Semi-Supervised Few-Shot Learning with Prototypical Random Walks
Authors: Ahmed Ayyad
Nassir Navab
Mohamed Elhoseiny
Shadi Albarqouni
Venue:  (2020)
Keywords: Few-Shot Learning
Semi-Supervised Learning
Random Walks

Abstract: Learning from a few examples is a key characteristic of human intelligence that inspired machine learning researchers to build data-efficient AI models. Recent progress has shown that few-shot learning can be improved with access to unlabelled data,  known as semi-supervised few-shot learning(SS-FSL). We introduce an SS-FSL approach, dubbed as Prototypical Random Walk Networks (PRWN), built on top of Prototypical Networks (PN). We develop a random walk semi-supervised loss that enables the network to learn representations that are compact and well-separated. Our work is related to the very recent development on graph-based approaches for few-shot learning. However, we show that achieved compact and well-separated class embeddings can be achieved by our prototypical random walk notion without needing additional graph-NN parameters or requiring a transductive setting where collective test set is provided. Our model outperforms prior art in most benchmarks with significant improvements in some cases. For example, in a mini-Imagenet 5-shot classification task, we obtain 69.65% accuracy to the 64.59% state-of-the-art. Our model, trained with 40% of the data as labelled, compares competitively against fully supervised prototypical networks, trained on 100% of the labels, even outperforming it in the 1-shot mini-Imagenet case with 50.89% to 49.4% accuracy.  We also show that our model is resistant to distractors, unlabeled data that does not belong to any of the training classes, and hence reflecting robustness to labelled/unlabelled class distribution mismatch. We also performed a challenging discriminative power test, showing a relative improvement on top of the baseline of 14% on 20 classes on mini-Imagenet and 60% on 800 classes on Ominiglot.

Under review as a conference paper at ICLR 2020
SEMI-SUPERVISER FEW-SHOT LEARNING WITH PRO- TOTYPICAL RANDOM WALKS
Anonymous authors Paper under double-blind review
ABSTRACT
Learning from few examples is a key characteristic of human intelligence that inspired machine learning researchers to build data efficient AI models. Recent progress has shown that few-shot learning can be improved with access to unla- belled data, known as semi-supervised few-shot learning(SS-FSL) We introduce an SS-FSL, approach, dubbed as Prototypical Random Walk Networks(PRWN), built on top of Prototypical Networks (PN) (Ren et al. 2018). We develop a ran- dom walk semi-superrised loss that enables the network to learn representations that are compact and well-separated. Our work is related to the very recent de- velopment on graph-based approaches for few-shot learning. However, we show that compact and well-separated class representations can be achieved by mod- eling our prototypical random walk notion without needing additional graph-NN parameters or requiring transductive setting where collective test set provided (e.g.. Kim et al. (2019). ). Our model outperforms prior art in most benchmarks with significant improvements in some cases. For example, in a 5-shot classification task, we obtain 69.65% accuracy to the 64.59% state-of oftth- art. Our model, trained with 40% of the data as labelled, compares competitively against fully supervised prototypical networks, trained on 100% of the labels, even outperforming it in the 1-shot Imageet case with 50.89% to 49.4% accuracy. We also show that our model is resistant to distractors, unlabeled data that does not belong to any of the training classes, and hence reflecting robustness to la- belled/unlabelled class distribution mismatch. We also performed a challenging discriminative power test, showing a relative improvement on top of the baseline of x: 14% on 20 classes on mini-Imagenn and Rx60% on 800 classes Omniglot. Our code will be released upon acceptance.
INTRODUCTION
Humans are capable of learning complex skills efficiently and quickly, raising a challenging ques- tion to scientists and philosophers: "How do our minds get much from little?" (B Tenenbaum ctt al.) 2011). In contrast, artificial learners require large amounts of labeled data to reach com- prable levels (Dodge & Karam, 2017). This gap motivated progress in few-shot learning (FSL.) and semi-supervised learning (SSL). Semi-supervised learning develops techniques that benefit from an abundance unlabeled of data for training. has gained big interest in the 90s and the early 2000s, guided not only with applications in natural language problems and text classification (Yarowsky
1995 Nigam & Kosovichev 1998 Blum & Mitchell| 1998; Collins & Singer 1999 Joachims, 1999 but also in computer vision as in segmentation Shi & Malik (000)); Li et al. (204)). Few- shot learning is an artificial learning skill of rapidly generalizing from limited supervisory data (few labeled examples), typically without the using of any unlabeled data (Koch et al. 2015) Miller jet al. 2000. Lake et al.] (20TT. Our work is at the intersection between few-shot learning and semi- supervised learning where we augment the capability of few-shot artificial learners with learning signal derived from unlabeled data.
Semi-supervised Few-shot Learning (SS-FSL): Few-shot learning methods typically adopt a super- vised learning setup (e.g.. (Vinyals et al. 2016 Ravi & Larochelle 2017b] Snell et al.) (017)). very recently, Ren et al. (2018) and Zhang al. (2018) developed Semi- remi-supervised few-shot learning approaches that can leverage additional unlabeled data. The machinery of both approaches adopts a meta-learning episodic training procedure with integrated learning signals from unlabeled data. Ren

---

Under review as a conference paper at ICLR 2020
Protonypical Random Walk (PPa))
Treatoo Phoaiih
Thcalle Troi calllllll adits SuPti
Erde
Class socppe
devee pains Guo Cat
Figure I: Our PRW aims at maximizing the probability of random walk begins at the class pro- totype Рj. taking steps among the unlabeled data, before it lands the same class prototype. This results in a more discriminative representation, where the embedding of the unlabeled data of a particular class got magnetized to its corresponding class prototype, denoted prototypical magnetization.
et al. 2018) build on top of prototypical (Pt)orks(PN) (Snell et al. 2017) better class prototypes can be learned with the help of the unlabeled data. Zhhng et al. 2018) proposed a GAN-based ap- proach, Meta-GAN, that helps making it easier for FSL models to learn better decision boundaries between different classes.
In this work, we propose Prototypical Random Walks (PRW), as an effective graph-based learning signal derived from unlabelled data. Our approach improves few-shot learning models by a random walk through the embeddings of unlabeled data starting from each class prototype passing through unlabeled data in the embedding space and encourages returning to the same prototype at the end of the prototypical walk (cf. Fig. [I] This PRW learning signal promotes a latent space where points of the same class are compactly clustered around their prototype, while being well isolated from other prototypes. We sometimes refer to this discriminative attraction to class prototypes as prototypical magnetization.
Since the PRW loss is computed over a similarity graph involving all the prototypes and unlabelled points in the episode, it takes global view of the data manifold. Due to the promoted prototypical magnetization property, this global view enables more efficient learning of discriminative embed- dings from few examples, which is the key challenge in few-shot learning. In contrast, there local SSL losses, where the loss is defined over each point individually, most notable of those approaches the state-of-the-ar Virtual Adversarial Training (VAT) (Miyato al. (0088). We show that in the FSL setting, our global consistency guided by our prototypical random walk loss adds a learning value compared to local consistency losses in VAT (Myyato et al., 2018).
Contribution.
We propose Prototypical Random Walk Networks (PRWN) where we promote pro- totypccal magnetization of the learning representation. We demonstrate the effectiveness of PRWN on popular few-shot image classification benchmarks. We also show that our model trained with fraction of the labels competitive with PN trained with all the labels. Moreover, we demon- strate that our loss is robust to "distractor" points which could accompany the unlabeled data yet not belong to of any of the training classes of the episode.
2
APPROACH
We build our approach on top of Prototypical Networks (PN) (Snell et al. 2017) and augment it with novel random walk loss leveraging the unlabelled data during the meta-training phase. The key message of our work is that more discriminative few-shot representations can be learned through training with prototypical random walks. We maximize the probability of random walk which starts from a class prototypes and walk through the embeddings of the unlabeled points to land back to the same prototype; see Fig. I Our random walk loss enforces the global consistency where the
2

---

Under review as a conference paper at ICLR 2020
overall structure of the manifold is considered. In this section, detail the problem definition and our loss.
2.1 PROBLEM SET-UP
The few-shot learning problem may be formulated as training over a distribution of classification tasks Prrain (T), in order to generalize to a related distribution of tasks (Test(T) at test time. This setting entails two levels of learning; meta-training is learning the shared model parameters(meta: parameters) to be used on future tasks, adaptation is the learning done within each task. Meta- training can be seen as the outer training loop, while adaptation being the inner loop.
Concretely, for -aos Wa- FSL, each task is an episode with a support set S containing N, labelled examples from each of N₂ classes, and query set Q of points to be classified into the Ne episode classes. The support set is used for adaptation, then the query set is used to evaluate our performance on the task and compute a loss for meta-training.
To run standard FSL experiment, we split our datasets such that each class is present exclusively in one of our train/val/test splits. To generate a training episode, we sample N₂ training classes from the train split, and sample N, samples from each class for the support set. Then we sample N₂ images from the same classes for the query set. Validation and test episodes are sampled analogously from their respective splits.
Following the SS-FSL setup in Ren et al. 2 Zhang et al. 2018): Liu et al. (2019). we split our training dataset into labelled/umlabelled; let DR.L denote all labeled points x E class (k), and Dx,u be all unlabeled points x E closs(k).. Analogous notation holds for our support and query set, S and Q To set up semi-supervised episode,, we simply need to add some unlabelled data to the support set. For every class c sampled for the episode, we sample Nu. samples from De,u and add them to S. In order to make the setting more realistic and challenging, we also test our model with the addition of distractor data. Those are unlabelled points added to the support set, but not belonging to the episode classes. We simply sample Na additional classes, and sample No, points from each class to add to the support set. We present pseudo-code for episode construction in appendix B
It worth mentioning that the unlabelled data may be present at either train or test time, or both. At training time, we want to use the unlabelled data for meta-training i.e. learning better model parameters. For unlabelled data test time, we want to use for better adaptation, i.e. performing better classification on the episode's s query set. Our loss operates on the meta-training level, to leverage unlabelled data for learning better meta-parameters. However, we also present a version of our model capable of using unlabelled data for adaptation, by using the semi-supervised inference from (Rnn et al., 2018) with our trained models.
Prototypical Networks. Prototypical networks (Snell al. 2017) aim to train neural net- work as an embedding function mapping from input space to a latent space where points of the same class tend to cluster. The emhedding function ((.) is used to compute a prototype for each class, by averaging the embeddings of all points in the support belonging to that class, De [... Em,es., (x;;;; 0).
where Pa is the prototype for our c-th class, and represents our meta- vetaa-parameters Once prototypes of all classes are obtained, query points are also embedded to the same space, and then classified based on their distances to the prototypes, via a softmax function. For a point Fú, with an embedding h4 ((x;;; 0), the probability of belonging to class e is computed by
21. = p(uel=)) = exp (-d(h,, Pc))
Enn exp (-d((;,pp)) De = EA,ESOUS, h4 -1,0
(1)
ΣNN Zi,e
where d(::) -) is the Euclidean distance. In the semi-supervised variant (Ren et al. 2018). PN use the unlabelled data to refine the class prototypes. This is achieved via a soft K-means step. First, the class probabilities for the unlabelled data ž₁, are computed as in [ and the labelled points have a hard assignment, i.e. ž is if E class(c) and 0 otherwise. Then the updated prototype P. is computed as the weighted average of the points assigned to it; see Eq. We can see this as a task adaptation step, which does not directly propagate any learning signal from the unlabelled points to our model parameters 0. In fact, it might be used only at the inference time, and results from (Ren) et al. 2018) show that it provides significant improvement when used such. When used during
3

---

Under review as a conference paper at ICLR 2020
meta-training by updating the model parameters from the unlabelled data, the performance improves only marginally (i.e., from 49.98 49.98% to 50.09% on mini mini-imagenet (Vinyals et al. 2016)). While this approach is powerful the adaptation step, it fails to fully exploit the unlabelled data during meta- training. SS-FSI. with adaption at test time. Our approach also allows using the former K-means refinement step inference time, analogous to the 'Semi-supervised inference' model from (Ren itt al., 2018). Orthogonal to (Ren et al. 2018), our approach can be thought as a meta-training regularizer that brings discriminative global characteristics to the learning representation efficiently
2.2 PROTOTYPICAL RANDOM WALK
Given the class prototypes Pe. computed using the labeled data in the support set St, and the embed- dings h; of unlabeled support set St. we construct similarity graph between the unlabeled points' embeddings and the prototypes. Our goal to have points of the same class form a compact cluster in latent space, well separated from other classes. Our Prototypical Random Walk(PRW) loss aims to aid this by efficiently magnetizing the unlabelled embeddings around the class prototypes(cf, Fig. [
This notion is translated into the idea that random walker over the similarity graph rarely crosses class decision boundaries. Here, we do not know the labels for our points or the right decision boundaries,
basically cannot optimize for this directly. Inspired by (Haeusser et al., 2017). imagine our walker starting at a prototype, taking step to an unlabeled point, and then stepping back prototype. The objective is to increase the probability that the walker returns to the same prototype it started from; we will refer to this probability as the landing probability. Additionally, we let our walker taking some steps between the unlabelled points, before taking step back prototype.
Concretely, for an episode with N class prototypes, and M unlabeled points overall, let A E RMM be the similarity matrix, such that each row contains the negative Euclidean distances between the embedding of an unlabelled point and the class prototypes. Similarly, we compute the similarity matrix between the unlabeled points B E RMMMM Mathematically speaking, A.j = - 1/,;
pyll? Bt,, = - ||h h2 where h; = (xx)) is the embedding of the i-th unlabeled sample, and Pj is the j-th class prototype. The diagonal entries Bi, are set to a small enough number to avoid self-loop.
Transition probability matrices for our random walker are calculated by taking a softmax over the rows of similarity matrices. For instance, the transition matrix from prototypes to points is obtained by softmaxing A", ((p=x) softmax(A"). such that ppz; I r(p-"a), Similarly, transition from points to prototypes (z--p), and transitions between points ((=-2), are computed by soft- maxing A, and B, respectively. Now, we define our random walker matrix as
T ( (r(+-t))) r(z-p)
where 7 denotes the number of steps taken between the unlabelled points, before stepping back to prototype. An entry Tr, denotes the probability of ending walk prototype j given that have started at prototype i, and the j-th row is the probability distribution over ending prototypes, given that we started at prototype The diagonal entries of T denote the probabilities of returning to the starting prototype: our landing probabilities. Our goal is to maximize those by minimizing cross-entropy loss between the identity matrix and our random walker matrix T. dubbed as Lwalken
Lwaaker Σ a' ((T, Loisit = H(U, P), Lnw = Loatterr + Luisit. 1=0
(3)
where (II,T)= Ei= logTi. Ti. and a is an exponential decay hyperparameter. However, one issue with Lwalker loss, that we could end up visiting a small subset of the unlabelled points. To remedy this problem, (Haeusser et al. 2017) introduce a 'visit loss', pressuring the walker to visit large set of unlabeled points. Hence, we assume that our walker equally likely to start at any prototype, then we compute the overall probability that each point would be visited when we
'To be exact, this is the average cross-entropy between the individual rows of I and T, since those are prohability distributions.
4

---

Under review as a conference paper at ICLR 2020
step from prototypes to points P= N. Ei= _ - r( where r( represents column of the matrix. Then add Luisit the standard cross-entropy between this probability distribution and the uniform distribution H. Hence, our final random walk loss is Law is the sum of Lwalker and
Cuisit: see Eq 3
Overall Loss. To put it all together, our objective function can be written as arg ming Ls + RRW where À is regularization parameter. While gradient of Ls = - pervised signal, the gradient of Rw encourages the "prototypical magnetization" " property guided by our random walk. This loss is minimized in expectation over randomly sampled semi-supervised episodes from our training data.
zi Ys log &i provides the su-
RELATED WORKS
PRWN Inspiration from Literature. Recently, Ren al. (2018) introduced the SS-FSL set- ting, and augmented PN with an adaptation step which leverages the unlabelled data. Later, ZZhag al. (2018) introduced another SS-FSL approach, dubbed MetaGAN, built on top of relation net- works (Sung et al. 2018), but employs an additional generator network (GANs) (Goodfellow et al.) 2014]. Analogous
(Dai al., 2017). the fundamental idea is to use the GAN generator gen- erate points in low density areas around the data. The discriminator is required to classify points into the K classes plus detect the fake points. This setup induces the discriminator to place decision boundaries in low density areas. On the other hand, SSL contains a rich toolbox of discriminative principlesteechniques which are simple, effective, and well-studied, yet have never been applied to the FSL setting (Miyato et al. [0118] Kamnitsas et al. 2018 Haeusser et al. 2017). We draw inspira- tion from those techniques, and design a state-of state-of-the-aa the-arterrrr art model which does not require an additional generator or adversarial training.
Local consistency. Unlabelled data gives information about the data density P P(x), and we somehow wish to use that information to improve a classifier modeling P(y|æ). Diserminative methods commonly do this by assuming some relation between the label distribution and the data density, and designing loss to enforce this prior. Most methods can be roughly said to enforce either local consistency or global consistency (Chapelle et al. [010 Zhou et al. 2004]. Local consistency means points which are close together hold similar labels. Global consistency assumes that point on the same structure have the same label. Much of local consistency methods are perturbation- based; where the objective is to minimize ((f((r), (z)). where D is a distance function, the classifier, and . is a perturbed version of z. VAT(Minyto et al. 2018) is one such method, where the perturbation made to x is an adversarial one.
Global Consistency and Graph-based Methods. Our loss falls into the global consistency meth- ods, more specifically graph-based methods (Zhu et al.] [005 Zhou et al.) [004 Kamnitsas et al., 2018 Haeusser et al.) 2017). These methods operate over graph with an adjacency matrix W. where Wi, is the similarity between samples T,, 2y E Dr U Dy. This graph is meant to reveal the structure of the data manifold. then points close over the manifold (high W.)), should have similar labels. Kamnitsas et al. (2018) and Hacusser et al. (2017) both use a random walk formulation, and encourage some notion of consistent walks, however, class prototypes are not involved. In Haeusser let al. (2017) the walker starting at a labelled point of class is required to return to any point of class In (Kamnitsas al.] 2018) improve on this approach by first performing label propagation to get labels for the unlabelled points, then an ideal transition matrix is constructed using those labels, and finally the cross-entropy between this ideal walker transitions, and the actual walker transitions is minimized. By involving prototypes in the graph, as the representatives of classes, our procedure simple, and better suited for prototypical networks; as we are ultimately interested in magnetizing the points around the prototypes.
TransducciveeSeni-upprvveed Adaptation Approaches. Apart from MetaGAN (Sung et al, 2018), existing cemii-uperrisee/trassuccci methods, use the unlabelled/query data as part of the classification procedure e.g., by defining better semi-supervised prototypes (Ren et al. 2018) or by replacing the K-means step with label propagation (Douze et al. 2018 Liu et al. 2019). None of those methods derive an additional training signal from the unlabelled data. In other words, our method focuses meta-training, the prior methods focus adaptation procedures which can leverage additional data. Kim et al. (2019) recently proposed an edge-labeling graph neural network (EGNN) approach achieve better shw-shot learning performance with direct exploitation of both
5

---

Under review as a conference paper at ICLR 2020
intra-cluster similarity and the inter-cluster dissimilarity. In contrast, our approach achieves better performance without (a) needing additional graph neural network parameters and hence is more re- sistant to over-fitting, (b) requiring transductive setting, where collective test set is provided during inference which is anyway orthogonal to our contribution; see Sec 4 for comparative results.
4 EXPERIMENTS
Overview. In our experiments, we cover two main results: with and without distractors (see See Sec where distractors present at train and test time when applied. In each, we discuss experiments with and without semi-superrvied adaptation where additional unlabelled data are used at test time. Note that whether not unlabelled data is available at test time, use the same trained model, the difference comes from adding the adaptation step in Eq. a test time to leverage that data.
4.1 EXPERIMENTAL SETUP
Datasets. We evaluated our work on the two commonly used SS-FSL benchmarks Omniglot and Mini-ImageNet. Omniglot (Lake et al.) (011) is dataset of 1,623 handwritten characters from 50 alphabets. Each character was drawn by 20 human subjects. We follow the few-shot setting proposed by (Vinyals et al. 2016). in which the images are resized to 28 x 28 px and rotations in multiples of 90" are applied, yielding 6,492 classes in total. These are split into 4, 12 training classes, 688 validation classes, and 1,692 testing classes. version of the ILSVRC-12 dataset (Russakovsky et al., 2015), in which 600 images, of size 84 x 84 px, for each of 100 classes were randomly chosen to be part of the dataset. We rely the class split used by Ravi & Larochelle (2017a). These splits use 64 classes for training, 16 for validation, and 20 for test. In our experiments, following (Ren et al. 2018 Zhang et al. (018), we sample 10% and 40% of the points in each class to form the labeled split for Omniglot and Mini-Imagenet, respectively; the rest forms the unlabeled split.
(Vinyals et al., 2016)) is modified
Implementation Details. We have provided full details of our experimental setting including net- work architectures, hyperparameter tuning on the validation set in appendix[] For fair compari- son, we opt for the same Conv-4 architecture (Vinyals et al., 2016) appeared in the prior SS-FSL art (Zhang et al. 2018 Ren et al. 2018).
Episode Composition. All testing is performed on 5-way episodes for both datasets. Unless stated otherwise, the analysis performed in sections 4.2 4.3 are performed by averaging results over 300 5-shot 5-way mini-imagenet episodes from the lest split, with =,.=00. Further detail is in appendix All accuracies reported are averaged over 3000 5-way episodes and reported with 95% confidence intervals.
Baselines. We evaluate our approach on standard SS-FSL benchmarks and compare to prior art; PN (Ren et al. 2018), MetaGAN (Zhang et al. 2018), and EGNN-Semi (Kim et al. 2019). We also compare PRWN with control models; the vanilla prototypical network (PN) trained on the fully labelled dataset, denoted PNat (the oracle), which is considered to be our target model, PN (Ren et al. 2018) model trained only on the labelled split of the data (40% of the labels), which is essentially PRWN without our random walk loss, and finally PN trained with the -f-th- VAT (Miyato et al. 2018) and entropy minimization as a strong baseline; we denote it as PNyAT.
4.2 SEMI-SUPERVISER META-LEARNING WITHOUT DISTRACTORS
For experiments without semi- supervupd adaptation, we observe from the third horizontal section of Table 3] that PRWN improves on the previous state-of-the-art MetaGAN (Zhang et al., 2018). and EGNN-Semi (Kim et al., 2019) on all experiments, with a significant improvement on 5-shot mini-imagenet. It is worth mentioning that our PRWN has less than half the trainable parameters of MetaGAN which empolys an additional larger generator.
Experiments with semi-supervised adaptation are presented in bottom section in Table 3 Note that PRWN already improves on prior art without the adaptation. With the added semi semi-supervised adaptation, PRWN improves significantly, and the gap widens. On the 5-shot mini-imagener task, PRWN achieves a relative improvement of 8.17%. 4,86% and 8,28% over the previous ofate-of-the- art, (Ren et al. 2018 Liu et al. 2019 Kim al. 2019) respectively.

---

Under review as a conference paper at ICLR 2020
Table
Semi- Suni--uuee Meta-Learning Ablation Study
Model
Omniglot 1-shot
Mini-Imagener
1-shot
5-shot
PNau Snell et al.
2017)
98.8
49.4
68.2
PN (Ren al. 2018)
94.62 + 0.09
43.61 + 0.27
59.08 + 0.22
MetaGAN Zhaan al.
2018
97.58 + 0.07
50.35
0.23 N/A 0.22
64.43 0.27
EGNN-Semi (Kim et al
2019
N/A 97.14 0.16
62.52 + N/A
PNy AT (Ours)
49.18
66.94 0.20
PRWN (Ours)
98.28 + 0.15
50.89 + 0.22
67.82 + 0.19
PN Semi-supervised inference Ren al. 2018
97.45 = 0.05
49.98 + 0.34
63.77 0.20
PN + Soft K-means Ren et al. 2018))
97.25 = 0.10
50.09 0.45
64.59 0.28
PN Soft K-means cluster Ren et al.
2018
97.68 + 0.07
49.03
0.24
63.08 0.18
PN + Masked soft K-means Ren et al.
2018
97.52 + 0.07
50.41
0.24
64.39 0.24
TPN-Semi (Liu al. 2018
N/A
52.78
0.27 N/A
66.42 0.21
EGNN-Semi(1] (Kmm ct al.
2019)
N/A
64.32 = N/A
PRWN + Semi-supervised inference (Ours)
99.23 0.08
56.65 0.24
69.65 0.20
ANALYSIS
Ablation study. From Table 3 we can see that our PRW loss improves the baseline PN significantly, boosting the accuracy of PRWN up 67.82% from 59. 59.08% on 5-shot mini-imagenee for example. Moreover, while PNv AT proves powerful model, competing with prior state-of-the still beats it on all tests. Furthermore, We trained PRWN on mini-imagenet with only 20% of the labels, and we obtain an accuracy of 64.8% on the 5-shot task; outperforming the SOTA of 64.43% which uses double the amount of labels. Most remarkably, PRWN performs competitively with the fully labelled PNall even outperforming it 1-shot mini-imagenet.
PRWN
Local Global consistency Analysis. evaluate the global consistency, we take look into behavior of our random walker for various models. We compute the landing probability over the graphs they generate: the probability a random walker returns to the starting prototype, given by Trace(T(()) from Eq. 2 We can see in Fig. 2a that even as 7 grows, PRWN generates graphs with the highest landing probs. Following is PN AN implying that enforcing local consistency still helps with global consistency. We can also see that PNau also does better than PN, indicating that the addition of extra labeled data also improves global consistency. To evaluate local consistency and adversarial robustness of our various models, we compute their average VAT loss. Unsurpris- ingly, PNy AT performs best with 1.1 loss, following are both PRWN and PNa with 3.1 & 2.91 respectively, then PN with 5.9. We see again that improving global consistency helps with local consistency, and does additional labelled data.
MAN
035
04:
30/00/
20C AMV
D00 WWV
20
20 Aty
D00
(a) Landing probabilities
(b) Higher-Waa Performance
(c) Improvement over PN
Figure 2: (a) Landing Probabilities on mini-ImageNet: The r-axis denotes the number of steps for the walk (7), and the y-axis shows the probability of returning to the right prototype. (b): The Higher-Way performance on Omniglot as we increase the number of test classes N.. (c): The
relative improvement of PRWN over PN increase the number of classes in Omniglot

---

Under review as a conference paper at ICLR 2020
Table 2: Experiments with distractor classes
Model
Omniglot 1-shot
Mini-Imagenet
1-shot
5-shot
PRWN (Ours)
97.76 0.11
50.96 + 0.23
67.64 + 0.18
PN+ Semi-supervised inference (Ren et al. 2018
95.08 + 0.09
47.42 = 0.33
62.62 + 0.24
PN+ Soft K-means (Ren et al. (018))
95.01 + 0.09
48.70 + 0.32
63.55 + 0.28
PN+ Soft K-means + cluster [Ren ef al. 2018
97.17 + 0.04
48.86 + 0.32
61.27 + 0.24
0.24
PN+ Masked soft K-means (Ren al. 2018
97.30 + 0.30
49.04 = 0.31
62.96
TPN-Semi (Liu et al. 2018
N/A 97.86 0.22
50,43 + 0.84
64.95
PRWN+ Semi-supervine sune--suee inference (Ours)
53.61 = 0.22
67.45 0.21
PRWN+ Semi- semi-super inference + filter (Ours)
99.04 + 0.18
54.51 + 0.23
68.77 = 0.20
Discriminative Power. order to study our approach and baselines in a more challenging setup, evaluate their performance a Higher- Baay classification. Fig. 2b shows that model still performs better than the baseline and close to PN (the oracle). The accuracy of PRWN, PNati: alls 64.43%, 65.57% and 39.84%, respectively. In Fig. 2c
and PN, 800-ways in Omniglot, show the relative improvement over PN reaching = 60% improvement on 800-ways classification. Similar behavior has been reported for mini-imagenet (Appendix F). This shows the performance gain from our PRW loss is robust and reflects its discriminative power.
adaptation approaches. (Liu al. al.; 2019 Ren et al. 2018: Douze et al. 2018) Our approach is orthogonal and can be integrated with these methods. In fact, PRWN semi-supervised inference is such an integration where K-means step is integrated from (Ren al., 2018). Tables 3 and 2 show that our network, combined with the K-means step at test time, perform far better than the networks trained with those adaptation methods. This supports our hypothesis that semi-supervised adaptation like the K-means step fails to fully exploit the unlabeled data during meta-training.
TransductiveeSSmiisuuperee
4.3 SEMI-SUPERVISED META-LEARNING WITH DISTRACTORS
The introduction of distractors by Ren et al. (2018) meant to make the whole setup realistic and challenging. To recap, the distractors are unlabelled points added to your support set, but they do not belong to any of the classes in that set i.e. the classes you currently classifying over. This "labelled/unnlbelleed class mismatch" was found by Oliver et al.] (2018) to be quite a challenge for SSL methods, sometimes even making the use of unlabelled data harmful for the model. We present our results in table 2 where the top row is our model without test time adaptation, and we can see that it already beats the previous state-of-the-ee below, which makes use of test time unlabelled data, even by a large margin in the 5-shot mini-imagene with relative improvement of 3,8%, and 6, % on TPN-Semi (Liu et al. 2019), and PN+Soft K-Means (Ren et al. 20188,, respectively. Moreover, it beats the MetaGAN (Zhang et al. 2018) model trained without distractors all tasks, and in fact performs closely to our own PRWN trained without distractors (cf. Table 3).
When we add the semi-supervised adaptation step, with distractors present among unlabelled data at test time, we see that our model does not benefit well from that step, and in the case the 5-shot mini-imagenet, the performance is slightly harmed. In the next subsection, we will explore why our model is robust to distractors during training, and how we can use the random walk dynamics to make the semi-supervised inference step useful when distractors are present.
DISTRACTOR ANALYSIS
We hypothesize that the reason our PRWN is robust against distractors, is because our random walker learns to largely avoid distractor points, and as such they are not magnetized towards our class prototypes; if anything by learning avoid them, the network is structuring the latent space such that points of each class are compact and well separated. This comes as a by-product of the "prototypical magnetization" property that our loss models.
8

---

Under review as a conference paper at ICLR 2020
To test this hypothesis, take PRWN model trained with distractors, we sample test episodes including distractors (Na = Ne = 5), construct our similarity graph, and compute the probabil- ity that our random walker visits distractor versus non-distractor points. Concretely,
compute P + Ex 1(p->x, where the summation over the columns, and an entry Pe represents the probability of visiting point i. We split P into Pataan and Paist, containing the entries for non- distractor and distractor points. respectively. Both probabilities Patean and Pdist should sum up to one. Whereas our baseline PN gets Pelean 0.67, and PN gets Palean = 0.76, our PRWN gets Petean = 0.81. So we see our Law is not only an attractive force bringing points closer to proto- types, but also has repelling force driving irrelevant points away from prototypes. Note this not only feature of the network, it is property of the loss function. For instance, the semi-supervised inference step (Ren et al. 20188) involves all points, distractor or not, equally in the prototype update, regardless of the geometry of the embeddings.
Distractors at semi-supervised inference. We also performed an experiment to further improve PRWN with the semi-supervised inference step. We exploit our random walk dynamics to order to filter out distractors. We compute the probability that a point is part of a successful walk; a walk which starts and ends at the same prototype. This is given by S = Exen ((p=s) c p(=-p), where @ is the Hadamard product, and the summation is over the columns of the resulting matrix. Then we simply discard the points that scored below the median. With this little step, we see our PRWN semi-supervised inference, become more robust to test time distractors, with 99.04% accuracy on omniglot, and 54.51 %% & 68.77% on mini-imagenet 1&5-shot, respectively. This simple filtering step just improved on the distractor state-of-the-aa as shown in Table[2[aast row).
More Distractors during Training, Back to training, so far we have only explored models trained with N₂- = Nr. = 5. In this case there are as many distractor points as there are clean points. We stress test PRWN by training it on mini-imagenet with N₂ > N 5, namely N. {10, 15}. For 5-shot performance, we get accuracies of 66.92% & 66.75%, respectively. For 1-shot performance, get 50.44 50.44% & 48.27%. We that the model still manages to improve significantly over the baseline PN (Ren et al. 2018), despite 75% of the unlabelled points being distractors. In fact, with Na set to 10, PRWN still beats MetaGAN, the previous rate-of-the-ar art model, trained on clean data in both mini-imagenet tasks(cf. Table B. This shows that PRWN is meaningful step towards real world settings, where unlabelled points are not guaranteed come from relevant classes.
5 CONCLUSION
SS-FSL is relatively unexplored yet challenging and important task. In this paper, we introduced state-of-the-ar SS-FSI. model, by introducing a semi-supervised meta-training loss, namely the Prototypical Random Walk, which enforces global consistency over the data manifold, and magne- tizes points around their class prototypes. We show that our model outperforms prior art and rivals its fully labelled counterpart in a wide range of experiments and analysis. We contrast the effects and performance of global versus local consistency, by training PN with VAT (Miyato et al.) 2018) and comparing with our model. While the local consistency loss has an improvement on the per- formance, we found that our global consistency loss significantly improves the performance in SS-FSL. Finally, we show that our model is robust to distractor classes even when they constitute the majority of unlabelled data. We show how this is related to the dynamic of PRW. We even create a simple distractor filter, and show its efficiency in improving semi-supervised inference (Ren et al., 2018). Our experiments and results set the state-of-the-art on most benchmarks.
REFERENCES
Joshua B Tenenbaum, Charles Kemp, Thomas Griffiths, and Noah D Goodman. How to grow a mind: Statistics, structure, and abstraction. Science (New York, N.Y.), 331:1279 85,, 03 2011. 1. doi: 10.1 1061s2///ci 192788.
Avrim Blum and Tom Mitchell. Combining labeled and unlabeled data with co-training. In Pro- ceedings of the eleventh annual conference on Computational learning theory, pp. 92-100. ACM, 1998.

---

Under review as a conference paper at ICLR 2020
Olivier Chapelle, Bernhard Schlkopf, and Alexander Zien. Saii-Supeeisedd Learning. The MIT Press, 1st edition, 2010. ISBN 0262514125, 9780262514125.
Michael Collins and Yoram Singer. Unsupervised models for named entity classification. In 1999 Joint SIGDAT Conference on Empirical Methods in Natural Language Processing and Very Large Corpora, 1999.
Zihang Dai, Zhilin Yang, Fan Yang, William W. Cohen, and Ruslan Salakhutdinov. Good semi- supervised learning that requires bad gan. In NIPS, 2017.
Samuel Dodge and Lina Karam. A study and comparison of human and deep learning recognition performance under visual distortions. In Computer Communication and Networks (ICCCN), 2017 26th International Conference on, pp. 1-7. IEEE, 2017.
Matthijs Douze, Arthur Szlam, Bharath Hariharan, and Hervé Jégou. Low-shot learning with large- scale diffusion. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recog- nition, pp. 3349-3358, 2018.
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural infor- mation processing systems, pp. 2672-2680, 2014.
Haeusser, A. Mordvintsev, and D. Cremers. Learning by association versatile semi- supervised training method for neural networks. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 626-635, July 2017. doi: 10.1109/CVPR.201..7.
Thorsten Joachims, Transductive inference for text classification using support vector machines, In Ieml, volume 99, pp. 200-209, 1999.
Konstantinos Kamnitsas, Daniel C. Castro, Loic Le Folgoc, Ian Walker, Ryutaro Tanno, Daniel Rueckert, Ben Glocker, Antonio Criminisi, and Aditya V. Nori. Semi-supervised learning via compact latent space clustering. In ICML, 2018.
Jongmin Kim, Taesup Kim, Sungwoong Kim, and Chang Yoo. Edge-labeling graph neural net- work for few-shot learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 11-20, 2019.
Gregory Koch, Richard Zemel, and Ruslan Salakhutdinov. Siamese neural networks for one-shot image recognition. In ICML deep learning workshop, volume 2, 2015.
Brenden Lake, Ruslan Salakhutdinov, Jason Gross, and Joshua Tenenbaum. One shot learning of simple visual concepts. In Proceedings of the Annual Meeting of the Cognitive Science Society, volume 33, 2011.
Yin Li, Jian Sun, Chi-Keung Tang, and Heung-Yeune Shum. Lazy snapping. ACM Transactions on Graphics (ToG), 23(3):303-308, 2004.
Yanbin Liu, Juho Lee, Minseop Park. Saehoon Kim, Eunho Yang. Sung Hwang, and Yi Yang. Learning to propagate labels: Transductive propagation network for few-shot learning. arXiv preprint arXiv: 10002, 2018
Yanbin Liu, Juho Lee, Minseop Park, Saehoon Kim, Eunho Yang, Sung Ju Hwang, and Yi Yang. Learning to propagate labels: Transductive propagation network for few-shot learning. ICLR, 2019.
Erik G Miller, Nicholas E Matsakis, and Paul A Viola. Learning from one example through shared densities transforms. In Proceedings IEEE Conference Computer Vision and Pattern Recog- nition. CVPR 2000 (Cat. No. PR00662), volume I, pp. 464-471. IEEE, 2000.
Takeru Miyato, Shin-ichi Maeda, Shin Ishii, and Masanori Koyama. Virtual adversarial training: regularization method for supervised and semi-supervised leaming. IEEE transactions on pattern analysis and machine intelligence, 2018.
10

---

Under review as a conference paper at ICLR 2020
R Nigam and AG Kosovichev. Measuring the sun's eigenfrequencies from velocity and intensity he- lioseismic spectra: Asymmetrical line profile-fitting fitteefitting formula. The Astrophysical Journal Letters, 505(1):L51, 1998.
Avital Oliver, Augustus Odena, Colin Raffel, Ekin Dogus Cubuk, and Ian Goodfellow. Realistic evaluation of semi-supervised learning algorithms. 2018. URL https: fittps://arxiv.orgg pdf
Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. 5th Interna- lional Conference on Learning Representations, 2017a.
Sachin Ravi and Hugo Larochelle. Optimization model for few-shot learning. In International Conference on Learning Representations, 2017b.
Mengye Ren, Sachin Ravi, Eleni Triantafillou, Jake Snell, Kevin Swersky, Josh B. Tenenbaum, Hugo Larochelle, and Richard S. Zemel. Meta-lcarning for semi-supervised few-shot classification. In International Conference on Learning Representations, 2018. pattps://openzeeee Bet/Foorum2IG+HUSSZ---
Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy. Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. ImageNet Large Scale Visual Recognition Challenge. International Journal of Computer Vision (IJCV), 115(3)211-255 1-22, 2015. doi: 10.1007/s1 1263-015-0816-y;
Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. TPAMI, pp. 107, 2000.
Jake Snell, Kevin Swersky, and Richard Zemel. Prototypical networks for few-shot learning. In Advances in Neural Information Processing Systems, pp. 4077-4084 2017. 2017,
Flood Sung, Yongxin Yang, Li Zhang, Tao Xiang, Philip HS Torr, and Timothy M Hospedales. Learning to compare: Relation network for few-shot learning. In Proceedings of the IEEE Con- ference Computer Vision and Pattern Recognition, pp. 1199-1208, 2018.
Oriol Vinyals, Charles Blundell, Timothy Lillicrap, Daan Wierstra, et al. Matching networks for shot learning. In Advances in neural information processing systems, pp. 3630-3638, 2016.
David Yarowsky. Unsupervised word sense disambiguation rivaling supervised methods. In 33rd annual meeting of the association for computational linguistics, 1995.
Ruixiang Zhang, Tong Che, Zoubin Ghahramani, Yoshua Bengio, and Yangqiu Song. Metagan: An adversarial approach to few-shot learning. In Advances in Neural Information Processing Systems, pp. 237 2370-, 2018.
Dengyong Zhou, Olivier Bousquet, Thomas N Lal, Jason Weston, and Bernhard Schölkopf. Learn- ing with local and global consistency. In Advances in neural information processing systems, pp- 321-328, 2004.
Xiaojin Zhu, John Lafferty, and Ronald Rosenfeld. Semi-supervised learning with graphs PhD thesis, Carnegie Mellon University, language technologies institute, school of .... 2005.

---

Under review as a conference paper at ICLR 2020
A APPENDIX
B EPISODE CONSTRUCTION
Algorithm Construct semi-supervised episode E, optionally with distractors. RANDOMSAMPLESS, N) denotes a set of N elements chosen randomly from set S, without re- placement. Items sampled from the labeled split tuples (Iz Vs), while items sampled from the unlabeled split are simply (æ:)
Require: No (The number of classes way)
N₂ (The number of examples per class or shor}
Ng (The number of query images per class}
No {The number of unlabeled examples per class in the support set}
Na (The number of distractor classes per episode}
V < RANDOMSAMPLE(()
K} Ne)
for k E V do
Sy. +- RANDOMSAMPLLEC N₂)
SK.U RANDOMSAAMPLECDS N.)
Qx RARDDOSSSMPLELOOO
Q + QUQ Q
S + S (S, USKU))
end for
if DISTRACTOR then
L RANDOMSAMPLE(11 for k E do S SU RANDOMSAMPLED.. N..)
N.)
end for end if'
C EXPERIMENTAL DETAILS
Architecture We the architecture from Vinyals al. (2016) composed of four convolutional blocks. Each block comprises a 64-filter 3 convolution, batch normalization layer, a ReLU non- linearity and 2 max-pooling layer. No other architectures were considered
Optimization We use ADAM for all our experiments with 31 = 0.9, 82 = 0.99. The initial learning rate for Omniglot experiments 0.001, and for all mini-imagenet 0.00025. For Omniglot, the learning rate in half every 2K episodes. For mini-imagenet we cut the rate in half every 12500 episodes. For omniglot, we train for 20K episodes, for mini-imagenet we train for 100K episodes. For the learning rate the range considered was from 0.0001 to 0,001. For the decay steps the range considered was 2k to 20k. The maximun training step considered was 120K.
Random walkFor all experiments the number of steps for our random walk r = with an eponential The weight given
decay a of 0.7, except on omniglot eperiments without distractors, where to for the semi-supervised loss À is 1.5 & 2 respectively for omniglot without and with distractors. For mini-imagenet,
0.5 for all experiments. We validated over 7 in the range from 5, a from 0.5 to 1, and À from 0.5 to 2.5.
C.1 EPISODE COMPOSITION
Omniglot For training without distractors, we use N, 20 and N,, = 10. For training with distrac- tors, use N. Na 5 and N, 10. And N, in all cases. For all experiments, N, = 5. For testing with additional unlabelled data, we use N, = for fair comparison with Ren et al. (018).
Mini-imagenet For training with distractors, N₂ = 5. For all experiments, N₂ = 5. For testing with additional unlabelled data, use N,, 20 for fair comparison with Ren et al. (2018).
N₂ 5, N. = and N., 10 for all experiments. When training
12

---

Under review as a conference paper at ICLR 2020
Table 3: Semi-Supervised Meta-Learing
Model
Tiered-Imagennt
1-shot
5-shot
RNeeen et al. 2018
46.52 0.52
66.15= 0.22 70.52 + 0.43
PRWN(Ours)
54.87 + 0.46
PN + Semi-supervised inference [Ren et al. 2018)
50.74 + 0.75
69.37 + 0.26
PN Soft K-means Ren et al. 2018)
51.52 + 0.36
70.25.59 + 0.31
PN + Soft K-means cluster Ren el al. 2018
51.85 + 0.24
69.42 + 0.17
Masked soft K-means Ren al. 2018)
52.39 + 0.44
69.88 0.20
TPN-Semi Semi (Liu et al. 2018
55.74
71.01
PRWN Semi-supervised inference (Ours)
59.17 + 0.41
71.06 0.39
D
TIEREDIMAGENET
E LATENT SPACE VISUALIZATION
Figure 3: (SNE visualization of the embeddings for 50 classes on Omniglot. The embeddings of un- labeled data got magnetized the class prototypes forming more compacted clusters in our PRWN right in contrast to the embeddings of PN left
F MINIIMAGENET HIGHER WAY CLASSIFICATION
13

---

Under review as a conference paper at ICLR 2020
PRIMN
Accursyy
15
20-way
Classifiation way
Figure 4: Left: Accuracy of our different models on 5-shot minilmageNet as we increase the number of classes No. Right: The relative improvement over PN as we increase the number of classes.
14


Reviews:
[{"review_id": "Syg4K6RjFS", "reviewer": "AnonReviewer2", "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 submission introduces a version of the random-walk regularizer introduced in Haeusser et al. 2017, in the setting of a Prototypical Network for semi-supervised few-shot learning. The authors show that using this regularizer, SOTA results can be obtained, notably on the popular miniImageNet. They also show that the random-walk can be used to successfully tackle the case with distractors.\n\nI'm a bit on the fence for this submission. I could be convinced to accept, due to the impressive effectiveness of the method despite its simplicity. However, the submission is not without faults:\n\n1. There are no results reported on tieredImageNet, despite it being used in the original paper on semi-supervised few-shot learning (Ren et al. 2018).\n\n2. The proposed methods remains a fairly simple extension of the regularizer of Haeusser et al. 2017.\n\nIf the authors could address point 1 and add results on tieredImageNet, I would be willing to increase my rating.\n\nVery small note: in the 4th section paragraph, is it possible that p(x_i|p_j) = \\Gamma_{i,j}^{(p\\rightarrow x)}, should be p(x_i|p_j) = \\Gamma_{j,i}^{(p\\rightarrow x)}?", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}, {"review_id": "Hyx7le6pYH", "reviewer": "AnonReviewer3", "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 suggests a method for semi-supervised few-shot learning. It is based on prototypical network, but in addition to the supervised loss a regularisation term that encourages unlabelled sample to be closer to the prototypes. This regularisation term is adapted from Haeusser et al. (2017) and is encouraging a random walk on a graph (where nodes are prototypes and unlabelled samples) that begins at a certain prototype to end at the same prototype. \n\nThe SS-FSL is indeed interesting and worth exploring. I also find the random walk on a graph of samples appealing and can potentially give insights on the structure of the embedding space. However, I think the paper is lacking in innovation, it is Haeusser et al. (2017) method applied to SS-FSL. The only difference is the usage of prototypes instead of labeled samples, this difference is also only relevant for 5-shot and not for 1-shot (where the prototype is the labeled sample) so there is only a single experiment (5-shot mini-imagenet) that is truly testing PRWN. Also, the choice of using prototypes (unlike Haeusser et al.) is neither justified theoretically nor empirically. Additionally, it is strange that the reported SS-FSL results are lower than standard FSL SOTA, e.g MetaOptNet (Lee et. al, 2019). \n\n\nUpdate after rebuttal:\nAfter reviewing the authors' response I'm changing my rating from reject to weak-reject  \n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "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.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "HkeeGhgaYB", "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 develops a random walk-based method on top of prototypical networks to address the semi-supervised few-shot learning, i.e. when each classification task can access only a few-shot labeled data but many unlabeled data. This paper defines a specific random walk: it walks from a prototype to an unlabeled sample, then walks for several steps between unlabeled samples, and then walk back to some prototype. They then propose two loss terms: one aims to maximize the probability of returning to the same prototype, and the other tries to make each unlabeled data having equal probability to be visited during the random walk. These two terms are added to the original prototypical network training loss and the resulted training procedure involves both the few-shot labeled data and the unlabeled data. Experiments on mini-ImageNet show that the proposed method outperforms the other baselines.\n\nIntuitively, the main idea makes some sense to me. The writing is clear to understand the main idea but can be improved in various places. My major concerns are the motivation and analysis of the proposed random walk and the training algorithm, whose details cannot be found in the paper. The paper uses a lot of spaces to review the existing works and problem settings, but only spends one page (Section 2.2) on the description of their contribution, and the description lacks any in-depth discussion about “why it is designed in this way but not others” or “how this objective helps the few-shot learning”: it simply lists the procedures without convincing explanation.\n\nDetailed comments:\n\n1. It is called “random walks” but is different from the random walks used in classical methods in many key points and thus might not have all the existing properties of random walks. For example, it is not clear whether the negative of the square of Euclidean distance is a valid similarity for random walks. It is also not clear why the random walk probability matrix is computed by softmax instead of normalized Laplacian. Moreover, it fixes the starting nodes and end nodes, and also fixes the propagation steps: this cannot give any guarantee of any convergence (or asymptotic properties, mixing rate, etc) as the original random walks hold. This could be a serious problem because the random walks can stop at any non-stationary state after tau steps, which cannot be used for training. \n\n2. It is not clear why the two additional loss terms (L_walker and L_visit) can help to improve the prototype training. The claimed motivation of minimizing these two terms cannot be soundly related to the final few-shot classification goal, though each of them independently makes some sense if applied to a different goal. Why does maximizing the probability of a prototype transit to itself give new information of improving few-shot classification? If prototypes are involved in the random walk nodes, why do we need to walk back to itself through many unlabeled nodes rather than simply walk to itself (which has the largest probability)? Why do we need to visit as many unlabeled data as possible? Isn’t the case that we hope to only visit the unlabeled data mostly related to the prototype and its class and rule out other unrelated ones since they introduce noises?\n\nHere is a counterexample, which is a trivial solution that can minimize the two terms but does make any sense here: it is easy to define a model that produces the same prototype for different classes (so L_walker is minimized), and achieve equal distance between all the unlabeled samples (so L_visit is minimized), but this does not help the prototype training at all. \n\n3. Another primary flaw here is that the training objective and the computational graph during training always change with the random walks, since the trajectory of the random walks keeps changing due to the randomness. Hence, the trained model does not have any guarantee and the convergence in the training is not the real convergence (it is not well-defined in the first place). If the random walks guarantee to converge to some stationary distribution, it might be possible to treat the varying computational graph as a stochastic one which has been analyzed in previous works. Unfortunately, due to the fixed number of steps and other issues mentioned above, this cannot hold. In Figure 2(a), we can see that even the largest tau they have tried cannot make the landing probability converge (not talking about the stationary distribution over all the nodes), which verifies my worries above.\n\n4. Is the final performance sensitive to the hyperparameters lambda and tau? How did you choose their values in the experiments? \n\n5. The methodology behind most existing semi-supervised few-shot learning methods, as also indicated in this paper’s introduction, is to apply or extend existing semi-supervised learning techniques on top of existing few-shot learning models. In fact, it is quite straightforward to do so and test all the semi-supervised learning techniques on few-shot learning tasks. Hence, I think it is necessary to compare to baselines that directly use, for example, consistency loss from mean teacher method and progressive training on pseudo labeling, or other SSL techniques mentioned in this paper: https://papers.nips.cc/paper/7585-realistic-evaluation-of-deep-semi-supervised-learning-algorithms. \n\n-------------\n\nUpdate:\n\nThanks for the authors' reply! After reading the rebuttal, I still think there are several main issues needed to be clarified or needing further study. Hence, I will keep my rating.", "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": "I carefully checked the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposed a semi-supervised few-shot learning method, on top of Prototypical Networks, wherein a regularization term that involves a random walk from a prototype to unlabeled samples and back to the same prototype.  SotA results were obtained in several experiments by using this method.  All reviewers agreed that the novelty of the paper is not such high compared with Haeusser et al. (2017) and the analysis and the experiments could be improved.
Decision: Reject