks not only for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "their simplicity, but also because they often appear as important building blocks of newly-proposed", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 671, + 493, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 493, + 684 + ], + "score": 1.0, + "content": "methods (e.g. Oreshkin et al. (2018); Cao et al. (2020); Gidaris et al. (2019); Yoon et al. 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It consists of organising training in a series of learning", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 232, + 470, + 244 + ], + "spans": [ + { + "bbox": [ + 141, + 232, + 470, + 244 + ], + "score": 1.0, + "content": "problems, each relying on small “support” and “query” sets to mimic the few-shot", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 243, + 470, + 255 + ], + "spans": [ + { + "bbox": [ + 141, + 243, + 470, + 255 + ], + "score": 1.0, + "content": "circumstances encountered during evaluation. In this paper, we investigate the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 254, + 469, + 266 + ], + "spans": [ + { + "bbox": [ + 141, + 254, + 469, + 266 + ], + "score": 1.0, + "content": "usefulness of episodic learning in Prototypical Networks, one of the most popu-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 265, + 470, + 277 + ], + "spans": [ + { + "bbox": [ + 141, + 265, + 470, + 277 + ], + "score": 1.0, + "content": "lar algorithms making use of this practice. Surprisingly, in our experiments we", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 275, + 470, + 289 + ], + "spans": [ + { + "bbox": [ + 141, + 275, + 470, + 289 + ], + "score": 1.0, + "content": "found that, for Prototypical Networks, it is detrimental to use the episodic learn-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 140, + 286, + 470, + 300 + ], + "spans": [ + { + "bbox": [ + 140, + 286, + 470, + 300 + ], + "score": 1.0, + "content": "ing strategy of separating training samples between support and query set, as it is", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 297, + 470, + 310 + ], + "spans": [ + { + "bbox": [ + 141, + 297, + 470, + 310 + ], + "score": 1.0, + "content": "a data-inefficient way to exploit training batches. This “non-episodic” version of", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "spans": [ + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "score": 1.0, + "content": "Prototypical Networks, which corresponds to the classic Neighbourhood Compo-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "spans": [ + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "score": 1.0, + "content": "nent Analysis, reliably improves over its episodic counterpart in multiple datasets,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 329, + 470, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 329, + 470, + 344 + ], + "score": 1.0, + "content": "achieving an accuracy that is competitive with the state-of-the-art, despite being", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 342, + 216, + 355 + ], + "spans": [ + { + "bbox": [ + 141, + 342, + 216, + 355 + ], + "score": 1.0, + "content": "extremely simple.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 11, + "bbox_fs": [ + 140, + 210, + 470, + 355 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 371, + 206, + 384 + ], + "lines": [ + { + "bbox": [ + 105, + 370, + 208, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 208, + 387 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 395, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 105, + 395, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 506, + 409 + ], + "score": 1.0, + "content": "The problem of few-shot learning (FSL) – classifying examples from previously unseen classes", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "given only a handful of training data – has considerably grown in popularity within the machine", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "learning community in the last few years. The reason is likely twofold. First, being able to perform", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "well on FSL problems is important for several applications, from learning new characters (Lake", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 452 + ], + "score": 1.0, + "content": "et al., 2015) to drug discovery (Altae-Tran et al., 2017). Second, since the aim of researchers in-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 450, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 464 + ], + "score": 1.0, + "content": "terested in meta-learning is to design systems that can quickly learn novel concepts by generalising", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "from previously encountered learning tasks, FSL benchmarks are often adopted as a practical way", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 472, + 304, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 304, + 486 + ], + "score": 1.0, + "content": "to empirically validate meta-learning algorithms.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 395, + 506, + 486 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 489, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "To the best of our knowledge, there is not a widely recognised definition of meta-learning. In", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 500, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 104, + 500, + 506, + 514 + ], + "score": 1.0, + "content": "a recent survey, Hospedales et al. (2020) informally describe it as “the process of improving a", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "score": 1.0, + "content": "learning algorithm over multiple learning episodes”. Several popular papers in the FSL community", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 535 + ], + "score": 1.0, + "content": "(e.g. Vinyals et al. (2016); Ravi & Larochelle (2017); Finn et al. (2017); Snell et al. (2017)) have", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "emphasised the importance of organising training into episodes, i.e. learning problems with a limited", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "amount of training and (pseudo-)test examples that resemble the test-time scenario. This popularity", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "has reached such a point that an “episodic” data-loader is often at the core of new FSL algorithms, a", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 566, + 475, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 475, + 579 + ], + "score": 1.0, + "content": "practice facilitated by frameworks such as Deleu et al. (2019) and Grefenstette et al. (2019).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5, + "bbox_fs": [ + 104, + 489, + 506, + 579 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "Despite the considerable strides made in FSL over the past few years, several recent works (e.g. Chen", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "et al. (2019); Wang et al. (2019); Dhillon et al. (2020); Tian et al. (2020)) showed that simple base-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "lines can outperform established meta-learning methods by using embeddings pre-trained with stan-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 629 + ], + "score": 1.0, + "content": "dard classification losses. These results have cast a doubt in the FSL community on the usefulness", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "of meta-learning and its pervasive episodes. Inspired by these results, we aim at understanding the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "practical usefulness of episodic learning in arguably the simplest method which makes use of it:", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "Prototypical Networks (Snell et al., 2017). We chose to analyse Prototypical Networks not only for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "their simplicity, but also because they often appear as important building blocks of newly-proposed", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 671, + 493, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 493, + 684 + ], + "score": 1.0, + "content": "methods (e.g. Oreshkin et al. (2018); Cao et al. (2020); Gidaris et al. (2019); Yoon et al. (2019)).", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 583, + 505, + 684 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 484, + 700 + ], + "score": 1.0, + "content": "With a set of ablative experiments, we show that for Prototypical Networks episodic learning", + "type": "text" + }, + { + "bbox": [ + 484, + 690, + 491, + 698 + ], + "score": 0.45, + "content": "a _ { . }", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 687, + 506, + 700 + ], + "score": 1.0, + "content": ") is", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 227, + 711 + ], + "score": 1.0, + "content": "detrimental for performance,", + "type": "text" + }, + { + "bbox": [ + 227, + 700, + 234, + 709 + ], + "score": 0.37, + "content": "^ b", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 699, + 506, + 711 + ], + "score": 1.0, + "content": ") is analogous to randomly discarding examples from a batch and", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "c) it introduces a set of unnecessary hyper-parameters that require careful tuning. We also show", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 721, + 506, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 732 + ], + "score": 1.0, + "content": "how, without episodic learning, Prototypical Networks are connected to the classic Neighbourhood", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 687, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "score": 1.0, + "content": "Component Analysis (NCA) (Goldberger et al., 2005; Salakhutdinov & Hinton, 2007) on deep em-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 505, + 107 + ], + "score": 1.0, + "content": "beddings. Without bells and whistles, our implementation of the NCA loss achieves an accuracy", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "score": 1.0, + "content": "that is competitive with the state-of-the-art on multiple FSL benchmarks: miniImageNet, CIFAR-FS", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 191, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 191, + 128 + ], + "score": 1.0, + "content": "and tieredImageNet.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "title", + "bbox": [ + 108, + 144, + 209, + 156 + ], + "lines": [ + { + "bbox": [ + 104, + 142, + 210, + 159 + ], + "spans": [ + { + "bbox": [ + 104, + 142, + 210, + 159 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 169, + 505, + 345 + ], + "lines": [ + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "score": 1.0, + "content": "Pioneered by the seminal work of Utgoff (1986), Schmidhuber (1987; 1992), Bengio et al. (1992)", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "score": 1.0, + "content": "and Thrun (1996), the general concept of meta-learning is several decades old (for a survey see Vi-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 191, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 204 + ], + "score": 1.0, + "content": "lalta & Drissi (2002); Hospedales et al. (2020)). However, in the last few years it has experienced a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 505, + 215 + ], + "score": 1.0, + "content": "surge in popularity, becoming the most used paradigm for learning from very few examples. Sev-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 213, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 506, + 227 + ], + "score": 1.0, + "content": "eral methods addressing the FSL problem by learning on episodes were proposed. MANN (Santoro", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "et al., 2016) uses a Neural Turing Machine (Graves et al., 2014) to save and access the information", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "score": 1.0, + "content": "useful to meta-learn; Bertinetto et al. (2016) propose a deep network in which a “teacher” branch", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 246, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "is tasked with predicting the parameters of a “student” branch; Matching Networks (Vinyals et al.,", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 257, + 504, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 504, + 270 + ], + "score": 1.0, + "content": "2016) and Prototypical Networks (Snell et al., 2017) are two non-parametric methods in which the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 267, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 505, + 281 + ], + "score": 1.0, + "content": "contributions of different examples in the support set are weighted by either an LSTM or a softmax", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "score": 1.0, + "content": "over the cosine distances for Matching Networks, and a simple average for Prototypical Networks;", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 290, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 505, + 302 + ], + "score": 1.0, + "content": "Ravi & Larochelle (2017) propose instead to use an LSTM to learn the hyper-parameters of SGD,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 299, + 505, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 505, + 314 + ], + "score": 1.0, + "content": "while MAML (Finn et al., 2017) learns to fine-tune an entire deep network by backpropagating", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 312, + 506, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 506, + 324 + ], + "score": 1.0, + "content": "through SGD. Despite these works widely differing in nature, they all stress on the importance of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 322, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 506, + 336 + ], + "score": 1.0, + "content": "organising training in a series of small learning problems (episodes) that are similar to those encoun-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 334, + 246, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 246, + 347 + ], + "score": 1.0, + "content": "tered during inference at test time.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 349, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 506, + 363 + ], + "score": 1.0, + "content": "In contrast with this trend, a handful of papers have recently shown that simple approaches that", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 362, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 374 + ], + "score": 1.0, + "content": "forego episodes and meta-learning can perform well on FSL benchmarks. These methods all have", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 371, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 386 + ], + "score": 1.0, + "content": "in common that they pre-train a feature extractor with the cross-entropy loss on the “meta-training", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "classes” of the dataset. Then, at test time a classifier is adapted to the support set by weight im-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "printing (Qi et al., 2018; Dhillon et al., 2020), fine-tuning (Chen et al., 2019), transductive fine-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "tuning (Dhillon et al., 2020) or logistic regression (Tian et al., 2020). Wang et al. (2019) suggest", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 416, + 489, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 489, + 430 + ], + "score": 1.0, + "content": "performing test-time classification by using the label of the closest centroid to the query image.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 433, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 446 + ], + "score": 1.0, + "content": "Different from these papers, we try to shed some light on one of the possible causes behind the poor", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 444, + 506, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 506, + 457 + ], + "score": 1.0, + "content": "performance of episodic-based algorithms like Prototypical Networks. An analysis similar to ours", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "score": 1.0, + "content": "in spirit is the one of Raghu et al. (2020). After showing that the efficacy of MAML in FSL is due", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "to the adaptation of the final layer and the “reuse” of the features of previous layers, they propose", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "a variant with the same accuracy and computational advantages. In this paper, we focus on an FSL", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 501 + ], + "score": 1.0, + "content": "algorithm just as popular and uncover inefficiencies that allow for a notable conceptual simplification", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 499, + 475, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 475, + 511 + ], + "score": 1.0, + "content": "of Prototypical Networks, which surprisingly also brings a significant boost in performance.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31 + }, + { + "type": "title", + "bbox": [ + 108, + 527, + 272, + 540 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 274, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 274, + 543 + ], + "score": 1.0, + "content": "3 BACKGROUND AND METHOD", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 553, + 505, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "This section is divided as follows: Sec. 3.1 introduces episodic learning and the formalism used", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 564, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 576 + ], + "score": 1.0, + "content": "in FSL, Sec. 3.2 reviews Prototypical Networks (often referred to as PNS from now on), Sec 3.3", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "score": 1.0, + "content": "describes the classic NCA loss and how exactly it relates to PNS, and Sec. 3.4 explains the three", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 585, + 475, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 475, + 599 + ], + "score": 1.0, + "content": "options we explored to perform FSL classification with an NCA-trained feature embedding.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + }, + { + "type": "title", + "bbox": [ + 108, + 612, + 220, + 623 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 221, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 221, + 624 + ], + "score": 1.0, + "content": "3.1 EPISODIC LEARNING", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 711 + ], + "lines": [ + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 442, + 644 + ], + "score": 1.0, + "content": "A common strategy to train few-shot learning algorithms is to consider a distribution", + "type": "text" + }, + { + "bbox": [ + 442, + 631, + 450, + 642 + ], + "score": 0.84, + "content": "\\hat { \\mathcal { E } }", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "over possible", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 642, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 457, + 656 + ], + "score": 1.0, + "content": "subsets of labels that is as close as possible to the one encountered during evaluation", + "type": "text" + }, + { + "bbox": [ + 458, + 643, + 474, + 654 + ], + "score": 0.83, + "content": "\\mathcal { E } ^ { \\mathrm { ~ I ~ } }", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 642, + 506, + 656 + ], + "score": 1.0, + "content": ". 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Without bells and whistles, our implementation of the NCA loss achieves an accuracy", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "score": 1.0, + "content": "that is competitive with the state-of-the-art on multiple FSL benchmarks: miniImageNet, CIFAR-FS", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 191, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 191, + 128 + ], + "score": 1.0, + "content": "and tieredImageNet.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5, + "bbox_fs": [ + 105, + 82, + 505, + 128 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 144, + 209, + 156 + ], + "lines": [ + { + "bbox": [ + 104, + 142, + 210, + 159 + ], + "spans": [ + { + "bbox": [ + 104, + 142, + 210, + 159 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 169, + 505, + 345 + ], + "lines": [ + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 505, + 182 + ], + "score": 1.0, + "content": "Pioneered by the seminal work of Utgoff (1986), Schmidhuber (1987; 1992), Bengio et al. (1992)", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 505, + 194 + ], + "score": 1.0, + "content": "and Thrun (1996), the general concept of meta-learning is several decades old (for a survey see Vi-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 191, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 506, + 204 + ], + "score": 1.0, + "content": "lalta & Drissi (2002); Hospedales et al. (2020)). However, in the last few years it has experienced a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 505, + 215 + ], + "score": 1.0, + "content": "surge in popularity, becoming the most used paradigm for learning from very few examples. Sev-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 213, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 506, + 227 + ], + "score": 1.0, + "content": "eral methods addressing the FSL problem by learning on episodes were proposed. MANN (Santoro", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "et al., 2016) uses a Neural Turing Machine (Graves et al., 2014) to save and access the information", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 505, + 248 + ], + "score": 1.0, + "content": "useful to meta-learn; Bertinetto et al. 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Despite these works widely differing in nature, they all stress on the importance of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 322, + 506, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 506, + 336 + ], + "score": 1.0, + "content": "organising training in a series of small learning problems (episodes) that are similar to those encoun-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 334, + 246, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 246, + 347 + ], + "score": 1.0, + "content": "tered during inference at test time.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 169, + 506, + 347 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 105, + 349, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 506, + 363 + ], + "score": 1.0, + "content": "In contrast with this trend, a handful of papers have recently shown that simple approaches that", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 362, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 374 + ], + "score": 1.0, + "content": "forego episodes and meta-learning can perform well on FSL benchmarks. These methods all have", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 371, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 386 + ], + "score": 1.0, + "content": "in common that they pre-train a feature extractor with the cross-entropy loss on the “meta-training", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "classes” of the dataset. Then, at test time a classifier is adapted to the support set by weight im-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "printing (Qi et al., 2018; Dhillon et al., 2020), fine-tuning (Chen et al., 2019), transductive fine-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "tuning (Dhillon et al., 2020) or logistic regression (Tian et al., 2020). Wang et al. 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NCA(mn)w(2)(m+n)²
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(2005) (and expanded to the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 199, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 199, + 244, + 212 + ], + "score": 1.0, + "content": "non-linear case by Salakhutdinov", + "type": "text" + }, + { + "bbox": [ + 244, + 200, + 253, + 210 + ], + "score": 0.27, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 199, + 505, + 212 + ], + "score": 1.0, + "content": "Hinton (2007)), except for a few important differences which", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 211, + 192, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 192, + 222 + ], + "score": 1.0, + "content": "we will now discuss.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 104, + 226, + 476, + 239 + ], + "lines": [ + { + "bbox": [ + 105, + 226, + 478, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 122, + 240 + ], + "score": 1.0, + "content": "Let", + "type": "text" + }, + { + "bbox": [ + 122, + 227, + 158, + 239 + ], + "score": 0.93, + "content": "i \\in [ 1 , b ]", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 226, + 332, + 240 + ], + "score": 1.0, + "content": "be the indices of the images within a batch", + "type": "text" + }, + { + "bbox": [ + 332, + 228, + 341, + 237 + ], + "score": 0.78, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 226, + 478, + 240 + ], + "score": 1.0, + "content": ". 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Due to the nature of episodic learning, PNS only consider pairwise distances between the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 141, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 141, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "query and the support set; the NCA instead uses all the distances within a batch and treats", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 516, + 268, + 528 + ], + "spans": [ + { + "bbox": [ + 141, + 516, + 268, + 528 + ], + "score": 1.0, + "content": "each example in the same way.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 129, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 129, + 528, + 141, + 538 + ], + "score": 1.0, + "content": "3.", + "type": "text" + }, + { + "bbox": [ + 141, + 527, + 211, + 539 + ], + "score": 1.0, + "content": "Because of how", + "type": "text" + }, + { + "bbox": [ + 211, + 527, + 219, + 537 + ], + "score": 0.48, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 527, + 224, + 539 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 225, + 527, + 233, + 537 + ], + "score": 0.61, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 527, + 252, + 539 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 253, + 527, + 262, + 538 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "are sampled in episodic learning, some images will be in-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 536, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 141, + 536, + 506, + 551 + ], + "score": 1.0, + "content": "evitably sampled more frequently than others, and some will likely never be seen during", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 141, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "training (this corresponds to sampling “with replacement”). NCA instead visits every im-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 560, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 142, + 560, + 505, + 572 + ], + "score": 1.0, + "content": "age of the dataset once and only once within each epoch (sampling “without replacement”).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 106, + 583, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "Notes on data-efficiency in batch exploitation. To expand on point 2 above, Fig. 1 illustrates", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 594, + 504, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 432, + 607 + ], + "score": 1.0, + "content": "the difference in batch exploitation. For PNS (left) and a training episode of", + "type": "text" + }, + { + "bbox": [ + 433, + 595, + 455, + 604 + ], + "score": 0.88, + "content": "w { = } 3", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 594, + 483, + 607 + ], + "score": 1.0, + "content": "ways,", + "type": "text" + }, + { + "bbox": [ + 484, + 595, + 504, + 605 + ], + "score": 0.85, + "content": "n { = } 3", + "type": "inline_equation" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 604, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 147, + 618 + ], + "score": 1.0, + "content": "shots and", + "type": "text" + }, + { + "bbox": [ + 148, + 606, + 171, + 615 + ], + "score": 0.88, + "content": "m { = } 1", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 604, + 462, + 618 + ], + "score": 1.0, + "content": "queries, the total number distances contributing to the loss consists of", + "type": "text" + }, + { + "bbox": [ + 462, + 606, + 504, + 616 + ], + "score": 0.82, + "content": "w m n = 9", + "type": "inline_equation" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 164, + 628 + ], + "score": 1.0, + "content": "positives and", + "type": "text" + }, + { + "bbox": [ + 164, + 616, + 243, + 628 + ], + "score": 0.93, + "content": "w ( w - 1 ) m n = 1 8", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "negatives 2. If we consider the same training batch in a non-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 103, + 624, + 507, + 643 + ], + "spans": [ + { + "bbox": [ + 103, + 624, + 389, + 643 + ], + "score": 1.0, + "content": "episodic way, when computing the NCA loss (Fig. 1 right) we have", + "type": "text" + }, + { + "bbox": [ + 389, + 627, + 448, + 641 + ], + "score": 0.93, + "content": "{ \\binom { m + n } { 2 } } w = 1 8", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 624, + 507, + 643 + ], + "score": 1.0, + "content": "positives and", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 107, + 639, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 107, + 640, + 185, + 654 + ], + "score": 0.92, + "content": "{ \\binom { w } { 2 } } ( m + n ) ^ { 2 } = 4 8", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 639, + 506, + 656 + ], + "score": 1.0, + "content": "negatives (we summarise these equations in Table 1). This difference in batch", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 653, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 433, + 667 + ], + "score": 1.0, + "content": "exploitation is significant; in Appendix A.8 we show that it grows exponentially as", + "type": "text" + }, + { + "bbox": [ + 433, + 653, + 501, + 666 + ], + "score": 0.92, + "content": "O ( w ^ { 2 } ( m ^ { 2 } + n ^ { 2 } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 653, + 505, + 667 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 670, + 503, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 670, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 670, + 505, + 683 + ], + "score": 1.0, + "content": "To investigate the effect of the three key differences between PNS and NCA illustrated in this sec-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 681, + 329, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 681, + 329, + 694 + ], + "score": 1.0, + "content": "tion, in Sec. 4 we conduct a wide range of experiments.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 701, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 117, + 698, + 506, + 715 + ], + "spans": [ + { + "bbox": [ + 117, + 698, + 425, + 715 + ], + "score": 1.0, + "content": "2The number of distances computed in the batch is actually even smaller for PNs:", + "type": "text" + }, + { + "bbox": [ + 425, + 702, + 454, + 711 + ], + "score": 0.83, + "content": "w m { = } 3", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 698, + 506, + 715 + ], + "score": 1.0, + "content": "positives and", + "type": "text" + } + ] + }, + { + "bbox": [ + 107, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 107, + 711, + 166, + 722 + ], + "score": 0.9, + "content": "w ( w - 1 ) m { = } 6", + "type": "inline_equation" + }, + { + "bbox": [ + 166, + 712, + 505, + 723 + ], + "score": 1.0, + "content": "negatives. 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In Appendix A.8", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 156, + 416, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 156, + 345, + 169 + ], + "score": 1.0, + "content": "we show that the extra number of pairs NCA can exploit grows as", + "type": "text" + }, + { + "bbox": [ + 345, + 156, + 410, + 168 + ], + "score": 0.92, + "content": "O ( w ^ { 2 } ( m ^ { 2 } + n ^ { 2 } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 156, + 416, + 169 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 135, + 505, + 169 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 188, + 506, + 222 + ], + "lines": [ + { + "bbox": [ + 106, + 188, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 201 + ], + "score": 1.0, + "content": "the Neighbourhood Component Analysis approach by Goldberger et al. (2005) (and expanded to the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 199, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 199, + 244, + 212 + ], + "score": 1.0, + "content": "non-linear case by Salakhutdinov", + "type": "text" + }, + { + "bbox": [ + 244, + 200, + 253, + 210 + ], + "score": 0.27, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 199, + 505, + 212 + ], + "score": 1.0, + "content": "Hinton (2007)), except for a few important differences which", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 211, + 192, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 192, + 222 + ], + "score": 1.0, + "content": "we will now discuss.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 106, + 188, + 505, + 222 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 226, + 476, + 239 + ], + "lines": [ + { + "bbox": [ + 105, + 226, + 478, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 122, + 240 + ], + "score": 1.0, + "content": "Let", + "type": "text" + }, + { + "bbox": [ + 122, + 227, + 158, + 239 + ], + "score": 0.93, + "content": "i \\in [ 1 , b ]", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 226, + 332, + 240 + ], + "score": 1.0, + "content": "be the indices of the images within a batch", + "type": "text" + }, + { + "bbox": [ + 332, + 228, + 341, + 237 + ], + "score": 0.78, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 226, + 478, + 240 + ], + "score": 1.0, + "content": ". The NCA loss can be written as:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 226, + 478, + 240 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 183, + 243, + 426, + 320 + ], + "lines": [ + { + "bbox": [ + 183, + 243, + 426, + 320 + ], + "spans": [ + { + "bbox": [ + 183, + 243, + 426, + 320 + ], + "score": 0.95, + "content": "\\mathcal { L } _ { \\mathrm { N C A } } ( X ) = - \\frac { 1 } { b } \\sum _ { i \\in 1 , \\dots , b } \\log \\left( \\frac { \\sum _ { j \\in 1 , \\dots , b } \\exp { - \\left\\| { \\mathbf z } _ { i } - { \\mathbf z } _ { j } \\right\\| ^ { 2 } } } { \\displaystyle \\sum _ { k \\in 1 , \\dots , b } \\exp { - \\left\\| { \\mathbf z } _ { i } - { \\mathbf z } _ { k } \\right\\| ^ { 2 } } } \\right) ,", + "type": "interline_equation", + "image_path": "7bf980569ec49caf9d5188cf52bccf493c4b8d1607d570ab4031f76422a76492.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 183, + 243, + 426, + 258.4 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 183, + 258.4, + 426, + 273.79999999999995 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 183, + 273.79999999999995, + 426, + 289.19999999999993 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 183, + 289.19999999999993, + 426, + 304.5999999999999 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 183, + 304.5999999999999, + 426, + 319.9999999999999 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 324, + 506, + 391 + ], + "lines": [ + { + "bbox": [ + 106, + 323, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 323, + 133, + 338 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 324, + 183, + 336 + ], + "score": 0.93, + "content": "\\mathbf { z } _ { i } = f _ { \\theta } ( \\mathbf { x } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 323, + 297, + 338 + ], + "score": 1.0, + "content": "is an image embedding and", + "type": "text" + }, + { + "bbox": [ + 297, + 326, + 307, + 336 + ], + "score": 0.85, + "content": "y _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 323, + 506, + 338 + ], + "score": 1.0, + "content": "its corresponding label. By minimising this loss,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "score": 1.0, + "content": "distances between embeddings from the same class will be minimised, while distances between", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 345, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 359 + ], + "score": 1.0, + "content": "embeddings from different classes will be maximised. This bears similarities to the (supervised)", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 358, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 369 + ], + "score": 1.0, + "content": "contrastive loss (Khosla et al., 2020; Chen et al., 2020a), which we discuss in Appendix A.3. For", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 369, + 505, + 380 + ], + "score": 1.0, + "content": "ease of discussion, we refer to the distances between pairs of embeddings from the same class as", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 379, + 488, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 488, + 392 + ], + "score": 1.0, + "content": "positives, and to the distances between pairs of embeddings from different classes as negatives.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 323, + 506, + 392 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 396, + 505, + 474 + ], + "lines": [ + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "score": 1.0, + "content": "Importantly, the concepts of support set and query set of Sec. 3.1 and 3.2 here do not apply. More", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 368, + 420 + ], + "score": 1.0, + "content": "simply, the images (and respective labels) constituting the batch", + "type": "text" + }, + { + "bbox": [ + 369, + 407, + 488, + 419 + ], + "score": 0.93, + "content": "B = \\{ ( \\mathbf { x } _ { 1 } , y _ { 1 } ) , \\dotsc , ( \\mathbf { x } _ { b } , y _ { b } ) \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "are", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "sampled i.i.d. from the training dataset, as normally happens in standard supervised learning. Con-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "sidering that in PNS there is no parameter adaptation happening at the level of each episodic batch", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 440, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 107, + 440, + 122, + 451 + ], + "score": 0.84, + "content": "B _ { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 122, + 440, + 125, + 452 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 126, + 441, + 134, + 450 + ], + "score": 0.72, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 440, + 151, + 452 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 151, + 440, + 161, + 451 + ], + "score": 0.76, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 440, + 446, + 452 + ], + "score": 1.0, + "content": "do not have a functional role in the algorithm, and their defining values", + "type": "text" + }, + { + "bbox": [ + 446, + 440, + 488, + 452 + ], + "score": 0.93, + "content": "\\{ w , m , n \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 440, + 505, + 452 + ], + "score": 1.0, + "content": "can", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "score": 1.0, + "content": "be interpreted as hyper-parameters controlling the data-loader during training. More specifically,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 461, + 281, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 281, + 475 + ], + "score": 1.0, + "content": "PNS differ from NCA in three key aspects:", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 396, + 506, + 475 + ] + }, + { + "type": "list", + "bbox": [ + 129, + 483, + 505, + 571 + ], + "lines": [ + { + "bbox": [ + 130, + 483, + 387, + 495 + ], + "spans": [ + { + "bbox": [ + 130, + 483, + 387, + 495 + ], + "score": 1.0, + "content": "1. PNS rely on the creation of prototypes, while NCA does not.", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 129, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 129, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "2. Due to the nature of episodic learning, PNS only consider pairwise distances between the", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 141, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "query and the support set; the NCA instead uses all the distances within a batch and treats", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 516, + 268, + 528 + ], + "spans": [ + { + "bbox": [ + 141, + 516, + 268, + 528 + ], + "score": 1.0, + "content": "each example in the same way.", + "type": "text" + } + ], + "index": 30, + "is_list_end_line": true + }, + { + "bbox": [ + 129, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 129, + 528, + 141, + 538 + ], + "score": 1.0, + "content": "3.", + "type": "text" + }, + { + "bbox": [ + 141, + 527, + 211, + 539 + ], + "score": 1.0, + "content": "Because of how", + "type": "text" + }, + { + "bbox": [ + 211, + 527, + 219, + 537 + ], + "score": 0.48, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 527, + 224, + 539 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 225, + 527, + 233, + 537 + ], + "score": 0.61, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 527, + 252, + 539 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 253, + 527, + 262, + 538 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "are sampled in episodic learning, some images will be in-", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 536, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 141, + 536, + 506, + 551 + ], + "score": 1.0, + "content": "evitably sampled more frequently than others, and some will likely never be seen during", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 141, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "training (this corresponds to sampling “with replacement”). NCA instead visits every im-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 560, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 142, + 560, + 505, + 572 + ], + "score": 1.0, + "content": "age of the dataset once and only once within each epoch (sampling “without replacement”).", + "type": "text" + } + ], + "index": 34, + "is_list_end_line": true + } + ], + "index": 30.5, + "bbox_fs": [ + 129, + 483, + 506, + 572 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 583, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "Notes on data-efficiency in batch exploitation. To expand on point 2 above, Fig. 1 illustrates", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 594, + 504, + 607 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 432, + 607 + ], + "score": 1.0, + "content": "the difference in batch exploitation. For PNS (left) and a training episode of", + "type": "text" + }, + { + "bbox": [ + 433, + 595, + 455, + 604 + ], + "score": 0.88, + "content": "w { = } 3", + "type": "inline_equation" + }, + { + "bbox": [ + 455, + 594, + 483, + 607 + ], + "score": 1.0, + "content": "ways,", + "type": "text" + }, + { + "bbox": [ + 484, + 595, + 504, + 605 + ], + "score": 0.85, + "content": "n { = } 3", + "type": "inline_equation" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 604, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 147, + 618 + ], + "score": 1.0, + "content": "shots and", + "type": "text" + }, + { + "bbox": [ + 148, + 606, + 171, + 615 + ], + "score": 0.88, + "content": "m { = } 1", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 604, + 462, + 618 + ], + "score": 1.0, + "content": "queries, the total number distances contributing to the loss consists of", + "type": "text" + }, + { + "bbox": [ + 462, + 606, + 504, + 616 + ], + "score": 0.82, + "content": "w m n = 9", + "type": "inline_equation" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 164, + 628 + ], + "score": 1.0, + "content": "positives and", + "type": "text" + }, + { + "bbox": [ + 164, + 616, + 243, + 628 + ], + "score": 0.93, + "content": "w ( w - 1 ) m n = 1 8", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "negatives 2. If we consider the same training batch in a non-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 103, + 624, + 507, + 643 + ], + "spans": [ + { + "bbox": [ + 103, + 624, + 389, + 643 + ], + "score": 1.0, + "content": "episodic way, when computing the NCA loss (Fig. 1 right) we have", + "type": "text" + }, + { + "bbox": [ + 389, + 627, + 448, + 641 + ], + "score": 0.93, + "content": "{ \\binom { m + n } { 2 } } w = 1 8", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 624, + 507, + 643 + ], + "score": 1.0, + "content": "positives and", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 107, + 639, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 107, + 640, + 185, + 654 + ], + "score": 0.92, + "content": "{ \\binom { w } { 2 } } ( m + n ) ^ { 2 } = 4 8", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 639, + 506, + 656 + ], + "score": 1.0, + "content": "negatives (we summarise these equations in Table 1). This difference in batch", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 653, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 433, + 667 + ], + "score": 1.0, + "content": "exploitation is significant; in Appendix A.8 we show that it grows exponentially as", + "type": "text" + }, + { + "bbox": [ + 433, + 653, + 501, + 666 + ], + "score": 0.92, + "content": "O ( w ^ { 2 } ( m ^ { 2 } + n ^ { 2 } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 653, + 505, + 667 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38, + "bbox_fs": [ + 103, + 583, + 507, + 667 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 670, + 503, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 670, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 670, + 505, + 683 + ], + "score": 1.0, + "content": "To investigate the effect of the three key differences between PNS and NCA illustrated in this sec-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 681, + 329, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 681, + 329, + 694 + ], + "score": 1.0, + "content": "tion, in Sec. 4 we conduct a wide range of experiments.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 106, + 670, + 505, + 694 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 83, + 341, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 343, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 343, + 95 + ], + "score": 1.0, + "content": "3.4 FEW-SHOT CLASSIFICATION DURING EVALUATION", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 103, + 505, + 137 + ], + "lines": [ + { + "bbox": [ + 105, + 102, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 130, + 117 + ], + "score": 1.0, + "content": "Once", + "type": "text" + }, + { + "bbox": [ + 131, + 104, + 141, + 115 + ], + "score": 0.87, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 102, + 505, + 117 + ], + "score": 1.0, + "content": "has been trained, there are many possible ways to perform few-shot classification during", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 115, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 504, + 126 + ], + "score": 1.0, + "content": "evaluation. In this paper we consider three simple approaches that are particularly aligned for em-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 126, + 364, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 364, + 138 + ], + "score": 1.0, + "content": "beddings learned via metric-based losses such as Eq. 2 or Eq. 3.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 145, + 505, + 191 + ], + "lines": [ + { + "bbox": [ + 106, + 144, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 106, + 146, + 113, + 155 + ], + "score": 0.75, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 144, + 223, + 159 + ], + "score": 1.0, + "content": "-NN. To classify an image", + "type": "text" + }, + { + "bbox": [ + 224, + 146, + 254, + 157 + ], + "score": 0.9, + "content": "\\mathbf q _ { i } \\in Q", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 144, + 505, + 159 + ], + "score": 1.0, + "content": ", we first compute the Euclidean distance to each support point", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 157, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 158, + 138, + 171 + ], + "score": 0.81, + "content": "\\mathbf { s } _ { j } \\in S", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 157, + 256, + 171 + ], + "score": 0.89, + "content": ": d _ { i j } = \\| f _ { \\boldsymbol \\theta } ( \\mathbf { q } _ { i } ) - f _ { \\boldsymbol \\theta } ( \\mathbf { s } _ { j } ) ) \\| ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 157, + 362, + 171 + ], + "score": 1.0, + "content": ". Then, we simply assign", + "type": "text" + }, + { + "bbox": [ + 362, + 158, + 385, + 170 + ], + "score": 0.93, + "content": "y ( \\mathbf { q } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 157, + 497, + 171 + ], + "score": 1.0, + "content": "to be majority label of the", + "type": "text" + }, + { + "bbox": [ + 497, + 158, + 504, + 168 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 169, + 505, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 285, + 181 + ], + "score": 1.0, + "content": "nearest neighbours. A downside here is that", + "type": "text" + }, + { + "bbox": [ + 286, + 170, + 292, + 179 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 169, + 505, + 181 + ], + "score": 1.0, + "content": "is a hyper-parameter that has to be chosen, although", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 180, + 432, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 420, + 192 + ], + "score": 1.0, + "content": "a reasonable choice in the FSL setup is to set it equal to the number of “shots”", + "type": "text" + }, + { + "bbox": [ + 421, + 182, + 428, + 190 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 180, + 432, + 192 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 200, + 503, + 235 + ], + "lines": [ + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 270, + 213 + ], + "score": 1.0, + "content": "1-NN with Class Centroids. Similar to", + "type": "text" + }, + { + "bbox": [ + 271, + 201, + 277, + 210 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 200, + 505, + 213 + ], + "score": 1.0, + "content": "-NN, we can perform classification by inheriting the label", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 209, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 104, + 209, + 235, + 228 + ], + "score": 1.0, + "content": "of the closest class centroid, i.e.", + "type": "text" + }, + { + "bbox": [ + 235, + 212, + 398, + 225 + ], + "score": 0.92, + "content": "\\begin{array} { r } { y ( { \\mathbf { q } } _ { i } ) = \\arg \\operatorname* { m i n } _ { j \\in \\{ 1 , \\dots , k \\} } \\| f _ { \\boldsymbol { \\theta } } ( { \\mathbf { x } } _ { i } ) - { \\mathbf { c } } _ { j } \\| } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 209, + 506, + 228 + ], + "score": 1.0, + "content": ". This is the approach used", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 223, + 335, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 335, + 236 + ], + "score": 1.0, + "content": "at test-time by Snell et al. (2017) and Wang et al. (2019).", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 243, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 242, + 505, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 505, + 256 + ], + "score": 1.0, + "content": "Soft Assignments. This is what the original NCA paper (Goldberger et al., 2005) used for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 253, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 104, + 253, + 252, + 267 + ], + "score": 1.0, + "content": "evaluation. To classify an image", + "type": "text" + }, + { + "bbox": [ + 252, + 255, + 291, + 266 + ], + "score": 0.89, + "content": "\\mathbf { q } _ { i } ~ \\in ~ { \\cal Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 253, + 399, + 267 + ], + "score": 1.0, + "content": ", we compute the values", + "type": "text" + }, + { + "bbox": [ + 399, + 254, + 505, + 267 + ], + "score": 0.89, + "content": "p _ { i j } ~ = ~ \\exp ( - \\| f _ { \\theta } ( { \\mathbf { q } } _ { i } ) ~ -", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 265, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 300, + 282 + ], + "score": 0.91, + "content": "\\begin{array} { r } { f _ { \\theta } ( \\mathbf { s } _ { j } ) ) \\vert \\vert ^ { 2 } ) / \\sum _ { \\mathbf { s } _ { k } \\in S } \\exp ( - \\vert \\vert f _ { \\theta } ( \\mathbf { q } _ { i } ) - f _ { \\theta } ( \\mathbf { s } _ { k } ) \\vert \\vert ^ { 2 } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 265, + 331, + 283 + ], + "score": 1.0, + "content": "for all", + "type": "text" + }, + { + "bbox": [ + 331, + 267, + 364, + 280 + ], + "score": 0.9, + "content": "\\mathbf { s } _ { j } ~ \\in ~ S", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 265, + 506, + 283 + ], + "score": 1.0, + "content": ", which is the probability that im-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 279, + 507, + 297 + ], + "spans": [ + { + "bbox": [ + 104, + 279, + 123, + 297 + ], + "score": 1.0, + "content": "age", + "type": "text" + }, + { + "bbox": [ + 123, + 282, + 128, + 290 + ], + "score": 0.71, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 279, + 224, + 297 + ], + "score": 1.0, + "content": "is sampled from image", + "type": "text" + }, + { + "bbox": [ + 224, + 282, + 230, + 292 + ], + "score": 0.75, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 279, + 424, + 297 + ], + "score": 1.0, + "content": ". We then compute the likelihood for each class", + "type": "text" + }, + { + "bbox": [ + 424, + 281, + 431, + 291 + ], + "score": 0.64, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 279, + 435, + 297 + ], + "score": 1.0, + "content": ":", + "type": "text" + }, + { + "bbox": [ + 435, + 280, + 484, + 295 + ], + "score": 0.91, + "content": "\\textstyle \\sum _ { s _ { j } \\in S _ { k } } p _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 279, + 507, + 297 + ], + "score": 1.0, + "content": ", and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 103, + 290, + 507, + 311 + ], + "spans": [ + { + "bbox": [ + 103, + 290, + 286, + 311 + ], + "score": 1.0, + "content": "choose the class with the highest likelihood", + "type": "text" + }, + { + "bbox": [ + 287, + 293, + 414, + 308 + ], + "score": 0.92, + "content": "y ( \\mathbf { q } _ { i } ) = \\arg \\operatorname* { m a x } _ { k } \\sum _ { s _ { j } \\in S _ { k } } p _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 290, + 507, + 311 + ], + "score": 1.0, + "content": ". This approach is the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 306, + 495, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 306, + 495, + 320 + ], + "score": 1.0, + "content": "only one closely aligned with the training procedure, and has a direct probabilistic interpretation.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 323, + 503, + 346 + ], + "lines": [ + { + "bbox": [ + 105, + 321, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 338 + ], + "score": 1.0, + "content": "We also experimented with using the NCA loss on the support set to perform adaptation at test time,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 334, + 251, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 251, + 347 + ], + "score": 1.0, + "content": "which we discuss in Appendix A.1.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 108, + 363, + 200, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 201, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 201, + 377 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 388, + 505, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "In the following, Sec. 4.1 describes our experimental setup. Sec. 4.2 shows the effect of the hyper-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 399, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 411 + ], + "score": 1.0, + "content": "parameters controlling the creation of episodes in PNS. In Sec. 4.3 we perform a set of ablation", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "score": 1.0, + "content": "studies to better illustrate the relationship between PNS and the NCA. Finally, in Sec. 4.4 we com-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 422, + 434, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 434, + 433 + ], + "score": 1.0, + "content": "pare our version of the NCA to several recent methods on three FSL benchmarks.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "title", + "bbox": [ + 107, + 447, + 229, + 458 + ], + "lines": [ + { + "bbox": [ + 106, + 447, + 230, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 230, + 459 + ], + "score": 1.0, + "content": "4.1 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 106, + 468, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "score": 1.0, + "content": "We conduct our experiments on miniImageNet (Vinyals et al., 2016), CIFAR-FS (Bertinetto et al.,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "score": 1.0, + "content": "2019) and tieredImageNet (Ren et al., 2018), using the ResNet12 variant first adopted by Lee et al.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 490, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 232, + 502 + ], + "score": 1.0, + "content": "(2019) as embedding function", + "type": "text" + }, + { + "bbox": [ + 232, + 490, + 243, + 501 + ], + "score": 0.86, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 490, + 505, + 502 + ], + "score": 1.0, + "content": ". A detailed description of benchmarks, architecture and imple-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 500, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 515 + ], + "score": 1.0, + "content": "mentation details is deferred to Appendix A.4, while below we discuss the most important choices", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 212, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 212, + 526 + ], + "score": 1.0, + "content": "of the experimental setup.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 590 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "Like Wang et al. (2019), for all our experiments (including those with Prototypical Networks) we", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "centre and normalise the feature embeddings before performing classification, as it is considerably", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 551, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 505, + 563 + ], + "score": 1.0, + "content": "beneficial for performance. After training, we compute the mean feature vectors of all the images", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 561, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 182, + 576 + ], + "score": 1.0, + "content": "in the training set:", + "type": "text" + }, + { + "bbox": [ + 182, + 561, + 287, + 576 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\bar { \\mathbf { x } } = \\frac { 1 } { | \\mathcal { D } ^ { \\mathrm { t r a i n } } | } \\sum _ { \\mathbf { x } \\in \\mathcal { D } ^ { t r a i n } } \\mathbf { x } . } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 561, + 506, + 576 + ], + "score": 1.0, + "content": ". Then, all feature vectors in the test set are updated as", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 103, + 572, + 290, + 592 + ], + "spans": [ + { + "bbox": [ + 103, + 572, + 290, + 592 + ], + "score": 1.0, + "content": "xi ← xi − x¯, and normalised by xi ← xikxik .", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 593, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 605 + ], + "score": 1.0, + "content": "We compared the inference methods discussed in Sec. 3.4 on miniImageNet and CIFAR-FS. Results", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "can be found in Table 2. We chose to use 1-NN with class centroids in all our experiments, as it per-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 230, + 628 + ], + "score": 1.0, + "content": "forms significantly better than", + "type": "text" + }, + { + "bbox": [ + 230, + 616, + 237, + 626 + ], + "score": 0.76, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "-NN or Soft Assignment. This might sound surprising, as the Soft", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "Assignment approach closely reflects the training protocol and outputs class probabilities. We spec-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 639, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 505, + 650 + ], + "score": 1.0, + "content": "ulate its inferior performance could be caused by poor model calibration (Guo et al., 2017): since", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "the classes between training and evaluation are disjoint, the model is unlikely to produce calibrated", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "probabilities. As such, within the softmax, outliers behaving as false positives can happen to highly", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "score": 1.0, + "content": "influence the final decision, and those behaving as false negatives can end up being almost com-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 682, + 506, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 506, + 695 + ], + "score": 1.0, + "content": "pletely ignored (their contribution is squashed toward zero). With the nearest centroid classification", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 693, + 423, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 423, + 705 + ], + "score": 1.0, + "content": "approach outliers are still clearly an issue, but their effect can be less dramatic.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 39.5 + }, + { + "type": "text", + "bbox": [ + 106, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "As standard, performance is assessed on episodes of 5-way, 15-query and either 1- or 5-shot. Each", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "model is evaluated on 10,000 episodes sampled from the test set (or the validation set, in some", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 307, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 83, + 341, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 343, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 343, + 95 + ], + "score": 1.0, + "content": "3.4 FEW-SHOT CLASSIFICATION DURING EVALUATION", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 103, + 505, + 137 + ], + "lines": [ + { + "bbox": [ + 105, + 102, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 130, + 117 + ], + "score": 1.0, + "content": "Once", + "type": "text" + }, + { + "bbox": [ + 131, + 104, + 141, + 115 + ], + "score": 0.87, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 102, + 505, + 117 + ], + "score": 1.0, + "content": "has been trained, there are many possible ways to perform few-shot classification during", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 115, + 504, + 126 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 504, + 126 + ], + "score": 1.0, + "content": "evaluation. In this paper we consider three simple approaches that are particularly aligned for em-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 126, + 364, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 364, + 138 + ], + "score": 1.0, + "content": "beddings learned via metric-based losses such as Eq. 2 or Eq. 3.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 102, + 505, + 138 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 145, + 505, + 191 + ], + "lines": [ + { + "bbox": [ + 106, + 144, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 106, + 146, + 113, + 155 + ], + "score": 0.75, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 144, + 223, + 159 + ], + "score": 1.0, + "content": "-NN. To classify an image", + "type": "text" + }, + { + "bbox": [ + 224, + 146, + 254, + 157 + ], + "score": 0.9, + "content": "\\mathbf q _ { i } \\in Q", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 144, + 505, + 159 + ], + "score": 1.0, + "content": ", we first compute the Euclidean distance to each support point", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 157, + 504, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 158, + 138, + 171 + ], + "score": 0.81, + "content": "\\mathbf { s } _ { j } \\in S", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 157, + 256, + 171 + ], + "score": 0.89, + "content": ": d _ { i j } = \\| f _ { \\boldsymbol \\theta } ( \\mathbf { q } _ { i } ) - f _ { \\boldsymbol \\theta } ( \\mathbf { s } _ { j } ) ) \\| ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 157, + 362, + 171 + ], + "score": 1.0, + "content": ". Then, we simply assign", + "type": "text" + }, + { + "bbox": [ + 362, + 158, + 385, + 170 + ], + "score": 0.93, + "content": "y ( \\mathbf { q } _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 157, + 497, + 171 + ], + "score": 1.0, + "content": "to be majority label of the", + "type": "text" + }, + { + "bbox": [ + 497, + 158, + 504, + 168 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 169, + 505, + 181 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 285, + 181 + ], + "score": 1.0, + "content": "nearest neighbours. A downside here is that", + "type": "text" + }, + { + "bbox": [ + 286, + 170, + 292, + 179 + ], + "score": 0.82, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 169, + 505, + 181 + ], + "score": 1.0, + "content": "is a hyper-parameter that has to be chosen, although", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 180, + 432, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 420, + 192 + ], + "score": 1.0, + "content": "a reasonable choice in the FSL setup is to set it equal to the number of “shots”", + "type": "text" + }, + { + "bbox": [ + 421, + 182, + 428, + 190 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 428, + 180, + 432, + 192 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 144, + 505, + 192 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 200, + 503, + 235 + ], + "lines": [ + { + "bbox": [ + 105, + 200, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 270, + 213 + ], + "score": 1.0, + "content": "1-NN with Class Centroids. Similar to", + "type": "text" + }, + { + "bbox": [ + 271, + 201, + 277, + 210 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 200, + 505, + 213 + ], + "score": 1.0, + "content": "-NN, we can perform classification by inheriting the label", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 209, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 104, + 209, + 235, + 228 + ], + "score": 1.0, + "content": "of the closest class centroid, i.e.", + "type": "text" + }, + { + "bbox": [ + 235, + 212, + 398, + 225 + ], + "score": 0.92, + "content": "\\begin{array} { r } { y ( { \\mathbf { q } } _ { i } ) = \\arg \\operatorname* { m i n } _ { j \\in \\{ 1 , \\dots , k \\} } \\| f _ { \\boldsymbol { \\theta } } ( { \\mathbf { x } } _ { i } ) - { \\mathbf { c } } _ { j } \\| } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 209, + 506, + 228 + ], + "score": 1.0, + "content": ". This is the approach used", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 223, + 335, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 335, + 236 + ], + "score": 1.0, + "content": "at test-time by Snell et al. (2017) and Wang et al. (2019).", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9, + "bbox_fs": [ + 104, + 200, + 506, + 236 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 243, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 105, + 242, + 505, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 505, + 256 + ], + "score": 1.0, + "content": "Soft Assignments. This is what the original NCA paper (Goldberger et al., 2005) used for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 253, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 104, + 253, + 252, + 267 + ], + "score": 1.0, + "content": "evaluation. To classify an image", + "type": "text" + }, + { + "bbox": [ + 252, + 255, + 291, + 266 + ], + "score": 0.89, + "content": "\\mathbf { q } _ { i } ~ \\in ~ { \\cal Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 253, + 399, + 267 + ], + "score": 1.0, + "content": ", we compute the values", + "type": "text" + }, + { + "bbox": [ + 399, + 254, + 505, + 267 + ], + "score": 0.89, + "content": "p _ { i j } ~ = ~ \\exp ( - \\| f _ { \\theta } ( { \\mathbf { q } } _ { i } ) ~ -", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 265, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 300, + 282 + ], + "score": 0.91, + "content": "\\begin{array} { r } { f _ { \\theta } ( \\mathbf { s } _ { j } ) ) \\vert \\vert ^ { 2 } ) / \\sum _ { \\mathbf { s } _ { k } \\in S } \\exp ( - \\vert \\vert f _ { \\theta } ( \\mathbf { q } _ { i } ) - f _ { \\theta } ( \\mathbf { s } _ { k } ) \\vert \\vert ^ { 2 } ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 265, + 331, + 283 + ], + "score": 1.0, + "content": "for all", + "type": "text" + }, + { + "bbox": [ + 331, + 267, + 364, + 280 + ], + "score": 0.9, + "content": "\\mathbf { s } _ { j } ~ \\in ~ S", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 265, + 506, + 283 + ], + "score": 1.0, + "content": ", which is the probability that im-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 279, + 507, + 297 + ], + "spans": [ + { + "bbox": [ + 104, + 279, + 123, + 297 + ], + "score": 1.0, + "content": "age", + "type": "text" + }, + { + "bbox": [ + 123, + 282, + 128, + 290 + ], + "score": 0.71, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 279, + 224, + 297 + ], + "score": 1.0, + "content": "is sampled from image", + "type": "text" + }, + { + "bbox": [ + 224, + 282, + 230, + 292 + ], + "score": 0.75, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 230, + 279, + 424, + 297 + ], + "score": 1.0, + "content": ". We then compute the likelihood for each class", + "type": "text" + }, + { + "bbox": [ + 424, + 281, + 431, + 291 + ], + "score": 0.64, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 279, + 435, + 297 + ], + "score": 1.0, + "content": ":", + "type": "text" + }, + { + "bbox": [ + 435, + 280, + 484, + 295 + ], + "score": 0.91, + "content": "\\textstyle \\sum _ { s _ { j } \\in S _ { k } } p _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 279, + 507, + 297 + ], + "score": 1.0, + "content": ", and", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 103, + 290, + 507, + 311 + ], + "spans": [ + { + "bbox": [ + 103, + 290, + 286, + 311 + ], + "score": 1.0, + "content": "choose the class with the highest likelihood", + "type": "text" + }, + { + "bbox": [ + 287, + 293, + 414, + 308 + ], + "score": 0.92, + "content": "y ( \\mathbf { q } _ { i } ) = \\arg \\operatorname* { m a x } _ { k } \\sum _ { s _ { j } \\in S _ { k } } p _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 290, + 507, + 311 + ], + "score": 1.0, + "content": ". This approach is the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 306, + 495, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 306, + 495, + 320 + ], + "score": 1.0, + "content": "only one closely aligned with the training procedure, and has a direct probabilistic interpretation.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 103, + 242, + 507, + 320 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 323, + 503, + 346 + ], + "lines": [ + { + "bbox": [ + 105, + 321, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 338 + ], + "score": 1.0, + "content": "We also experimented with using the NCA loss on the support set to perform adaptation at test time,", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 334, + 251, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 251, + 347 + ], + "score": 1.0, + "content": "which we discuss in Appendix A.1.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 321, + 505, + 347 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 363, + 200, + 375 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 201, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 201, + 377 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 388, + 505, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "In the following, Sec. 4.1 describes our experimental setup. Sec. 4.2 shows the effect of the hyper-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 399, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 411 + ], + "score": 1.0, + "content": "parameters controlling the creation of episodes in PNS. In Sec. 4.3 we perform a set of ablation", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "score": 1.0, + "content": "studies to better illustrate the relationship between PNS and the NCA. Finally, in Sec. 4.4 we com-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 422, + 434, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 434, + 433 + ], + "score": 1.0, + "content": "pare our version of the NCA to several recent methods on three FSL benchmarks.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 387, + 506, + 433 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 447, + 229, + 458 + ], + "lines": [ + { + "bbox": [ + 106, + 447, + 230, + 459 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 230, + 459 + ], + "score": 1.0, + "content": "4.1 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 106, + 468, + 505, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "score": 1.0, + "content": "We conduct our experiments on miniImageNet (Vinyals et al., 2016), CIFAR-FS (Bertinetto et al.,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "score": 1.0, + "content": "2019) and tieredImageNet (Ren et al., 2018), using the ResNet12 variant first adopted by Lee et al.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 490, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 232, + 502 + ], + "score": 1.0, + "content": "(2019) as embedding function", + "type": "text" + }, + { + "bbox": [ + 232, + 490, + 243, + 501 + ], + "score": 0.86, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 490, + 505, + 502 + ], + "score": 1.0, + "content": ". A detailed description of benchmarks, architecture and imple-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 500, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 515 + ], + "score": 1.0, + "content": "mentation details is deferred to Appendix A.4, while below we discuss the most important choices", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 511, + 212, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 212, + 526 + ], + "score": 1.0, + "content": "of the experimental setup.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 468, + 506, + 526 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 590 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 542 + ], + "score": 1.0, + "content": "Like Wang et al. (2019), for all our experiments (including those with Prototypical Networks) we", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "centre and normalise the feature embeddings before performing classification, as it is considerably", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 551, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 505, + 563 + ], + "score": 1.0, + "content": "beneficial for performance. After training, we compute the mean feature vectors of all the images", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 561, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 182, + 576 + ], + "score": 1.0, + "content": "in the training set:", + "type": "text" + }, + { + "bbox": [ + 182, + 561, + 287, + 576 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\bar { \\mathbf { x } } = \\frac { 1 } { | \\mathcal { D } ^ { \\mathrm { t r a i n } } | } \\sum _ { \\mathbf { x } \\in \\mathcal { D } ^ { t r a i n } } \\mathbf { x } . } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 561, + 506, + 576 + ], + "score": 1.0, + "content": ". Then, all feature vectors in the test set are updated as", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 103, + 572, + 290, + 592 + ], + "spans": [ + { + "bbox": [ + 103, + 572, + 290, + 592 + ], + "score": 1.0, + "content": "xi ← xi − x¯, and normalised by xi ← xikxik .", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32, + "bbox_fs": [ + 103, + 528, + 506, + 592 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 593, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 605 + ], + "score": 1.0, + "content": "We compared the inference methods discussed in Sec. 3.4 on miniImageNet and CIFAR-FS. Results", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "can be found in Table 2. We chose to use 1-NN with class centroids in all our experiments, as it per-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 230, + 628 + ], + "score": 1.0, + "content": "forms significantly better than", + "type": "text" + }, + { + "bbox": [ + 230, + 616, + 237, + 626 + ], + "score": 0.76, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "-NN or Soft Assignment. This might sound surprising, as the Soft", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "Assignment approach closely reflects the training protocol and outputs class probabilities. We spec-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 639, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 505, + 650 + ], + "score": 1.0, + "content": "ulate its inferior performance could be caused by poor model calibration (Guo et al., 2017): since", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "the classes between training and evaluation are disjoint, the model is unlikely to produce calibrated", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "probabilities. As such, within the softmax, outliers behaving as false positives can happen to highly", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "score": 1.0, + "content": "influence the final decision, and those behaving as false negatives can end up being almost com-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 682, + 506, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 506, + 695 + ], + "score": 1.0, + "content": "pletely ignored (their contribution is squashed toward zero). With the nearest centroid classification", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 693, + 423, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 423, + 705 + ], + "score": 1.0, + "content": "approach outliers are still clearly an issue, but their effect can be less dramatic.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 594, + 506, + 705 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "As standard, performance is assessed on episodes of 5-way, 15-query and either 1- or 5-shot. Each", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "model is evaluated on 10,000 episodes sampled from the test set (or the validation set, in some", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "score": 1.0, + "content": "experiments). To further reduce the variance, we trained each model five times with five different", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 379, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 505, + 390 + ], + "score": 1.0, + "content": "random seeds, for a total of 50,000 episodes per configuration, from which error bars are computed.", + "type": "text", + "cross_page": true + } + ], + "index": 15 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 709, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 226, + 88, + 384, + 171 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 310, + 81, + 355, + 89 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 309, + 79, + 356, + 91 + ], + "spans": [ + { + "bbox": [ + 309, + 79, + 356, + 91 + ], + "score": 1.0, + "content": "miniImageNet", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 226, + 88, + 384, + 171 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 226, + 88, + 384, + 171 + ], + "spans": [ + { + "bbox": [ + 226, + 88, + 384, + 171 + ], + "score": 0.96, + "html": "
method5-shot val5-shot test
Soft Assignment79.11 ± 0.2777.16 ± 0.10
k-NN75.82 ± 0.2173.52 ±0.12
1-NN centroid80.61±0.2078.30 ± 0.14
CIFAR-FS
Soft Assignment76.12 ± 0.3283.31 ± 0.37
k-NN73.46 ± 0.3980.94 ± 0.38
1-NN centroid77.80±0.3585.13 ±0.32
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Models trained using NCA,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 304, + 336 + ], + "score": 1.0, + "content": "or Proto-nets with different configurations: 1-shot with", + "type": "text" + }, + { + "bbox": [ + 304, + 325, + 323, + 334 + ], + "score": 0.88, + "content": "a { = } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 324, + 380, + 336 + ], + "score": 1.0, + "content": "and 5-shot with", + "type": "text" + }, + { + "bbox": [ + 381, + 325, + 399, + 334 + ], + "score": 0.83, + "content": "a { = } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 324, + 505, + 336 + ], + "score": 1.0, + "content": ", 16 or 32. Values correspond", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 334, + 480, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 480, + 345 + ], + "score": 1.0, + "content": "to the mean accuracy of five models trained with different random seeds. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 108, + 367, + 504, + 389 + ], + "lines": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "score": 1.0, + "content": "experiments). To further reduce the variance, we trained each model five times with five different", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 379, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 505, + 390 + ], + "score": 1.0, + "content": "random seeds, for a total of 50,000 episodes per configuration, from which error bars are computed.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5 + }, + { + "type": "title", + "bbox": [ + 107, + 404, + 365, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 366, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 366, + 416 + ], + "score": 1.0, + "content": "4.2 CONSIDERATIONS ON EPISODES AND DATA EFFICIENCY", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 423, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 504, + 435 + ], + "score": 1.0, + "content": "Despite Prototypical Networks being one of the simplest FSL methods, the creation of episodes", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 291, + 447 + ], + "score": 1.0, + "content": "requires the use of several hyper-parameters", + "type": "text" + }, + { + "bbox": [ + 292, + 434, + 336, + 447 + ], + "score": 0.91, + "content": "( \\{ w , m , n \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 337, + 434, + 505, + 447 + ], + "score": 1.0, + "content": ", Sec. 3.1) which can significantly affect", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 446, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 353, + 459 + ], + "score": 1.0, + "content": "performance. Snell et al. (2017) state that the number of shots", + "type": "text" + }, + { + "bbox": [ + 353, + 448, + 361, + 456 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 446, + 505, + 459 + ], + "score": 1.0, + "content": "between training and testing should", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 327, + 469 + ], + "score": 1.0, + "content": "match and that one should use a higher number of ways", + "type": "text" + }, + { + "bbox": [ + 327, + 459, + 335, + 466 + ], + "score": 0.69, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 456, + 506, + 469 + ], + "score": 1.0, + "content": "during training time. In their experiments,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 228, + 480 + ], + "score": 1.0, + "content": "they train 1-shot models with", + "type": "text" + }, + { + "bbox": [ + 228, + 468, + 263, + 478 + ], + "score": 0.85, + "content": "w = 3 0", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 467, + 267, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 267, + 468, + 295, + 478 + ], + "score": 0.83, + "content": "n = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 467, + 299, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 299, + 468, + 335, + 478 + ], + "score": 0.87, + "content": "m = 1 5", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 467, + 434, + 480 + ], + "score": 1.0, + "content": "and 5-shot models with", + "type": "text" + }, + { + "bbox": [ + 435, + 468, + 469, + 478 + ], + "score": 0.85, + "content": "w = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 467, + 473, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 473, + 468, + 501, + 478 + ], + "score": 0.85, + "content": "n = 5", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 467, + 505, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 479, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 143, + 489 + ], + "score": 0.9, + "content": "m = 1 5", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 479, + 504, + 491 + ], + "score": 1.0, + "content": ". This makes the corresponding batch sizes of these episodes 480 and 400, respectively.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "Since, as seen in Sec. 3.3, the number of positives and negatives grows rapidly for both PNS and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "score": 1.0, + "content": "NCA (although at a different rate), this makes a fair comparison between models trained on different", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 512, + 213, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 213, + 524 + ], + "score": 1.0, + "content": "types of episodes difficult.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 617 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 542 + ], + "score": 1.0, + "content": "We investigate the effect of changing these hyper-parameters in a systematic manner. To compare", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "configurations fairly across episode/batch sizes, we define each configuration by its number of shots", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 107, + 552, + 114, + 560 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 550, + 174, + 562 + ], + "score": 1.0, + "content": ", the batch size", + "type": "text" + }, + { + "bbox": [ + 174, + 551, + 180, + 560 + ], + "score": 0.55, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 550, + 345, + 562 + ], + "score": 1.0, + "content": "and the total number of images per class", + "type": "text" + }, + { + "bbox": [ + 345, + 552, + 352, + 560 + ], + "score": 0.68, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "(which accounts for the sum between", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 202, + 573 + ], + "score": 1.0, + "content": "support and query set,", + "type": "text" + }, + { + "bbox": [ + 202, + 562, + 256, + 572 + ], + "score": 0.89, + "content": "a = n + m ,", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 561, + 456, + 573 + ], + "score": 1.0, + "content": "). For example, if we train a 5-shot model with", + "type": "text" + }, + { + "bbox": [ + 456, + 562, + 486, + 572 + ], + "score": 0.9, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 140, + 582 + ], + "score": 0.88, + "content": "b = 2 5 6", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 572, + 376, + 585 + ], + "score": 1.0, + "content": ", it means that its corresponding training episodes will have", + "type": "text" + }, + { + "bbox": [ + 376, + 573, + 402, + 583 + ], + "score": 0.88, + "content": "n = 5", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 572, + 406, + 585 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 406, + 572, + 464, + 583 + ], + "score": 0.89, + "content": "q = 8 - 5 = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 572, + 484, + 585 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 485, + 573, + 505, + 583 + ], + "score": 0.85, + "content": "w =", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 156, + 595 + ], + "score": 0.89, + "content": "2 5 6 / 8 = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 582, + 506, + 596 + ], + "score": 1.0, + "content": ". Using this notation, we train configurations of PNS covering several combinations of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "these hyper-parameters so that the resulting batch size corresponds to an episode is 128, 256 or 512.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 604, + 484, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 484, + 617 + ], + "score": 1.0, + "content": "Then, we train three configurations of NCA, where the only hyper-parameter is the batch size.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 107, + 622, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 476, + 634 + ], + "score": 1.0, + "content": "Results for CIFAR-FS can be found in Fig. 2, where we report results for NCA and PNS with", + "type": "text" + }, + { + "bbox": [ + 477, + 622, + 501, + 632 + ], + "score": 0.88, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 621, + 506, + 634 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "score": 1.0, + "content": "16 or 32. Results for miniImageNet observe the same trend and are deferred to Appendix A.6. Note", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 642, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 226, + 658 + ], + "score": 1.0, + "content": "that the results of 1-shot with", + "type": "text" + }, + { + "bbox": [ + 227, + 644, + 257, + 654 + ], + "score": 0.89, + "content": "a = 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 642, + 275, + 658 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 275, + 644, + 306, + 654 + ], + "score": 0.9, + "content": "a = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 642, + 506, + 658 + ], + "score": 1.0, + "content": "are not reported, as they fare significantly worse.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "score": 1.0, + "content": "Several things can be noticed. First, NCA performs better than all PNS configurations, no matter the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "score": 1.0, + "content": "batch size. Second, PNS is very sensitive to different hyper-parameter configurations. For instance,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 379, + 690 + ], + "score": 1.0, + "content": "with batches of size 128, PNS trained with episodes of 5-shot and", + "type": "text" + }, + { + "bbox": [ + 380, + 677, + 412, + 687 + ], + "score": 0.9, + "content": "a = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "performs significantly", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 331, + 700 + ], + "score": 1.0, + "content": "worse than a PNS trained with episodes of 5-shot and", + "type": "text" + }, + { + "bbox": [ + 332, + 688, + 365, + 698 + ], + "score": 0.9, + "content": "a = 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 687, + 505, + 700 + ], + "score": 1.0, + "content": ". Finally, we can also notice that,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "contrary to what has been previously reported (Snell et al., 2017; Cao et al., 2020), the 5-shot model", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "with the best configuration is always strictly better than any 1-shot configuration. We speculate that", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 721, + 486, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 486, + 733 + ], + "score": 1.0, + "content": "this is probably due to the fact that we compare configurations keeping the batch size constant.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 307, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 226, + 88, + 384, + 171 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 310, + 81, + 355, + 89 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 309, + 79, + 356, + 91 + ], + "spans": [ + { + "bbox": [ + 309, + 79, + 356, + 91 + ], + "score": 1.0, + "content": "miniImageNet", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 226, + 88, + 384, + 171 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 226, + 88, + 384, + 171 + ], + "spans": [ + { + "bbox": [ + 226, + 88, + 384, + 171 + ], + "score": 0.96, + "html": "
method5-shot val5-shot test
Soft Assignment79.11 ± 0.2777.16 ± 0.10
k-NN75.82 ± 0.2173.52 ±0.12
1-NN centroid80.61±0.2078.30 ± 0.14
CIFAR-FS
Soft Assignment76.12 ± 0.3283.31 ± 0.37
k-NN73.46 ± 0.3980.94 ± 0.38
1-NN centroid77.80±0.3585.13 ±0.32
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Models trained using NCA,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 304, + 336 + ], + "score": 1.0, + "content": "or Proto-nets with different configurations: 1-shot with", + "type": "text" + }, + { + "bbox": [ + 304, + 325, + 323, + 334 + ], + "score": 0.88, + "content": "a { = } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 324, + 380, + 336 + ], + "score": 1.0, + "content": "and 5-shot with", + "type": "text" + }, + { + "bbox": [ + 381, + 325, + 399, + 334 + ], + "score": 0.83, + "content": "a { = } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 324, + 505, + 336 + ], + "score": 1.0, + "content": ", 16 or 32. Values correspond", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 334, + 480, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 480, + 345 + ], + "score": 1.0, + "content": "to the mean accuracy of five models trained with different random seeds. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 108, + 367, + 504, + 389 + ], + "lines": [], + "index": 14.5, + "bbox_fs": [ + 106, + 367, + 505, + 390 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 404, + 365, + 414 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 366, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 366, + 416 + ], + "score": 1.0, + "content": "4.2 CONSIDERATIONS ON EPISODES AND DATA EFFICIENCY", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 423, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 504, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 504, + 435 + ], + "score": 1.0, + "content": "Despite Prototypical Networks being one of the simplest FSL methods, the creation of episodes", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 291, + 447 + ], + "score": 1.0, + "content": "requires the use of several hyper-parameters", + "type": "text" + }, + { + "bbox": [ + 292, + 434, + 336, + 447 + ], + "score": 0.91, + "content": "( \\{ w , m , n \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 337, + 434, + 505, + 447 + ], + "score": 1.0, + "content": ", Sec. 3.1) which can significantly affect", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 446, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 353, + 459 + ], + "score": 1.0, + "content": "performance. Snell et al. (2017) state that the number of shots", + "type": "text" + }, + { + "bbox": [ + 353, + 448, + 361, + 456 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 446, + 505, + 459 + ], + "score": 1.0, + "content": "between training and testing should", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 327, + 469 + ], + "score": 1.0, + "content": "match and that one should use a higher number of ways", + "type": "text" + }, + { + "bbox": [ + 327, + 459, + 335, + 466 + ], + "score": 0.69, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 456, + 506, + 469 + ], + "score": 1.0, + "content": "during training time. In their experiments,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 467, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 228, + 480 + ], + "score": 1.0, + "content": "they train 1-shot models with", + "type": "text" + }, + { + "bbox": [ + 228, + 468, + 263, + 478 + ], + "score": 0.85, + "content": "w = 3 0", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 467, + 267, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 267, + 468, + 295, + 478 + ], + "score": 0.83, + "content": "n = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 467, + 299, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 299, + 468, + 335, + 478 + ], + "score": 0.87, + "content": "m = 1 5", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 467, + 434, + 480 + ], + "score": 1.0, + "content": "and 5-shot models with", + "type": "text" + }, + { + "bbox": [ + 435, + 468, + 469, + 478 + ], + "score": 0.85, + "content": "w = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 467, + 473, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 473, + 468, + 501, + 478 + ], + "score": 0.85, + "content": "n = 5", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 467, + 505, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 479, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 143, + 489 + ], + "score": 0.9, + "content": "m = 1 5", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 479, + 504, + 491 + ], + "score": 1.0, + "content": ". This makes the corresponding batch sizes of these episodes 480 and 400, respectively.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "Since, as seen in Sec. 3.3, the number of positives and negatives grows rapidly for both PNS and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 513 + ], + "score": 1.0, + "content": "NCA (although at a different rate), this makes a fair comparison between models trained on different", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 512, + 213, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 213, + 524 + ], + "score": 1.0, + "content": "types of episodes difficult.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 424, + 506, + 524 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 617 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 542 + ], + "score": 1.0, + "content": "We investigate the effect of changing these hyper-parameters in a systematic manner. To compare", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 551 + ], + "score": 1.0, + "content": "configurations fairly across episode/batch sizes, we define each configuration by its number of shots", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 107, + 552, + 114, + 560 + ], + "score": 0.71, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 550, + 174, + 562 + ], + "score": 1.0, + "content": ", the batch size", + "type": "text" + }, + { + "bbox": [ + 174, + 551, + 180, + 560 + ], + "score": 0.55, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 550, + 345, + 562 + ], + "score": 1.0, + "content": "and the total number of images per class", + "type": "text" + }, + { + "bbox": [ + 345, + 552, + 352, + 560 + ], + "score": 0.68, + "content": "a", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "(which accounts for the sum between", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 561, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 202, + 573 + ], + "score": 1.0, + "content": "support and query set,", + "type": "text" + }, + { + "bbox": [ + 202, + 562, + 256, + 572 + ], + "score": 0.89, + "content": "a = n + m ,", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 561, + 456, + 573 + ], + "score": 1.0, + "content": "). For example, if we train a 5-shot model with", + "type": "text" + }, + { + "bbox": [ + 456, + 562, + 486, + 572 + ], + "score": 0.9, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 561, + 505, + 573 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 107, + 572, + 140, + 582 + ], + "score": 0.88, + "content": "b = 2 5 6", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 572, + 376, + 585 + ], + "score": 1.0, + "content": ", it means that its corresponding training episodes will have", + "type": "text" + }, + { + "bbox": [ + 376, + 573, + 402, + 583 + ], + "score": 0.88, + "content": "n = 5", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 572, + 406, + 585 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 406, + 572, + 464, + 583 + ], + "score": 0.89, + "content": "q = 8 - 5 = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 572, + 484, + 585 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 485, + 573, + 505, + 583 + ], + "score": 0.85, + "content": "w =", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 582, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 156, + 595 + ], + "score": 0.89, + "content": "2 5 6 / 8 = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 582, + 506, + 596 + ], + "score": 1.0, + "content": ". Using this notation, we train configurations of PNS covering several combinations of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "these hyper-parameters so that the resulting batch size corresponds to an episode is 128, 256 or 512.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 604, + 484, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 484, + 617 + ], + "score": 1.0, + "content": "Then, we train three configurations of NCA, where the only hyper-parameter is the batch size.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 29.5, + "bbox_fs": [ + 105, + 527, + 506, + 617 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 622, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 476, + 634 + ], + "score": 1.0, + "content": "Results for CIFAR-FS can be found in Fig. 2, where we report results for NCA and PNS with", + "type": "text" + }, + { + "bbox": [ + 477, + 622, + 501, + 632 + ], + "score": 0.88, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 621, + 506, + 634 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 506, + 646 + ], + "score": 1.0, + "content": "16 or 32. Results for miniImageNet observe the same trend and are deferred to Appendix A.6. Note", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 642, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 226, + 658 + ], + "score": 1.0, + "content": "that the results of 1-shot with", + "type": "text" + }, + { + "bbox": [ + 227, + 644, + 257, + 654 + ], + "score": 0.89, + "content": "a = 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 642, + 275, + 658 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 275, + 644, + 306, + 654 + ], + "score": 0.9, + "content": "a = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 642, + 506, + 658 + ], + "score": 1.0, + "content": "are not reported, as they fare significantly worse.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "score": 1.0, + "content": "Several things can be noticed. First, NCA performs better than all PNS configurations, no matter the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 679 + ], + "score": 1.0, + "content": "batch size. Second, PNS is very sensitive to different hyper-parameter configurations. For instance,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 379, + 690 + ], + "score": 1.0, + "content": "with batches of size 128, PNS trained with episodes of 5-shot and", + "type": "text" + }, + { + "bbox": [ + 380, + 677, + 412, + 687 + ], + "score": 0.9, + "content": "a = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "performs significantly", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 331, + 700 + ], + "score": 1.0, + "content": "worse than a PNS trained with episodes of 5-shot and", + "type": "text" + }, + { + "bbox": [ + 332, + 688, + 365, + 698 + ], + "score": 0.9, + "content": "a = 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 687, + 505, + 700 + ], + "score": 1.0, + "content": ". Finally, we can also notice that,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "contrary to what has been previously reported (Snell et al., 2017; Cao et al., 2020), the 5-shot model", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "with the best configuration is always strictly better than any 1-shot configuration. We speculate that", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 721, + 486, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 486, + 733 + ], + "score": 1.0, + "content": "this is probably due to the fact that we compare configurations keeping the batch size constant.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 621, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 147, + 83, + 452, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 147, + 83, + 452, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 147, + 83, + 452, + 183 + ], + "spans": [ + { + "bbox": [ + 147, + 83, + 452, + 183 + ], + "score": 0.966, + "type": "image", + "image_path": "378d174e86a8463b548944cdf9989681b1fa7f1af0417280c46488bd5b815969.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 147, + 83, + 452, + 116.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 147, + 116.33333333333334, + 452, + 149.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 147, + 149.66666666666669, + 452, + 183.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 186, + 505, + 236 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 186, + 506, + 197 + ], + "spans": [ + { + "bbox": [ + 106, + 186, + 506, + 197 + ], + "score": 1.0, + "content": "Figure 3: 1-shot and 5-shot accuracies on the miniImageNet test set for models trained with a batch size of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 195, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 205, + 207 + ], + "score": 1.0, + "content": "256 while only sampling a", + "type": "text" + }, + { + "bbox": [ + 206, + 196, + 214, + 205 + ], + "score": 0.8, + "content": "\\%", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 195, + 506, + 207 + ], + "score": 1.0, + "content": "of the total number of available pairs. Reported values correspond to the mean", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 205, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 104, + 205, + 506, + 218 + ], + "score": 1.0, + "content": "accuracy of five models trained with different random seeds. Individual points contain models trained using", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 218, + 227 + ], + "score": 1.0, + "content": "PNS which are plotted on the", + "type": "text" + }, + { + "bbox": [ + 218, + 217, + 224, + 225 + ], + "score": 0.53, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "-axis based on the relative percentage of distance pairs that are used in their", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 226, + 418, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 418, + 236 + ], + "score": 1.0, + "content": "computation compared to NCA on the same batch size. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "score": 1.0, + "content": "Episodic batches vs random sub-sampling of standard batches. Despite the NCA outperform-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 273, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 505, + 285 + ], + "score": 1.0, + "content": "ing all PNS configurations (Fig. 2), one might posit that by using more distances within a batch,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 284, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 505, + 296 + ], + "score": 1.0, + "content": "NCA is more computationally costly and thus the episodic strategy of PNS can sometimes be ad-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "vantageous (e.g. real-time applications with large batches). To investigate this, we perform an exper-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 305, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 506, + 318 + ], + "score": 1.0, + "content": "iment where we train NCA models by randomly sampling a fraction of the total number of distances", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "used in the loss. Then, for comparison, we include different PNS models after having computed to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 327, + 475, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 475, + 340 + ], + "score": 1.0, + "content": "which percentage of discarded pairs (in a normal batch) their episodic batch corresponds to.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 344, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "Results can be found in Fig. 3. As expected, we can see how sub-sampling a fraction of the total", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 356, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 505, + 367 + ], + "score": 1.0, + "content": "available number of pairs within a batch negatively affects performance. To answer to possible", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "concerns on computational efficiency, we can notice that the PNS points lie very close to the under-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "sampling version of the NCA, which signals that the episodic strategy of PNS is roughly equivalent", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 461, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 461, + 400 + ], + "score": 1.0, + "content": "to train with the NCA and only exploiting a fraction of the distances available in a batch.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 505, + 471 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "We see as we move right on the curve in Fig. 3, that the PN performance increases as well. In", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 416, + 506, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 506, + 428 + ], + "score": 1.0, + "content": "Appendix A.9 we look more carefully whether the difference in performance between the different", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "score": 1.0, + "content": "episodic batch setups of Fig. 2 can be explained by the differences in the number of distance pairs", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 438, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 506, + 450 + ], + "score": 1.0, + "content": "used in the batch configurations. We indeed find that generally speaking the higher the number of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "score": 1.0, + "content": "pairs the better, however, one should also consider the positive/negative balance and the number of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 460, + 229, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 229, + 471 + ], + "score": 1.0, + "content": "classes present within a batch.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 107, + 489, + 239, + 500 + ], + "lines": [ + { + "bbox": [ + 105, + 488, + 241, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 241, + 502 + ], + "score": 1.0, + "content": "4.3 ABLATION EXPERIMENTS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 511, + 505, + 566 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "score": 1.0, + "content": "To better analyse why NCA performs better than PNS, in this section we consider the three key", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "score": 1.0, + "content": "differences discussed earlier by performing a series of ablations on models trained on batches of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 533, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 505, + 545 + ], + "score": 1.0, + "content": "size 256. Results are summarised in Fig. 4. We refer the reader to Appendix A.1 to obtain detailed", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "steps describing how these ablations affect Eq. 2 and Eq. 3, while Appendix A.7 contains the same", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 555, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 289, + 567 + ], + "score": 1.0, + "content": "analysis also for batches of size 128 and 512.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 572, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "First, we compare two variants of NCA: one in which the sampling of the training batches happens", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "sequentially and without replacement, as it is standard in supervised learning, and one where the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "batches are sampled with replacement. Interestingly, this modification (row 1 and 2 of Fig. 4) has", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "a negligible effect across the two datasets and four splits considered, meaning that the replacement", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 616, + 442, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 442, + 628 + ], + "score": 1.0, + "content": "sampling introduced by episodic learning will not interfere with the other ablations.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "We then perform a series of ablations on episodic batches, i.e. sampled with the method described", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "in Sec. 3.1. 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Reported values correspond to the mean", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 205, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 104, + 205, + 506, + 218 + ], + "score": 1.0, + "content": "accuracy of five models trained with different random seeds. Individual points contain models trained using", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 218, + 227 + ], + "score": 1.0, + "content": "PNS which are plotted on the", + "type": "text" + }, + { + "bbox": [ + 218, + 217, + 224, + 225 + ], + "score": 0.53, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "-axis based on the relative percentage of distance pairs that are used in their", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 226, + 418, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 418, + 236 + ], + "score": 1.0, + "content": "computation compared to NCA on the same batch size. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "spans": [ + { + "bbox": [ + 106, + 262, + 505, + 274 + ], + "score": 1.0, + "content": "Episodic batches vs random sub-sampling of standard batches. Despite the NCA outperform-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 273, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 505, + 285 + ], + "score": 1.0, + "content": "ing all PNS configurations (Fig. 2), one might posit that by using more distances within a batch,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 284, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 505, + 296 + ], + "score": 1.0, + "content": "NCA is more computationally costly and thus the episodic strategy of PNS can sometimes be ad-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "vantageous (e.g. real-time applications with large batches). To investigate this, we perform an exper-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 305, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 506, + 318 + ], + "score": 1.0, + "content": "iment where we train NCA models by randomly sampling a fraction of the total number of distances", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 505, + 329 + ], + "score": 1.0, + "content": "used in the loss. Then, for comparison, we include different PNS models after having computed to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 327, + 475, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 475, + 340 + ], + "score": 1.0, + "content": "which percentage of discarded pairs (in a normal batch) their episodic batch corresponds to.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 262, + 506, + 340 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 344, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "Results can be found in Fig. 3. As expected, we can see how sub-sampling a fraction of the total", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 356, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 505, + 367 + ], + "score": 1.0, + "content": "available number of pairs within a batch negatively affects performance. To answer to possible", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 505, + 378 + ], + "score": 1.0, + "content": "concerns on computational efficiency, we can notice that the PNS points lie very close to the under-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "sampling version of the NCA, which signals that the episodic strategy of PNS is roughly equivalent", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 461, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 461, + 400 + ], + "score": 1.0, + "content": "to train with the NCA and only exploiting a fraction of the distances available in a batch.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 344, + 505, + 400 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 505, + 471 + ], + "lines": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 505, + 417 + ], + "score": 1.0, + "content": "We see as we move right on the curve in Fig. 3, that the PN performance increases as well. In", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 416, + 506, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 506, + 428 + ], + "score": 1.0, + "content": "Appendix A.9 we look more carefully whether the difference in performance between the different", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 506, + 440 + ], + "score": 1.0, + "content": "episodic batch setups of Fig. 2 can be explained by the differences in the number of distance pairs", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 438, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 506, + 450 + ], + "score": 1.0, + "content": "used in the batch configurations. We indeed find that generally speaking the higher the number of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "score": 1.0, + "content": "pairs the better, however, one should also consider the positive/negative balance and the number of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 460, + 229, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 229, + 471 + ], + "score": 1.0, + "content": "classes present within a batch.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 405, + 506, + 471 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 489, + 239, + 500 + ], + "lines": [ + { + "bbox": [ + 105, + 488, + 241, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 241, + 502 + ], + "score": 1.0, + "content": "4.3 ABLATION EXPERIMENTS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 511, + 505, + 566 + ], + "lines": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "score": 1.0, + "content": "To better analyse why NCA performs better than PNS, in this section we consider the three key", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 535 + ], + "score": 1.0, + "content": "differences discussed earlier by performing a series of ablations on models trained on batches of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 533, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 505, + 545 + ], + "score": 1.0, + "content": "size 256. Results are summarised in Fig. 4. We refer the reader to Appendix A.1 to obtain detailed", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 544, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 558 + ], + "score": 1.0, + "content": "steps describing how these ablations affect Eq. 2 and Eq. 3, while Appendix A.7 contains the same", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 555, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 289, + 567 + ], + "score": 1.0, + "content": "analysis also for batches of size 128 and 512.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 510, + 506, + 567 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 572, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 505, + 584 + ], + "score": 1.0, + "content": "First, we compare two variants of NCA: one in which the sampling of the training batches happens", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "sequentially and without replacement, as it is standard in supervised learning, and one where the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "batches are sampled with replacement. Interestingly, this modification (row 1 and 2 of Fig. 4) has", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "a negligible effect across the two datasets and four splits considered, meaning that the replacement", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 616, + 442, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 442, + 628 + ], + "score": 1.0, + "content": "sampling introduced by episodic learning will not interfere with the other ablations.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 572, + 505, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "We then perform a series of ablations on episodic batches, i.e. sampled with the method described", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "in Sec. 3.1. For each ablation, we perform experiments on PNS trained with 1-shot and 5-shot, both", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 127, + 668 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 127, + 655, + 154, + 665 + ], + "score": 0.89, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 154, + 654, + 506, + 668 + ], + "score": 1.0, + "content": ". This means that both the 1-shot and 5-shot models have 32 classes and 8 images per", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "class, allowing a fair comparison. The batch size is 256 for the NCA too. We first train standard PNS", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "models. Next, we train a PNS model where “prototypes” are not computed (point 1 of Sec. 3.3),", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 687, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 701 + ], + "score": 1.0, + "content": "meaning that distances are considered between individual points, but a separation between query and", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "support set remains. Then, we perform an ablation where we ignore the separation between support", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 707, + 506, + 725 + ], + "spans": [ + { + "bbox": [ + 104, + 707, + 506, + 725 + ], + "score": 1.0, + "content": "and query set (point 2 of Sec. 3.3), and compute the NCA on the union of the support and query", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "score": 1.0, + "content": "set, while still computing prototypes for the points that would belong to the support set. Last, we", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 228, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 242 + ], + "score": 1.0, + "content": "perform an ablation where we consider all the previous points together: we sample with replacement,", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 241, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 505, + 252 + ], + "score": 1.0, + "content": "we ignore the separation between support and query set and we do not compute prototypes. This", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 250, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 105, + 250, + 505, + 263 + ], + "score": 1.0, + "content": "amounts to the NCA loss, except that it is computed on batches with a fixed number of classes and", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 262, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 505, + 273 + ], + "score": 1.0, + "content": "a fixed number of images per class. Notice that in Fig. 4 there is only one row dedicated to 1-shot", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 271, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 286 + ], + "score": 1.0, + "content": "models. This is because we cannot generate prototypes from 1-shot models, so we cannot have", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 284, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 296 + ], + "score": 1.0, + "content": "a “no proto” ablation. Furthermore, for 1-shot models the “no S/Q” ablation is equivalent to the", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 294, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 307 + ], + "score": 1.0, + "content": "NCA with a fixed batch composition. From Fig. 4, we can see that disabling prototypes (row 6)", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 305, + 506, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 506, + 319 + ], + "score": 1.0, + "content": "negatively affects the performance of 5-shot (row 5), albeit slightly. On the other hand, enabling", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 317, + 504, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 504, + 329 + ], + "score": 1.0, + "content": "the computation between all pairs increases the performance (last row), Importantly, enabling all the", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 327, + 380, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 380, + 340 + ], + "score": 1.0, + "content": "ablations (row 3) completely recovers the performance lost by PNS.", + "type": "text", + "cross_page": true + } + ], + "index": 14 + } + ], + "index": 41, + "bbox_fs": [ + 104, + 632, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 126, + 79, + 482, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 126, + 79, + 482, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 79, + 482, + 183 + ], + "spans": [ + { + "bbox": [ + 126, + 79, + 482, + 183 + ], + "score": 0.965, + "type": "image", + "image_path": "d846cc09a7dd57288e9008e707f160d4426fa3c70630d43f864c50e40d192fb7.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 126, + 79, + 482, + 113.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 126, + 113.66666666666666, + 482, + 148.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 126, + 148.33333333333331, + 482, + 182.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 186, + 503, + 207 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 186, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 106, + 186, + 505, + 198 + ], + "score": 1.0, + "content": "Figure 4: Ablation experiments on NCA and Prototypical Networks, both on batches or episodes of size 256", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 196, + 428, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 428, + 208 + ], + "score": 1.0, + "content": "on the validation set of miniImageNet and CIFAR-FS. Please refer to Sec. 4.3 for details.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 107, + 228, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 105, + 228, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 242 + ], + "score": 1.0, + "content": "perform an ablation where we consider all the previous points together: we sample with replacement,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 241, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 505, + 252 + ], + "score": 1.0, + "content": "we ignore the separation between support and query set and we do not compute prototypes. This", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 250, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 105, + 250, + 505, + 263 + ], + "score": 1.0, + "content": "amounts to the NCA loss, except that it is computed on batches with a fixed number of classes and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 262, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 505, + 273 + ], + "score": 1.0, + "content": "a fixed number of images per class. Notice that in Fig. 4 there is only one row dedicated to 1-shot", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 271, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 286 + ], + "score": 1.0, + "content": "models. This is because we cannot generate prototypes from 1-shot models, so we cannot have", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 284, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 296 + ], + "score": 1.0, + "content": "a “no proto” ablation. Furthermore, for 1-shot models the “no S/Q” ablation is equivalent to the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 294, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 307 + ], + "score": 1.0, + "content": "NCA with a fixed batch composition. From Fig. 4, we can see that disabling prototypes (row 6)", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 305, + 506, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 506, + 319 + ], + "score": 1.0, + "content": "negatively affects the performance of 5-shot (row 5), albeit slightly. On the other hand, enabling", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 317, + 504, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 504, + 329 + ], + "score": 1.0, + "content": "the computation between all pairs increases the performance (last row), Importantly, enabling all the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 327, + 380, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 380, + 340 + ], + "score": 1.0, + "content": "ablations (row 3) completely recovers the performance lost by PNS.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 344, + 505, + 433 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "The fact that each single ablation does not have much influence on the performance, but their combi-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 356, + 505, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 367 + ], + "score": 1.0, + "content": "nation does, could be explained by the number of distance pairs exploited by the individual ablations.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "score": 1.0, + "content": "Using the formulas described at the end of Section 3.3, we compute the number of positives and neg-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 505, + 389 + ], + "score": 1.0, + "content": "atives used for each ablation. For row 6 there are 480 positives, and 14,880 negatives. For row 7", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "there are 576 positives and 20,170 negatives. In both cases, the number is significantly lower than", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "the corresponding NCA, which gets 896 positives and 31,744 negatives, and this could explain the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 506, + 423 + ], + "score": 1.0, + "content": "jump in performance from row 6/7 to 3. Moreover, from row 5/6 to 7 we see a slight increase in", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 421, + 471, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 471, + 434 + ], + "score": 1.0, + "content": "performance, which can also be explained by the (slightly) larger number of distance pairs.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 438, + 505, + 505 + ], + "lines": [ + { + "bbox": [ + 106, + 437, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 451 + ], + "score": 1.0, + "content": "These experiments nonetheless highlight that the separation of roles between the images belonging", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "score": 1.0, + "content": "to support and query set, which is typical of episodic learning (Vinyals et al., 2016), is detrimental", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 460, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 505, + 471 + ], + "score": 1.0, + "content": "for the performance of Prototypical Networks. Instead, using the NCA loss on standard mini-batches", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "score": 1.0, + "content": "allows full exploitation of the training data and significantly improves performance. 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For example, we only report the results of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "the main approach proposed by Tian et al. 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(2020) and not their sequential self-distillation (Furlanello", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 649, + 503, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 503, + 662 + ], + "score": 1.0, + "content": "et al., 2018) variant, which requires re-training multiple times and can be applied to most methods.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 604, + 506, + 662 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 665, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "Results can be found in Table 3 for miniImageNet and CIFAR-FS and Table 4 for tieredImageNet.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 689 + ], + "score": 1.0, + "content": "In Table 3 we report Prototypical Networks results for both the episodic setup from Snell et al.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 299, + 699 + ], + "score": 1.0, + "content": "(2017) and the best one (batch size 512, 5-shot,", + "type": "text" + }, + { + "bbox": [ + 299, + 688, + 324, + 698 + ], + "score": 0.87, + "content": "a { = } 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 688, + 505, + 699 + ], + "score": 1.0, + "content": ") found from the experiment of Fig. 2, which", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "brings a considerable improvement over the original. We did not optimised for a new setup for Pro-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 709, + 506, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 721 + ], + "score": 1.0, + "content": "totypical Networks on tieredImageNet, as the larger dataset and the higher number of classes would", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "have made the hyper-parameter search too demanding. Notice how our vanilla NCA is competi-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 424, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 506, + 437 + ], + "score": 1.0, + "content": "tive or superior to recent methods, despite being extremely simple. It fairs surprisingly well against", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "methods that use meta-learning (and episodic learning), and also against the high-performing simple", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 446, + 345, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 345, + 460 + ], + "score": 1.0, + "content": "baselines based on pre-training with the cross-entropy loss.", + "type": "text", + "cross_page": true + } + ], + "index": 14 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 666, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 121, + 83, + 488, + 257 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 293, + 81, + 335, + 88 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 293, + 81, + 335, + 88 + ], + "spans": [], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 121, + 83, + 488, + 257 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 121, + 83, + 488, + 257 + ], + "spans": [ + { + "bbox": [ + 121, + 83, + 488, + 257 + ], + "score": 0.979, + "html": "
minilmageNetCIFAR-FS
1-shot5-shot1-shot5-shot
Episodic methods
adaResNet (Munkhdalai et al.,2018)56.88 ±0.6271.94 ± 0.57
TADAM(Oreshkin et al., 2018)58.50 ±0.3076.70 ± 0.30
Shot-Free (Ravichandran et al.,2019)60.71±n/a77.64±n/a69.2±n/a84.7±n/a
TEAM (Qiao et al.,2019)60.07±n/a75.90±n/a
MTL (Sun et al.,2019)61.20 ± 1.8075.50 ±0.80
TapNet (Yoon et al.,2019)61.65 ± 0.1576.36 ±0.10
MetaOptNet-SVM(Lee et al.,2019)62.64 ± 0.6178.63 ± 0.4672.0±0.784.2 ±0.5
Variatonal FSL (Zhang et al., 2019)61.23±0.2677.69 ±0.17
Simple baselines
Transductive finetuning (Dhillon et al., 2020)62.35 ±0.6674.53 ± 0.5470.76 ± 0.7481.56 ±0.53
RFIC-simple (Tian et al.,2020)62.02±0.6379.64 ± 0.4471.5 ±0.886.0±0.5
Meta-Baseline (Chen et al.,2020b)63.17±0.2379.26 ± 0.17
Our implementations:
Proto-nets (Snell et al. (2017) setup)59.93±0.2375.89 ±0.1670.20±0.2283.96 ±0.16
Proto-nets (our setup)61.32 ±0.2377.77 ± 0.1570.41 ± 0.3184.46 ±0.29
SimpleShot (Wang et al.,2019)62.16 ±0.2378.33 ± 0.1770.01 ± 0.2184.50 ± 0.11
NCA (ours)62.52±0.2478.3±0.1472.48±0.4085.13±0.29
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tieredImageNet
Method1-shot5-shot
Shot-Free (Ravichandran et al.,2019)63.52±n/a82.59±n/a
RFIC-simple (Tian et al., 2020)69.74±0.7284.41±0.55
Meta-Baseline (Chen et al.,2020b)68.62 ± 0.2783.29 ±0.18
MetaOptNet-SVM(Lee et al.,2019)65.99 ± 0.7281.56 ± 0.53
Our implementations:
Proto-nets (Snell et al. (2017) setup)65.45 ± 0.2381.14 ± 0.17
SimpleShot (Wang et al., 2019)66.17 ± 0.1580.64±0.20
NCA (ours)68.36 ± 0.1183.20±0.18
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It fairs surprisingly well against", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "methods that use meta-learning (and episodic learning), and also against the high-performing simple", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 446, + 345, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 345, + 460 + ], + "score": 1.0, + "content": "baselines based on pre-training with the cross-entropy loss.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 108, + 470, + 195, + 482 + ], + "lines": [ + { + "bbox": [ + 104, + 468, + 197, + 486 + ], + "spans": [ + { + "bbox": [ + 104, + 468, + 197, + 486 + ], + "score": 1.0, + "content": "5 CONCLUSION", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 497, + 505, + 629 + ], + "lines": [ + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "score": 1.0, + "content": "Towards the aim of understanding the reasons behind the poor competitiveness of meta-learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 505, + 522 + ], + "score": 1.0, + "content": "methods with respect to simple baselines, in this paper we start by investigating the role of episodes", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 532 + ], + "score": 1.0, + "content": "in the popular Prototypical Networks. We found that their performance is highly sensitive to the set", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 531, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 505, + 544 + ], + "score": 1.0, + "content": "of hyper-parameters used to sample the episodes. By replacing the Prototypical Networks’ loss with", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 541, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 505, + 555 + ], + "score": 1.0, + "content": "the classic Neighbourhood Component Analysis, we are able to ignore these hyper-parameters while", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "significantly improving the few-shot classification accuracy. With a series of experiments, we found", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 563, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 577 + ], + "score": 1.0, + "content": "out that the performance discrepancy mostly arises from the separation between support and query", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "score": 1.0, + "content": "set within each episode, and that Prototypical Networks’ episodic strategy is almost empirically", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "score": 1.0, + "content": "equivalent to randomly discarding a large fraction of distances within a standard mini-batch. Finally,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 596, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 505, + 608 + ], + "score": 1.0, + "content": "we show that our variant of the NCA achieves an accuracy on multiple popular FSL benchmarks that", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 608, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 505, + 620 + ], + "score": 1.0, + "content": "is comparable or superior with state-of-the-art methods of similar complexity, making it a simple and", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 618, + 249, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 249, + 630 + ], + "score": 1.0, + "content": "appealing baseline for future work.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21.5 + }, + { + "type": "title", + "bbox": [ + 108, + 650, + 175, + 663 + ], + "lines": [ + { + "bbox": [ + 106, + 650, + 176, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 176, + 664 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 672, + 504, + 694 + ], + "lines": [ + { + "bbox": [ + 105, + 670, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 505, + 686 + ], + "score": 1.0, + "content": "Kelsey R Allen, Evan Shelhamer, Hanul Shin, and Joshua B Tenenbaum. Infinite mixture prototypes", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 116, + 683, + 437, + 695 + ], + "spans": [ + { + "bbox": [ + 116, + 683, + 437, + 695 + ], + "score": 1.0, + "content": "for few-shot learning. In International Conference on Machine Learning, 2019.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 503, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "score": 1.0, + "content": "Han Altae-Tran, Bharath Ramsundar, Aneesh S Pappu, and Vijay Pande. Low data drug discovery", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 116, + 720, + 323, + 732 + ], + "spans": [ + { + "bbox": [ + 116, + 720, + 323, + 732 + ], + "score": 1.0, + "content": "with one-shot learning. ACS central science, 2017.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 306, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 121, + 83, + 488, + 257 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 293, + 81, + 335, + 88 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 293, + 81, + 335, + 88 + ], + "spans": [], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 121, + 83, + 488, + 257 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 121, + 83, + 488, + 257 + ], + "spans": [ + { + "bbox": [ + 121, + 83, + 488, + 257 + ], + "score": 0.979, + "html": "
minilmageNetCIFAR-FS
1-shot5-shot1-shot5-shot
Episodic methods
adaResNet (Munkhdalai et al.,2018)56.88 ±0.6271.94 ± 0.57
TADAM(Oreshkin et al., 2018)58.50 ±0.3076.70 ± 0.30
Shot-Free (Ravichandran et al.,2019)60.71±n/a77.64±n/a69.2±n/a84.7±n/a
TEAM (Qiao et al.,2019)60.07±n/a75.90±n/a
MTL (Sun et al.,2019)61.20 ± 1.8075.50 ±0.80
TapNet (Yoon et al.,2019)61.65 ± 0.1576.36 ±0.10
MetaOptNet-SVM(Lee et al.,2019)62.64 ± 0.6178.63 ± 0.4672.0±0.784.2 ±0.5
Variatonal FSL (Zhang et al., 2019)61.23±0.2677.69 ±0.17
Simple baselines
Transductive finetuning (Dhillon et al., 2020)62.35 ±0.6674.53 ± 0.5470.76 ± 0.7481.56 ±0.53
RFIC-simple (Tian et al.,2020)62.02±0.6379.64 ± 0.4471.5 ±0.886.0±0.5
Meta-Baseline (Chen et al.,2020b)63.17±0.2379.26 ± 0.17
Our implementations:
Proto-nets (Snell et al. (2017) setup)59.93±0.2375.89 ±0.1670.20±0.2283.96 ±0.16
Proto-nets (our setup)61.32 ±0.2377.77 ± 0.1570.41 ± 0.3184.46 ±0.29
SimpleShot (Wang et al.,2019)62.16 ±0.2378.33 ± 0.1770.01 ± 0.2184.50 ± 0.11
NCA (ours)62.52±0.2478.3±0.1472.48±0.4085.13±0.29
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tieredImageNet
Method1-shot5-shot
Shot-Free (Ravichandran et al.,2019)63.52±n/a82.59±n/a
RFIC-simple (Tian et al., 2020)69.74±0.7284.41±0.55
Meta-Baseline (Chen et al.,2020b)68.62 ± 0.2783.29 ±0.18
MetaOptNet-SVM(Lee et al.,2019)65.99 ± 0.7281.56 ± 0.53
Our implementations:
Proto-nets (Snell et al. (2017) setup)65.45 ± 0.2381.14 ± 0.17
SimpleShot (Wang et al., 2019)66.17 ± 0.1580.64±0.20
NCA (ours)68.36 ± 0.1183.20±0.18
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We tried training a positive semi-definite matrix", + "type": "text" + }, + { + "bbox": [ + 406, + 178, + 415, + 188 + ], + "score": 0.65, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 178, + 505, + 190 + ], + "score": 1.0, + "content": "on the outputs of the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "score": 1.0, + "content": "trained neural network, which corresponds to learning a Mahalanobis distance metric as in Gold-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 200, + 504, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 504, + 212 + ], + "score": 1.0, + "content": "berger et al. (2005). However, we found that there was no meaningful increase in performance.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 379, + 223 + ], + "score": 1.0, + "content": "Differently, we did find that fine-tuning the whole neural network", + "type": "text" + }, + { + "bbox": [ + 380, + 211, + 390, + 222 + ], + "score": 0.87, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 209, + 408, + 223 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 408, + 211, + 485, + 223 + ], + "score": 0.84, + "content": "\\operatorname { a r g m i n } _ { \\theta } { \\mathcal { L } } _ { \\mathrm { N C A } } ( S )", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 209, + 505, + 223 + ], + "score": 1.0, + "content": "was", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 220, + 505, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 235 + ], + "score": 1.0, + "content": "beneficial (see Table 5). However, given the computational cost, we opted for non performing adap-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 233, + 324, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 324, + 245 + ], + "score": 1.0, + "content": "tation to the support sets in our experiments of Sec. 4.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 252, + 505, + 306 + ], + "lines": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "Features concatenation. For NCA, we also found that concatenating the output of intermediate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "score": 1.0, + "content": "layers modestly improves performance at (almost) no additional cost. We used the output of the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 274, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 505, + 286 + ], + "score": 1.0, + "content": "average pool layers from all ResNet blocks except the first and we refer to this variant as NCA", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 285, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 285, + 505, + 297 + ], + "score": 1.0, + "content": "multi-layer. However, since this is an orthogonal variation that can be applied to several methods,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 314, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 314, + 308 + ], + "score": 1.0, + "content": "we do not consider it for our experiments of Sec. 4.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 354, + 324 + ], + "lines": [ + { + "bbox": [ + 106, + 311, + 355, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 311, + 355, + 325 + ], + "score": 1.0, + "content": "Results on miniImageNet an CIFAR-FS are shown in Table 5.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "title", + "bbox": [ + 107, + 336, + 379, + 348 + ], + "lines": [ + { + "bbox": [ + 106, + 336, + 380, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 380, + 349 + ], + "score": 1.0, + "content": "A.2 DETAILS ABOUT THE ABLATION STUDIES OF SECTION 4.3", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 506, + 390 + ], + "lines": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "Referring to the three key differences between the Prototypical Networks and the NCA losses listed", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "in Sec. 3.3, in this section we detail how to obtain the ablations we used to perform the experiments", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 378, + 155, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 155, + 390 + ], + "score": 1.0, + "content": "of Sec. 4.3.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 409 + ], + "score": 1.0, + "content": "We can “disable” the creation of prototypes (point 1), which will change the prototypical loss of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 405, + 142, + 421 + ], + "spans": [ + { + "bbox": [ + 104, + 405, + 142, + 421 + ], + "score": 1.0, + "content": "Eq. 2 to", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5 + }, + { + "type": "interline_equation", + "bbox": [ + 165, + 416, + 446, + 468 + ], + "lines": [ + { + "bbox": [ + 165, + 416, + 446, + 468 + ], + "spans": [ + { + "bbox": [ + 165, + 416, + 446, + 468 + ], + "score": 0.94, + "content": "\\mathcal { L } ( S , Q ) = - 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The only difference now is the separation of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 489, + 261, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 261, + 502 + ], + "score": 1.0, + "content": "the batch into a query and support set.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 505, + 332, + 517 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 333, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 333, + 520 + ], + "score": 1.0, + "content": "Independently, we can “disable” point 2, which gives us", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "interline_equation", + "bbox": [ + 153, + 517, + 457, + 594 + ], + "lines": [ + { + "bbox": [ + 153, + 517, + 457, + 594 + ], + "spans": [ + { + "bbox": [ + 153, + 517, + 457, + 594 + ], + "score": 0.95, + "content": "\\mathcal { L } ( S , Q ) = - \\frac { 1 } { | Q | + | S | } \\sum _ { ( \\mathbf { z } _ { i } , y _ { i } ) \\in Q \\cup C } \\log ( \\frac { \\sum _ { y _ { j } , y _ { j } ) \\in Q \\cup C } \\exp { - 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However, we found that there was no meaningful increase in performance.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 379, + 223 + ], + "score": 1.0, + "content": "Differently, we did find that fine-tuning the whole neural network", + "type": "text" + }, + { + "bbox": [ + 380, + 211, + 390, + 222 + ], + "score": 0.87, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 209, + 408, + 223 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 408, + 211, + 485, + 223 + ], + "score": 0.84, + "content": "\\operatorname { a r g m i n } _ { \\theta } { \\mathcal { L } } _ { \\mathrm { N C A } } ( S )", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 209, + 505, + 223 + ], + "score": 1.0, + "content": "was", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 220, + 505, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 235 + ], + "score": 1.0, + "content": "beneficial (see Table 5). However, given the computational cost, we opted for non performing adap-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 233, + 324, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 324, + 245 + ], + "score": 1.0, + "content": "tation to the support sets in our experiments of Sec. 4.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 167, + 505, + 245 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 252, + 505, + 306 + ], + "lines": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "Features concatenation. For NCA, we also found that concatenating the output of intermediate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "score": 1.0, + "content": "layers modestly improves performance at (almost) no additional cost. We used the output of the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 274, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 505, + 286 + ], + "score": 1.0, + "content": "average pool layers from all ResNet blocks except the first and we refer to this variant as NCA", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 285, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 285, + 505, + 297 + ], + "score": 1.0, + "content": "multi-layer. However, since this is an orthogonal variation that can be applied to several methods,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 314, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 314, + 308 + ], + "score": 1.0, + "content": "we do not consider it for our experiments of Sec. 4.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 252, + 505, + 308 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 354, + 324 + ], + "lines": [ + { + "bbox": [ + 106, + 311, + 355, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 311, + 355, + 325 + ], + "score": 1.0, + "content": "Results on miniImageNet an CIFAR-FS are shown in Table 5.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 106, + 311, + 355, + 325 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 336, + 379, + 348 + ], + "lines": [ + { + "bbox": [ + 106, + 336, + 380, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 380, + 349 + ], + "score": 1.0, + "content": "A.2 DETAILS ABOUT THE ABLATION STUDIES OF SECTION 4.3", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 506, + 390 + ], + "lines": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "Referring to the three key differences between the Prototypical Networks and the NCA losses listed", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "in Sec. 3.3, in this section we detail how to obtain the ablations we used to perform the experiments", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 378, + 155, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 155, + 390 + ], + "score": 1.0, + "content": "of Sec. 4.3.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 357, + 505, + 390 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 409 + ], + "score": 1.0, + "content": "We can “disable” the creation of prototypes (point 1), which will change the prototypical loss of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 405, + 142, + 421 + ], + "spans": [ + { + "bbox": [ + 104, + 405, + 142, + 421 + ], + "score": 1.0, + "content": "Eq. 2 to", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 394, + 506, + 421 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 165, + 416, + 446, + 468 + ], + "lines": [ + { + "bbox": [ + 165, + 416, + 446, + 468 + ], + "spans": [ + { + "bbox": [ + 165, + 416, + 446, + 468 + ], + "score": 0.94, + "content": "\\mathcal { L } ( S , Q ) = - 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The only difference now is the separation of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 489, + 261, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 261, + 502 + ], + "score": 1.0, + "content": "the batch into a query and support set.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 28, + "bbox_fs": [ + 106, + 466, + 505, + 502 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 505, + 332, + 517 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 333, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 333, + 520 + ], + "score": 1.0, + "content": "Independently, we can “disable” point 2, which gives us", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 504, + 333, + 520 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 153, + 517, + 457, + 594 + ], + "lines": [ + { + "bbox": [ + 153, + 517, + 457, + 594 + ], + "spans": [ + { + "bbox": [ + 153, + 517, + 457, + 594 + ], + "score": 0.95, + "content": "\\mathcal { L } ( S , Q ) = - 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method1-shot5-shot1-shot5-shot
NCA62.52 ± 0.2478.3 ± 0.1472.48 ± 0.4085.13± 0.29
NCA multi-layer63.21 ± 0.0879.27 ±0.0872.44 ± 0.3685.42 ± 0.29
NCA (ours) multi-layer + ss-79.79 ± 0.08-85.66 ± 0.32
", + "type": "table", + "image_path": "2e0369acdd7e6721aeb0cb9cfe97d1125f8fbadee2de066d1d7fc15a1393e247.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 123, + 91, + 486, + 107.66666666666667 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 123, + 107.66666666666667, + 486, + 124.33333333333334 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 123, + 124.33333333333334, + 486, + 141.0 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 157, + 505, + 198 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 156, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 156, + 505, + 171 + ], + "score": 1.0, + "content": "Table 5: Comparison between vanilla NCA, NCA using multiple evaluation layers and NCA performing", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 168, + 505, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 505, + 179 + ], + "score": 1.0, + "content": "optimisation on the support set (ss). The NCA can only be optimised in the 5-shot case, since there are not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 176, + 506, + 192 + ], + "spans": [ + { + "bbox": [ + 104, + 176, + 506, + 192 + ], + "score": 1.0, + "content": "enough positives distances in the 1-shot case. Support set is optimised for 5 epochs using Adam with learning", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 187, + 333, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 333, + 199 + ], + "score": 1.0, + "content": "rate 0.0001 and weight decay 0.0005. For details, see Sec. A.1", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6.5 + } + ], + "index": 2.0 + }, + { + "type": "title", + "bbox": [ + 108, + 221, + 400, + 232 + ], + "lines": [ + { + "bbox": [ + 106, + 220, + 401, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 220, + 401, + 233 + ], + "score": 1.0, + "content": "A.3 DIFFERENCES BETWEEN THE NCA AND CONTRASTIVE LOSSES", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 241, + 505, + 329 + ], + "lines": [ + { + "bbox": [ + 105, + 240, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 506, + 254 + ], + "score": 1.0, + "content": "Eq. 3 is similar to the contrastive loss functions (Khosla et al., 2020; Chen et al., 2020a) that are", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "used in self-supervised learning and representation learning. The main differences are that 1.) In", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "contrastive losses, the denominator only contains negative pairs and 2.) the inner sum in the nu-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "score": 1.0, + "content": "merator is moved outside of the logarithm in the supervised contrastive loss function from Khosla", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "et al. (2020). We opted to work with the NCA loss because we found it performs better than the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 296, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 505, + 309 + ], + "score": 1.0, + "content": "supervised constrastive loss in a few-shot learning setting. Using the supervised contrastive loss we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 308, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 205, + 320 + ], + "score": 1.0, + "content": "only managed to obtain", + "type": "text" + }, + { + "bbox": [ + 206, + 308, + 238, + 318 + ], + "score": 0.84, + "content": "5 1 . 0 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 308, + 286, + 320 + ], + "score": 1.0, + "content": "1-shot and", + "type": "text" + }, + { + "bbox": [ + 286, + 308, + 318, + 318 + ], + "score": 0.84, + "content": "6 3 . 3 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 308, + 506, + 320 + ], + "score": 1.0, + "content": "5-shot performance on the miniImagenet test", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 123, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 123, + 330 + ], + "score": 1.0, + "content": "set.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5 + }, + { + "type": "title", + "bbox": [ + 108, + 344, + 249, + 355 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 251, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 251, + 356 + ], + "score": 1.0, + "content": "A.4 IMPLEMENTATION DETAILS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 368, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "score": 1.0, + "content": "Benchmarks. In our experiments, we use three popular FSL benchmarks. miniImageNet (Vinyals", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "et al., 2016) is a subset of ImageNet generated by randomly sampling 100 classes, each with 600 ran-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "domly sampled images. We adopt the commonly used splits of Ravi & Larochelle (2017) who use", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "score": 1.0, + "content": "64 classes for meta-training, 16 for meta-validation and 20 for meta-testing. CIFAR-FS was pro-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 412, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 104, + 412, + 506, + 425 + ], + "score": 1.0, + "content": "posed by Bertinetto et al. (2019) as an anagolous version of miniImagenet for CIFAR-100. It uses the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "score": 1.0, + "content": "same sized splits and same number of images per split as miniImageNet. tieredImageNet (Ren et al.,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "score": 1.0, + "content": "2018) is also constructed from ImageNet, but contains 608 classes, with 351 training classes, 97 val-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 445, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 458 + ], + "score": 1.0, + "content": "idation classes and 160 test classes. The class split have been generated using WordNet (Miller,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 455, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 505, + 469 + ], + "score": 1.0, + "content": "1995) to ensure that the training classes are semantically “distant” to the validation and test classes.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 466, + 294, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 261, + 480 + ], + "score": 1.0, + "content": "For all datasets, we use images of size", + "type": "text" + }, + { + "bbox": [ + 261, + 468, + 290, + 478 + ], + "score": 0.88, + "content": "8 4 \\times 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 466, + 294, + 480 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 542 + ], + "lines": [ + { + "bbox": [ + 106, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 166, + 499 + ], + "score": 1.0, + "content": "Architecture.", + "type": "text" + }, + { + "bbox": [ + 182, + 487, + 294, + 500 + ], + "score": 1.0, + "content": "In all our experiments,", + "type": "text" + }, + { + "bbox": [ + 295, + 488, + 306, + 499 + ], + "score": 0.75, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 487, + 506, + 500 + ], + "score": 1.0, + "content": "is represented by a ResNet12 with widths", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "[64, 160, 320, 640]. We chose this architecture, initially introduced by Lee et al. (2019), as it is", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 510, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 505, + 522 + ], + "score": 1.0, + "content": "the one which is most frequently adopted by recent FSL methods. Unlike most methods, we do not", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "use a DropBlock regulariser (Ghiasi et al., 2018), as we did not notice it to meaningfully contribute", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 532, + 172, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 172, + 544 + ], + "score": 1.0, + "content": "to performance.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 551, + 505, + 607 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "Optimisation. To train all the models used for our experiments, unless differently specified, we", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "used a SGD optimiser with Nesterov momentum, weight decay of 0.0005 and initial learning rate of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 573, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 473, + 586 + ], + "score": 1.0, + "content": "0.1. For miniImageNet and CIFAR-FS we decrease the learning rate by a factor of 10 after", + "type": "text" + }, + { + "bbox": [ + 473, + 574, + 493, + 584 + ], + "score": 0.87, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 573, + 506, + 586 + ], + "score": 1.0, + "content": "of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 585, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 598 + ], + "score": 1.0, + "content": "epochs have been trained, and train for a total of 120 epochs. As data augmentations, we use random", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 594, + 267, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 267, + 610 + ], + "score": 1.0, + "content": "horizontal flipping and centre cropping.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 612, + 505, + 690 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "score": 1.0, + "content": "Only for the experiments of Sec. 4.4, we slightly change our training setup. On CIFAR-FS, we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 624, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 479, + 636 + ], + "score": 1.0, + "content": "increase the number of training epochs from 120 to 240, which improved accuracy of about", + "type": "text" + }, + { + "bbox": [ + 479, + 624, + 501, + 634 + ], + "score": 0.87, + "content": "0 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 624, + 505, + 636 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "score": 1.0, + "content": "For tieredImageNet, we train for 120 epochs and decrease the learning rate by a factor of 10 after", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 645, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 126, + 656 + ], + "score": 0.84, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 645, + 146, + 659 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 146, + 646, + 166, + 656 + ], + "score": 0.86, + "content": "7 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 645, + 506, + 659 + ], + "score": 1.0, + "content": "of the training progress. For tieredImageNet only we increased the batch size to", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 656, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 505, + 669 + ], + "score": 1.0, + "content": "1024, as we found it being beneficial. For the other datasets it did not improve performance. These", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 668, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 680 + ], + "score": 1.0, + "content": "changes affect all our methods and baselines: NCA, Prototypical Networks (with both old and new", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 678, + 307, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 307, + 691 + ], + "score": 1.0, + "content": "batch setup), and SimpleShot (Wang et al., 2019).", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "Projection network. 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method1-shot5-shot1-shot5-shot
NCA62.52 ± 0.2478.3 ± 0.1472.48 ± 0.4085.13± 0.29
NCA multi-layer63.21 ± 0.0879.27 ±0.0872.44 ± 0.3685.42 ± 0.29
NCA (ours) multi-layer + ss-79.79 ± 0.08-85.66 ± 0.32
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The NCA can only be optimised in the 5-shot case, since there are not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 176, + 506, + 192 + ], + "spans": [ + { + "bbox": [ + 104, + 176, + 506, + 192 + ], + "score": 1.0, + "content": "enough positives distances in the 1-shot case. Support set is optimised for 5 epochs using Adam with learning", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 187, + 333, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 333, + 199 + ], + "score": 1.0, + "content": "rate 0.0001 and weight decay 0.0005. For details, see Sec. A.1", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6.5 + } + ], + "index": 2.0 + }, + { + "type": "title", + "bbox": [ + 108, + 221, + 400, + 232 + ], + "lines": [ + { + "bbox": [ + 106, + 220, + 401, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 220, + 401, + 233 + ], + "score": 1.0, + "content": "A.3 DIFFERENCES BETWEEN THE NCA AND CONTRASTIVE LOSSES", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 241, + 505, + 329 + ], + "lines": [ + { + "bbox": [ + 105, + 240, + 506, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 506, + 254 + ], + "score": 1.0, + "content": "Eq. 3 is similar to the contrastive loss functions (Khosla et al., 2020; Chen et al., 2020a) that are", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 253, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 505, + 265 + ], + "score": 1.0, + "content": "used in self-supervised learning and representation learning. The main differences are that 1.) In", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "contrastive losses, the denominator only contains negative pairs and 2.) the inner sum in the nu-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 505, + 287 + ], + "score": 1.0, + "content": "merator is moved outside of the logarithm in the supervised contrastive loss function from Khosla", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "et al. (2020). 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Using the supervised contrastive loss we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 308, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 205, + 320 + ], + "score": 1.0, + "content": "only managed to obtain", + "type": "text" + }, + { + "bbox": [ + 206, + 308, + 238, + 318 + ], + "score": 0.84, + "content": "5 1 . 0 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 308, + 286, + 320 + ], + "score": 1.0, + "content": "1-shot and", + "type": "text" + }, + { + "bbox": [ + 286, + 308, + 318, + 318 + ], + "score": 0.84, + "content": "6 3 . 3 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 308, + 506, + 320 + ], + "score": 1.0, + "content": "5-shot performance on the miniImagenet test", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 123, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 123, + 330 + ], + "score": 1.0, + "content": "set.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 240, + 506, + 330 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 344, + 249, + 355 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 251, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 251, + 356 + ], + "score": 1.0, + "content": "A.4 IMPLEMENTATION DETAILS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 368, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "score": 1.0, + "content": "Benchmarks. In our experiments, we use three popular FSL benchmarks. miniImageNet (Vinyals", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "score": 1.0, + "content": "et al., 2016) is a subset of ImageNet generated by randomly sampling 100 classes, each with 600 ran-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "domly sampled images. We adopt the commonly used splits of Ravi & Larochelle (2017) who use", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 414 + ], + "score": 1.0, + "content": "64 classes for meta-training, 16 for meta-validation and 20 for meta-testing. CIFAR-FS was pro-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 412, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 104, + 412, + 506, + 425 + ], + "score": 1.0, + "content": "posed by Bertinetto et al. (2019) as an anagolous version of miniImagenet for CIFAR-100. It uses the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "score": 1.0, + "content": "same sized splits and same number of images per split as miniImageNet. tieredImageNet (Ren et al.,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 505, + 447 + ], + "score": 1.0, + "content": "2018) is also constructed from ImageNet, but contains 608 classes, with 351 training classes, 97 val-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 445, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 458 + ], + "score": 1.0, + "content": "idation classes and 160 test classes. The class split have been generated using WordNet (Miller,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 455, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 505, + 469 + ], + "score": 1.0, + "content": "1995) to ensure that the training classes are semantically “distant” to the validation and test classes.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 466, + 294, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 261, + 480 + ], + "score": 1.0, + "content": "For all datasets, we use images of size", + "type": "text" + }, + { + "bbox": [ + 261, + 468, + 290, + 478 + ], + "score": 0.88, + "content": "8 4 \\times 8 4", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 466, + 294, + 480 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5, + "bbox_fs": [ + 104, + 369, + 506, + 480 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 487, + 505, + 542 + ], + "lines": [ + { + "bbox": [ + 106, + 487, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 166, + 499 + ], + "score": 1.0, + "content": "Architecture.", + "type": "text" + }, + { + "bbox": [ + 182, + 487, + 294, + 500 + ], + "score": 1.0, + "content": "In all our experiments,", + "type": "text" + }, + { + "bbox": [ + 295, + 488, + 306, + 499 + ], + "score": 0.75, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 487, + 506, + 500 + ], + "score": 1.0, + "content": "is represented by a ResNet12 with widths", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "[64, 160, 320, 640]. We chose this architecture, initially introduced by Lee et al. (2019), as it is", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 510, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 505, + 522 + ], + "score": 1.0, + "content": "the one which is most frequently adopted by recent FSL methods. Unlike most methods, we do not", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "use a DropBlock regulariser (Ghiasi et al., 2018), as we did not notice it to meaningfully contribute", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 532, + 172, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 172, + 544 + ], + "score": 1.0, + "content": "to performance.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 487, + 506, + 544 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 551, + 505, + 607 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "Optimisation. To train all the models used for our experiments, unless differently specified, we", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "used a SGD optimiser with Nesterov momentum, weight decay of 0.0005 and initial learning rate of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 573, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 473, + 586 + ], + "score": 1.0, + "content": "0.1. For miniImageNet and CIFAR-FS we decrease the learning rate by a factor of 10 after", + "type": "text" + }, + { + "bbox": [ + 473, + 574, + 493, + 584 + ], + "score": 0.87, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 573, + 506, + 586 + ], + "score": 1.0, + "content": "of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 585, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 598 + ], + "score": 1.0, + "content": "epochs have been trained, and train for a total of 120 epochs. As data augmentations, we use random", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 594, + 267, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 267, + 610 + ], + "score": 1.0, + "content": "horizontal flipping and centre cropping.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 552, + 506, + 610 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 612, + 505, + 690 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "score": 1.0, + "content": "Only for the experiments of Sec. 4.4, we slightly change our training setup. On CIFAR-FS, we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 624, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 479, + 636 + ], + "score": 1.0, + "content": "increase the number of training epochs from 120 to 240, which improved accuracy of about", + "type": "text" + }, + { + "bbox": [ + 479, + 624, + 501, + 634 + ], + "score": 0.87, + "content": "0 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 624, + 505, + 636 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 634, + 505, + 647 + ], + "score": 1.0, + "content": "For tieredImageNet, we train for 120 epochs and decrease the learning rate by a factor of 10 after", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 645, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 126, + 656 + ], + "score": 0.84, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 645, + 146, + 659 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 146, + 646, + 166, + 656 + ], + "score": 0.86, + "content": "7 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 645, + 506, + 659 + ], + "score": 1.0, + "content": "of the training progress. For tieredImageNet only we increased the batch size to", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 656, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 505, + 669 + ], + "score": 1.0, + "content": "1024, as we found it being beneficial. For the other datasets it did not improve performance. These", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 668, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 680 + ], + "score": 1.0, + "content": "changes affect all our methods and baselines: NCA, Prototypical Networks (with both old and new", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 678, + 307, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 307, + 691 + ], + "score": 1.0, + "content": "batch setup), and SimpleShot (Wang et al., 2019).", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 611, + 506, + 691 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "Projection network. Similarly to (Khosla et al., 2020; Chen et al., 2020a), we also experimented", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "(for both PNS and NCA) with a projection network (but only for the comparison of Sec. 4.4). The", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 104, + 718, + 507, + 735 + ], + "spans": [ + { + "bbox": [ + 104, + 718, + 277, + 735 + ], + "score": 1.0, + "content": "projection network is a single linear layer", + "type": "text" + }, + { + "bbox": [ + 278, + 720, + 328, + 731 + ], + "score": 0.91, + "content": "A \\in \\mathbb { R } ^ { M \\times P }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 718, + 426, + 735 + ], + "score": 1.0, + "content": "that is placed on top of", + "type": "text" + }, + { + "bbox": [ + 426, + 721, + 437, + 732 + ], + "score": 0.88, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 718, + 507, + 735 + ], + "score": 1.0, + "content": "at training time,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 233, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 133, + 245 + ], + "score": 1.0, + "content": "where", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 133, + 234, + 145, + 244 + ], + "score": 0.74, + "content": "M", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 145, + 233, + 325, + 245 + ], + "score": 1.0, + "content": "is the output dimension of the neural network", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 325, + 234, + 335, + 245 + ], + "score": 0.87, + "content": "f _ { \\theta }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 336, + 233, + 352, + 245 + ], + "score": 1.0, + "content": "and", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 353, + 234, + 362, + 243 + ], + "score": 0.82, + "content": "P", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 362, + 233, + 466, + 245 + ], + "score": 1.0, + "content": "is the output dimension of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 466, + 234, + 475, + 243 + ], + "score": 0.69, + "content": "A", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 475, + 233, + 505, + 245 + ], + "score": 1.0, + "content": ", which", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 244, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 327, + 258 + ], + "score": 1.0, + "content": "can be considered as a hyper-parameter. The output of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 327, + 245, + 336, + 254 + ], + "score": 0.8, + "content": "A", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 336, + 244, + 505, + 258 + ], + "score": 1.0, + "content": "is only used during training. At test time,", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 256, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 106, + 256, + 217, + 268 + ], + "score": 1.0, + "content": "we do not use the output of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 217, + 256, + 225, + 265 + ], + "score": 0.74, + "content": "A", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 226, + 256, + 344, + 268 + ], + "score": 1.0, + "content": "and directly use the output of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 345, + 256, + 355, + 267 + ], + "score": 0.86, + "content": "f _ { \\theta }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 355, + 256, + 505, + 268 + ], + "score": 1.0, + "content": ". For CIFAR-FS and tieredImageNet,", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "we found this did not help performance. For miniImageNet however we found that this improved", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 211, + 290 + ], + "score": 1.0, + "content": "performance, and we set", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 211, + 277, + 253, + 288 + ], + "score": 0.89, + "content": "P = 1 2 8", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 253, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "(which worked best for both PNS and NCA). Note that this", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "is not an unfair advantage over other methods. Compared to SimpleShot (Wang et al., 2019) and", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 298, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 312 + ], + "score": 1.0, + "content": "other simple baselines, we actually use fewer parameters without the projection network (effectively", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 309, + 506, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 323 + ], + "score": 1.0, + "content": "making our ResNet12 a ResNet11) since they use an extra fully connected layer to minimise cross", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 320, + 219, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 219, + 335 + ], + "score": 1.0, + "content": "entropy during pre-training.", + "type": "text", + "cross_page": true + } + ], + "index": 17 + } + ], + "index": 47, + "bbox_fs": [ + 104, + 698, + 507, + 735 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 145, + 90, + 464, + 156 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 258, + 81, + 312, + 90 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 258, + 79, + 313, + 92 + ], + "spans": [ + { + "bbox": [ + 258, + 79, + 313, + 92 + ], + "score": 1.0, + "content": "miniImageNet", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_caption", + "bbox": [ + 383, + 81, + 423, + 90 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 383, + 80, + 424, + 92 + ], + "spans": [ + { + "bbox": [ + 383, + 80, + 424, + 92 + ], + "score": 1.0, + "content": "CIFAR-FS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 145, + 90, + 464, + 156 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 145, + 90, + 464, + 156 + ], + "spans": [ + { + "bbox": [ + 145, + 90, + 464, + 156 + ], + "score": 0.949, + "html": "
method1-shot5-shot1-shot5-shot
PNs (SimpleShot)57.99 ±0.2174.33 ± 0.1653.76 ±0.2268.54± 0.19
PNs (ours)62.79 ±0.1278.82 ± 0.0959.60 ± 0.1374.64± 0.11
NCA (SimpleShot)61.21 ± 0.2276.39 ± 0.1659.41± 0.2473.29 ± 0.19
NCA (ours)64.94 ± 0.1380.12 ±0.0962.07 ± 0.1476.26 ±0.10
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The output of", + "type": "text" + }, + { + "bbox": [ + 327, + 245, + 336, + 254 + ], + "score": 0.8, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 244, + 505, + 258 + ], + "score": 1.0, + "content": "is only used during training. At test time,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 256, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 106, + 256, + 217, + 268 + ], + "score": 1.0, + "content": "we do not use the output of", + "type": "text" + }, + { + "bbox": [ + 217, + 256, + 225, + 265 + ], + "score": 0.74, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 226, + 256, + 344, + 268 + ], + "score": 1.0, + "content": "and directly use the output of", + "type": "text" + }, + { + "bbox": [ + 345, + 256, + 355, + 267 + ], + "score": 0.86, + "content": "f _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 355, + 256, + 505, + 268 + ], + "score": 1.0, + "content": ". For CIFAR-FS and tieredImageNet,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "we found this did not help performance. For miniImageNet however we found that this improved", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 211, + 290 + ], + "score": 1.0, + "content": "performance, and we set", + "type": "text" + }, + { + "bbox": [ + 211, + 277, + 253, + 288 + ], + "score": 0.89, + "content": "P = 1 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "(which worked best for both PNS and NCA). Note that this", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "is not an unfair advantage over other methods. 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method1-shot5-shot1-shot5-shot
PNs (SimpleShot)57.99 ±0.2174.33 ± 0.1653.76 ±0.2268.54± 0.19
PNs (ours)62.79 ±0.1278.82 ± 0.0959.60 ± 0.1374.64± 0.11
NCA (SimpleShot)61.21 ± 0.2276.39 ± 0.1659.41± 0.2473.29 ± 0.19
NCA (ours)64.94 ± 0.1380.12 ±0.0962.07 ± 0.1476.26 ±0.10
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In particular:", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 366, + 505, + 412 + ] + }, + { + "type": "list", + "bbox": [ + 132, + 420, + 505, + 595 + ], + "lines": [ + { + "bbox": [ + 132, + 419, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 132, + 419, + 505, + 432 + ], + "score": 1.0, + "content": "• We always use the normalisation strategy of Wang et al. (2019), as it is beneficial also for", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 429, + 165, + 442 + ], + "spans": [ + { + "bbox": [ + 141, + 429, + 165, + 442 + ], + "score": 1.0, + "content": "PNs.", + "type": "text" + } + ], + "index": 24, + "is_list_end_line": true + }, + { + "bbox": [ + 137, + 441, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 137, + 441, + 505, + 454 + ], + "score": 1.0, + "content": "Unless expressively specified, we always used PNs 5-shot model, which in our implemen-", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 142, + 452, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 142, + 452, + 505, + 465 + ], + "score": 1.0, + "content": "tation outperforms the 1-shot model (for both 1-shot and 5-shot evaluation). Instead, (Snell", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 463, + 377, + 475 + ], + "spans": [ + { + "bbox": [ + 141, + 463, + 377, + 475 + ], + "score": 1.0, + "content": "et al., 2017) train and tests with the same number of shots.", + "type": "text" + } + ], + "index": 27, + "is_list_end_line": true + }, + { + "bbox": [ + 139, + 475, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 139, + 475, + 506, + 487 + ], + "score": 1.0, + "content": "Apart from the episodes hyper-parameters of PNs, which we did search and optimise over", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 141, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 141, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "to create the plots of Fig. 2, the only other hyper-parameters of PNs are those related to the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 497, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 141, + 497, + 505, + 508 + ], + "score": 1.0, + "content": "training schedule, which are the same as the NCA. To set them, we started from the simple", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 141, + 507, + 505, + 520 + ], + "score": 1.0, + "content": "SGD schedule used by Wang et al. (2019) and only marginally modified it by increasing the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 518, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 141, + 518, + 505, + 532 + ], + "score": 1.0, + "content": "number of training epochs to 120, increasing the batch size to 512 and setting weight decay", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 529, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 141, + 529, + 220, + 541 + ], + "score": 1.0, + "content": "and learning rate to", + "type": "text" + }, + { + "bbox": [ + 220, + 529, + 245, + 540 + ], + "score": 0.34, + "content": "5 e { - 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 529, + 505, + 541 + ], + "score": 1.0, + "content": "and 0.1, respectively. As a sanity check, we trained both the NCA", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 540, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 142, + 540, + 506, + 552 + ], + "score": 1.0, + "content": "and PNs with the exact training schedule used by Wang et al. (2019). Results are reported", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 141, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "in Table 6, and show that the schedule we used for this paper is considerably better for", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 142, + 562, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 142, + 562, + 505, + 574 + ], + "score": 1.0, + "content": "both PNs and NCA. In general, we observed that the modifications were beneficial for both", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 141, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "NCA and PNs, and improvements in performance in NCA and PNs were highly correlated.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 142, + 584, + 481, + 596 + ], + "spans": [ + { + "bbox": [ + 142, + 584, + 481, + 596 + ], + "score": 1.0, + "content": "This is to be expected given the high similarity between the two methods and losses.", + "type": "text" + } + ], + "index": 38, + "is_list_end_line": true + } + ], + "index": 30.5, + "bbox_fs": [ + 132, + 419, + 506, + 596 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 608, + 288, + 619 + ], + "lines": [ + { + "bbox": [ + 106, + 608, + 289, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 608, + 289, + 621 + ], + "score": 1.0, + "content": "A.6 ADDITIONAL RESULTS FOR SEC. 4.2", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39, + "bbox_fs": [ + 106, + 608, + 289, + 621 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 629, + 323, + 640 + ], + "lines": [ + { + "bbox": [ + 105, + 627, + 324, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 324, + 642 + ], + "score": 1.0, + "content": "Fig. 5 complements the results of Fig. 2 from Sec. 4.2", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 627, + 324, + 642 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 653, + 287, + 664 + ], + "lines": [ + { + "bbox": [ + 106, + 653, + 289, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 653, + 289, + 666 + ], + "score": 1.0, + "content": "A.7 ADDITIONAL RESULTS FOR SEC. 4.3", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 677, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "Matching Networks (Vinyals et al., 2016) are closely related to PNs (Snell et al., 2017), and even", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 687, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 506, + 701 + ], + "score": 1.0, + "content": "equivalent in the 1-shot case. The difference is in the use of the support set in the multi-shot case.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "Whereas PNs generate prototypes by averaging the embedding of the support set, Matching Net-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "works adopt a weighted nearest-neighbour approach using an attention mechanism. If the attention", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "mechanism is a softmax over the distances (which the authors suggest in Sec. 2.1.1 of their paper),", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "score": 1.0, + "content": "we obtain the soft-assignment approach discussed in Sec. 3.4 of this paper. The only two differences", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "between Matching Networks with a softmax attention mechanism and PNs are the lack of protoypes", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "score": 1.0, + "content": "and the use of the cosine distance, instead of the Euclidean distance (Snell et al. (2017) has shown", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 441, + 321, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 321, + 453 + ], + "score": 1.0, + "content": "that the Euclidean distance is a better choice in FSL).", + "type": "text", + "cross_page": true + } + ], + "index": 15 + } + ], + "index": 44, + "bbox_fs": [ + 106, + 677, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 82, + 460, + 191 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 82, + 460, + 191 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 82, + 460, + 191 + ], + "spans": [ + { + "bbox": [ + 146, + 82, + 460, + 191 + ], + "score": 0.972, + "type": "image", + "image_path": "1a21157d9635de40bd189e50aa5d659788e69c1d7626e81e35fb91c9365b4c2c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 82, + 460, + 118.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 118.33333333333334, + 460, + 154.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 154.66666666666669, + 460, + 191.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 202, + 505, + 243 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 203, + 504, + 213 + ], + "spans": [ + { + "bbox": [ + 107, + 203, + 504, + 213 + ], + "score": 1.0, + "content": "Figure 5: 1-shot (left) and 5-shot accuracies (right) on the validation set of miniImageNet for different batch", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 213, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 441, + 223 + ], + "score": 1.0, + "content": "sizes. Models are trained using NCA or Proto-nets with different configurations: 1-shot with", + "type": "text" + }, + { + "bbox": [ + 441, + 213, + 464, + 222 + ], + "score": 0.89, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 213, + 505, + 223 + ], + "score": 1.0, + "content": "and 5-shot", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 222, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 222, + 125, + 234 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 125, + 223, + 149, + 232 + ], + "score": 0.87, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 222, + 505, + 234 + ], + "score": 1.0, + "content": ", 16 or 32. Reported values correspond to the mean accuracy of five models trained with different", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 233, + 271, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 233, + 271, + 244 + ], + "score": 1.0, + "content": "random seeds. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "image", + "bbox": [ + 126, + 256, + 483, + 361 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 126, + 256, + 483, + 361 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 126, + 256, + 483, + 361 + ], + "spans": [ + { + "bbox": [ + 126, + 256, + 483, + 361 + ], + "score": 0.969, + "type": "image", + "image_path": "586df99c2485d5b98fbdda21783b89aab8b28de2fff9ca8be0efc3534b6a407a.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 126, + 256, + 483, + 291.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 126, + 291.0, + 483, + 326.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 126, + 326.0, + 483, + 361.0 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 364, + 504, + 385 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Figure 6: Ablation experiments on NCA and Matching Networks, both on batches or episodes of size 256 on", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 373, + 491, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 373, + 491, + 386 + ], + "score": 1.0, + "content": "the validation set of miniImageNet and CIFAR-FS. All methods use soft assignment (Sec. 3.4) at test time.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + } + ], + "index": 9.25 + }, + { + "type": "text", + "bbox": [ + 107, + 408, + 505, + 452 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "score": 1.0, + "content": "we obtain the soft-assignment approach discussed in Sec. 3.4 of this paper. The only two differences", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "between Matching Networks with a softmax attention mechanism and PNs are the lack of protoypes", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 442 + ], + "score": 1.0, + "content": "and the use of the cosine distance, instead of the Euclidean distance (Snell et al. (2017) has shown", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 441, + 321, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 321, + 453 + ], + "score": 1.0, + "content": "that the Euclidean distance is a better choice in FSL).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 106, + 457, + 505, + 568 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 471 + ], + "score": 1.0, + "content": "Given this similarity, and because of the relevance Matching Networks has in the few-shot learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 469, + 505, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 481 + ], + "score": 1.0, + "content": "community, we repeated the ablation experiment of Fig. 4. The results can be found in Table 6.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 480, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 505, + 492 + ], + "score": 1.0, + "content": "In particular, we perform experiments on Matching Networks (without a Full Context Embedding)", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "using the softmax attention mechanism, and using a Euclidean distance metric instead of a cosine", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "score": 1.0, + "content": "distance metric. At training time, Matching Networks corresponds to the “no prototype” method", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 511, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 104, + 511, + 506, + 526 + ], + "score": 1.0, + "content": "in row 6 of Fig. 4. Therefore, the only difference between Matching Networks and NCA during", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 523, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 506, + 536 + ], + "score": 1.0, + "content": "training is the separation between the support and query set, leaving us with only one ablation to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 534, + 506, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 547 + ], + "score": 1.0, + "content": "perform. At test time, evaluating Matching Networks is equivalent to using the soft-assignment", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "approach described in Sec. 3.4. Therefore, for a fair comparison, for both NCA and “NCA fixed-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 557, + 444, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 557, + 444, + 568 + ], + "score": 1.0, + "content": "batch composition” methods we also use the soft-assignment evaluation at test time.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 107, + 573, + 505, + 640 + ], + "lines": [ + { + "bbox": [ + 106, + 574, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 585 + ], + "score": 1.0, + "content": "As we can see, disregarding the separation between the support and query set also improves the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 584, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 584, + 506, + 597 + ], + "score": 1.0, + "content": "performance of Matching Networks, and significantly so. This corroborates the findings of Sec. 4.3:", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 594, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 609 + ], + "score": 1.0, + "content": "the separation of roles between images in the support and query sets, typical of episodic learning,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "score": 1.0, + "content": "is detrimental to the performance of not only PN, but also Matching Networks. Instead, using the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 616, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 631 + ], + "score": 1.0, + "content": "(closely related) NCA on standard random mini-batches allows for better exploitation of the training", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 628, + 357, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 357, + 640 + ], + "score": 1.0, + "content": "data, while simultaneously simplifying the training procedure.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 649, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "Ablation experiments for different batch sizes. We repeated the ablation experiments done for", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "score": 1.0, + "content": "batch size 256 (Fig. 4) also for size 128 and 512. Results can be found in Fig. 7 and Fig. 8. As we", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "can see, the overall trend is maintained. A difference is the meaningful gap in performance between", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 682, + 390, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 390, + 694 + ], + "score": 1.0, + "content": "row 1 and 3 in Fig. 7 (size 128), which disappers in Fig. 8 (batch 512).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "This is likely due to the number of positives available in an excessively small batch size. Since our", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 710, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 504, + 722 + ], + "score": 1.0, + "content": "vanilla NCA relies on using distance pairs and creates batches by simply sampling images randomly", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 720, + 506, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 506, + 732 + ], + "score": 1.0, + "content": "from the dataset, there is a limit to how small a batch can be (which depends on the number of classes", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + } + ], + "page_idx": 15, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 301, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 306, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 82, + 460, + 191 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 82, + 460, + 191 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 82, + 460, + 191 + ], + "spans": [ + { + "bbox": [ + 146, + 82, + 460, + 191 + ], + "score": 0.972, + "type": "image", + "image_path": "1a21157d9635de40bd189e50aa5d659788e69c1d7626e81e35fb91c9365b4c2c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 82, + 460, + 118.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 118.33333333333334, + 460, + 154.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 154.66666666666669, + 460, + 191.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 202, + 505, + 243 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 203, + 504, + 213 + ], + "spans": [ + { + "bbox": [ + 107, + 203, + 504, + 213 + ], + "score": 1.0, + "content": "Figure 5: 1-shot (left) and 5-shot accuracies (right) on the validation set of miniImageNet for different batch", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 213, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 441, + 223 + ], + "score": 1.0, + "content": "sizes. Models are trained using NCA or Proto-nets with different configurations: 1-shot with", + "type": "text" + }, + { + "bbox": [ + 441, + 213, + 464, + 222 + ], + "score": 0.89, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 213, + 505, + 223 + ], + "score": 1.0, + "content": "and 5-shot", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 222, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 222, + 125, + 234 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 125, + 223, + 149, + 232 + ], + "score": 0.87, + "content": "a = 8", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 222, + 505, + 234 + ], + "score": 1.0, + "content": ", 16 or 32. Reported values correspond to the mean accuracy of five models trained with different", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 233, + 271, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 233, + 271, + 244 + ], + "score": 1.0, + "content": "random seeds. Please see Sec. 4.2 for details.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "image", + "bbox": [ + 126, + 256, + 483, + 361 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 126, + 256, + 483, + 361 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 126, + 256, + 483, + 361 + ], + "spans": [ + { + "bbox": [ + 126, + 256, + 483, + 361 + ], + "score": 0.969, + "type": "image", + "image_path": "586df99c2485d5b98fbdda21783b89aab8b28de2fff9ca8be0efc3534b6a407a.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 126, + 256, + 483, + 291.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 126, + 291.0, + 483, + 326.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 126, + 326.0, + 483, + 361.0 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 364, + 504, + 385 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Figure 6: Ablation experiments on NCA and Matching Networks, both on batches or episodes of size 256 on", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 373, + 491, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 373, + 491, + 386 + ], + "score": 1.0, + "content": "the validation set of miniImageNet and CIFAR-FS. All methods use soft assignment (Sec. 3.4) at test time.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + } + ], + "index": 9.25 + }, + { + "type": "text", + "bbox": [ + 107, + 408, + 505, + 452 + ], + "lines": [], + "index": 13.5, + "bbox_fs": [ + 105, + 408, + 505, + 453 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 457, + 505, + 568 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 471 + ], + "score": 1.0, + "content": "Given this similarity, and because of the relevance Matching Networks has in the few-shot learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 469, + 505, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 481 + ], + "score": 1.0, + "content": "community, we repeated the ablation experiment of Fig. 4. The results can be found in Table 6.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 480, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 505, + 492 + ], + "score": 1.0, + "content": "In particular, we perform experiments on Matching Networks (without a Full Context Embedding)", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "using the softmax attention mechanism, and using a Euclidean distance metric instead of a cosine", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 506, + 515 + ], + "score": 1.0, + "content": "distance metric. At training time, Matching Networks corresponds to the “no prototype” method", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 511, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 104, + 511, + 506, + 526 + ], + "score": 1.0, + "content": "in row 6 of Fig. 4. Therefore, the only difference between Matching Networks and NCA during", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 523, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 506, + 536 + ], + "score": 1.0, + "content": "training is the separation between the support and query set, leaving us with only one ablation to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 534, + 506, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 547 + ], + "score": 1.0, + "content": "perform. At test time, evaluating Matching Networks is equivalent to using the soft-assignment", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 104, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "approach described in Sec. 3.4. Therefore, for a fair comparison, for both NCA and “NCA fixed-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 557, + 444, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 557, + 444, + 568 + ], + "score": 1.0, + "content": "batch composition” methods we also use the soft-assignment evaluation at test time.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 20.5, + "bbox_fs": [ + 104, + 455, + 506, + 568 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 573, + 505, + 640 + ], + "lines": [ + { + "bbox": [ + 106, + 574, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 585 + ], + "score": 1.0, + "content": "As we can see, disregarding the separation between the support and query set also improves the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 584, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 104, + 584, + 506, + 597 + ], + "score": 1.0, + "content": "performance of Matching Networks, and significantly so. This corroborates the findings of Sec. 4.3:", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 594, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 609 + ], + "score": 1.0, + "content": "the separation of roles between images in the support and query sets, typical of episodic learning,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "score": 1.0, + "content": "is detrimental to the performance of not only PN, but also Matching Networks. Instead, using the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 616, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 631 + ], + "score": 1.0, + "content": "(closely related) NCA on standard random mini-batches allows for better exploitation of the training", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 628, + 357, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 357, + 640 + ], + "score": 1.0, + "content": "data, while simultaneously simplifying the training procedure.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5, + "bbox_fs": [ + 104, + 574, + 506, + 640 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 649, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "Ablation experiments for different batch sizes. We repeated the ablation experiments done for", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 673 + ], + "score": 1.0, + "content": "batch size 256 (Fig. 4) also for size 128 and 512. Results can be found in Fig. 7 and Fig. 8. As we", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "can see, the overall trend is maintained. A difference is the meaningful gap in performance between", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 682, + 390, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 390, + 694 + ], + "score": 1.0, + "content": "row 1 and 3 in Fig. 7 (size 128), which disappers in Fig. 8 (batch 512).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 648, + 506, + 694 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "This is likely due to the number of positives available in an excessively small batch size. Since our", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 710, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 504, + 722 + ], + "score": 1.0, + "content": "vanilla NCA relies on using distance pairs and creates batches by simply sampling images randomly", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 720, + 506, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 506, + 732 + ], + "score": 1.0, + "content": "from the dataset, there is a limit to how small a batch can be (which depends on the number of classes", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 334, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 505, + 345 + ], + "score": 1.0, + "content": "of the dataset). As an example, consider the extreme case of a batch of size 4. For the datasets", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "considered, it is very likely that such a batch will contain no positive pairs. For a batch size of 128", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 505, + 369 + ], + "score": 1.0, + "content": "and a training set of 64 classes, with a parameter-free sampler the NCA will have in expectation only", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 506, + 379 + ], + "score": 1.0, + "content": "one positive pair per class. Conversely, the NCA ablation with a fixed batch composition (i.e. with a", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "score": 1.0, + "content": "set number of images per class) will have a higher number of positive pairs (at the cost of a reduced", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 389, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 401 + ], + "score": 1.0, + "content": "number of classes per batch). We believe this can explain the difference, as positive pairs constitute", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "a less frequent (and potentially more informative) training signal. For the sake of simplicity, and", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 423 + ], + "score": 1.0, + "content": "since this only affects smaller batch sizes, we opted to use a vanilla, parameter-free sampler for the", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 421, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 475, + 434 + ], + "score": 1.0, + "content": "NCA in the rest of our experiments. 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( m + n - 2 ) ! } w } \\\\ & { \\qquad = \\frac { 1 } { 2 } ( m + n ) ( m + n - 1 ) w } \\\\ & { \\qquad = \\frac { 1 } { 2 } ( m ^ { 2 } + 2 m n - m + n ^ { 2 } - n ) w } \\\\ & { \\qquad = \\frac { 1 } { 2 } ( m ( m - 1 ) + 2 m n + n ( n - 1 ) ) w } \\\\ & { \\qquad \\geq \\frac { 1 } { 2 } ( 2 m n ) w = w m n . } \\end{array}", + "type": "interline_equation", + "image_path": "8e8618f61e6e4dbcf13f817dae44879ada466c8a5289be0009de027ff15aa060.jpg" + } + ] + } + ], + "index": 31.5, + "virtual_lines": [ + { + "bbox": [ + 200, + 585, + 411, + 597.6 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 200, + 597.6, + 411, + 610.2 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 200, + 610.2, + 411, + 622.8000000000001 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 200, + 622.8000000000001, + 411, + 635.4000000000001 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 200, + 635.4000000000001, + 411, + 648.0000000000001 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 200, + 648.0000000000001, + 411, + 660.6000000000001 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 200, + 660.6000000000001, + 411, + 673.2000000000002 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 200, + 673.2000000000002, + 411, + 685.8000000000002 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 200, + 685.8000000000002, + 411, + 698.4000000000002 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 200, + 698.4000000000002, + 411, + 711.0000000000002 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 719, + 452, + 734 + ], + "lines": [ + { + "bbox": [ + 105, + 718, + 454, + 735 + ], + "spans": [ + { + "bbox": [ + 105, + 718, + 326, + 735 + ], + "score": 1.0, + "content": "Similarly, we can show for negative distance pairs that", + "type": "text" + }, + { + "bbox": [ + 327, + 720, + 449, + 734 + ], + "score": 0.93, + "content": "{ \\binom { w } { 2 } } ( m + n ) ^ { 2 } > w ( w - 1 ) m n", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 718, + 454, + 735 + ], + "score": 1.0, + "content": ":", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 718, + 454, + 735 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 205, + 80, + 406, + 148 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 205, + 80, + 406, + 148 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 205, + 80, + 406, + 148 + ], + "spans": [ + { + "bbox": [ + 205, + 80, + 406, + 148 + ], + "score": 0.976, + "html": "
rankmethod# pos#neg# total pairs
1NCA1792129024130816
25-shot a=1617605456056320
35-shot a=89606048061440
45-shot a=3221603240034560
51-shot a=84482822428672
", + "type": "table", + "image_path": "e041b4b0db49f93bc0e5285daf6406d82523b20300296106f1ff1bdcd0b86d41.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 205, + 80, + 406, + 93.6 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 205, + 93.6, + 406, + 107.19999999999999 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 205, + 107.19999999999999, + 406, + 120.79999999999998 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 205, + 120.79999999999998, + 406, + 134.39999999999998 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 205, + 134.39999999999998, + 406, + 147.99999999999997 + ], + "spans": [], + "index": 4 + } + ] + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 137, + 156, + 472, + 167 + ], + "lines": [ + { + "bbox": [ + 136, + 154, + 474, + 169 + ], + "spans": [ + { + "bbox": [ + 136, + 154, + 474, + 169 + ], + "score": 1.0, + "content": "Table 7: Number of positives and negatives used in the batch size 512 experiments of Fig. 2.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "interline_equation", + "bbox": [ + 205, + 203, + 406, + 294 + ], + "lines": [ + { + "bbox": [ + 205, + 203, + 406, + 294 + ], + "spans": [ + { + "bbox": [ + 205, + 203, + 406, + 294 + ], + "score": 0.94, + "content": "\\begin{array} { l } { { { \\binom { w } { 2 } } ( m + n ) ^ { 2 } = \\displaystyle \\frac { w ! } { 2 ! ( w - 2 ) ! } ( m ^ { 2 } + 2 m n + n ^ { 2 } ) } } \\\\ { { \\mathrm { } } } \\\\ { { \\mathrm { } = \\displaystyle \\frac { 1 } { 2 } w ( w - 1 ) ( m ^ { 2 } + 2 m n + n ^ { 2 } ) } } \\\\ { { \\mathrm { } } } \\\\ { { \\mathrm { } > \\displaystyle \\frac { 1 } { 2 } w ( w - 1 ) ( 2 m n ) } } \\\\ { { \\mathrm { } = w ( w - 1 ) m n . } } \\end{array}", + "type": "interline_equation", + "image_path": "b83c8ef008ebe0d15dc5377c9321fa75c9635c6c255492460feb513b6c7ea201.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 205, + 203, + 406, + 216.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 205, + 216.0, + 406, + 229.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 205, + 229.0, + 406, + 242.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 205, + 242.0, + 406, + 255.0 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 205, + 255.0, + 406, + 268.0 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 205, + 268.0, + 406, + 281.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 205, + 281.0, + 406, + 294.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 303, + 505, + 326 + ], + "lines": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "This means that the NCA has at least the same number of positives as Prototypical Networks, and", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 315, + 282, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 282, + 328 + ], + "score": 1.0, + "content": "always has strictly more negative distances.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 108, + 330, + 440, + 344 + ], + "lines": [ + { + "bbox": [ + 105, + 329, + 441, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 330, + 346 + ], + "score": 1.0, + "content": "The total number of extra pairs that NCA can rely on is", + "type": "text" + }, + { + "bbox": [ + 331, + 331, + 437, + 345 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\frac { w } { 2 } ( w ( m ^ { 2 } + n ^ { 2 } ) - m - n ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 329, + 441, + 346 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 357, + 415, + 368 + ], + "lines": [ + { + "bbox": [ + 106, + 357, + 415, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 415, + 369 + ], + "score": 1.0, + "content": "A.9 DETAILS ABOUT NUMBER OF PAIRS DESCRIPTION OF SECTION 4.2", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 377, + 505, + 443 + ], + "lines": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 505, + 390 + ], + "score": 1.0, + "content": "In Table 7 we plot the number of positives and negatives (gradients contributing to the loss) for the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "score": 1.0, + "content": "NCA and different episodic configurations of PNs, to see whether the difference in performance can", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 399, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 506, + 412 + ], + "score": 1.0, + "content": "be explained by the difference in the number of distance pairs that can be exploited in a certain batch", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 505, + 422 + ], + "score": 1.0, + "content": "configuration. This is often true, as the ranking can almost be fully explained by the number of total", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 421, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 104, + 421, + 437, + 434 + ], + "score": 1.0, + "content": "pairs in the right column. However, there are two exceptions to this: 5-shot with", + "type": "text" + }, + { + "bbox": [ + 437, + 421, + 459, + 432 + ], + "score": 0.8, + "content": "\\mathsf { a } { = } 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 421, + 506, + 434 + ], + "score": 1.0, + "content": "and 5-shot", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 432, + 147, + 444 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 126, + 444 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 127, + 433, + 143, + 442 + ], + "score": 0.76, + "content": "\\scriptstyle \\mathbf { a } = { } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 432, + 147, + 444 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 106, + 449, + 505, + 538 + ], + "lines": [ + { + "bbox": [ + 105, + 448, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 430, + 462 + ], + "score": 1.0, + "content": "To understand this, we can see that the number of positive pairs is much higher for", + "type": "text" + }, + { + "bbox": [ + 430, + 450, + 452, + 460 + ], + "score": 0.84, + "content": "_ { \\mathrm { a } = 1 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 448, + 485, + 462 + ], + "score": 1.0, + "content": "than for", + "type": "text" + }, + { + "bbox": [ + 485, + 450, + 501, + 460 + ], + "score": 0.78, + "content": "\\scriptstyle \\mathrm { a = } 8", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 448, + 505, + 462 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 459, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 505, + 473 + ], + "score": 1.0, + "content": "Since the positive pairs constitute a less frequent (and potentially more informative) training signal,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 471, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 249, + 482 + ], + "score": 1.0, + "content": "this can explain the difference. The", + "type": "text" + }, + { + "bbox": [ + 250, + 471, + 271, + 482 + ], + "score": 0.78, + "content": "\\scriptstyle \\mathbf { a } = 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 471, + 479, + 482 + ], + "score": 1.0, + "content": "variant has an even higher number of positives than", + "type": "text" + }, + { + "bbox": [ + 480, + 471, + 501, + 482 + ], + "score": 0.83, + "content": "\\mathsf { a } { = } 1 6", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 471, + 505, + 482 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 481, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 496 + ], + "score": 1.0, + "content": "but the loss in performance there could be explained by a drastically lower number of negatives,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 505, + 505 + ], + "score": 1.0, + "content": "and by the fact that the number of ways used during training is lower. So, while indeed generally", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 503, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 506, + 518 + ], + "score": 1.0, + "content": "speaking the higher number of pairs the better (which is also corroborated by Fig. 3, where moving", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 515, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 155, + 527 + ], + "score": 1.0, + "content": "right on the", + "type": "text" + }, + { + "bbox": [ + 155, + 516, + 162, + 525 + ], + "score": 0.26, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 515, + 505, + 527 + ], + "score": 1.0, + "content": "-axis sees higher performance for both NCA and PNs), one should also consider how", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 526, + 495, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 526, + 495, + 538 + ], + "score": 1.0, + "content": "this interacts with the positive/negative balance and the number of classes present within a batch.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 26.5 + } + ], + "page_idx": 17, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 307, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2021", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "score": 1.0, + "content": "18", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 205, + 80, + 406, + 148 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 205, + 80, + 406, + 148 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 205, + 80, + 406, + 148 + ], + "spans": [ + { + "bbox": [ + 205, + 80, + 406, + 148 + ], + "score": 0.976, + "html": "
rankmethod# pos#neg# total pairs
1NCA1792129024130816
25-shot a=1617605456056320
35-shot a=89606048061440
45-shot a=3221603240034560
51-shot a=84482822428672
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This is often true, as the ranking can almost be fully explained by the number of total", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 421, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 104, + 421, + 437, + 434 + ], + "score": 1.0, + "content": "pairs in the right column. 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