Clustered Task-Aware Meta-Learning by Learning from Learning Paths
Authors: Danni Peng
Sinno Pan
Venue: ICLR 2022 Submitted (2022)

Abstract: To enable effective learning of new tasks with only few samples, meta-learning acquires common knowledge from the existing tasks with a globally shared meta-learner. To further address the problem of task heterogeneity, recent developments balance between customization and generalization by incorporating task clustering to generate the task-aware modulation to be applied on the global meta-learner. However, these methods learn task representation mostly from the features of input data, while the task-specific optimization process with respect to the base-learner model is often neglected. In this work, we propose a Clustered Task-Aware Meta-Learning (CTML) framework with task representation learned from its own learning path. We first conduct a rehearsed task learning from the common initialization, and collect a set of geometric quantities that adequately describes this learning path. By inputting this set of values into a meta path learner, we automatically abstract path representation optimized for the downstream clustering and modulation. To further save the computational cost incurred by the additional rehearsed learning, we devise a shortcut tunnel to directly map between the path and feature cluster assignments. Extensive experiments on two real-world application domains: few-shot image classification and cold-start recommendation demonstrate the superiority of CTML compared to state-of-the-art baselines.

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CLUSTERED TASK-AWARE META-LEARNING BY LEARNING FROM LEARNING PATHS
Anonymous authors Paper under double-blind review
ABSTRACT
To enable effective learning of new tasks with only few samples, meta-learning acquires common knowledge from the existing tasks with globally shared meta- learner. To further address the problem of task heterogeneity, recent developments balance between customization and generalization by incorporating task cluster- ing to generate the task-aware modulation to be applied on the global meta-learner. However, these methods learn task representation mostly from the features of in- put data, while the task-specific optimization process with respect to the base- learner model often neglected. In this work, we propose Clustered Task- Aware Meta-Learning (CTML) framework with task representation learned from both features and learning path. We first conduct rehearsed task learning from the common initialization, and collect a set of geometric quantities that adequately de- scribes this learning path. By inputting this set values into a meta path learner, we automatically abstract path representation optimized for the downstream clus- tering and modulation. To further save the computational cost incurred by the additional rehearsed learning, devise shortcut tunnel directly map between the path and feature cluster assignments. Extensive experiments on two real-world application domains: few-shot image classification and cold-start recommenda- tion demonstrate the superiority of CTML compared to state-of-the-art baselines.
INTRODUCTION
The astonishing performance of deep learning relies on large amounts data, which are not always available. Humans, the other hand, are able to learn new tasks much more quickly, leveraging prior experience to relate knowledge among tasks. Inspired by this property of human intelligence, meta-learning (also known as learning to learn) (Thrun & Pratt, 1998) acquires transferable com- monalities from existing tasks for more efficient learning of new tasks. Although recent advances in meta-learning have demonstrated success in fields like few-shot image classification and cold-start recommendation (Vinyals et al., 2016; Snell et al., 2017; Ravi & Larochelle, 2016; Munkhdalai & Yu, 2017), most of them typically assume that all the tasks are drawn from single distribution and face the challenge of handling tasks that come from different underlying distributions, a problem known as lask heterogeneity (Devos & Dandi, 2020; Yao al., 2020; Suo al., 2020).
To overcome this challenge, many recently developed works leverage task-specific information to customize the global meta-learner (Vuorio al., 2019; Oreshkin et al., 2018; Requeima al., 2019; Finn et al., 2018; Yoon et al., 2018; Li et al., 2019; Rusu et al., 2018). To further consider gener- alization among related tasks, methods that perform various types of task clustering are proposed (Yao et al.. 2019; 2020: Suo et al., 2020; Lu et al., 2020; Dong et al., 2020; Lin et al., 2021). De- spite their effectiveness in improving over the globally shared meta-learning algorithms, they learn task representations only based on the input data distribution in (original or projected) feature space, while the interaction between data and the base-learner is often neglected.
The amount of information contained in the task-specific data about network that is responsible for performing the task can be seen as a good representation of the task itself. This can be manifested as the gradients of the network parameters with respect to the task-specific loss, or Fisher Information Matrix (FIM) which indicates the importance of different network parameters in solving the task.
Achille et al. (2019) introduce task embedding method based on FIM to assist the meta task of selecting a pre-trained feature extractor. To alleviate the conflict issue of the global initialization methods, Baik et al. (2020) utilize task gradients the initialization as task representation to produce

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attenuation. However, these methods represent task based gradients only single point in parameter space (e.g., at the initialization), while the potential of exploiting a wider range on the task manifold remains unexplored.
For the parameter initialization approach, the key of success lies in that the task adaptation process is accounted for when training the meta-learner. This task-specific learning may involve multiple gradient descent steps, and thus constitute a learning trajectory on the loss surface (Flennerhag et al., 2018; Zenke et al., 2017). To better characterize the task optimization behaviors, it is more beneficial to look at the complete learning trajectory as opposed to only the first gradient step at the initialization, as is likely that tasks with similar gradients at first will have their learning paths diverged as the update proceeds. With that in mind, we are motivated to leverage the entire learning path for better task representation, which will then be used to condition the global initialization.
In particular, we propose a Clustered Task-aware Meta-Learning (CTML) framework, building upon the well-known global initialization method Model-Agnostic Meta-Learning (MAML) (Finn et al., 2017). To address the problem of task heterogeneity with good balance between customiza- tion and generalization, we modulate the common initialization based on task representation learned from both its local task-specific information and global clustering results. In addition to using the input features to represent task, we further leverage the task learning path with respect to the base- devise
learner to characterize task from the perspective of optimization. To facilitate clustering, GRU-based meta path learner which automatically abstracts path representations from the step-wise geometric quantities. We realize that it may be too costly rehearse the entire learning process for task representation. Hence, we further propose a shortcut tunnel to bypass the rehearsed task learning during meta-testing and predict path cluster assignment directly from the feature cluster assignment. We carefully study the effectiveness of CTML in two real-world application domains: few-shot image classification and cold start recommendation, and show that our method able to outperform the baselines with comparable inference time.
2 RELATED WORK
To address the problem of task heterogeneity, recent developments often tailor the shared meta- learner to different tasks using task-specific information. Finn et al. (2018) and Yoon et al. (2018) model the uncertainty exists in task distribution with probabilistic framework. Oreshkin al. (2018), Li et al. (2019), Requeima et al. (2019) and Bateni et al. (2020) condition the base network on task- specific data by designing a meta adaptation network. To enable more robust training. Rusu et al. (2018) propose to learn lower-dimensional latent space specific to each task to generate the base network parameters. Relevant to our work, Vuorio et al. (2019) build upon MAMI. and modulate the global initialization based on the task representation learned from an encoder network.
However, customizing the common knowledge to individual task without considering the relations among similar tasks may lead to poor generalization. In regard to this, Dong et al. (2020) and Lin et al. (2021) apply K-means clustering on users (treated as tasks) based on their profile information to address the cold-start problem in recommender systems. Yao et al. (2019) employ hierarchical structure to model the nested relationships inherent in domains with clear taxonomy, such as image classification. Yao et al. (2020) further develop an automatic relational graph method by constructing a meta knawlegg graph to preserve and propagate the global structural information. Suo et al. (2020) take advantages of an external knowledge base to facilitate task clustering. Despite their effectiveness in generalizing across tasks, they rely solely on input features for task representation, while the interaction between task data and the base-learner (e.g.. gradients) is often neglected.
The idea of using gradients for task representation is commonly adopted in continual learning (Kirk- patrick et al. 2017: Zenke et al.. 2017: Aljundi al., 2018). In the context of task-aware meta- learning, Achille et al. (2019) propose to use the FIM of a "probe" network to represent task, and Baik et al. (2020) leverage gradients of the globally initialized parameters to generate task-specific attenuation. However, these methods utilize gradients only at single point in parameter space, whereas meta-learning often incorporates the entire task learning trajectory while learning the meta- learner. Garcia et al. (2021) perform task clustering at each adaptation step and aggregate the gradi- ents for more stable task adaptation. Flennerhag et al. (2018) highlight the benefits of leveraging the learning paths for deriving the common knowledge, but the proposed algorithm only relies on one geometric quantity- - the length of the path, which can be limited in characterizing the learning paths, and the initialization is not tailored to specific task. Our work serves to address the above-mentiones
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limitations, whereby higher-order behaviours of the learning path are also taken into account to learn a better task representation for modulating the global initialization.
3 PRELIMINARIES AND PROBLEM STATEMENT
In task-heterogeeneous setting, tasks (T1, T2, ...; TN) are sampled from a mixture of task distributions {pi (T), P2 (T)),, where the number of underlying distributions is usually unknown. The goal of meta-lcarning is to learn the sharable knowledge by training the meta-learner on a set of meta- training tasks T = {TiJi=1 and test it on a set of meta-testing tasks T = {T:),= -fJi=Ne++1 For each task T: E T UTe, its samples are further divided into a training set (also termed support set) D.F- = [(x,, (iss::ii.)): )= together form an "episode" (Vinyals et al., 2016). This episodic scheme allows to learn fast during meta-training, and test the learning performance of new tasks in the same way during meta-testing. For few-shot learning, the size of the training set n is usually small.
ni and a test set (also termed query set) Dif {(xx.) (.ss)::.,)))) (e,)) +1 which
train tasks
Our work builds upon Model-Agnostic Meta-Learning (MAML) (Finn et al., 2017). implements the meta-learner as an initialization of parameters On RD. of the base-learner fo responsible for the prediction task. During meta-training, the global initialization 0g is first adapted to each meta- training task T T by learning on the respective training set D.F, which yields the task-specific parameters TT. After that, loss is computed on the test set D4; based on 0y, and backward propa- gated to update 8g. Taking one step adaptation as an example, the metm-oppiiizztiin is as follows:
0 arg min
Σ C(for, D4.)) arg Σ [[fer-avo TRETt
D4.), (1)
On
Oo TeET
where a is the adaptation rate, C(Je. D) can be mean square error loss for regression prob- lem (i.c., [D E(xx)ED(V - fx())) or cross-entropy loss for classification problem (i.e., (xx,))D yog (x()). During meta-testing, the learned initialization 0g is adapted to each meta-testing task Ti E T using Dj and the learning performance is evaluated on Di;-
However, with globally shared initialization, MAML is not capable handling task heterogeneity. Though task-specic methods have been developed to tailor the global initialization, they lack explicit modeling of the global clustering structure. Hence, a framework considering both ssecifpcciiic information and global structure is desired.
4 METHODOLOGY
Grounded on MAML, our CTML framework modulates the common initialization based on task representation learned from different perspectives enhanced with the clustering information. Specifically, given the training set of a specific task, we first conduct rehearsed learning of the task from the common initialization and compute set of step-wise quantities along the learning path. This set of values will be inputted into the meta path learner to generate a task-specific path embedding. On the other hand, imput features of the given task will also be extracted to form the feature embedding. Both feature and path embeddings will then undergo soft K-means clustering in their respective latent space. Finally, the two embeddings enriched with cluster information will be aggregated to produce the task-aware modulation to be applied on the global initialization. From this modulated intialization, standard MAML follows, which conducts the actual task learning on the training set and perform meta-update across tasks using the test sets. To further improve the inference efficiency during meta-testingg a shortcut tunnel is used to bypass the rehearsed learning process and generate the path cluster assignment directly from the feature cluster assignment. An overview of CTMLL framework is shown in Figure 1.
In the following sections, first elaborate task representation learning based on learning path and features respectively, and then introduce the aask- modulation and the shortcut tunnel.
4.1 TASK REPRESENTATION BASED ON LEARNING PATH
4.1.1
PATH CONSTRUCTION
To obtain representation of task T. based on learning path, we first conduct a 7-step rehearsed learning from the global initialization On on training set Djr. Applying the same gradient de- scent update in MAMI, we obtain the updated parameters each step t E (1,2...,T) by:
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Centice Bi]
Fentere
Dutnceer
FC
S
Teal Awars
updnn Rehwarsed Learing Actual lonk Loaring
Recosemuttion LosG
6ur
Loarning Pach
Parh Leamer
Big
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Pash Erileddnn
0%
Tehes sad
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Figure 1: Overview of CTML framework. For each incoming task
Figure 2: Illustration of
Tú part (a) extracts path representation and performs clustering; part
CTML task learning process. Tasks with similar rehearsed learning paths will produce similar modulations.
(b) extracts feature representation and performs clustering; part (c)
generates task-aware modulation for global initialization; part (d) re-
constructs path cluster assignment from feature cluster assignment.
04. = T. aVoL(J=== D4,,, where 09; = 0-- The overhead is used to differentiate between the parameters updated from the rehearsed learning and from the actual learning.
Joining the discrete points {(04, )== constitutes the rehearsed learning path of T; (we write L(fay
y; ).: Cty for brevity) the unique task manifold MT; E PR+ characterized by the base-learner function and the task-specific data distribution. We collect the coordinates of point (04, (4,) at each update step E 1,., to indicate the exact learning trajectory. To account for higher-order behaviours of the learning path, we further incorporate the gradients V VeCy, and the Fisher Information Matrix (FIM) Ft at each step, which specify the direction and curvature respectively. Note that by definition, the FIM is equivalent to the Hessian matrix in expectation for cross-entropy loss: F+ Exx.vT,IVVe....
x, y) veVelffo, x) [ x, y)]. It provides measure of the amount of information that task Tú contains about the parameters O (Gianfelici & Battistelli, 2009). Following Achille et al. (2019), we assume negligible correlation among different parameters and consider only the diagonal entries of 17,, denoted by F7. As a result, we obtain a set of step-wise quantities {(0),: Ci VoCi, Fi Di that adequately describes the rehearsed learning path.
As opposed to looking at only single point in the parameter space (e.g., use gradients at the ini- tialization to represent task (Baik et al., 2020)), it is benificial to take into account the entire learn- ing path traversed, which gives more complete picture of the optimization process. Take for instance, two tasks To and To may have gradients forming a small angle Vo at the initialization, ie., (0,))) O. However, it is likely that their learning paths will diverge the gradient update proceeds, i.e., the accumulated angle Σz= cos(v) < 0 (see dotted paths of Tz and Ts in Figure 2). Conversely, the tasks may have gradients pointing at different directions at first, but eventu- ally converge towards the same direction as the learning proceeds (see dotted paths of Ti and T2). Considering a single step only can be restrictive for task representation from the optimization per- spective. Looking further down the paths allows better characterization of the learning behaviors and even the flexibility to determine the "important" steps (as shown in experiments later), producing more informative task representations. Furthermore, leveraging path representations serves to pro- vide a stronger inductive bias to condition the initialization in favorable direction, as the rehearsed learning path can be considered encoding the quality of the initialization with respect to the task (i.e., tasks with longer and more zigzag paths imply that the initialization is not a good one for them).
4.1.2 PATH REPRESENTATION
Having collected the step-wise quantities ((0%, Fr) along the rehearsed learn- ing path, the problem now is how to evaluate "similarity" among different task learning paths for clustering. Previous works with single-step gradients usually compute dot product or cosine sim- ilarity between gradients of two tasks (Riemer et al., 2018; Katoch et al., 2019; Yu et al., 2020; Baik et al.. 2020). With multiple steps, straightforward adaptation will be to simply sum up the similarity scores at all steps. However, this human-defined rule may not be the best way of mea- suring path similarity. Instead, propose to employ meta path learner to automatically learn
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path embedding from the step-wise quantities, and then measure similarity based on these vector representations. In other words, the meta path learner induces a latent space on which the distance metric best characterizes what is considered as "similar" (or "disimilar") among task learning paths.
Before we delve into the design of the path learner, we first elaborate how we construct the functional input from the step-wise quantities. Recall that at each step t, we have f7.: F, E R and CT IR. To obtain regularly shaped input, we duplicate L to form D-dimensional vector and stack it together with the other 3 components form a matrix P E IR*x,, Further stacking the 7+1 1 steps gives the overall 3-D matrix PT, E [[(+1)x4XD) To avoid high model complexity, we apply the meta path learner coordinate-wise on the base-learner parameters. That is, the same path learner is used to process the matrix Pd E R(r+1)x4 independently for all E (1,2,.., D}-
For the path learner design, we propose to leverage the Gated Recurrent Units (GRUs) to model the sequential dependencies among steps'. Specifically, the hidden state h at step & is obtained by inputting the t-th sliced vector P E I of P4, and the hidden state h d.t-1 step - 1 into the GRU cell:
! = (W, [ 1n P Pi,,), 2.tt = = [h. d.1--1 .P..D.
h tanh (W; (e hg 1 P(,,,,
h h (1-
d
2 d.f on.
where | denotes concatenation, a--) is the sigmoid activation, ri d.t d.t (0, are gates that control how much of past and present information to be retained, and W., W W are learnable weights shared across all steps. For step
22
we use zero-initialized input hidden state.
The path representation hę at the d-th dimension is obtained from the final step hidden state h via a linear transformation: he = W. h + b,- Concatenating the path representations at all D dimensions and passing it through fully-connected layer gives the final path embedding path Rd for task T;: co.th FC h,!TT).
T,
Inspired by (Suo et al., 2020; Dong et al., 2020; Lin et al., 2021), we handle task heterogeneity without jeopardizing generalization among similar tasks by employing a simple yet effective soft K-means clustering on the path embeddings². Specifically, we maintain kpath learnable cluster Apee xd. for path embeddings. The cluster-enhanced path embedding s E dR is simply the weighted sum of the cluster centroids:
centroids {agoth
VVj E [1, ]
awath
1= dij
Apach path aooth
(3)
(I (1+11022 pach puth
where Li (1+1le
1 is the probability of assigning path to cluster j. computed using the Student's -distribution kernel, following Xie al. (2016).
path
4.2 TASK REPRESENTATION BASED ON FEATURES
Task representation based on learning path can be interpreted as encoding the conditional distribu- tion p(y]x) (as the learning path is informed by the labels), whereas task best described by the joint distribution p(x, v) = p(v x)). Therefore, we further incorporate the marginal distribution of input features by learning another representation solely based on features, as what have been done in most of the existing task-aware meta-learning methods (Vuorio et al., 2019; Yao et al., 2019; 2020; Lin et al., 2021). Another significance of including feature-based representation is that, we create a mapping between the path and feature representations to bypass the rehearsed learning during the meta-testing phase (details will be claborated in Section 4.4).
Generally, the design of the feature extractor may vary for different application domains. Let E-) denote an arbitrary feature extractor, the feature embedding e E TRd. for task T₁ is obtained by
aggregating the extracted features of all samples in the training set: e
(E(xx,))
Similar to the path embeddings, we also employ soft K-means clustering to promote generaliza- tion among related feature embeddings. Specifically, given kfeat cluster centroids (a. foat [Vj
'Other network designs are possible for the meta path learner. We compare their efficacy in ablation study. Otter clustering algorithms are possihle. We leave it future work.
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[1, kfeail } E Reat the
feature embedding T,
feat RR is obtained by:
ef
kfout
Feat feat a
T
Pij
(4)
you 113)= (1+1l07 foat a
where Oij
feat
the probability of assigning ey, cluster j.
(,+ coul 11)-1
4.3 TASK-AWARE MODULATION
We aggregate the path and feature embeddings via learnable weight vector À to generate the final lask representation. This task representation will then be used to produce a modulation to tailor the global initialization On specific task. The modulated initialization Oo: for task T; is obtained by:
lor = ( (Ae @ (1
2)07
feat + b) @ 0o:
(5)
where W, b, À are learnable parameters, a(-) is the sigmoid function, + and C denote element-wise addition and element-wise multiplication respectively.
From this modulated initialization, task Ti will undergo regular task adaptation learning for T steps. After that, the meta-leamer & will be updated by optimizing loss across all the test sets, the same procedure as in MAMI.. The meta-optimization objective is:
min TiETir
L( Eiod voliing DF) D
(6)
where & includes the global initialization Og, the learnable parameters used to generate the cluster- enhanced path and feature embeddings, and also the final modulation.
4.4 IMPROVING META-TESST TESTING EFFICIENCY VIA SHORTCUT TUNNEL
The need to conduct rehearsed learning before the actual learning of each task inevitably leads to twice the inference time compared to the original MAMI., Though it is not possible to bypass the rehearsed learning during meta-training downstream cluster centroids, it is possible to improve the inference efficiency during meta-testing with the well-traines cluster centroids. Note that the cluster- enhancd path embedding apath used to generate modulation is obtained based on the path cluster centroids and the soft assignment (see equation 3). If we can estimate the path cluster assignment without actually going through the path rehearsed learning process to obtain CT, we will be able to reduce the inference time by half.
we need to optimize the meta path learner and the
Inspired by this, we devise shorteut tunnel to predict the path cluster assignment directly from the feature cluster assignment of the same task. The assumption behind is that there exists one-to- one mapping between the feature cluster assignments and the path cluster assignments, which can be linear or non-linear. For better expressivity, we employ two-layer fully connected network to approximate the mapping and use it to reconstruct the path cluster assignment of T, from its feature cluster assignment:
q gatt sooftmax Ceftimax(Fss(q" (raat)
where q feat Igfret ...., lik Bikyeot yeat mapping handles cases where knoth * kfoat and allows for different softness of cluster assignments. To align the reconstructed and the actual assignment distributions, we the Jensen-Shannon (JS) divergence (a symmetrized version of Kullback-I
feat JT E Rijeatt and q q.uthh [aaath
Saat
E
R Riach The
(KI.) divergence) as the reconstruction loss:
(.())) = JS(
path path [|q math)
1 2
+ KL(q. path [p:),
1
(8)
where p, = (4 math + o path) and (L(q))p) = E, dj log 3L is the KL divergence. During meta-
training, the reconstruction loss is optimized together with the loss in equation 6, resulting in the following overall objective:
min
L(S a Eied vollos :4.) D4) (D4)
T.E
where ( controls the weight of (D(F), and é now further includes the shortcut tunnel parameters.
To apply the shorteut tunnel during meta-testing, we simply replace q; gath with q gooth in equation 3 to obtain the custeee- path embedding aPoth i... a Ehath spath path, The overall meta-training and meta-testing procedures of CTML. are summarized Algorithm and 2.

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Algorithm 1: Meta- Vetan-rainnnn of CTML.
Algorithm 2: Meta-Testing of CTML.
Required:
Meta-training tasks T [Ti)==:
Required: Meta-testing tasks T = (Ti NT 41
Number of steps r; Adaptation rate o;
Number of steps T; Adaptation rate as Number of clusters kpath and kyeat; Meta-trained +
Meta-update rate B3 Number of clusters
Kputh and feut
Randomly initialize all learnable parameters while not converged do
for Ti E T do
Extract feat and cluster to obtain feat T; if use shortcut appraximation then Generate path assignment via the shortcut tunnel to obtain 77
Sample batch of tasks B from T for T: E B do
Extract feut and cluster to obtain e/ feot Extract e/t from the 7-step rehearsed learning and cluster to obtain an Aggregate e7; and T, to generate Oo: Evaluate [[J07, Dff) and (P%)
else
Extract et from the 7-step rehearsed learning and cluster to obtain e% Aggregate e7,
Feat and spoth to generate Oo:
Meta-update 4-
Φ B EnealCUer, Df.) (D.)
Evaluate L[So,,
5
EXPERIMENTS
To test the effectiveness of the proposed CTML framework, we conduct experiments on two real- world application domains: few-shot image classification and cold-start recommendation.
5.1 FEW-SHOT IMAGE CLASSIFICATION
Datasets and Settings In few-shot image classification, each task is defined as assigning images to N classes after training with K samples (i.e., N-way K-shot) (Vinyals et al., 2016). To simulate task heterogeneity, we construct the Mixture-Of-Datasee consisting of 6 widely used benchmark datasets: LUB-200-2011 (Bird) (Wah et al., 2011), I), FGVC-Aireraft (Aircraft) (Maji et al., 2013), FGVCX-Fungi (Fungi) (Schroeder & Cui, 2018), VGG Flower (Flower) (Nilsback & Zisserman, 2008), Describable Textures (Texture) (Cimpoi et al., 2014), and GTSRB Traffic Signs (Traffic Sign) (Stallkamp et al., 2012). Following Yao et al. (2019), we create each task by sampling N classes from one of the 6 sub-datasets. This step ensures that tasks are drawn from different underlying distributions. Apart from the Mixture-Of-Datasef, we also conduct experiments on the Minilma- genet (Ravi & Larochelle, 2016), which can be considered as a task-homogeneous setting as tasks are sampled from a single dataset (results on Minilmagenet are discussed in Appendix D.2). More details on datasets and pre-pree pre-processing can be found in Appendix A.1.
Baselines and Our Method We compare the performance of our method against 5 baselines: (1) global initialization method: MAMI. (Finn et al., 2017); (2) task-specific initialization methods: MMAML (Feature-based customization) (Vuorio et al., 2019) and L2F ggradient-based customiza- tion) (Baik et al., 2020); (3) cluster-enhanced initialization methods: HSML (feature-based hicrar- chical clustering) (Yao et al., 2019) and ARML (feature- based relational graph) (Yao et al., 2020). For our proposed CTML, we report both the original meta-testing performance (CTML) and the one applying shorteut approximation (CTML(approx.), We further implement 2 variants com- pare with the baselines: CTML-feet which only depends on feature representation and CTML-path which only depends on path representation. Following Finn al. (2017), adopt both the feature extractor E() and the base-leamer fe as a four-layer 3 x 3 convolutions with 32 filters for all the compared methods (experiments on deeper network for base-lcarner can be found Appendix D. Further details on hyper-parameten settings can be found in Appendix B.1.
Baseline Comparison Table la presents the 5-way 1-shot & 5-shot classification performance on Mixture-Of -ftttaaes (disentangled performance on individual sub-datasets are included in Ap- pendix D.3). First of all, we see that all the task-aware methods outperform the globally initialized MAML in mask-heterogeneuus setting. L2F with gradient-based conditioning on the initialization performs better than the feature-basse MMAML. After considering generalization across similar tasks with some clustering techniques, HSML and ARMI further improve over MMAMI. Under our proposed CTML. framework, CTML-feat with K-means clustering on features exhibits compara- ble performance as HSML and ARMI.. For CTMh-ppah, the improvements over baselines are more
All experiments conducted using NVIDIA Tesla P100 GPU with 16GB memory.

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Table 1: Few-shot classification performance on Mixture-Of-Datasets for (a) baseline comparison and (b) ablation study. We sampled 1000 tasks for meta-testing. The results are reported in the form of mean accuracy (%) + std over 8 trials. We also report the inference time (in milliseconds) per task during meta-testing for the 5-way 1-shot scenario for baseline comparison.
(b) Ablation Study
(a) Baseline Comparison
Mixture-Of Oaiee-OFDDuuu Df-Datasets
Mixture-Ce Of Datasets
Variants
Methods
5-way I-shot
S-way 5-shot
5-way I-shot
5-way S-shot
runtime
Remove T
56.74 + 1.03
71.38 0.52
MMAML
MAMI.
54.28 = 1.30
52.83 1.54
66.54
67,82
1 0.59
83.2
82.9
Remove E
57.24 + 1,20
71.50 4: 0.71
L2F
56.61 1.21
68.45
117.9
Remove V Ti
57.89 + 1.33
71,76 +: 0.61
HSML
56.32 = 1.16
68,73
041
101.3
Remove Fiz 72
58.13 + 1.12
71,88 0.67
ARML
57.21 = 1.68
69.29 1: 0.42
93.0
Linear Path Learner
57.52 # 1.09
71.44 +: 0.47
CTM---feat
57.14 = 1.38
68.71 0.52
84,3
FC Path Learne
58.37 = 1.02
71,62 0.30
CTML-path
57.74 1: 0.67
70.63
171.2
Attention Path Learner
58.67 + 1,40
71.83 +: 0.56
CTML
59,03 = 0.84
72.18 0.42
181.0
No Clustering
57.29 4: 1.24
71,06 J: 0.62
CTML(approx.)
58.91 +: 0,95
71.69 0.61
85.7
CTML
59.03 :: 0.84
72.18 0.42
Aircraf:
0.5-
-0.5
Flower
CUTTE
-1.0
-05
0.0
0.5
1.0
1.5
1m-7
Bin CDVE KCR
KAU 9,07
_
Traffic
Sign
KITH
DAMI
WSTW 0500
-05
0.0
55
1.0
PC1
0
(a)
(b)
Figure 3: Understanding the path learning mechanism. (a) 6 tasks (5-way 1-shot) are randomly sampled from Aireraft, Flower and Traffic Sign sub-datasets. (b) PCA visualization of the 5-step rehearsed learning paths (upper plot) and the corresponding path embeddings generated by the GRU (lower plot) for the 6 tasks. (c) Visualization of z gate (how much to retain for the current step input) and gate (how much to retain for the previous step memory) of GRU at each step & for the 6 tasks.
significant, especially for the 5-shot scenario where the learning paths are more reliable with more training data. The final CTML combining the advantages of the two representations achieves further improvements and outperforms the strongest baseline by a significant margin. Nevertheless, we can see that the meta-testing time of CTML. is about twice that of the baselines due to the additional rehearsed learning process. After applying the shortcut approximation, we are able to cut down the inference time by half with just a small compromise on performance.
Ablation Study We further conduct ablation study to test the efficacy of various CTML designs, including the step-wise input components, the path learner design, and the effects of clustering. From the results in Table 1b, we see that the lower-order quantities seem more important. Regarding the path learner design, our proposed GRU-based model achieves the best result due to its ability to capture the sequential dependencies among the steps. Attention model is also a competitive alterna- tive, as the positional encodings and the causal mask serve to constrain the sequential order (detailed descriptions of the different path learner designs can be found in Appendix C). As for clustering, we see that it indeed helps to generalize better as the global structure is explicitly considered.
Understanding the Path Learning Mechanism To understand what has actually been learned by the GRU path learner, we randomly sample 6 tasks (5-way 1 1-shot) from Aircraft, Flower and Traffic Sign sub-datasets (Figure 3a) and visualize their path learning results. In Figure 3b, we plot the 5- step rehearsed learning paths (upper) and the corresponding path embeddings generated by the GRU (lower) on the first two PCA components. We can see that the learning paths of tasks from the same sub-dataset generally move along the same direction, and the corresponding path embeddings are able to encode the path geometric information and positioned closely for similar tasks in the latent space. In Figure 3c, we further visulize the gates and gates of the GRU at each step t, which control how much to retain for the current step input and previous step memory respectively. We can see that the GRU path learner is able to identify the "important" steps (darker-blue blocks) and absorbs a larger portion of the inputs at these steps into the final path embedding. More examples on path visualization can be found in Appendix D.5
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Table 2:
Prediction performance in MAE
Number of path clusters Kuo
16 20
6.500
(lower the better) for 3 datasets. We port the mean MAE over trials, where the standard deviations are all less than 0.001.
Feature Cluster Assipmment
Shortout
0.766
13
Reconstrurted Parh Cluster
Mothods
MovieLens
Yelp
Amazon
Approcn.
McLU
0.8164
0.9464
0,7216
0,750
PAML
0.7725
0.9280
0.7150
MAMO
0.8084
0.8965
0.7207
Number feature clusters
Path Assignemet
MctaHIN
0.7727
0,8832
0.6743
(a)
(b)
CTML-feat
0,7560
0.9023
0.6804
Figure 4: (a) Effect of varying feat and kpach for
CTML-path
0.7592
0,8714
0.6286
MovieLens dataset. (b) Shortcut approximation of path
CTML
0.7543
0.8603
0.6048
cluster assignment for user from MovieLens dataset,
(TML(spprox.)
0.7555
0.8679
0.6087
where feeat 8 and kpath 16.
5.2 COLD-START RECOMMENDATION
Datasets and Settings In the field of recommender systems, meta-learning has been applied to solve the cold-start problem, which refers to making recommendations related to new items or new users unseen before (Vartak al., 2017: Volkovs et al., 2017; Lee et al., 2019). Here, we focus on the user cold-start problem, where recommending for each user is treated as a task. This setting lusk-heterogeneouus in nature as users may belong to different preference groups. We conduct experiments on 3 public datasets: Moviel IM (Harper & Konstan, 2015), Yelp (Dataset, 2019), and Amazon- (McAuley et al., 2015), consisting of user's ratings on movies, business services and CD products respectively. We split each dataset into meta-train/val/tesl by ratio 7/1/2 according to the timestamps of ratings. For each user, we use the first 10 samples as training set, and the rest as test set. Further details about datasets and pre- pre-processing
be found in Appendix A.2.
Baselines and Our Method We choose 4 baselines that specifically tackle the user cold-start problem in recommender systems developed based on MAML. MeLU (Lee al., 2019) is the first to adopt MAML in recommender systems with locally adapted decision layers; MetaHIN (Lu et al., 2020) further incorporates Heterogeneous Information Networks (HIN) for data augmentation and multi-faceted adaptations: MAMO (Dong et al.. 2020) involves global memory module to group users based on profile information and personalizes the initial bias; PAMI, (Yu et al., 2021) per- sonalizes the adaptation learning rate to allow for better fitting of the minor users. Following the baselines, we implement the feature extractor E-) as several embedding lookup matrices for differ- ent features, and the base-learner fe general recommender system model consists of embedding matrices followed by multiple fully-connected layers (Lee et al., 2019). Detailed
settings can be found in Appendix B.2.
Baseline Comparison error (MAE) on 3 datasets, reported in Table (more detailed results can be found in Appendix D.4). From the results, we can see that PAML and MAMO with personalized adaptation rate and initial- ization achieve better performance than MELU. Our CTML surpasses all the baselines, including MetaHIN which leverages HIN for data augmentation. Furthermore, we notice that for Moviel ens, CTML--feat slightly better than CTM,--path, while for the other two datasets, CTML.-path sig- nificantly outperforms CTML-feat. Given that the MovieLens dataset contains more complete user profile, this result implies the potential of representing users based on learning paths when the side information is seriously lacking inaccurate, which is often the case in real-world applications.
We evaluate the rating prediction performance in terms of mean absolute
Number of Clusters For recommendation problem, there is no ground-truth grouping of users. In Figure 4a, we investigate the effect of varying the number of clusters kyoth and keea for MovieLens dataset. We see that the best performance occurs at smaller k feat values and larger kipath values, which implies greater complexity for clustering the learning paths. Our design of the shortcut tunnel allows flexibility to set different kipath and Feat. In Figure 4b, we visualize the shorteut approxi- mation of path assignment from feature assignment for a random user Movielens, We can see that the shortcut tunnel is rather reliable the reconstructed path assignment highly resembles the actual path assignment. More examples on shortcut approximation are provided in Appendix D.6.
CONCLUSION
In this work, we introduce a CTML framework which leverages both features and learning paths for task representation. We employ a GRU-based meta path learnrr to process the step-wise wise geometric quantities, and introduce a shortcut tunnel to bypass the rehearsed learning during meta-testing. Experiments on real-world application domains demonstrate the effectiveness of our framework.

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7
REPRODUCIBILITY STATEMENT
Our code can be accessed at:
For data pre-processing and hyper-parameters settings, please see Appendix A and B.
ETHICS STATEMENT
Since the proposed method is general meta-leamiin framework, do not foresee any potential ethic issue to the best our knowledge.
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A DATASETS AND PRE-PROCESSING DETAILS
If not specially mentioned, datasets downloaded from the respective official websites, where we have tried our best to seek permission for usage if applicable. The open-source datasets are licensed under CCO: Public Domain. For recommendation datasets, all records anonymized and no personal identifiable information is involved.
A.1 IMAGE DATASETS
In our experiments, Ceeture-Of-Datasets consist of six widely used benchmark datasets. For the CUB-200-2011 (Bird), FGVC-Aireraft (Aircraft), FGVCX-Fungi (Fungi), and DTD (Texture) datasets, we directly acquire the pre-processed version released by the authors of HSML (Yao et al., 2019). Pre-processing details of these four sub-datasets can be found in the original paper of HSML. We have obtained the authors' consent to use this asset for our research.
For the VGG Flower (Flower) and GTSRB (Traffic Sign) datasets, download the raw datasets from the respective official websites. We follow the pre-processing protocols of Finn et al. (2017) to resize all the images to 84 x 84 x 3. We also try maintain the same cocta-train/valideee aaiin/vliiatiiontess ratio as Yao et al. (2019) for class splits. For VGG Flower, there are in total 102 flower classes, and each class consists of 40 to 258 images. For GTSRB, traffic sign classes, and each class has 30 images.
the official training data which contains 43
For Minilmagenet, we acquire the dataset as well as the metaa-taiin/validttionnes splits from Ravi & Larochelle (2016). Table summarizes the metaa-train//aliidationnees splits for each of the sub- datasets as well Minilmagenet.
Table 3: Metaa-taain/validdtiionnes splits of sub-datasets and Minilmagenet.
Datasets
#Metn- Classes
Validation Classes
CUB-200-208 118-200-2011 (Bird) (Wah al., 2011)
64
16
20
RGVC-Aireraf (Airemfit (Maji et al., 2013)
64
16
20
RGVCX-Fungi (Fungi) (Schrozder & Cui, 2018)
64
16
24
VGG Flower (Flower) (Nilsback Zisserman, 2008)
16
22
DTD (Texture) (Cimpui al., 2014)
30
7
10
GTSRB (Traffic Sign) (Stallkamp et al., 2012)
Minilmagenet (Ravi & Larochelle, 2016)
64
20
16
A.2
RECOMMENDATION DATASETS
A.2.1 MOVIELENS-IM
Mo dataset (Harper & Konstan, 2015) contains 1,000,209 anonymous ratings on around 3,900 movies made by 6,040 users. We acquire the additional side information released by the authors of McLU (Lee et al., 2019), which contains user profile information of gender, age group, occupation, zipcode, and movie profile information of rate, genre, director and actor.
The dataset is split into ttt.--rriinvaiiaaiinieeee set according to the timestamps of ratings by ratio 7/1/2. As a result, the start time is 2000-04-26 the meta-train cut-off time is 1000-11-22, the meta- validation cut-off time is 2000-12-02, and the end time is 2003-03-01. Users with less than 30 samples in each split are removed. In the end, the average sample size for each user is 163. The statisties of the pre-processed MovieLens-IIM IM dataset and the number of segta-rain/valiiationnee users are recorded in Table 4 and 5. Note that it is possible for meta-train users to appear in meta- validation and meta-test set, and these users are termed warm users. Conversely, meta-validation or meta-test users that have never appeared in the meta-train set are termed cold users.
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A.2.2 YELP
Yelp' dataset (Dataset, 2019) contains 8,635,403 reviews for 160,585 business services made by 2,189,45 users. We extract the star ratings from the reviews for our experiments. For each business service, collect the city resides and the categories it belongs from the business metadata. However, for the user, the personal information is lacking, and we only have access to the user ID.
The dataset is split into meta- setaa-ttainnvliiaaiiooi/oe set according to the timestamps of ratings by ratio 7/1/2. As result, the start time is 1004-10-12, the meta-train cut-off time is 201 8-02-07, the meta- validation cut-off time 2018-09-04, and the end time 2019-12-13. Users with less than 30 samples in each split are removed. In the end, the average sample size for each user is 89, The statistics of the pre-processed Yelp dataset and the number of meta-train/validationnl/ users are recorded in Table and 5.
A.2.3 AMAZON-CDS
Amazon-CDD " dataset (McAuley et al., 2015) contains 3.749,004 ratings for 544,442 CD and Vinyl products made by 1,578,597 users. For each CD, we collect its brand and category, while for the user, the personal profile information is lacking and we only have access to the user II).
The dataset is split into meta-train/validatiinness set according to the timestamps of ratings by ratio 7/1/2. As result, the start time is 1997-09-13, the meta-train cut-off time is 2012-01-13, the meta- validation cut-off time 2013-03-05, and the end time 2014-07-23. Users with less than 30 samples in each split are removed. In the end, the average sample size for each user is 82. The statistics of the pre-processed Amazon-CDl dataset and the number meta- train/ validation/test users recorded in Table 5.
Table 4: Statistics of recommendation datasets.
Datasets
Features
#IDs
User
5,255
Gender
2
Age Group
Occupation
21
Zipcode
3,402
MovieLLns-IMM (Harper & Konstan, 2015)
Mevie
3,697
Rate
Genre
25
Director
2.186
Actor
8,030
User
25,206
Yolp (Dataset, 2019)
Business Service
159,611
Category
1.317
City
User
3.876
(MeAuley et al., 2015)
CD Category Brand
132,209
490
49,283
Table 5: Number of meta-traiin/validatoonn users of recommendation datasets.
#Meta Validation Users
#Meta- Teat Users
Datasets
#Meta-Train Users
All
Warm
Cold
All
Warn
Cold
MovieLens. IM (larper & Konstan, 2015)
4,119
621
122
499
1,229
485
744
Yelp (Dataset, 2019)
1,281
3,442
Amazon-CDs (McAuley al., 2015)
3,584
202
110
92
355
119
236
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B HYPER-PARAMETERS SETTINGS
B.1 FEW-SHOT IMAGE CLASSIFICATION
For fair comparison, we adopt the same feature extractor and base-learner for all the compared methods. Following Finn et al. (2017), the feature extractor is a four-layer 3 x 3 convolutions with 32 filters, followed by one-layer fully-connected layer that maps the extracted features into the task embedding dimension de- The base-learner is also four-layer 3 x 3 convolutions with 32 filters, followed by a one-layer fully-connected layer that projects the output to prediction scores for 5 classes. Each convolution layer is accompanied with batch normalization, ReLU nonlinearity, and 2 x 2 max-pooling.
For all the compared methods, we follow the hyper- parametetsttrss settings for meta-training in MAML (Finn et al., 2017), which sets the adaptation learning rate a as 0.01, the meta-update learning rate as 0.001, the number of adaptation steps T 5, the meta batch size [B] 4, the size of test set [Di]] as 15, and the number of meta-update iterations as 60,000. For all the task-aware modulation methods (i.e., MMAML (Vuorio al., 2019), L2F (Baik et al., 2020), HSML (Yao et al., 2019), ARML (Yao et al., 2020)), we set the dimension of task embedding de as 128 (following Yao et al. (2019)). Additionally. for HSML (Yao al., 2019), we set the number of clusters the first and second layer of hierarchical tree as 4 and 2 respectively. For ARML (Yao et al., 2020), we set the number of vertices in the meta- weree-knowledgge graph as For our proposed CTML,, we set the number of clusters for both feature and path representations as 6, i.e., Kpath = kfeut 6.
B.2 COLD-START RECOMMENDATION
Different from the image dataset, recommendation dataset typically consists of user-item interac- tions and profile features for both sides. The feature extractor is implemented several embedding lookup tables, each corresponds to one categorical feature. We set the embedding dimension as for all features. The base-learner implemented as a general deep learning-basse recommender system model, composed of embedding matrices followed by a two-layer fully connected layer that models the interaction between different features. The embedding dimension for beae-learner is set to 8, and the hidden sizes for the fully-connected layers is set to [32, 16].
For all the compared methods, we follow the hyper-parameters settings for meta-training MeLU (Lee et al., 2019), which sets the adaptation learning rate a as 5e-3, the meta-update learning rate as 5e-5, the number of adaptation steps т as 5. For other hyper-parameters that are not explicitly specified by Lee et al. (2019), we set the meta batch size [8] as 1, the size of training set [Dt] for each user 10 (the remaining are used as test set D for that user, whose size varies for different users), and the number meta-training epuchs as 20. For MAMO (Dong et al., 2020) which also CTML.
employs K- K-means clustering, we apply the same syper-parameters tuning procedure That is, we tune both kpath and fe in {4,8 8, 12, 16, 20), and tune the dimension of task embedding de in {64, 128, 256, 512, 1024). Other byper-parameters settings specific the baseline methods are directly adopted from the source codes released by the authors.
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C OTHER PATH LEARNER DESIGNS
In addition to the GRU-based meta path learner design descrihed in equation 2, we also experiment on 3 other network designs test their effectiveness modeling the step-wise geometric quantities.
Recall that the meta path learner is applied coordinate-wise on the base-learner parameters. That is, the same meta path learner is used to process the sequence of step-wise tuples P7, E R(++1)x4 independently for all parameters at different dimensions E {1,2, DJ.
The first design linearly transforms the vectorized P4 with learnable weight and bias:
Linear:
h = W vec (P+, b.
(10)
The second one employs multiple fully-connected layers with nonlinear activation a(-):
FC: u = vec 77))
u =o('' - +b+b"',
(11)
u² o (WL. 1- b²),
h L.
The third design applies multiple self-attention layers on the sequence with scaled dot-product sim- ilarity following Vaswani et al. (2017). To inform about the sequential order, we apply sinusoid positional encodings at the input level, and also apply causal mask prevent interaction with future steps (i.e., set the upper triangular entries of the similarity matrix to oo before inputting into soft- max). The final representation h given by the (r + 1)-th row (i.e., the last row) of the final-layer output:
Attention:
U
P4. positional encodings.
Q' Q dda
U softmax
V2
Q Q4. VL.
U softmax
Vdaa
(12)
h = U
where
Q' =(( Wy + bb2) ((
K' o(Ul-1. w + +b(x) R((+1)xds
V o(U--1 W. + bb)) [[(+1]xd.
Concatenating the path representations at all dimensions and passing through a fully-connected path
layer gives the final path embedding c. E Rd for task Te:
path (h T.
(13)
17

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Under review as a conference paper at ICLR 2022
D ADDITIONAL EXPERIMENTAL RESULTS
D.1 PERFORMANCE ON RESNET-12
We have conducted additional experiments to the effectiveness of our method using a deeper network ResNet-12 as the backbone (i.e., the base-learner). We follow the implementation of Sun al. (2019) which adopts (64-128-256-512) for the number of filters the four blocks.
It was shown recently that, with deeper backbone, simple training paradigm like pre-training and fine-tuning (Tian et al., 2020; Chen et al., 2018) can achieve very satisfactory performance. We therefore further include the following baselines for comparison on ResNet-12:
Finetune: This baseline simply pretrains a global feature extractor on the entire training dataset and then finetunes the classifier for individual tasks.
Finetune-distance (Chen al., 2018): This method modifies Finetune by computing cosine distance between the input feature vector and the class vectors for the classifier.
Finetume-distill (Tian et al., 2020): This method modifies Finetune by employing a sequen- tial self-distillation technique pretrain the feature extractor.
Table below presents the 5-way 1-shot performance on the Mixture-Of-Datasee with 2 differ- backbones: Conv-4 and ResNet-12. We can see that the gaps between Finetune methods and MAML are narrower for deeper backbone, which can be attributed to that the deeper models have larger capacity accommodate the transferable knowledge obtained from the pre-training (in line with the findings of Chen et al. (2018)). However, under this hese-heterogenouus setting, the task- conditioned methods still yield better performance than MAMI. and the Finetune baselines for ResNet- 12, demonstrating the effectiveness of task-conditioning even for deeper backbone. And our method with path representation yiclds the best result.
Table 5-way 1-shot performance (mean accuracy (%) + std over 8 trials) on Of-ttre-Of-Datasetts for Conv-4 and ResNet-12
Mixture- Conturre-O--ataaseee Datassts
Methods
Conv-4
ResNet-12
Finetune
45.76
53.48
Finetune-
46.82 + 1.32
54.67 # 1.44
Finctune-distill
47.41 + 1.67
55.72
=: 1.07
MAML
52.83 + 1.54
56.84
1.38
MMAML
54.28 1.30
59.12
1.61
L2F
+ 56.61
61.57
HSML
56.32 + 1.16
64.03 # 0.89
ARML
57.21 + 1.48
61.06 1.19
CTML
59.03 + 0,54
63.18
: 1.02
(aprox))
58.91 + 0.95
62.69 1.32
D.2 PERFORMANCE ON MINILMAGENET
Table 7 presents the results on Minilmagenet benchmark (Ravi & Larochelle, 2016), where tasks are constructed from a single dataset (i.e.. there is only one underlying distribution) and hence can be considered as fask-homogenede advantages over the global initialization methods, we see that all the baselines have comparable performance the original MAML. Nevertheless, the results show that though the task-aware mod- ulation is rendered less meaningful in task-homon hakkhoooggeeuuss setting, CTML will yield performance at least comparable to the global initialization method in this scenario.
setting, Since in this case, task-aware methods do not have
18

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Under review as a conference paper at ICLR 2022
Table Few-shot classification performance on Minilmagenet. Since for all the baselines on Mini- Imagenet, the results are reported in the form of 95% confidence interval of accuracy (%) based on 1000 meta-testing tasks, we also report our results in the same format for direct comparison.
Minilmagenet
Methods
5-way 1-shot
5-way 5-shot
MAML
48.70 1.84
63.11 0,0
MMAML
49.86 1.3
63.73 + 091
L2F#
50.78 #: 50.38 + 1.85
64.06 +
HSML
64.03 +: 0.00
ARML
50.42 + 1.79
64.12 + 0.50
CTML-ffat
50.29 + 1.82
64.05 :: 0.87
CTML-path
50.43 + 1.82
64.07 + 0.50
CTML
50.47 + 1.83
64.15 +: 0.90
(aproxaprrx.)
50.25 + 1.84
64.03 : 0.93
reproduced due to different implementation of base-lcarner.
D.3 PERFORMANCE ON SUB-DATASETS
Table presents the few-shot classification performance of CTML and the baselines on each sub- dataset. We see that CTML consistently outperforms all the baselines for all the sub-datasets. Other trends are similar to that of the overall results in Table la.
Table 8: Few-shot classification performance on individual sub-datasets. We sample 1000 tasks from each sub-datased for meta-testing. The results reported in the form of mean accuracy (%) + std over trials.
Methods
Bird
Aircraft
Fungi
Flower
Texture
Traffic
52.73
1.42
31,80
MMAMI.
54.02 = 1.36
$1.81
1.08
41.99 + 1.27
64.36
+ 121
32,83
+ 1.54
92.07 : 1.13
57.13
54.23
1.14
1: 1.31
64.79
1 1.47
33.64
1 1.52
92.61
0.87
HSML
55.75 1.14
53,02
43.03
8: 124
64.15
162
34.07
à: 1.48
92.01 4: 1.08
way I-shot
ARML
58.12 = 1,53
54.11
+ 1.52
44.15
+: 1.32
65.36
+ 1.01
33.87
+ 1.39
93.76 + 1.12
CTML-feat
58.72 =: 1.33
53.87 1.00
44.21 à: 1.37
65.41 4: 1.22
33:07
+: 1.51
92.95 :: 1.31
CTMh--pth
1.37
67.08
+ 1.07
CTMLLaprok.)
60.73 1.42
55.92
44,72 1.61
67.32 1.5
34.98 +: 1.26
94.71 1.07
MAMI.
71.02 2 0.82
63.64
53.61
75.29 0.55
44.76 + 0.63
97.01 0.18
MMAML
71.22 +: 0.48
67.01 + 0.54
$2.80 +: 0.43
77.63 + 0.84
45.29 + 0.38
98.13 + 0.57
0.87
HSML.
71.73 = 0.62
71.26
0.39
56.48 0:77
79.12 1 0.49
46.11 + 0.84
98.22 0.33
5-way
ARML
73.84 0.61
72.07
1: 0.15
55.87 1: 0.52
79.67
0.44
45.48 :1 0.36
98.52
0.26
S-shot
CTML-feat
71.92 +: 0.73
72.19 0.45
55.64 +: 0.58
78.94 +: 0.82
45.43 +: 0.46
98.43 + 0.37
CTML-path
73.65
74.03
56.78
80.92
46.18
98.95
46.88
CTML(appoxx))
74.57 = 0.41
73,51 0.41
57.41 0.51
80.71 + 0.71
46.81 + 0.51
98.72 + 0.31
D.4 PERFORMANCE ON RECOMMENDATION DATASETS
Table presents the rating prediction performance 3 datasets evaluated in two metrics: mean absolute enror (MAE) and normalized discounted cumulative gain at top 20 (NDCG@20), The meta-testing users further divided into warm and cold users, where warm are those that have appeared in the vecaattaiinin set, and cold users are those that have not!! From the results, we see that CTML consistently outperforms the baselines.
Note that for few-shot image classification, all the meta-testing tasks unseen during meta-training, while for recommendation, is possible that the meta-testing users also appeared meta-training set.
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Under review as a conference paper at ICLR 2022
Table Rating prediction performance datasets in MAE and NDCG@20, Note that the results under 'All Users' are the same as that in Table 2.
NDCG@20 f
Datasets
Methods
Cold
All
Cold
MeLU
0.8164
0.8112
0.8197
0.7839
0,7935
0.7716
PAML
0.7725
0.7575
0.7879
0.8255
0.8165
MAMO
0.8084
0,8073
0.8091
0.8118
0,8274
0.8030
MovieLens- 1M
CTML-feet
0,7482
0.8384
CTML--pth
0.7592
0.7474
0.7690
0.8493
0.8499
0.8437
CTML
0.7543
0.7415
0.7626
0,8562
0.8634
0.8487
CTML/approx.
0.7555
0.7411
0.7652
0.8531
0.8627
0.8418
McLU
0.9464
0.9100
0.9576
0.8149
0,8161
0.8139
PAML
0.9151
0.9336
0.8215
0.8204
MAMO
0.8965
0,9125
0.8840
0.8332
0.8296
0.8384
MetaHIN
0.8832
0,9021
0.8767
0.8375
0.8324
0.8412
Yelp
CTML-feal
0.9U23
0,9107
0.8949
0.8295
0,8301
U,8254
CTML path
CTML
0,8603
0.8700
0.8533
0.8467
0.8364
0.8524
CTML/sppox.)
0.8679
0.8721
0.86077
0,8433
0,8319
0.8497
MeLU
0.68400
0,9026
U,9020
PAML
0.7150
0.6813
0.7317
0.9083
0.9096
0,9051
MetaHIN
0.6743
0.6675
0.6804
0.9111
0.9082
0,9153
Amazon-CDs
CTMI
0.6804
0.6697
0.6874
0,9122
0,9078
0.9179
CTML-path
0.6286
0.6207
0.6372
0.9201
0.9180
0.9238
CTML
0.6048
0.6080
0.6011
0.9279
0.9244
0.9293
CTML/agprx.)
0.6144
20

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Under review as a conference paper at ICLR 2022
D.5 ADDITIONAL LEARNING PATH VISUALIZATION
D.5.1 FEW-SHOT IMAGE CLASSIFICATION
Here we provide more examples for visualizing the path learning results for the few-shot image classification experiments. Figure and 7 each shows the path learning results of tasks randomly sampled from 3 of the sub-datasets.
We see that in this application scenario, the overall direction of the learning path plays an important role in determining the task representation. Looking the GRU gates at each step, seems that the first 2 to 3 steps are often the most importantinformatie steps, after which the learning begins to converge and the subsequent steps longer provide useful information about the learning direction.
10-
Bird
CIMIT
A310
C.541 KI1
00.5
COOM
B30W
(34)
KIW
Fungi
-.0
-0.5
1.0
16-7
E:40) 1.04
Texture
S4ND
03:3 E314
63817 CARE
PC1
(b)
(c)
Figure 5: Visualizing path learning results of 6 tasks (5-way 1-shot) randomly sampled from Bird, Fungi and Texture sub-datasets (2 tasks from each sub-dataset).
1.0
Bird
0.5
SCOR
0.0
KLUM
-0.5
Aircraft
-1.0
C1DI
1.0
(112)
A304
Traffic Sign
PC2
ASTAN
(144)
A300
64T11
01OTE 0597
-1.0
-0.5
0.0
PC1
16-5
(b)
Figure 6: Visualizing path learning results of 6 tasks (5-way 1-shot) randomly sampled from Bird, Aircraft and Traffic Sign sub-datasets (2 tasks from each sub-dataset).
ECINI
2201
CUBIT
EIEN
B3TM
Fungi
KCDM
0200
6360
4350
8320)
-0.5
KSPW
DU01
E304
KIUM
Flower
1+-7
-0.5
0.0
0.5
1.0
2012
5308
E1041
831M
X1171
6.774
001
6154
Texture
0.296
-0.5
PC1
(a)
(b)
(c)
Figure 7: Visualizing path learning results of 6 tasks (5-way I-shot) randomly sampled from Fungi, Flower and Texture sub-datasets (2 tasks from each sub-dataset).
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Under review as a conference paper at ICLR 2022
D.5.2 GOLD-START RECOMMENDATION
We also provide examples for visualizing the learning paths for the cold-start recommendation ex- periments. Figure 8 and 9 each shows the path learning results of 6 users randomly selected from the MovieLens- 1M dataset, and Figure 10 and 11 each shows the results of 6 users sampled from the Amazon-CDs dataset.
In this application scenario, we notice that apart from the overall direction of the path, the length of the path also plays an important role in determining the task representation. For instance, in Figure 11, the blue, orange, green and brown paths (upper plot) are clustered closely in the representation space (lower plot) due to similar lengths, although they pointing very different directions. Similar observation can also found in Figure 8. Although blue and orange paths are pointing at the same directions, their embeddings are positioned far away from each other due to the big difference in path lengths.
RIATT
8:00
B15
6710
CRL 5430
1427 516
Q
LEM 5112
1150
PC1
1e-2
-13
-25
PC1
1.0
Figure 8: Visualizing path learning results of 6 users randomly selected from MovieLens- IM.
Figure 9: Visualizing path learning results of 6
users randomly selected from MovieLens- IM.
rgata
1.5
Cioc
74-
-23
0
-2.
00
-25
25
50
3.5
PC1
Figure 10: Visualizing path learning results of users randomly selected from Amazon-CDs.
Figure 11: Visualizing path learning results of users randomly selected from Amazon-CDi
22

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Under review as a conference paper at ICLR 2022
D.6 ADDITIONAL SHORTCUT APPROXIMATION VISUALIZATION
In this section, we give more examples to verify the effectiveness of the shortcut approximation. Figure 12 shows the approximation results of 2 users sampled from the MovieLens- 1M dataset, and Figure 13 shows the results of tasks sampled from 3 different image sub-datasets. We can see that the shortcut tunnel able to learn and accommodate different mappings, provide guarantee on the performance of the approximated model.
@1
3
a
a
a1
A4
a
Feature Cluster Assignment Shortcut Tunnel
Feature Cluster Assignment Shortcut Tunnel
a1
A2
33
84
85
a6
a7
aB
@1
a2
a3
24
35
36
a7
ag
810
811
a14
29
811
A14
Reconstructed Path Cluster Assignment
Reconstructed Path Cluster Assignment
Approx.
Approx.
83
36
31
33
84
a6
87
a6
8g
810
811
812
813
814
Ø15
B16
ag
a10
011
012
013
A14
015
a16
Path Cluster Assignment
Path Cluster Assignment
(a)
(b)
Figure 12: Shorteut approximation of path cluster assignment from feature cluster assignment for users sampled from MovieLens- IMM dataset. Here, we set feat 8 and kpath
16.
a4
a2
33
35
a3
ab
Feature Cluster Assignment
Feature Cluster Assignment
Feature Cluster Assignment
Shortcut Tunnel
Shortcut Tunnel
Shortcut Tunnel
@2
a4
a6
a2
a5
a3
a6
Reconstructed Path Cluster Assignment
Reconstructed Path Cluster Assignment
Reconstructed Path Cluster Assignment
Approx.
Approx.
Approx.
a4
22
a5
a3
a6
Path Cluster Assignment
Path Cluster Assignment
Path Cluster Assignment
(b)
Figure 13: Shortcut approximation of path cluster assignment from feature cluster assignment for tasks sampled from 3 different image sub-datasets. Here, we set keeat kpath 6.
23


Reviews:
[{"review_id": "reh76LYWo9D", "reviewer": "Reviewer_9y7H", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "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": "Utilizing feature embeddings jointly with path embeddings drawn from several steps of the inner-loop optimization is novel to the best of my knowledge, and an interesting direction. The authors do a good job of motivating the need to consider geometric information from more than just the initialization point. The paper is also nicely written, well organized and for the most part easy to follow. However, I have a few concerns, primarily relating to the placement of this work into the previous literature. More details below.\n\n- Limited comparisons with state-of-the-art methods. The experimental comparisons are only against similar MAML-based meta-learning methods. These are not state-of-the-art for few-shot classification, so considering only these in the table (though indeed they are most relevant to the proposed method) is misleading. In fact, it was recently shown that transfer learning approaches can match or surpass the performance of meta-learning methods [4,5], especially when using larger architectures than a 4-layer-convnet, while also having the advantage of being simpler and more computationally efficient. On mini-ImageNet, according to the results presented in the Appendix, there is a large gap between the proposed approach and recent work e.g. [4], which isn’t included in that table. Despite the nice ideas presented in this paper, the significance of the work is low if the results aren’t comparable with conceptually simpler and computationally more efficient baselines.\n\nRelationship to related work:\n- [1,2] should also be cited in the context of task-conditioned meta-learners (non-MAML-like in this case)\n- It is unfortunate that the authors construct a new collection of datasets and name it Meta-Dataset, since Meta-Dataset is already the name of a few-shot classification benchmark [3] which actually has high overlap with the datasets chosen here. In fact, Meta-Dataset [3] is a good evaluation benchmark for approaches that deal with task heterogeneity like the one proposed here.\n- “Though task-specific methods have been developed to tailor the initialization, they overlook generalization among similar tasks” - I would argue that this isn’t necessarily the case. Approaches that use a network to predict a task encoding, and then condition on that encoding (like Oreshkin et al, and [1], [2], etc) *do* consider relationships between tasks implicitly, since similar tasks are likely to cluster close to each other in the learned task embedding space, even if an explicit clustering objective isn’t employed. I would revise this sentence to more fairly describe previous work.\n\nScalability considerations\n- The architecture considered for few-shot learning is a small 4-layer convnet. Is this method easy to scale up to larger ones like the resnet-12 and resnet-18 that are commonly used more recently [3,4,5]?\n- How many steps of gradient descent were performed in these experiments? It seems that this method would not scale well to large numbers of steps which might be more appropriate for larger support set sizes? The evaluation here is constrained to 1-shot and 5-shot tasks.\n\nAdditional ablation\n- It would be good to also ablate the effect of the clustering, for both the path and feature embeddings.\n\nLess important comments and typos \n- ‘The amount of information contained in the task-specific data about a “probe” network can be seen as a good representation of the task itself’. It should be explained what a “probe” network is\n- ‘while the interaction between task data and the base-learner (e.g., gradients) is often not neglected.’ – I think you meant “is often neglected” here (without the not).\n- ‘However, these methods utilize gradients only at a single point in parameter space’ - I would say ‘only at the initialization’, to make it clearer what the single point is, compared to what is proposed in this work.\n- ‘we first elaborate task representation learning’ - the word ‘on’ missing after ‘elaborate’\n\nSuggestion: I encourage the authors to consider the methodology of [1], which meta-learns the task-conditioning networks that are used to predict task-specific parameters for a pre-trained (and now frozen) feature extractor. This combination of pre-training and meta-learning is very effective and competitive with state-of-the-art in Meta-Dataset. Can some of the ideas presented here be used in the context of a meta-learning phase on a pre-trained feature extractor too? In contrast to the proposed method of this work, [1] only uses feature embeddings and doesn’t consider path embeddings (in fact there is no gradient descent adaptation in that work, it’s an amortized model).\n\nReferences\n- [1] Fast and Flexible Multi-Task Classification Using Conditional Neural Adaptive Processes. Requeima et al. NeurIPS 2019.\n- [2] Improved Few-shot Visual Classification. Bateni et al. CVPR 2020.\n- [3] Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples. Triantafillou et al. ICLR 2020.\n- [4] Rethinking Few-Shot Image Classification: a Good Embedding Is All You Need? Tian et al.\n- [5] A Closer Look at Few-shot Classification. Chen et al. ICLR 2019.\n", "summary_of_the_paper": "This paper proposes a meta-learning approach based on MAML but with a task-conditioned initialization, which takes into account both information extracted from the features of the task (support set) data, as well as geometric information from a “rehearsed” learning path (obtained by gradient descent on the support set). The geometric information includes the parameters, loss, gradient and fisher matrix for different steps of the task adaptation process. They propose a GRU architecture to process this information across the different steps, yielding a path embedding. For both the feature and path embeddings, they utilize clustering, motivated by the need to share knowledge across similar tasks. They then combine the path and feature embeddings via an additional neural network to generate the final task-specific initialization. Computing the path embedding requires rehearsing which is computationally expensive (it’s akin to training twice on the task, once for rehearsing, and then training from the task-conditioned initialization). To amend this at inference time, they meta-learn a ‘tunnel’ connection that predicts the path embedding from the feature embedding. At test time, only a forward pass through this meta-learned connection is required instead of rehearsing. They experimentally evaluate their approach on few-shot classification and cold-start recommender problems and show performance gains over similar MAML-based approaches. They also perform ablation studies and analyses to understand the contribution of different parts of this system to downstream performance.", "summary_of_the_review": "Overall, while the paper presents some nice ideas, is technically novel, well-organized and easy to follow, I have some concerns primarily about the relationship to prior work that make me lean towards rejection at this stage. \n\n########\nEdit after rebuttal:\nDuring the discussion with the authors, they have addressed some of my concerns by running additional ablations (removing the clustering component), comparisons to transfer learning methods, and experimenting with deeper backbones. They also have commented on the scalability of their approach, and discussed pros and cons w.r.t efficiency at training time vs deployment for transfer learning vs meta-learning methods. Overall, my view is that test-time efficiency is important for certain applications, which makes meta-learning methods a good candidate, and the particular variant proposed here seems especially suited at the important problem of handling heterogeneous data and outperforms previous MAML-based meta-learning methods that were designed for this. Based on these, I updated my score from a 5 to a 6 to reflect that the paper is slightly above the publication bar in my opinion.\n\nTo strengthen the work further, I recommend comparing against recent methods developed for heterogeneous data on common benchmarks. Some examples are the following:\n- Fast and Flexible Multi-Task Classification Using Conditional Neural Adaptive Processes. Requeima et al. NeurIPS 2019.\n- Selecting Relevant Features from a Multi-domain Representation for Few-shot Classification. Dvornik et al. ECCV 2020.\n- A Universal Representation Transformer Layer for Few-Shot Image Classification. Liu et al. ICLR 2021.\n- Learning a Universal Template for Few-shot Dataset Generalization. Triantafillou et al. ICML 2021.\n- Universal Representation Learning from Multiple Domains for Few-shot Classification. Li et al.\n- Memory Efficient Meta-Learning with Large Images. Bronskill et al. NeurIPS 2021.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "pgFRdkb-lNq", "reviewer": "Reviewer_fGEV", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "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": "The proposed idea that adopts a learning path to improve the parameter initialization is interesting. Code is provided and experiment results look persuasive.\n\nSome of the critical technical points are not sufficiently justified, e.g.\n(1)\twhy is using the trajectory of rehearsed path helpful to learn a good parameter initialization? \n(2)\tin section 4.2, the reason for modeling task representation is explained as encoding the predictive distribution. But I can't see the connection between them.\n  I would like the author to use several sentences to explain the insights of these points.\n", "summary_of_the_paper": "This paper proposes a clustered task-aware meta-learning algorithm. The proposed algorithm firstly collects the learning path and uses the path to train a sequence module. The sequence module output is combined with the task feature. The task feature is derived from the weighted sum of the soft cluster centers. The combination is then used as initialization of the model parameter for task adaptation. Experiments on image classification and cold-start recommendation demonstrate superior performance compared to baseline algorithms.", "summary_of_the_review": "The proposed algorithm is interesting and well-supported by experiments. My concerns are that a more intuitive description should be added to make the motivation, rationality, and insight of algorithm design easy to follow.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "gUyr9EYMr5r", "reviewer": "Reviewer_kvxn", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "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": "Strengths\n\nCharacterizing a task using the trajectory is an interesting perspective. The authors provide sufficient intuition and motivation behind the proposed characterization (the four entities in the tuple given as input to the GRU) of the task using trajectory information. \n\nThough superficial, the analysis on trying to demystify the GRU’s learnings is interesting. \n\nThe paper is well written. \n\nConcerns\n\nThe assumption behind the shortcut tunnel is that the tasks with similar feature assignments will also have identical path assignments. If that is the case, why does one have to rely on path characterization? Isn’t it going against the basic premise of the paper?\n\nThe improvements over the current state-of-the-art approaches on meta-dataset and the miniimagenet (in the appendix) are marginal at best. The goal of the meta-learning framework, such as the one used in the paper, is to learn a well-generalizable meta-model. Recent works have demonstrated significant improvements in the performances by using deep architectures. The gain on miniimagenet for both 5.1 and 5.5 settings is over 10% (Liu et al. 2020). Furthermore, it appears that CTML does not yield even the marginal gains when the number of shots increases (based on the results from the miniimagenet dataset). Thus, I am not convinced about the utility of such a complex method to squeeze out the last drop in performance when better models are readily available. It would be interesting to see the results of these deeper networks-based meta-learning models on the meta-dataset curated by the authors. \n", "summary_of_the_paper": "The paper proposes to apply the task-aware-modulation on global Meta-learning for learning on tasks sampled from heterogeneous distributions. This paper builds on prior work on the feature-based task characterization to integrate the rehearsed task gradient descent trajectory into task representation. As the rehearsal task is computationally expensive, the authors learn a different network to estimate the rehearsed task-trajectory characterization from the feature representation. The proposed framework is tested on few-shot image classification (meta dataset and miniimagenet) and cold-start recommendation tasks.\n", "summary_of_the_review": "Overall, it is a well-written paper with interesting and, at times, conflicting ideas. I deeply appreciate the amount of work invested by the authors. However, I am not convinced about the approach’s utility.\n\n---post rebuttal update\n\nThank you for the clarification on the 'shortcut tunnel assumption. The assumption results in estimating the path cluster assignments through feature cluster assignments. This means that the information related to the path cluster assignments is already present (linear or non-linear relationship) in the feature cluster assignments. Thus, I am not entirely convinced that the model is getting any additional information to justify the improvement in the results because of the addition of the path cluster assignments.\n\nThe additional experiments using the heavier backbone strengthen the result.  I agree that on the curated 'meta-data set the proposed approach has an edge over prior methods. The authors have incorporated these results in the updated draft.\n", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "Ofi5eEN-2DQ", "reviewer": "Reviewer_oNDW", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "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": "My opinion is that the work has some significant positives, for example:\n\n- The paper is well written, mostly clear besides some small details (see \"Minor points\" below)\n- The authors report experiments on several benchmarks and several ablation studies. \n- Visualization of the rehearsed learning paths (figure 3b) is nice.\n\nHowever, there are some problems with the study that make it fall slightly short, in particular:\n\n1) It is actually not true that this is the first meta-learning work doing clustering on multi-step optimization trajectories. The work of https://arxiv.org/abs/2103.04691 is conceptually very similar, they run gradient descent in the inner loop for a few steps and they cluster the resulting trajectories across tasks. There are several differences with the author's work, trajectories are not processed by a RNN, and the method is applied to a very different context (multi-language inferece), but is otherwise very similar conceptually.\n\n2) I'm not entirely convinced that the 1% or 2% gains with respect to other methods reported in table 1 and table 2 are due to the superiority of the proposed architecture. Is the capacity (e.g. number of parameters) of the different models taken into account? Furthermore, some of the performances reported in table one falls within the standard deviation of other methods, so it is not clear whether differences are significant. \n\n3) In section 4.4., while deriving the \"shortcut tunnel\", the authors justify their method by stating that \"tasks with similar feature assignments will also have similar path assignments.\" If that is true, then the entire motivation of the study breaks, since the method is formulated under the assumption that path representations actually add significant information that is not avaiable in the feature representations.\n\nMinor points:\n- Why talking about Natural gradient in section 4.1.1? That seems completely out of context. Besides, it is not true that the Fisher is equivalent to the Hessian for cross entropy loss in general, that is true only for very special models.\n- It is unclear to me why \"learning path can be interpreted as encoding the predictive distribution\"\n- Along the entire paper it remains unclear what the authors mean by \"lower order\" and \"higher order geometric quantities\"\n- There is actually a dataset that is called \"Meta-dataset\" (http://arxiv.org/abs/1903.03096), which is different from the one the authors define. It would be great to do some effort to avoid confusion between the two. \n ", "summary_of_the_paper": "This paper looks at the problem of meta-learning with heterogeneous tasks.\nThis is an interesting problem that is receiving increasing attention in the past two or three years.\nSeveral previous work address this problem by clustering task representations and let the meta-learner exploit the information about task cluster.\nThe authors claim that, for the first time, they cluster tasks not only at the level of the input representation (features), but also at the level of the optimization trajectory in parameter space.\n", "summary_of_the_review": "Given the above points 1, 2 and 3 I think the paper is marginally below the acceptance threshold", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposed a cluster-based task-aware meta-learning (CTML) approach with task representation learned from its own learning path. Based on the prior work of feature-based task characterization, it integrates the rehearsed task gradient descent trajectory into task representation, and further improves computational efficiency by learning a different network to estimate the rehearsed task-trajectory characterization from the feature representation. Experiments were conducted on few-shot image classification (meta dataset and miniimagenet) and cold-start recommendation tasks. 

Reviewers had raised various concerns about the work including technical novelty, the shortcut-tunnel assumption, empirical comparison, scalability issue, more ablations for in-depth analysis, etc. The reviewers and AC appreciate authors for putting good efforts in the rebuttal by replying the review questions carefully and making changes to improve their experiments and paper. 

Overall, this paper is a borderline case, where reviewers agree some clear merits (well-written, easy to follow, good execution of an interesting idea with code provided, etc). Despite the improvements during rebuttal, some major concerns on the weaknesses still remain (e.g., technical novelty, more convincing justification on the assumption, significance of empirical gains). Therefore, I cannot recommend it for acceptance at its current form, but I hope to see it accepted in the near future after these issues are fully addressed.
Decision: Reject