Automated Relational Meta-learning
Authors: Huaxiu Yao
Xian Wu
Zhiqiang Tao
Yaliang Li
Bolin Ding
Ruirui Li
Zhenhui Li
Venue:  (2020)
Keywords: meta-learning
task heterogeneity
meta-knowledge graph

Abstract: In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, a critical challenge in meta-learning is the task heterogeneity which cannot be well handled by traditional globally shared meta-learning methods. In addition, current task-specific meta-learning methods may either suffer from hand-crafted structure design or lack the capability to capture complex relations between tasks. In this paper, motivated by the way of knowledge organization in knowledge bases, we propose an automated relational meta-learning (ARML) framework that automatically extracts the cross-task relations and constructs the meta-knowledge graph. When a new task arrives, it can quickly find the most relevant structure and tailor the learned structure knowledge to the meta-learner. As a result, the proposed framework not only addresses the challenge of task heterogeneity by a learned meta-knowledge graph, but also increases the model interpretability. We conduct extensive experiments on 2D toy regression and few-shot image classification and the results demonstrate the superiority of ARML over state-of-the-art baselines.

Published as a conference paper at ICLR 2020
AUTOMATED RELATIONAL META-LEARNING
Huaxiu Yao":, Xian Wu², Zhiqiang Tao Valiang Li', Bolin Ding', Ruirui Li,, Zhenhui Li! Pennsyyvvani State University, PUniversity of Notre Dame, "Northeastern University AAlibaba Group, University of Califormia, Los Angeles
(hhuaxiiuua uyaa,, JessieLi (8psu edu, 2xwu9ênd.c edu, 3 'zqtaoßece neu.edu
(yaliang 1i, bolin. ding ) ea aawaaaalaaiiinn com, Prrli@es, ucla.
ABSTRACT
In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, critical challenge in meta-learning is the task heterogeneity which cannot be well handled by traditional globally shared meta-leariing methods. In addition, current task-specific meta-learning methods may either suffer from hand-crafted structure design or lack the capability capture complex relations between tasks. In this paper, motivated by the way of knowledge organization in knowledge bases, we propose an automated relational meta-learning (ARML) framework that automat- ically extracts the cross-task relations and constructs the meta-knowledt When a new task arrives, it can quickly find the most relevant structure and tailor the learned structure knowledge to the meta-learner. As result, the proposed framework not only addresses the challenge of task heterogeneity by a learned mnta-knowledde graph, but also increases the model interpretability. We conduct extensive experiments on 2D toy regression and few-shot image classification and the results demonstrate the superiority of ARML over state-of-ther of-the-art baselines.
graph.
INTRODUCTION
Learning quickly is the key characteristic of human intelligence, which remains a daunting problem in machine intelligence. The mechanism of meta-learning is widely used to generalize and transfer prior knowledge learned from previous tasks to improve the effectiveness of learning new tasks,
which has benefited various applications, such as computer vision (Kang et al.) 2019: Liu et al. 2019))
natural language processing (Gu et al., 2018: Lin et al. 2019) and social good (Zhang al. 2019
Yao et al. 2019a). Most of existing meta-learning algorithms learn a globally shared meta- earner (e.g., parameter initialization (Finn et al.] 2017 2018). meta-optimizer (Ravi & Larochelle 2016). metric space (Snell et al.
2017] Garcia & Bruna 2017 Oreshkin et al., (018)). However, globally shared meta-lcarners fail handle tasks lying different distributions, which is known as task
heterogemeity (Vuorio et al. 2018 Yao et al., 2019b). Task heterogeneity has been regarded as one of the most challenging issues meta-learning, and thus is desirable design meta-learning models that effectively optimize each of the heterogeneous tasks.
The key challenge to deal with task heterogeneity is how to customize globally shared meta-learner by using task-specific information? Recently, a handful of works try to solve the problem by learning task mask-specific representation for tailoring the transferred knowledge to each task (Oreshkin et al.. 2018)
Vuorio al. 2018 Lee & Choi 2018). However, the expressiveness of these methods is limited due to the impaired knowledge generalization between highly related tasks. Recently, learning the underlying structure across tasks provides
effective way for balancing the customization and generalization. Representatively, Yao et al. propose a hierarchically structured meta-learning method customize the globally shared knowledge to each cluster (Yao et al.) 2019b). Nonetheless, the hierarchical clustering structure completely relies on the handcrafted design which needs to be tuned carefully and may lack the capability to capture complex relationships.
Hence, we are motivated to propose a framework to automatically extract underlying relational structures from historical tasks and leverage those relational structures to facilitate knowledge
Work was done when Huaxiu Yao, Xian Wu, Zhiqiang Tao interned in Alibaba Group

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Published as a conference paper at ICLR 2020
customization a new task. This inspiration comes from the way of structuring knowledge in knowledge bases (i.e., knowledge graphs). In knowledge bases, the underlying relational structures across text entities automatically constructed and applied to new query to improve the searching efficiency. In the meta-learning problem, similarly, we aim at automatically establishing the meta- knowledge graph between prior knowledge learned from previous tasks. When new task arrives, it queries the meta veeta-knoweedg graph and quickly attends to the most relevant entities (vertices), and then takes advantage of the relational knowledge structures between them to boost the learning effectiveness with the limited training data.
The proposed meta-learning framework is named as Automated Relational Meta-Learmin (ARML). Specifically, the ARML automatically builds the meta-knowlest graph from meta- training tasks to memorize and organize learned knowledge from historical tasks, where each vertex represents one type of knotledee (e.g., the common contour between birds and aircrafts). To learn the meta-knowledge graph at meta-training time, for each task, we construct a prototype- basedd relational graph for each class, where each vertex represents one prototype. The prototype-basee relational graph not only captures the underlying relationship behind samples, but alleviates the potential effects of abnormal samples. The meta- wett-knowwldgge graph is then learned by summarizing the information from the corresponding prototype- based relational graphs of meta- ceta-training tasks. After constructing the knotleenoweegge graph, when new task comes in, the prototype- new task taps into the meta-knowledge graph for acquiring the most relevant knowledge, which further enhances the task representation and facilitates its training process.
relational graph of the
Our major contributions of the proposed ARML are three-fold: (1) it automatically constructs the meta-knowledge graph facilitate learning a new task; (2) it empirically outperforms the state-of- the-art meta-learning algorithms; (3) the meta-knowledge graph well captures the relationship among tasks and improves the interpretability of veta-learning algorithms.
RELATED WORK
Meta-leariig designs models to learn new tasks or adapt new environments quickly with a few training examples. There are mainly three research lines of meta-learning: (1) black-box amortized methods design black-box learners to infer the model parameters (Ravi Larochelle, 2016) Andrychowicz et al., 2016, Mishra et al. 2018 Gordon et al.) 2019); (2) gradient-based methods aim to learn an optimized initialization of model parameters, which can be adapted to new tasks by a few steps of gradient descent (Finn et al., 2017: 2018 Lee & Choi 2018 Yoon et al. 2018: Grant et al., 2018); (3) non-parametric methods combine parametric meta-learned and non parrpaaaeiiiic learners to learn appropriate distance metric for few-shot classification (Snell et al. 2017 Vinyals et al. 2016 Yang et al. 2018: Oreshkin et al. 2018 Yoon et al.) 2019: Garcia & Bruna 2017).
Our work is built upon the gradient-basee meta-learning methods. In the line of gradient- baseed meta-learning, most algorithms learn a globally shared meta-learners from previous tasks (Finn et al. 2017 Li et al. 2017; Flennerhag al.) 2201), to improve the effectiveness of learning process on new tasks. However, these algorithms typically lack the ability to handle heterogeneous tasks (i.e., tasks sample from sufficient different distributions). To tackle this challenge, recent works tailor the globally shared initialization to different tasks by customizing initialization (Vuorio et al.) 2018 Yao al. (219b) and using probabilistic models (Yoon et al.) 2018)] Finn et al.] 2018). Representatively, HSML customizes the globally shared initialization with a manually designed hierarchical clustering structure to balance the generalization and customization (Yao et al., 2019b). However, the hand- crafted designed hierarchical structure may not accurately reflect the real structure and the clustering structure constricts the complexity of relationship. Compared with these methods, ARML leverages the most relevant structure from the automatically constructed meta-knowledge graph. Thus, ARML not only discovers more accurate underlying structures to improve the effectiveness of meta-learning algorithms, but also the meta- eetta-nnowwegge graph further enhances the model interpretabilityy
3 PRELIMINARIES
Few-shot Learning Considering task T., the goal of few-shot learning is to learn a model with a dataset D; = (D.", D)*}, where the labeled training set D = (xf",y] VVj E [I] only has a few samples and D represents the corresponding test set. A learning model (a.k.a., base model)
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with parameters 0 are used to evaluate the effectiveness D by minimizing the expected empirical loss on D."" i... L(D;, 0), and obtain the optimal parameters 0,. For the regression problem. the loss function is defined based on the mean square enror (i.e., Σix, x)))p [x,) - y,1lă) and for the clas- sification problem, the loss function uses the cross-entropy loss (i.e., -E(x, ,,, log ply, |X,, fo)). Usually, optimizing and learning parameter for the task T, with few labeled training samples is difficult. To address this limitation, meta-learning provides us a new perspective to improve the performance by leveraging knowledge from multiple tasks.
Meta-lcarning and Model-agnostic Meta-learning In meta-learning, a sequence of tasks (Ti....; Tr) are sampled from a task-level probability distribution p(T), where each one is few-shot learning task. To facilitate the adaption for incoming tasks, the meta-lcarning algorithm aims to find well-generalized meta-learner optimal meta-learner is applied to adapt the new tasks T.. In this way, meta-learning algorithms are capable of adapting to tasks efficiently even with shortage of training data for new task.
/ training tasks at meta-learning phase. At meta-testing phase, the
agnostic meta- weta-learning (MAML) (Finn et al. 2017), one of the representative algorithms in gradient-based meta-learning, regards the meta-learner the initialization of parameter i.e., fo. and learns well-generalized initialization 0% during the meta-training process. The optimization problem is formulated as (one gradient step exemplary):
0 arg min Σ C(fe, D = arg min
Σ Co
a0 D.
At the meta-testing phase, to obtain the adaptive parameter Oe for each new task Te, we finetune the initialization of parameter 0g by performing gradient updates a few steps, i.c., Soc Soz - aVol(s.P(()
METHODOLOGY
In this section, we introduce the details of the proposed ARMI. To better explain how it works, we show its framework in Figure | The goal of ARML is to facilitate the learning process of new tasks by leveraging transferable knowledge learned from historical tasks. To achieve this goal, we introduce weta--knoweedge graph, which is automatically constructed at the meta-training time, to organize and memorize historical learned knowledge. Given a task, which built as a prototype- based relational structure, it taps into the meta keetl-knowwedge graph to acquire relevant knowledge for enhancing its own representation. The enhanced prototype representations further aggregate and incorporate with meta-learner for fast and effective adaptions by utilizing modulating function. In the following subsections, we elaborate three key components: prototype-basee sample structuring, automated meta- kettllnnoweegg graph construction and utilization, and task-specific knowledge fusion and adaptation, respectively.
4.1 PROTOTYPE-BASED SAMPLE STRUCTURING
Given task which involves either classifications or regressions regarding set of samples, we first investigate the relationships among these samples. Such relationship is represented by a graph, called proiotype-basee relational graph in this work, where the vertices in the graph denote the prototypes of different classes while the edges and the corresponding edge weights are created based on the similarities between prototypes. Constructing the relational graph based on prototypes instead of raw samples allows us to alleviate the issue raised by abnormal samples. As the abnormal samples, which locate far away from normal samples, could pose significant concerns especially when only limited number of samples are available for training. Specifically, for classification problem, the prototype, denoted by cf IRd is defined as:
N N Σ Ex,),
C
(
where No denotes the number of samples in class k. E is embedding function, which projects xj into a hidden space where samples from the same class are located closer to each other while samples from different classes stay apart. For regression problem, is not straightforward to construct
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Propagation
Prototype-based Relational Structure &
Meta-knowledge Graph g
Prototypes
0g
Aggregator
Modulation
Aggregator
nt
0:
The framework of ARML. For each task T;, ARML first builds a prototype- based relational structure R2 by mapping the training samples D into prototypes, with each prototype represents one class. Then, R, interacts with the meta-knowledge graph G to acquire the most relevant historical knowledge by information propagation. Finally, the task-specific modulation tailors the globally shared initialization 0g by aggregating of raw prototypes and enriched prototypes, which absorbs relevant historical information from the meta weta-knooledde graph.
Figure 1:
the prototypes explicitly based on class information. Therefore, we cluster samples by learning an assignment matrix P. Rx Specifically, we formulate the process as:
P. Softmax (WannaxxWWPeFF) W.E" (X) bp), ci P.))
(3)
where [k( represents the k-th row of P.. Thus, training samples are clustered K clusters, which serve the representation of prototypes.
After calculating all prototype representations {et vk E [1, K]}, which serve as the vertices in the the prototype-based relational graph R,, we further define the edges and the corresponding edge weights. The edge weight AR, (c/, c) between two prototypes of and ct"h is gauged by the the similarity between them. Formally:
(4) where W, and b, represents learnable parameters, 7, is a scalar and a is the Sigmoid function, which normalizes the weight between 0 and 1. For simplicity, as R, = (CR, ). where CR, {c]IV) [1, K]} E R xd represent a set vertices, with each corresponds the prototype from class, while AR, [|AR, c/"),, E [1, K} R gives the adjacency matrix, which indicates the proximity between prototypes.
AR, (c/, (W.((c -,"" b,),
denote the prototype-baset relational graph
4.2 AUTOMATED META-KNOWLEDGS GRAPH CONSTRUCTION AND UTILIZATION
In this section, we first discuss how to organize and distill knowledge from historical learning process and then expound how leverage such knowledge to benefit the training of new tasks. To organize and distill knowledge from historical learning process, we construct and maintain a meta-knowledge graph. The vertices represent different types of meta-knowledge (e.g., the common contour between aircrafts and birds) and the edges are automatically constructed to reflect the relationship between meta-know netta-nnowledge. When serving new task, we refer to the meta- knowledge, which allows to efficiently and automatically identify relational knowledge from previous tasks. In this way, the training of a new task can benefit from related training experience and get optimized much faster than otherwise possible. In this paper, the meta-knowledde graph is automatically constructed the meta-tran aata-training phase. The details of the construction are claborated as follows:
Assuming the representation of vertex g is given by he E Rd, we define the knowlknn graph as ç =
where Hę [h'lVj E []] E R@xd and Ag = (Ag(h' h MV"" vj E GI) G denote the vertex feature matrix and vertex adjacency matrix, respectively. To better explain the construction of the meta- knowledge graph, we first discuss the vertex representation Hg.
During meta-training, tasks arrive after another in sequence and their corresponding vertices
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representations are expected to be updated dynamically in timely manner. Therefore, the vertex representation of meta- kett-knoweedge graph are defined to get parameterized and learned at the training time. Moreover, to encourage the diversity of mntal-nnoweedee encoded in the meta- meta-knowledge graph, the vertex representations are randomly initialized. Analogous to the definition of weight in the prototype-base baatepeeebseddddee based relational graph R; in equation 4 constructed as:
the weight between pair of vertices j and m is
Ag hm) = a (W.(h hn'l//)) + bo),
(5)
where W. and b. represent learnable parameters and Yo is a scalar.
To enhance the learning of new tasks with involvement of historical knowledge, we query the prototype-based relational graph in the meta-knowledge graph to obtain the relevant knowledge in history. The ideal query mechanism is expected to optimize both graph representations simultancously at the meta- veta-training time, with the training of one graph facilitating the training of the other. In light of this, we construct a super-graph S. by connecting the prototype-base peaeet relational graph R. with the meta- knowledge graph G for each task T; The union of the vertices in R; and g contributes to the vertices in the super-graph. The edges in R. and G are also reserved the super-graph. We connect R, with G by creating links between the prototype-based relational graph with the meta-knowledge graph. The link between prototype ef in prototype-based relational graph and vertex h" in meta- knowledge graph is weighted by the similarity between them. More preciscly, for each prototype ey. the link weight As(c,, h²") is calculated by applying softmax over Euclidean distances between cj and [h"]/Vm [1, G1] as follows:
As(c,, = exp(-I1(c; h 1/T01///22 exp(-lic,_-b)//n.lPe 21'=1 exp(-I((c h" 1/>a1//2)
(6)
where 7/8 is a scaling factor. We denote the intra-adjacent matrix as As (As(c], Sosfc/.."")) \[
[1. [] [1, G]) E &xx Thus, for task Tú, the adjacent matrix and feature matrix of super-gran graph S: = (A., H.) is defined as A. = (AR., As; AT, As) E R(K-G)x(X+() and H. = (CR,; Ha) E
R(K+G)xd respectively.
After constructing the super-graph S,, we are able to propagate the most relevant knowledge from meta-knowledge graph G to the prototype-based relational graph R, by introducing Graph Neural Networks (GNN), In this work, following the imessage-passingg framework (Gilmer et al. 2017). the GNN is formulated as:
H (++) = MP(A,, H W
where MP(-) is the message passing function and has several possible implementations (Hamilton
et al. 2017: Kipf& & Welling 2017 Veličković al. 2018 H.") is the vertex embedding after (
layers of GNN and w is a learnable weight matrix of layer 1. The input H H. After stacking L GNN layers, we get the information dnformation-proppgateed feature representation for the prototype-basee
relational graph R2 as the top-K rows of H("), which is denoted as Cr, = {ée E [1,
4.3 TASK-SPECIFIC KNOWLEDGE FUSION AND ADAPTATION
After propagating information form meta-knowledge graph to prototype- -based relational graph, in this section, we discuss how learn well-generalized meta-learner for fast and effective adaptions to new tasks with limited training data. To tackle the challenge of task heterogeneity, in this paper, we incorporate task-specific information customize the globally shared meta-learner (e.g.. initialization here) by leveraging a modulating function, which has been proven to be effective to provide customized initialization in previous studies (Wang et al.) 2019: Vuorio al. 2018).
The modulating function relies on well-discriminated task representations, while it is difficult to learn all representations by merely utilizing the loss signal derived from the test set D/+, To encourage such stability, we introduce two reconstructions by utilizing two auto-encoders. There are two collections of parameters, i.c, CR, and ČR,, which contribute the most to the creation of the task-specific meta-learner. CR, express the raw prototype information without tapping into the meta-knowledge graph, while ČR, give the prototype representations after absorbing the relevant knowledge from the mewwelno graph. Therefore. the two reconstructions
built CR, and ČR,- To reconstruct CR,, an aggregator (G) (c.g.. recurrent network, fully connected layers) is involved to encode Cr, into a dense representation, which is further fed into decoder AGga(() to achieve reconstructions.
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Algorithm 1 Meta-Training Process of ARML
Require: p(7): distribution over tasks; K: Number of vertices in meta- graph; a: stepsize for gradient descent of each task (i.e., inner loop stepsize); 3: stepsize for meta-optmiiztion (i.e., outer loop stepsize); μı, jazi balancing factors in loss function
1: Randomly initialize all learnable parameters db
2: while not done do
3: Sample a batch of tasks {Tilá E [1, }]} from p(T)
4: for all do
5: Sample training set D and testing set T
6:
Construct the prototype-based relational graph R, by computing prototype in equation
and weight in equation []
7: Compute the similarity between each prototype and meta weta-knowledge vertex in equation and construct the super-graph S;
8:
Apply GNN on super-graph and get the information-propagaale representation CR, Aggregate CR, in equation 8 and CR, in equation 9 to get the representations qi and reconstruction loss Lq, Lt
9:
10:
Compute the task-specific initialization la in equation 10 and update parameters 0, Our aJo,(Js, (e D(")
11:
end for
12:
Update < + - Vo Ele (Uo., + puCa + p2L,
end while
Then, the corresponded task representation q: of CR, is summarized by applying mean pooling operator over prototypes on the encoded dense representation. Formally,
= MeanP = N j=1
(AG C, =|iRC,, AG (AG'(CR,))
(8)
Similarly, we reconstruct CR, and get the corresponded task representation t, as follows:
Nrr
t, MeanPool(AA
N Σ (AG) f. ||CR, (AGe
The reconstruction errors Equations S and pose an extra constraint to enhance the training stability, leading to improvement of task representation learning.
After getting the task representation q, and t,, the modulating function is then used to tailor the task-specific information the globally shared initialization 8.. which is formulated as:
lor o (t: qi) b,) Co.
(10)
where W, and b, learnable parameters of fully connected layer. Note that adopt the Sigmoid gating as exemplary and more discussion about different modulating functions can be found in ablation studies of Section
For each task T,, we perform the gradient descent process from oor and reach its optimal parameter 0, Combining the reconstruction loss and E, with the meta-learning loss defined in equation I the overall objective function of ARMI.
min C..: min L P.L, + #2L, min Σ -U D.") + HiC, + u2C,,
(11)
where and μ2 are introduced to balance the importance of these three items. & represents all learnable parameters. The algorithm of meta-training process of ARML is shown Alg. 2 The details of the meta-testing process of ARML are available in Appendix A
5
EXPERIMENTS
In this section, we conduct extensive experiments to demonstrate the effectiveness of the ARML on 2D regression and few-shot classification.

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5.1 EXPERIMENTAL SETTINGS
Methods for Comparison We compare our proposed ARML with two types of baselines: (1)
Gradient-basel meta-learning methods: both globally shared methods (MAML. (Finn et al. (017).
Meta-SGD (Li et al. 2017)) and task-specific methods (MT-Net (T.ee & Choil, 2018), MUMO-
MAML (Vuorio ct al. 2018). HSML (Yao et al. al.] 2019b), BMAML (Yoon et al. 2018)) are considered for comparison. (2) Other meta-learning methods para-maaaettric and black box amortized meth-
ods): we select globally shared methods VERSA (Gordon et al.] 2019), Prototypical Network (ProtoNet) (Snell et al. 2017), TapNet (Yoon et al., 2019) and task- method TADAM (Ore shkin et al. 2018) as baselines. Following the traditional settings, non- con-paametrrc baselines are only used in few-shot classification. Detailed implementations of baselines are discussed in Appendix B.3
Hyperparameter Settings For the aggregated function in autoencoder structure (AG', AG AG
AG we use the GRU as the encoder and decoder in this structure. We adopt one layer GCN (Kipt & Welling 2017) with tanh activation as the implementation of GNN in equation 7 For the modulation network, we test sigmoid, tanh and Film modulation, and find that sigmoid modulation achieves best performance. Thus, in the future experiment, we set the sigmoid modulation as modulating function. More detailed discussion about experiment settings are presented in Appendix B
5.2 2D REGRESSION
Dataset Description In 2D regression problem. we adopt the similar regression problem settings
as (Finn et al.) 2018 Vuorio et al. 2018 Yao et al. 2019b] Rusu et al. (211)), which includes several families of functions. In this paper, to model more complex relational structures, we design a 2D regression problem rather than traditional ID regression. Input I U[0.0, 5.0] and y U[0.0, 5.0] are sampled randomly and random Gaussian noisy with standard deviation 0.3 is added to the output. Furthermore, six underlying functions are selected, including (1) Sinusoids: =(x, y) agsin(w,e (w,r + bc), where ag ~ U[0.1, 5.0). by ~ U'0, 2m] w, ~ U[0.8, 1.2]; (2) Line: 2(x, = a + bi, where a U[-3.0, 3.0), ~ U[-3.0, (3) Quadratic: z(x. ag 2 b, + Coz where ag U1-0.2, 0.2), by ~ 2.0,, C, ~ U1-3.0, 3.0]; (4) Cubic: 2(x, y) = aax"" + bott + cot + de. where da 0111,, be 0.22, Co U1- 2.0), de ~ U[-3.0,3.0]: (5) Quadratic
Surface: 2(2, = agua" + by."", where ag. U[0 1.0], byg ~ U[-10. 1.0]; (6) Ripple: 2(xx v) sin(-a, (a + w²)) + br, where a, ~ U[-0.2,00 0.2). b, U[-3.0, 3.0). Note that, function 1-4 are located in the subspace of y 1. Follow (Finn et al. 2017). we use two fully connected layers with 40 neurons as the base model. The number of vertices of kntallno graph set as
Results and Analysis In Figure 2 we summarize the interpretation of meta--knowledge graph (see top figure, and more cases are provided in Figure Appendix G.4) and the the qualitative results (see bottom table) of 10-shot 2D regression. In the bottom table, we can observe that ARMI. achieves the best performance as compared competitive gradient-based meta-learning methods, i.e., globally shared models and task-specific models. This finding demonstrates that the meta-knowledge graph necessary to model and capture task-specific information. The superior performance can also be interpreted in the top figure. In the left, we show the heatmap between prototypes and meta-knowledge vertices (darker color means higher similarity). We can see that sinusoids and line activate V1 and V4, which may represent curve and line, respectively. VI and V4 also contribute to quadratic and quadratic surface, which also show the similarity between these two families of functions. V3 is activated in PO of all functions and the quadratic surface and ripple further activate V1 in PO, which may show the different between 2D functions and 3D functions (sinusoid, line, quadratic and cubic lie in the subspace). Specifically, in the right figure, we illustrate the meta-knowledge graph, where we set a threshold to filter the link with low similarity score and show the rest. We can see that V3 is the most popular vertice and connected with V1, V5 (represent curve) and V4 (represent line). V1 is further connected with V5, demonstrating the similarity of curve representation.
5.3 FEW-SHOT CLASSIFICATION
Dataset Deseription and Settings In the few-shot classification problem, first use the bench- mark proposed in Yao et al.) 2019b), where four fine-grained image classification datasets are included (i.e., CUB-200-2011 (Bird), Describable Textures Dataset (Texture), FGVC of Aircraft
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11
V2
VO
VI V2
V3 V4 V5
VO VI V2
V3 V4 V5
Sinuzoids
Line
91
50
VD
V0 V1 V2
V3
V4 V5
VO VI
V4 V5
Quadaricc
Cubic
11
90
VO VI
V2
V3
V4 V5
VO V1 V2
V3
V4 V5
Quadrabic Surface
Ripple
Model
MAML
Meta SGD
BMAML
NeN
MUMOMAML
HSSML
ARMI.
10-shot
2.29
U.16
2.91 = 0.23
1.65 + U.10
1.76 + 0.12
0.52 = 0.04
0.49 0.04
0.44
0.03
Figure 2: In the top figure, we show the interpretation of meta-knowledge graph. The left heatmap shows the similarity between prototypes (PO, P1) and meta-knowledee vertices (VO-V5). The right part show the meta-knowledde graph. In the bottom table, we show the overall performance (mean square error with 95% confidence) of 10-shot 2D regression.
(Aircraft), and FGVCX-Fungi (Fungi)). For each few-shot classification task, it samples classes from one of four datasets. In this paper, we call this dataset Plain-Multi and each fine-grained dataset as subdataset.
Then, to demonstrate the effectiveness of our proposed model for handling more complex underlying structures, in this paper, we increase the difficulty of few-shot classification problem by introducing two image filters: blur filter and pencil filter. Similar to (Jerfel et al. 2019), for each image in Plain- Multi, one artistic filters are applied to simulate a changing distribution of few-shot classification tasks. After applying the filters, the total number of subdatasets is 12 and each task is sampled from one of them. This data is named as Art-Multi. More detailed descriptions of the effect of different filters are discussed in Appendix C
Following the traditional meta-learning settings, all datasets are divided into meta- vetaa-raiiinn,, meta- validation and sesta-tstting classes. The traditional N-way K-shot settings are used split training and test set for each task. We adopt the standard four-block convolutional layers as the base learner (Finn al., 2017 Snell al. 2017) for ARMI, and baselines for a fair comparison. The number of vertices of meta-know ledge graph for Plain-Multi and Art-Multi datasets are set as 4 and 8, respectively. Additionally, for the minilmagenet and tieredlmagenet (Ren et al. 2018), similar to (Finn et al.] 2018),, which tasks are constructed from single domain and do not have heterogeneity, we compare our proposed ARML with baseline models and present the results in Appendix
Overall Performance Experimental results for Plain-Multi and Art-Multi are shown Table and Table respectively. For each dataset, the performance accuracy with 95% confidence interval reported. Due to the space limitation, in Art-Multi dataset, we only show the average value of each filter here. The full results shown in Table of Appendix [E] In these two tables, first, can observe that task-specific gradient-basee based models (MT-Net, MUMOMAMI, HSML, BMAML) significantly outperforms globally shared models (MAML, Meta-SGD). Second, compared ARML with other task-specific gradient-based meta-learning methods, the better performance confirms that ARML can model and extract task-specific information more accurately by leveraging the constructed meta-knowledde graph. Especially, the performance gap between the ARML and HSML verifies the benefits of relational structure compared with hierarchical clustering structure. Third, as gradient- based meta meta-learning algorithm, ARML can also outperform methods of other research lines (i.e., ProtoNet, TADAM, TapNet and VERSA). Finally, to show effectiveness of proposed components in ARML, we conduct comprehensive ablation studies in Appendix F The results further demonstrate the effectiveness of prototype- prassdd based relational graph and meta- detta-knowledge graph.
Analysis of Constructed Meta-knowledge Graph this section, we conduct extensive qualita- tive analysis for the constructed meta-knowledd graph, which is regarded the key component in ARML. Due to the space limit, we present the results on Art-Multi datasets here and the analysis of Plain-Multi with similar observations is discussed in Appendix G.T We further analyze the effect of
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Table Overall few-shot classification results (accuracy + 95% confidence) on Plain-Multi dataset.
Settings
Algorithms
Data: Bird
Data: Texture
Data: Aircraft
Data: Fungi
VERSA
53,40 + 1.41%
30.43 = 1.30%
50.60 + 1.34%
40.40 +: 1.40%
ProtoNet
54.11 + 1.38%
32.52 = 1.28%
50.63 + 1.35%
41.05 + 1.37%
TapNet
54.90 1.34%
32.44 = 1.23%
51.22 1.34%
42.88 1.35%
5-way
TADAM
56.58 1.34%
33.34 = 1.27%
53.24 E 1.33%
43.06 = 1.33%
1-shot
MAML
53.94 1.45%
31.66 = 1.31%
51.37 1.38%
42.12 1.36%
MetaSGD
55.58 1.43%
32.38 = 1.32%
52.99 1.36%
41.74 1.34%
BMAML
54.89 + 1.48%
32.53 = 1.33%
53.63 + 1.37%
42.50 + 1.33%
MT-Net
58.72 + 1.43%
32.80 = 1.35%
47.72 1.46%
43.11 + 1.42%
MUMOMAML
56.82 + 1.49%
33.81 1.36%
53.14 1.39%
42.22 = 1.40%
HSML
60.98 1.50%
35.01 = 1.36%
57.38 1 1.40%
44.02 1.39%
ARML
62.33 1.47%
35.65 1 1.40%
58.56 1.41%
44.82 1 1.38%
VERSA
65.86 + 0.73%
37.46 0.65%
62.81 + 0.66%
48.03 + 0.78%
ProtoNet
68.67 1 0.72%
45.21 0.67%
65.29 1 0.68%
51.27 1 0.81%
TapNet
69.07 0.74%
45.54 = 0.68%
67.16 0.66%
51.08 0.80%
5-way
TADAM
69.13 0.75%
45.78 = 0.65%
69.87 1 0.66%
53.15 1 0.82%
5-shot
MAML
68.52 0.79%
44.56 - 0.68%
66.18 0.71%
51.85 0.85%
MetaSGD
67.87 + 0.74%
45.49 = 0.68%
66.84 0.70%
52.51 - 0.81%
BMAML
69.01 + 0.74%
46.06 = 0.69%
65.74 0.67%
52.43 = 0.84%
MT-Net
69.22 + 0.75%
46.57 = 0.70%
63.03 + 0.69%
53.49 - 0.83%
MUMOMAML
70.49 0.76%
45.89 = 0.69%
67.31 0.68%
53.96 + 0.82%
HSML
71.68 0.73%
48.08 = 0.69%
73.49 + 0.68%
56.32 + 0.80%
ARML
73.34 0.70%
49.67 + 0.67%
74.88 + 0.64%
57.55 0.82%
different number of vertices in meta meta-knowledge graph in Appendix G.2 and conduct comparison with HSML about the learned structure in Appendix G.3
To analyze the learned nnowele graph, for each subdataset, we randomly select one task as SnvendixG..4]oor f.r more cases). For each task, in the left part of Figure 3 we show the similarity heatmap between prototypes and vertices in meta-knowledge graph, where deeper color means higher similarity. VO- V8 and P1-P5 denote the different vertices and prototypes, respectively. The meta- netta-nnoweddge graph is also illustrated in the right part. Similar to the graph in 2D regression, we set a threshold to filter links with low similarity and illustrate the rest of them. First,
exemplary (see Figure of of Appendix
that the VI is mainly activated by bird and aircraft (including all filters), which may reflect the shape similarity between bird and aircraft. Second, V2, V3, V4 are firstly activated by texture and they form loop in the meta-knowledde graph. Especially, V2 also benefits images with blur and pencil filters. Thus, V2 may represent the main texture and facilitate the training process on other subdatasets. The detta-knowledge graph also shows the importance of V2 since it connected with almost all other vertices. Third, when we use blur filter, in most cases (bird blur, texture blur, fungi blur), V7 activated. Thus, V7 may show the similarity of images with blur filter. In addition, the connection between V7 and V2 and V3 show that classifying blur images may depend on the texture information. Fourth, V6 (activated by aircraft mostly) connects with V2 and V3, justifying the importance of texture information to classify the aircrafts.
CONCLUSION
In this paper, to improve the effectiveness of meta-learning for handling heterogencous task, propose a new framework called ARML, which automatically extract relation across tasks and construct meta-know meta-knowwedde graph. When new task comes in, it can quickly find the most relevant relations through the metal-nowledde graph and use this knowledge to facilitate its training process. The experiments demonstrate the effectiveness of our proposed algorithm.
In the future, we plan to investigate the problem in the following directions: (1) we are interested to investigate the more explainable semantic meaning in the meta-knowledge graph on this problem; (2)

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Table 2: Overall few-shot classification results (accuracy + 95% confidence) on Art-Multi dataset.
Settings
Algorithms
Avg. Original
Avg. Blur
Avg. Pencil
VERSA
43.91 1.35%
41.98 + 1.35%
38.70 1.33%
Protonet
42.08 1 1.34%
40.51 + 1.37%
36.24 +: 1.35%
TapNet
42.15 1 1.36%
41.16 + 1.34%
37.25 + 1.33%
TADAM
44.73 1 1.33%
42.44 + 1.35%
39.02 1.34%
5-way, 1 1-shot
MAML
42.70 +: 1.35%
10.53 + 1.38%
36.71 + 1.37%
MetaSGD
44.21 + 1.38%
42.36 = 1.39%
37.21 1.39%
MT-Net
43.94 1.40%
41.64 1.37%
37.79 1.38%
BMAML
43,66 +: 1.36%
41.08 + 1.35%
37.28 1.39%
MUMOMAMI.
45.63 + 1.39%
41.59 + 1.38%
39.24 1.36%
HSMI.
45.68 + 1.37%
42.62 + 1.38%
39.78 1.36%
ARML
47.92 + 1.34%
44.43 + 1.34%
1.34+1.344%
VERSA
55.03 1 0.71%
53.41 1 0.70%
47.93 1 0.70%
Protonet
58.12 + 0.74%
55.07 + 0.73%
50.15 0.74%
TapNet
57.77 = 0.73%
55.21 = 0. 0.72%
50.68 0.71%
TADAM
60.35 0.72%
58.36 = 0.73%
53.15 0.74%
5-way, 5-shot
MAML
58.30 + 0.74%
55.71 = 0. 74%
49.59 + 0.73%
MetaSGD
57.82 + 0.72%
55.54 + 0.7%
50.24 0.72%
BMAML
58.84 0.73%
56.21 + 0.71% %
51.22 0.73%
MT-Net
57.95 + 0.74%
54.65 + 0.73%
49.18 + 0.73%
MUMOMAML
58.60 + 0.75%
56.29 + 0.72%
51.15 0.73%
HSML
60.63 + O. 73%
57.91 + 0. 0.72%
53.93 1 0.72%
ARML
61.78 1 0.74%
58.73 1 0.75%
55.27 1 0.73%
55555554 45655585
0.5.5.555 4955555
V1
V2
2: 1i 22
Armat
Fung
V7
1nd Pencil
Tonure Pendi
Aircaft Foncl
Turgi Pencl
Figure 3: Interpretation of meta-knowledge graph on Art-Multi dataset. For each subdataset, we randomly select one task from them. In the left, we show the similarity heatmap between prototypes (PO-P5) and meta-know knowledge vertices (V0-V7). the right part, we show the meta neta-knowwedge graph. graph.
we plan to extend the ARML the continual learning scenario where the structure of meta-knowledge graph will change over time; (3) our proposed model focuses on tasks where the feature space, the label space shared. We plan to explore the relational structure tasks with different feature and label spaces.
ACKNOWLEDGMENTS
The work supported in part by NSF awards #1652525 and #1618448. The views and conclusions contained in this paper are those of the authors and should not be interpreted as representing any funding agencies.
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REFERENCES
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A ALGORITHM IN META-TESTING PROCESS
Algorithm 2 Meta-Testing Process of ARML
Require:
Training data D of a new task T, 1: Construct the prototype-based relational graph R, by computing prototype in equation 2 and weight in equation
2: Compute the similarity between each prototype and mnta-lnnwwedge vertice in equation 6 and construct the super-graph S.
3: Apply GNN super-graph S, and get the updated prototype representation Čr.
4: Aggregate CR, in equation 8 CR, in equation 9 and get the representations qr. t.
5: Compute the task-specific initialization dur in equation I0
6: Update parameters 0, for Voo(ff D
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B HYPERPARAMETERS SETTINGS
B. 2D REGRESSION
In 2D regression problem, we the inner-loop stepsize (i.e., (r) and outer-loop stepsize (i.e., (8) as 0.001 and 0.001, respectively. The embedding function is set as one layer with 40 neurons. The autoencoder aggregator is constructed by the gated recurrent structures. We set the meta-batch size as 25 and the inner loop gradient steps as 5.
B.2 FEW-SHOT IMAGE CLASSIFICATION
few-shot image classification, for both Plain-Multi and Art-Multi datasets, we the corresponding inner stepsize (i.e., ()) as 0.001 and the outer stepsize (i.e., 3) as 0.01. For the embedding function & we employ two convolutional layers with x 3 filters. The channel size these two convolutional layers are 32. After convolutional layers, use two fully connected layers with 384 and 128 neurons for each layer. Similar to the hyperparameter settings 2D regression, the autoencoder aggregator is constructed by the gated recurrent structures, i.e. AG', AGk... AG", AG all GRUs. The meta-batch size is set as 4. For the inner loop, we use 5 gradient steps.
B.3 DETAILED BASELINE SETTINGS
For the gradient-based baselines (i.e., MAML, MetaSGD, MT-Net, BMAML. MUMOMAML, HSML), we use the same inner loop stepsize and outer loop stepsize rate as our ARML. As for non-parametric based meta-learning algorithms, both TADAM and Prototypical network, we use the same meta- meta-training and meta-testing process as gradient-baat based models. Additionally, TADAM uses the same embedding function & ARML, for fair comparison (i.e., similar expressive ability).
C ADDITIONAL DISCUSSION OF DATASETS
In this dataset, pencil and blur filers change the task distribution. To investigate the effect of pencil and blur filters, we provide one example in Figure 4 We can observe that different filters result in different data distributions. All used filters provided by OpenCV[]
(a): Plain Image
(b) with blur filter Figure 4: Effect of different filters.
(c) with pencil filter
D RESULTS ON MINTIMAGENET AND TIBREDIMAGENET
For miniimagenet and maaeee since do not have characteristic of task heterogeneity, we show the results in Table and Table 4 respectively. In this table, compare model with other gradient-based meta-lcarnin models (the top baselines are globally shared models and the bottom baselines task-specific models). Similar (Finn al., 2018), also apply the standard 4-block convolutional layers for each baseline. For MT-Net on Minil Imagenet, we use the reported results in (Yao et al., 2219b)), which control the model with the same expressive power. Most task-specific models including ARML achieve the similar performance on the standard benchmark due to the homogeneity between tasks.
https://openevoorg/
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Table 3: Performance comparison on the 5-way, 1-shot Minilmagenet dataset.
Algorithms
5-way 1-shot Accuracy
MAMI, (Finn et al.
2017
48.70 + 1.84%
LLAMA [Finn & Levine
2018
49.40 1.83%
Reptile (Nichol & Schulman 2018
49.97 0.32%
MetaSGD (Li et al.
2017)
50.47 = 1.87%
MT-Net (Lee & Choi (0018)
49.75 = 1.83%
MUMOMAML (Vuorio et al. 2018
49.86 1.85%
HSML Yao et al. (2019b
50.38 = 1.85%
PLATIPUS (Finn et al. 2018
50.13 1.86%
ARML
50.42 1.73%
Table 4: Performance comparison the 5-way, 1-shot tieredlmagenet dataset.
Algorithms
5-way 1-shot Accuracy
MAML (Finn et al.
2017)
51.37 + 1.80%
Reptile (Nichol Schulman 2018)
49.41 1.82%
MetaSGD (Li et al.
2017)
51.48 + 1.79%
MT-Net (Lee & Choi 2018
51.95 = 1.83%
MUMOMAMI Vuorio et al. 2018)
52.59 1.80%
HSML Yao al.
2019b)
52.67 1.85%
ARML
52.91 1.83%
E ADDITIONAL RESULTS OF FEW-SHOT IMAGE CLASSIFICATION
We provide the full results table of Art-Multi Dataset Table g ARML outperforms almost all baselines in every sub-datasets.
In this table, we can see our proposed
F ABLATION STUDY
In this section, perform the ablation study of the proposed ARML to demonstrate the effectiveness of each component. The results of ablation study on 5-way, 5-shot scenario for Art-Multi and Plain- Multi datasets are presented in Table[]aan Table respectively. Specifically, show the effectiveness of prototype-based relational graph, in ablation I, we apply the mean pooling to aggregate each sample and then feed it to interact with meta-knowledge graph. In ablation II, we use all samples construct the sample-level relational graph without constructing prototype. In ablation III, we remove the links between prototypes. Compared with ablation I, II and IIII the better performance of ARML shows that structuring samples can (1) better handling the underlying relations (2) alleviating the effeet of potential anomalies by structuring samples as prototypes.
In ablation IV, we remove the meta- mnta-kno graph and use the prototype- prototype-based based relational graph with aggregator AG" as the task representation. The better performance of ARML demonstrates the effectiveness of meta-knowledge graph for capturing the relational structure and facilitating the classification performance. We further remove the reconstruction loss in ablation V and replace the encoder/decoder structure as MLP in ablation VI. The results demonstrate that the autocncoder structure benefits the process of task representation learning and selected encoder and decoder.
In ablation VII, share the gate value within each filter in Convolutional layers. Compared with VII, the better performance ARML indicates the benefit customized gate for each parameter. In ablation VIII and IX, change the modulate function to Film (Perez al.) (2088) and tanh, respectively. We can see that ARML is not very sensitive to the modulating activation, and Sigmoid function is slightly better in most cases.
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Table 5:
Full evaluation results of model ablation study on Art-Multi dataset. B, T, A, represent bird, texture, aircraft, fungi, respectively. Plain means original image.
Model
Plain
B Blur
B Pencil
Plain
T Blur
T Pencil
no protolype-bant based graph
72. 72.08%
71.06%
66.83%
45.23%
39.97%
41.67%
II. no prototype
72.99%
70.92%
67.19%
45.17%
40.05%
41.04%
III. no prototype links
72.53%
71.09%
67.11%
45.08%
40.12%
41.01%
IV. no meta-knowledge graph
70.79%
69.5 39.53%
64.87%
43.37%
39.80 39.86%
41.23%
V. no reconstruction loss
70.82%
69.87%
65.32%
44.02%
40.18%
40.52%
VL replace encoder/decoder as MLP
71.36%
70.25%
66.38%
44.18%
39.97%
41.85%
VII share the gate within Conv. filter
72.03%
68. 68.15%
65.23%
43.98%
40.13%
39.71%
VIII tanh
72.70%
69.53%
66.85%
45.81%
40.79%
38.64%
IX. film
71.52%
68.70%
64.23%
43.83%
40.52%
39.49%
ARML
73.05%
71.31%
67. 67.14%
45.32%
40.15%
41.98%
Model
A Plain
A Blur
A Pencil
F Plain
F Blur
F Penciil
I. no prototype-based graph
70.06%
68.02%
60.66%
55.81%
54.39%
50.01%
II. no prototype
71.10%
67.59%
61.07%
56.11%
54.82%
49.95%
III. no prototype links
71.56%
67.91%
60.83%
55.76%
54.60%
50.08%
IV. meta-knowledge graph
69.97%
68.03%
59.72%
55.84%
53.72%
48.91 %
no reconstruction loss
66.83%
65. 73%
55.98%
54. 54.62%
53.02%
48. 48.01%
VL. replace encoder/decoder as MLP
70.93%
68. 12%
60.95%
56.02%
53.83%
50.22%
VII. share the gate within Conv. filter
71.25%
67.49%
58.09%
55.36%
54.25%
49.90%
VIII. tanh
73.96%
69.709 70%
60.75%
56 56.87%
54.30%
49. 49.82%
IX. film
63.13%
66.93%
55.59%
55.77%
53.72%
48.92%
ARML
71.89%
68.59%
61.41%
56.8%%
54.87%
50.53%
Table 6: Results of Model Ablation (5-way, 5-shot results) on Plain-Multi dataset.
Ablation Models
Bird
Texture
Aircraft
Fungi
I. no prototype-based graph
71.96 + 0.72%
48.79 + 0.67%
74.02 + 0.65%
56 03.83 + 0.80%
prototype
86
0.74%
0.69%
0.65%
0.81%
III. no protolype links
72.53 1 0.72%
49.25 1 0.68%
74.46 :: 0.64%
57.10 1: 0.81%
IV. keetl-knowledg graph
71.23 + 0.75%
47 17.96-2 + 0.68%
73.71 + 0.69%
55.97 + 0.82%
no reconstruction loss
70.99
0.74%
48.00 03 0.69%
69.86 0.66%
55.78 0.83%
VI. replace encoden/decnler MI.
0.72% 72.36
48.93 0.67%
74.28 0.65%
56.91 0.83%
share gate within Cony. filter
72.83 0.72%
68.6%
74.13 0.66%
83 0.81% 57. .7 + 0.80%
VIII. tanh
73.45 + 0.71%
19.2 23 = 0.66%
71.39 + 0.65%
IX. lilm
72.95 0.73%
49.18 0.69%
73.82 0.68%
56.89 16.89 0.80%
ARML
73.31 + 0.70%
19.67 + 0.67%
74.88 +: 0.64%
57 55 + 0.82%
G ADDITIONAL ANALYSIS OF META-KNOWLEDGE GRAPH
G.1 QUALITATIVE ANALYSIS ON MUAIT-MULTI DATASET
Then, we analyze the meta-knowledge graph on Plain-Multi dataset by visualizing the learned meta- knowledge graph on Plain-Multi dataset (as shown in Figure [5). In this figure, we can see that different subdatasets activate different vertices. Specifically, V2, which is mainly activated by texture, plays significantly important role in aircraft and fungi. Thus, V2 connects with V3 and VI in the meta- knowlegeowwddg graph, which is mainly activated by fungi and aircraft, respectively. In addition, VO is also activated by aireraft because of the similar contour between aircraft and bird. Furthermore, in meta- knowlennowwege graph, VO connects with V3, which shows the similarity of environment between bird images and fungi images.
15

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Published as a conference paper at ICLR 2020
v/
V1
V1
V0
40
P4 P5
P1
P2 PS M4 P5
V2
Bird
Texture
VO
V3
V3
12
42
41
V3
v0
40
Aircraft
Fungi
Figure 5: Interpretation of meta- knowl-nnowwegge graph Plain-Multi dataset. For each subdataset, one task is randomly selected from them. In the left figure, we show the similarity heatmap between prototypes (P1-P5) and meta-knowledge vertices (denoted as E1-F4), where deeper color means higher similarity. the right part, we show the meta-knowledge graph, where a threshold is also set to filter low similarity links.
G.2 PERFORMANCE V.S. VERTICE NUMBERS
We first investigate the impact of vertice numbers in meta- neeal-nooleedge graph. The results of Art-Multi (5-way, 5-shot) are shown Table 7 From the results, we can notice that the performance saturates as the number of vertices around 8. One potential reason is that 8 vertices are enough to capture the potential relations. If we have a larger datasets with more complex relations, more vertices may be needed. In addition, if the meta-knowledge graph does not have enough vertices, the worse performance suggests that the graph may not capture enough relations across tasks.
Table 7: Full evaluation results of performance v.s. # vertices of meta-knowledge graph Art-Multi. B, T, A, represent bird, texture, aircraft, fungi, respectively. Plain means original image.
# of Vertices
B Plain
Blur
B Pencil
T Plain Blur
T Pencil
4
72.29%
70.36%
67.88%
45.37%
41.05%
41.43%
8
73.05%
71.31%
67.14%
45.32%
40.15%
11.98%
73.45%
70.64%
67.11%
44.53%
41.41%
41.05%
16
72.68%
70.18%
68.34%
45.63%
41.43%
12.18%
20
73.41%
71.07%
68.64%
46. 46.26%
41.80%
41.61%
# of Vertices
A Plain
A Blur
A Pencil
F Plain
F Blur
F Pencil
70.98%
67.36%
60.46%
56.07%
53.77%
50.08%
8
71.89%
68.59%
61.41%
56.83%
54.87%
50.53%
12
71.78%
67.26%
60.97%
56.87%
55.14%
50.86%
16
71.96%
68.55%
61.14%
56.76%
54.54%
49.41%
72.02%
68.29%
60.59%
55.95%
54.53%
50.13%
G.3 DISCUSSION BETWEEN ARML AND HSML
In this part, we provide the case study to visualize the task structure of HSML and ARML. HSML is one of representative task-specific meta-learning methods, which adapts transferable knowledge by introducing task-specific representation. It proposes a tree structure to learn the relations between tasks. However, the structure requires massive labor efforts to explore the optimal structure. By contrast. ARML automatically learn the relation across tasks by introducing the knowledge graph. In addition, ARML fully exploring there types of relations simultancously. ie., the prototpe--pooooyy prototype-knowledge and mnowledge-knowledge relations.
16

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Published as a conference paper at ICLR 2020
To compare these two models, show the case studies of HSML and ARML in Figure 6 and Figure 7 For tasks sampled from bird, bird blur, aircraft and aireraft blur are selected for this comparison. Following case study settings in the original paper (Yao et al. 2019b), for each task, we show the soft-assignment probability to each cluster and the learned hierarchical structure. For ARMI., l show the learned meta-knowledge and the similarity heatmap between prototypes and meta-knows meta-knowledge vertices. In this figures we can observe that ARML constructs relations in more flexible way by introducing the graph structure. More specifically, while HSML activate relevant node in fixed two-layer hierarchical way, ARML provides more possibilities to leverage previous learned tasks by leveraging prototypes and the learned eetteenoweedge graph.
N6
N7
NB
N6
N7
NB
N2
N3
N4
AS
N2
N4
NS
N1
N2
N3
N4
N5
N1
N2
N3
N4
N5
Bird
Bird Blur
N6
N7
NB
NZ
N2
NG
MS
N2
N4
N1 N2
N5
N1 N2
N3
N4
N5
Aircraft
Aircraft Blur
Figure 6: Case study for learned structure of HSMI. For each task, the top heatmap shows the soft-assignment probability with each cluster and the top tree show the learned hierarchical structure.
<9
45
48
V2
VO
VB
PM
Bird
Bird Blur
44
46
VG
P3 P4 P5
Aircraft
Aircraft Blur
Figure Case study for learned structure ARML. Both the learned graph and the similarity heatmap between prototypes and knowllnoo vertices illustrated.
17

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Published as a conference paper at ICLR 2020
G.4 ADDITIONAL CASES NETTAKNNWEEDGE GRAPH ANALYSIS
We provide additional case study in this section. In Figure g we show the cases of 2D regression and the additional cases of Art-Multi are illustrated in Figure We the additional cases also support our observations and interpretations.
V1
P1
PI
V2
PO
PO
VO
VI
V2
V3
V4 V5
VO
V1
V2
V3
V4
V5
P1
P1
PO
VO
V4
Quadratic
Cubic
P1
PO
PO
V0
V1
V2
V3
V4
V5
VO
V1
V2 V3 V4 V5
Quadratic Surface
Ripple
Figure 8: Additional cases on 2D regression.
48
055395
48
F2
6
6
<9
P2 Ps
Blur
Aircraft Blur
V6
46
5
V5
4
43
4
Bird Pencil
Texture Pencil
Airoreft Pencl
Fung Pencl
Figure 9: Additional cases of Art-Multi.
18

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Published as a conference paper at ICLR 2020
F Pencil
36. 20%
34.36%
35.46% 55.46%
36.27%
35. 55.38%
36.30%
35.51%
37.965 37.96%
36.52%
37.01% 1
38 38.36 33%
43.54%
46.3 (6.33%
46.69%
47.85%
46.5 39%
46. 43.43%
48.21 1
47.02%
47. 17.79%
49. 19.40%%
50. 60.53%
Table 8: Full results on Multi dataset. In this table, B, A, F represent bird, texture, aircraft, fungi, respectively, Plain means original image.
Blar
26%
38 05.00%
39 50.
40.000 40.09%
38. 53.588
40 10.38%
39 .6.6
42. 22.64%
10.08%
41 21%
42. 42. 13%
50.30 30%
60.56%
50.66 60.66%
54.04%
52.0 12.02%
52.26%
53. 18%
11.70%
52. 82%
54.60%
54.8 54.87%
F Plain
13%
37.71%
37.54%
41.73%
39 37%
41 11.88%
.9%
43 02.0%
12.97%
42.58%
44. 169%
51.18%
51 31.45%
53 73.92%
56 66.04%
54.00 44.08%
53. 18%
.6%
54.01%
54. 44.89%
55.97%
56 56.8399 83%
A Peneil
41. ..70%
35. 49%
36 65.66%
40.1 10.17%
34. 41.52%
35 55.98%
36. 08.
33.739 73%
39.61%
(0.87%
41 .93%
53. 00%
54.08%
54.73%
59. 99.09%
49 2..20%
52.31%
51.91%
46. 12%
52. 17%
59. 40%
61.41%
A Blur
.89%
43.9 13.94%
44 44.0%
47 47.59%
42 12.24%
47 .29%
63%
40.08%
13.36%
45.79%
47 99.9
62. 73%
63 63.41%
64. 29%
68.56 08.56%
02.54%
63 33.36%
63 33%
58. 28.29%
61 11.55%
67. 17.63%
68 68.59 59%
A Plain
51 03.%%
45. 15.54%
46. 18%
50. 42%
45. 45.599 59.59%
51. 51.24%
83%
43 64%
49. 99.95
49. 10.98%
51 $1.99%
64. 82%
65.84%
65. 16%
70.35%
64. 68%
64.88% 88%
66.57 57%
63 63.399 39%
63. 33.36%
70. 12%
71 89%
T Pencil
74%
28. 48%4
29 09.08%
30 82%
28. 39%
28 38%
29 69%
29 23%
29 99.90%
30.1 10.17%
31 31.51%
33 83%
38. 40%
38 60%
40. 18%
38 87%
37 91%
39. 39.76% 76%
39 20.20%%
40. 10.07%
41 11.33%
41 98%
T Blur
29. 10%
29. 99.08%
29. 48%
29. .00%
28. .5%
28. 70%
29. 11%
29 63%
29. 79.
30 21.
30. 30.77% 77%
35. 49%
38 43%
37 87.86%
41 80%
39 59%
37. 79%
30 83%
39 39.429 42%
40.31%
40. 13%
40. 15%
T Plain
30 0.%%
31 1.%3%
31 56%
32 03%
30 57%
29. 28%
31 020
32. 13%
31 31.88%
32.01%
32.31 %
38 85%
44.78%
43 43.41%
44.93%
42. 96%
41 80%
43. 18%
43 13.23%
4..57%
44 68%
45. 32%
Pencil
80%
46, .6%
47. 76%
48 85.85%
48 585
48. 48.18% 18%
47 83%
50 25%
50 50.96%
51 51.09%
52. 97%
60.76% 76%
61 11.82%
62.69%
65. 45%
63 93%
64.33%
1..00%%
68. 28%
64.57%
65. 62%
67 14%
B Blur
51 .56%
50. 00.9%
51.14%
52. 18%
52. 52.62 62%
53 03.08%
52. 87%
54.21%
53.18%
53 20%
54. 89.%
65. 65. 12%
67. 67.90%
68. 08%
69.055 99.05%
68. 68.65% 65%
68. 73%
68.52 51%
69. 20%
70.50%
69. 31%
71.31% %
B Plain
52. 46%
63.67%
53. 13.30%
54.76%
55. 25.27%
55. 23%
56. 71%
56. 99%
57. 73%
58. 15%
59. 59.67% 67%
66. 28%
70. 42%
68. 68.60%
70. 08.08%
71. 71.51%
71 11.31%
71. .66%
71.18%
71 11.77
71.75%
73. 03.05%
MUMOMAML
MUMOMAMI
Algorithms
VERSA
ProtoNet
TapNet
TADAM
MAML
MetaSGD
BMAMM
MI--Nt
HSML
ARMI.
VERSA
ProtoNet
TapNet
TADAM
MAML
MclaSGD
BMAML
MT-Net
HSML
ARML
|
Settings
5-way I-shot
5-way 5-shot
19


Reviews:
[{"review_id": "rJenyvF6YB", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "################################################################################\nSummary:\n\nThe paper provides a interesting direction in the meta-learning filed. In particular, it proposes to enhance meta learning performance by fully exploring relations across multiple tasks. To capture such information, the authors develop a heterogeneity-aware meta-learning framework by introducing a novel architecture--meta-knowledge graph, which can dynamically find the most relevant structure for new tasks.\n\n\n################################################################################\nReasons for score:\n\nOverall, I vote for accepting. I like the idea of mining the relation between tasks and handle it by the proposed meta-knowledge graph. My major concern is about the clarity of the paper and some additional ablation models (see cons below). Hopefully the authors can address my concern in the rebuttal period. \n\n################################################################################\nPros:\n\n1. The paper takes one of the most important issue of meta-learning: task heterogeneity. For me, the problem itself is real and practical.\n\n2. The proposed meta-knowledge graph is novel for capturing the relation between tasks and address the problem of task heterogeneity. \nGraph structure provides a more flexible way of modeling relations.\nThe design for using the prototype-based relational graph to query the meta-knowledge graph is reasonable and interesting.\n\n3. This paper provides comprehensive experiments, including both qualitative analysis and quantitative results,  to show the effectiveness of the proposed framework. The newly constructed Art-Multi dataset further enhances the difficulty of tasks and makes the performance more convincing.\n\n################################################################################\nCons:\n\n1. Although the proposed method provides several ablation studies, I still suggest the authors to conduct the following ablation studies to enhance the quality of the paper:\n(1) It might be valuable to investigate the modulation function. In the paper, the authors compare sigmoid, tanh, and Film layer. Can the authors analyze the results by reducing the number of gating parameters in Eq. 10 by sharing the gate value of each filter in Conv layers?\n\n(2) What is the performance of the proposed model by changing the type of aggregators?\n\n2. For the autoencoder aggregator, it would be better to provide more details about it, which seems not very clear to me. \n\n3. In the qualitative analysis (i.e., Figure 2 and Figure 3), the authors provide one visualization for each task. It would be more convincing if the authors can provide more cases in the rebuttal period.\n\n\n################################################################################\nQuestions during rebuttal period:\n\nPlease address and clarify the cons above\n\n################################################################################\nSome typos:\n(1) Table 7: I. no sample-level graph -> I. no prototype-based graph\n(2) 5.1 Hyperparameter Settings: we try both sigmoid, tanh Film -> we try both sigmoid, tanh, \nFilm.\n(3) parameteric -> parametric\n(4) Table 2: Origninal -> original\n(5) Section 4 first paragraph:  The enhanced prototype representation -> The enhanced prototype representations\n\n\nUpdates: Thanks for the authors' response. The newly added experimental results address my concerns. I believe this paper will provide new insights for this field and I recommend this paper to be accepted.\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "BkeCLhJAtr", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper mainly tackles the problem of heterogeneous tasks in meta-learning by proposing a new meta-learning framework ARML, which contains a module extracting relations across classes and a module representing meta-knowledge. When processing a new task, a graphical task representation is firstly constructed based on class prototypes, and then information propagation is conducted on a super-graph to find the most relevant meta-knowledge in the meta-knowledge graph. Ideally, the higher similarity between a prototype and a meta-knowledge node means the higher the correlation between a class and a specific type of meta-knowledge. In order to construct task-specific meta-learners, the authors utilize two auto-encoders to encode task representations with and without meta-knowledge graph. After that, a modulating function is applied to a set of shared parameters, which finishes the calculation of task-specific parameters. The authors empirically evaluated the proposed method on several datasets and it seems that ARML outperforms some compared methods.\n\nThis paper should be rejected. Firstly, the proposed method is not well motivated. It’s true that tasks in meta-learning may be sampled from a complex (or multi-modal) task distribution, but why to represent a task as a graph? I think the relation between tasks can be simply obtained from instances (CNN embeddings). Secondly, it’s hard to say the meta-knowledge graph can really capture knowledge with ‘exact meanings’ even though in some situations, a subset of nodes is activated and others are not.\n\nMain arguments\n1.\tThe whole framework is too complex and it’s hard to say every module in the framework really works even ablation study is done.\n2.\tThe meta-knowledge graph lacks interpretability. From my perspective, it’s just a set of learnable parameters without any exact meanings. Authors tried to analyze the constructed meta-knowledge graph by some experiments, but these discussions are farfetched.\n\nThings to improve the paper\n1.\tSimplify the proposed method.\n2.\tMake it clear why should we represent a task as a graph.\n3.\tSome most widely used benchmark datasets such as mini-imagenet and tiered-imagenet are not used. For a fair and convincing comparison, I suggest the authors test the proposed method on these benchmark datasets. Moreover, more methods should be compared.", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "BJeu-JE2FB", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposed a knowledge-based meta-learning framework, called ARML(Automated Relational Metal-Learning) that automatically extracts cross-task relations and constructs a meta-knowledge graph. ARML wanted to solve the task heterogeneity problem in meta-learning through knowledge graph learning using graph neural networks. To do this, the authors introduced a framework consisting of (1) finding a prototype-based relational structure, (2) constructing a meta-knowledge graph, and (3) adapting the task-specific knowledge. Experimental results show that the proposed algorithm outperforms other competitive algorithms in few-shot learning tasks, which is justified by experimentally showing that the learned meta-knowledge graph has a meaningful interpretation.\n\nThe paper was well-motivated and well-written, which made it very interesting to read. Looking at the task heterogeneity problem of meta-learning as a knowledge graph learning problem is the most important contribution of this paper. Since then, the framework's proposal to learn it as a graph neural network is a very natural extension, which can greatly increase the performance of existing few-shot learning tasks.\n\nThe question here is whether the meta-learning method for finding relational structures through knowledge graphs is the first one proposed in this paper. The paper \"Few-shot learning with graph neural networks, ICLR-2018\" performed the few-shot learning task with very similar motivation. What is the difference compared to this paper?\n\nAnd as mentioned in the paper, HSML is the closest study to ARML in that it considers high-level relations between cross-tasks. The reviewer is very curious about the qualitative comparison of the high-level structures found by the two algorithms, and I confident that this comparison will enrich the paper.", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes to deal with task heterogeneity in meta-learning by extracting cross-task relations and constructing a meta-knowledge graph, which can then quickly adapt to new tasks. The authors present a comprehensive set of experiments, which show consistent performance gains over baseline methods, on a 2D regression task and a series of few-shot classification tasks. They further conducted some ablation studies and additional analyses/visualization to aid interpretation.

Two of the reviewers were very positive, indicating that they found the paper well-written, motivated, novel, and thorough, assessments that I also share. The authors were very responsive to reviewer comments and implemented all actionable revisions, as far as I can see. The paper looks to be in great shape. I’m therefore recommending acceptance.  
Decision: Accept (Poster)