Improving Task-Specific Generalization in Few-Shot Learning via Adaptive Vicinal Risk Minimization
Authors: Long-Kai Huang
Ying Wei
Venue: NeurIPS 2022 Accept (2022)
Keywords: Few-shot learning
Vicinal risk minimization
Task-specific generalization

Abstract: Recent years have witnessed the rapid development of meta-learning in improving the meta generalization over tasks in few-shot learning. However, the task-specific level generalization is overlooked in most algorithms.  For a novel few-shot learning task where the empirical distribution likely deviates from the true distribution, the model obtained via minimizing the empirical loss can hardly generalize to unseen data. A viable solution to improving the generalization comes as a more accurate approximation of the true distribution; that is, admitting a Gaussian-like vicinal distribution for each of the limited training samples. Thereupon we derive the resulting vicinal loss function over vicinities of all training samples and minimize it instead of the conventional empirical loss over training samples only, favorably free from the exhaustive sampling of all vicinal samples.
It remains challenging to obtain the statistical parameters of the vicinal distribution for each sample. To tackle this challenge, we further propose to estimate the statistical parameters as the weighted mean and variance of a set of unlabeled data it passed by a random walk starting from training samples. To verify the performance of the proposed method, we conduct experiments on four standard few-shot learning benchmarks and consolidate the superiority of the proposed method over state-of-the-art few-shot learning baselines. 

Improving Task-Specific Generalization in Few-Shot Learning via Adaptive Vicinal Risk Minimization
Long-Kai Huang Tencent Al Lab hlongkai@gmail com
Ying Wei" City University of Hong Kong yingvei@cityu. edu.hk .kk
Abstract
Recent years have witnessed the rapid development of meta-learning in improving the meta generalization over tasks in few-shot learning. However, the task-specific level generalization is overlooked in most algorithms. For novel few-shot learning task where the empirical distribution likely deviates from the true distribution, the model obtained via minimizing the empirical loss hardly generalize to unseen data. viable solution to improving the generalization comes as a more accurate approximation of the true distribution; that is, admitting Gaussian-like vicinal distribution for each the limited training samples. Thereupon we derive the resulting vicinal loss function over vicinities of all training samples and minimize it instead of the conventional empirical loss over training samples only, favorably free from the exhaustive sampling of all vicinal samples. remains challenging to obtain the statistical parameters of the vicinal distribution for each sample. To tackle this challenge, we further propose to estimate the statistical parameters as the weighted mean and variance of set of unlabeled data it passed by random walk starting from training samples. To verify the performance of the proposed method, we conduct experiments on three standard few-shot learning benchmarks and consolidate the superiority of the proposed method over state-of-the-an few-shot learning baselines.
Introduction
In recent years, deep learning algorithms have made tremendous progress and have been widely applied in vision [16], language (37] and speech [10 areas. Despite the prevalence, deep learning algorithms rely heavily on a sufficient amount of labeled data and often fail when only a limited number of labeled samples available. Considering the high cost of extensive data collection and annotation, it has attracted increasing attention to developing algorithms lcarning from a limited number of training samples, which has been widely known few-shot learning 39 5
The recent focus of few-shot learning is built on the meta-learning framework of meta-learning is to train model that can be quickly adapted to new task with a small number of labeled samples by leveraging the knowledge from previous related tasks. Typically, a meta-learning model consists of the meta-training stage where well-generalized feature extractor is learned from meta-training tasks and the meta-testing stage during which a classifier built on top the feature extractor for novel tasks. While the majority of meta-lcarning works revolved around developing better meta-training strategies to reduce the meta-genente settt-eennrallzation error over all tasks, how to fully leverage the meta-trained feature extractor build a robust classifier and improve task-specific generalization in the meta-testing stage remains less explored.
33
The goal
"Correspondence Ying Wei.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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(b)
Figure 1: (a) The classifier overfits few-shot examples that inadequately represent the true distribu- tion. (b) The vicinal distribution without adjusting the means slightly improves the classifier. (c) The vicinal distribution with updated means contributes gell-general classifier.
The challenge to building such a classifier lies in the significant deviation of the empirical distribution (i.e. the distribution formed by the training data) from the population distribution (i.e. the true distribution). As illustrated in Figure L a model well fitting the training data (support set) may generalize poorly on the testing data (query set) from the true distribution due to the bias in the empirical distribution. One viable solution is to approximate the true distribution more accurately by viewing the empirical distribution as the assembling of delta functions located on each training sample, Chapelle et al. [4]] proposed the Vicinal Risk Minimization loss function where the delta functions are replaced by some density estimate in the vicinity of each training data. In the era of deep learning, the VRM learning principle is implemented as Mixup [47 38
which is simple yet effective given sufficiently large number of training data. However, as we have verified in Table the performance improvement by applying Mixup on the support set is limited in few-shot learning where the vicinal distributions assembled by Mixup is still significantly biased. To improve the generalization of few-shot classifier during meta-testing, we are motivated to revisit the VRM principle to 1) generate adaptive vicinal distribution for each sample support set and 2) minimize the expected vicinal loss over the vicinal distributions. However, both are challenging.
Without loss of generality, we assume that the vicinity of each training point admits Gaussian distribution. In 4. the means of the vicinal distributions are located on the original training points. As illustrated in Figure [(b) however, setting the mean in this way is not sufficient to approximate the true distribution, as an original training point likely deviates from the mean of the ground-trute distribution of its corresponding class. In fact, it is difficult to estimate the mean and variance based only on the labeled training samples. In this paper, we assume that unlabeled samples are also available, and leverage these unlabeled samples to estimate the mean and variance of the vicinal distribution for each labeled sample. Concretely, inspired by [4]], we first construct transition probability matrix based on pairwise distances between features of all samples, and secondly perform the lazy random walk among unlabeled samples starting from each labeled sample. After walking a certain number of steps, we obtain the visit probabilities of all the samples and infer the vicinal distribution whose mean and variance are the weighted mean and variance of all samples visited.
All that remains the loss function over the vicinal distributions of all training samples. An intuitive way to do this is to exploit the Monte Carlo method, which repeats random sampling to explicitly generate data points from each vicinal distribution and minimizes the loss on all the sampled data points. Unfortunately, it requires drawing large amount of samples to minimize the Monte Carlo approximation error, which significantly increases the computation cost. Instead, we follow 4 to derive closed form of the expected vicinal loss over the vicinal distributions. In this paper. we focus classifier in optimization-base
on building an optimization-ban which has been proved with much more adaptability and generalization capacity in novel meta-testing tasks than a neighst- classifier metric-based meta-learning algorithms [39 <
meta-learning algorithms [Р 19].
Particularly, we consider both the rross-entrppy loss and the SVM loss functions which are used as classifier in the state-of-the-an meta-learning algorithms 4 |9] For the vicinal version of cross- entropy loss, it cannot be computed in closed form. We instead derive its quadratic approximation. For SVM, we derive its closed-form vicinal loss.
In summary, our contributions are threefold:
We revisit vicinal risk minimization (VRM) in deep few-shot learning and derive the resulting expected vicinal loss functions for both the cross-entropy loss and SVM.

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We propose to harness unlabeled data and a lazy random walk algorithm to generate adaptive statistical parameters for the vicinal distribution of each training sample.
We have validated the superiority of the proposed algorithm with extensive experiments three benchmarks, ie., minilmageNet, CUB, CIFAR-FS.
Related Works
2.1 Few-Shot Learning and Meta-Learning
Few-shot learning aims to recognize novel classes with insufficient labeled instances. The recent focus of few-shot learning algorithms has been on the meta- veta-learning framework, which trains the model with multiple episodes to enable quick learning and applies the model to improve learning in novel tasks. The meta-learning methods fall into two major categories; metric-based methods and optimization-
based methods. Metric-based methods 15
39 33
45 learn a metric to compare two samples'
feature embeddings encoded by the feature extractor and classify a sample in the query set based
on its distances to the samples in the support set. Optimization based approaches [9] 27 BI B35 I1
learn good initialization such that it can be fast adapted to novel tasks based few instances.
To tackle the data deficiency issue in few-shot learning, researchers have explored the idea of exploiting unlabeled data and developed transductive learning semi-supervised learning techniques for few-shot learning, either by leveraging nearest neighbor graph for propagating labels 4 14 21
or by leveraging predicted soft or hard labels on unlabeled samples to update the class prototypes 45 Our method not built on a metric-based method. We make use of the unlabeled data to derive the vicinal distribution for each support sample and optimize the consequential vicinal loss to learn a classifier. Our approach shares a similar spirit of [43]. Yang et al.
or metric [29
43 proposed to calibrate the distribution of the support samples by transferring statisties from the base classes and trained the classifier on a set of samples sampled from the calibrated distributions. Unlike 43). method obtains more accurate vicinal distributions by making of the unlabeled data from the same task. Besides, instead of sampling extensive data from the distributions, our model directly optimizes the expected vicinal loss over the distributions, resulting in more efficient training and higher performance.
2.2 Vicinal Risk Minimization
The Vicinal Risk Minimization (VRM) principle is introduced in 4 36 It assumes each training sample admits a vicinal distribution and optimizes the expected loss over the vicinal distributions. In [. only binary VRM classifiers are considered. Our method considers multi-class classifiers and the cross-entropy loss, which is more challenging to derive the expected vicinal loss. Besides, Chapelle et al. 4 consider Gaussian vicinities but only estimate the variances, keeping the mean the same as the original training sample. Our approach further estimates the mean with the unlabeled data.
In the era of deep learning, the most popular technique under the VRM principle is Mixup 47 38 Mixup constructs the vicinal distributions as the convex combination of the training data, which can be understood as data augmentation technique that encourages the model to behave linearly in-between training examples. It has been demonstrated that Mixup simple yet efficient and improves the generalization of deep models given sufficiently many training samples. Mixup has been introduced on the meta-learning algorithm in 4 6 but applied to the query set, focusing on improving the meta generalization. As the experiment results in [ (Table 6) and in Table 5 shows, applying Mixup on the support set could even hurt the performance. Our method instead improves the performance by producing an accurate estimate of the vicinal distribution for the small support set using unlabeled data.
Adaptive Vicinal Few-Shot Learning
In this section, we will introduce the proposed algorithm, ADaptive Vicinal Few-Shot Learning (ADV). We will first introduce the VRM, then derive the expected vicinal loss for a linear classifier train with cross-entropy loss and for SVM, respectively, and finally propose the algorithm based on lazy random walks to obtain the adaptive vicinal distribution for each labeled support sample. We summarize the proposed method in Algorithm I Note that our method focuses on improving the

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task-specific generalization in meta-testing set and is compatible with feature extractor trained by any meta-learning algorithm.
3.1
Vicinal Risk Minimization
Given data following the distribution P(x, y), the loss function L, we would like to optimize a model (x) by minimizing the expected risk
[(0) - e(fo(z).)) dP(2, v).
Here, x is the input data, is its label and 0 is the model parameters. In practice, P(z. y) is unknown and a set of training data {I,, V1 1N is available, where is the size of training data. To learn a model, one can minimize the empirical risk, which is equivalent to minimizing the expected loss with respect to empirical density estimate d dP v) N Σx (2) (v), where d, (-))) is Dirac delta function centered at a.
Given limited number of training sample, the empirical density estimate dl'(1, (ar, y) could bias from the true density (f( y). For a more accurate density estimate, Chapelle al. 4 proposed to replace the delta functions 82, (1r) by some estimate of density in the vicinity of zyz. Given a vicinal distribution of I; Px, (z), the improved density estimate is Pz(z,)) And the corresponding vicinal risk is defined as
N Σ Ps. (z),,), (v).
N Σ / [(fo(z)) dP,,
N
(. - e(fo(z).)) dP.
3.2 Vicinal Loss
In this paper, assume the feature extractor is trained and fixed for novel tasks. Each task is C-way K-shot, consisting of N = CK data support samples {(0 y0) To perform VRM, we assume the feature 2; of each sample 2; in the support admits Gaussian vicinal distribution NW,, Ej) such that sample is drawn from the vicinal distribution with probability (3) = det(2xE,) 1 exp(- - (z- p4) E (ž - pt)), where μ4 and Σg is the mean and variance of the vicinal distribution of 24-
T
3.2.1 Vicinal Cross-Entropy Loss
We first focus on linear classifier with Cross- cooss-Entoppy loss. A linear classifier fe(z) TW 2 b) maps a feature z E Rdd to its logits, where W E R and E RC is the parameter of the classifier.
The cross-entropy loss is defined as l(h, y) -e] log( (sfotttaa((ff(())) where E 1, C' is the label; ey is a one-hot vector with the y-th element being 1. The expected loss cross entropy over Gaussian vicinal distribution of is defined as
(fo())))))) = -ej -ej (og(softmax((o(3)) aP:(2) = / ((f(()))))) (P) Ep Ep.tol((fo(3)..))) (1)
Due to the softmax function, the expected loss 1 cannot be computed in closed form. Instead, we utilize Taylor expansion to derive an approximation of Eqn. ① By taking the second-order Taylor expansion of e(fo (2))2))) y) around the mean of the vicinal distribution 2,, ie.. μ4, we obtain
(()())) se E(folm).)) v) + G(2 ()) + 3 H H(2 14),
(2)
where G the gradient and H is the Hessian w.r.t. input μ.. Note that H W (diag(h) hh T where h = softmax (Jo (1)) and diag(h) is diagonal matrix whose diagonal elements are equal to h By taking the expectation over é, we have
EP.(a) [G(2 [4]] = 0,
(3)
C Σ k=1
C ΣΣ j=1
Ep (p - M) H(: 10]
hyh W T.WWE
(4)

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Algorithm Adaptive Vicinal Few-Shot Learning (ADV)
1: Input: Support data (zz, 3. unlabeled data {ug J lazy stay parameter 3, number of step in lazy
random walk '''
2: Compute the distance matrix D and Du by and
3: for all & do
4: Compute the transition probabilitics matrix P. by and
Compute the step visit probability us by
6: Compute 14, and E, as the weighted mean of variance of 2, and {a, Na with the weights being
7: end for
8: Compute objective the vicinal cross-entropy loss in or the Vicinal SVM 9
9: Optimize objective until convergence
where E is the variance of Σ, hy is the k-th elements of h. We is the k-th column of W. We define (E)E) as the RHS of Eqn. (4). Plugging ( ( and (4) into ① we obtain the approximated expected
vicinal cross-entropy loss for the linear classifier as
1 N
[folue) un (o(2
(.
3.2.2 Vicinal SVM
SVM is used as classifier for meta-learning algorithms and Singer formulation of multi-class SVM linear multi-class SVM is obtained as:
19 43
We follow 19 to use the Crammer the dual formulation of the objective for
7
In
1V
C
N
N
max a
(a
+
a
yi
(6)
2
k= 1,1=1
1=1
C Σ
s.t. a v X; a 0
Vk + ys
= Vi,
where at is the dual variable and X is regularization parameter. The linear classifier for the k-th Note that here is unseen data. We assume only
class is f (2) _. z. where wi Σm= i=1 a. labeled data admit vicinal distributions while unseen data does not admit vicinal distributions. If each 2 admits a vicinal distribution N ((,, Σ,), the vicinal expectation for the term 2, 2g in (6 becomes
RE ~ H,,,,,,,,) 2 2y]
14 Mg.
and the classifier becomes
E E.
Σ
a 14
If [4; = 24, the objective of the vicinal SVM reduces to the original SVM objective in Eqn. Even when μ4 # 2,. the objective of the vicinal SVM still does not take the variance of the vicinal distribution into consideration and may result in suboptimal performance. To exploit the variance information improve the vicinal SVM classifier, consider nonlinear classifier, i.c. the kernel-based SVM.
Multi-class kernel-based SVM uses kernel (. admits dual formulation similar to 6 but replaces the inner product of 2, and 2j in ( by K(2,, And the classifier becomes fø (2)
Σ, a AC(,, z). In this paper, we consider the widely-used RBF kernel K(2,, x') exp( - where a hyper-parameter.
In vicinal multi-class kernel-based SVM, we define M(z, 2,) = Es x Ex, 8,, AC 2/)
and ((2,,)) =) X, 2) and obtain their computation
|
2(
IA( + E exp
|* mullãs.)
|A(
1 M4 1B4rs)
M(sr, = [A(o2) + E, + +
exp
- |//4
(8)
5

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The detailed derivation is available in Appendix A. Here, A(o²) E R is diagonal matrix with
diagonal elements being o²; M; (A(o²) + Σ,)= M,j (A(o²) + Σ +,, ",)";; the operator
||=||3r =s. Note that for computation simplification, in vicinal SVM, we assume the variance
Σ; is diagonal and set its non-diagonal elements to zeros.
Now achieve the vicinal objective for multi-class kernel-based SVM
max
1
+
Σ 1=1
(9)
s.l. 0 S X; 50 #
ys Σ a 0 Vi,
with the classifier being (=) - E a Ozz, z). The objective in is a quadratic program (QP) over dual variables {of} and can be solved by using differentiable GPU-based QP solver 1
3.3 Lazy Random Walk for an Adaptive Vicinal Distribution
As illustrated in Figure D the performance of the model learned by VRM relies heavily on how close the vicinal distribution is to the true distribution. However, is almost impossible to estimate accurate proximate distributions from small support set. Therefore, ie., the unlabeled data from the same task, to reduce the estimation error of the statistical parameters for the vicinal distribution and, thus, improve the performance of the model.
propose exploit extra data,
We assume that a well-trained feature extractor on the meta-training tasks can preserve the similarity between the data in the feature space. Data from the same class in the novel task would have similar features with high probability. Then, we apply the lazy random walk algorithm 4S] to estimate the probability that the unlabeled data will be visited starting from support sample, and compute the statistical parameters as the weighted mean and variance of the samples visited by the lazy random walk.
To perform lazy random walk, we first compute the distance DU between the support sample 2; and the unlabeled data {" and compute the distance Dou between the unlabeled data as:
D
2
Uy 11: uyll
and itj i=j
(10)
au.
D
(11)
00
Secondly, we transform these distances into transition probabilities by softmaxing the distance matrix over columns with temperature T:
exp
DSU
Σ
csp
(-
3'
(12)
(--D
1 crp
(-1
D -_
exp
Note that we set D oo such that PCU O.
Thirdly, we construct the transition probabilities matrix for 2; in lazy random walk by combining
PSU and PUU and setting the lazy stay probability: 3 E (0, 1) as:
B.
(1 P
P.
(13)
ON.
3In. + (1 PUU
where PSU is the i-th row of pSu 0 is a all zero vector, and Nv., is an identity matrix.
We then compute the visit probability of at the t-th step for
=
(14)
where E (N++1)xx1 is one-hot vector with the first element being 1. For computational efficiency, we keep only the top m nearest neighbors of a data visitable and set DCU (D$U) to zero if uy is not in the top nearest neighbors of u, (2²). Finally, obtain μ, and L, the weighted

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Table 1: Comparison with baselines 5-way 1-shot and 5-way 5-shot classification accuracy (%) on minilmageNer, CUB and CIFAR-FS with 95% confidence intervals. For the backbone, CONV denotes network consisting of 4 convolution layer; ResNet denotes ResNet-12; WRN denotes WideResNet-288. The best two accuracies are highlighted in bold.
minilmageNet way
CUB 5 5-way
CIFAR FS 5-way
Methods
Backhone
I-shot
5-shot
1-shot
5-shot
I-shot
5-shot
MAML
CONV
48.70
63.11
50.45
0.97
59.60
0.84
$8.9
71.5 LO
MetaSGD AD]
CONV
50.47 1: 1.87
64.03 1 0.94
53.34
1 0.97
67.59 1: 0.82
NatchningNet
56.53
0.85
ProtoNet
1:
CONY
49,42 0.78
68.20 + 0,66
58,43
75.22
55,5 + 0.7
72.0 0.6
Relation Not
CONV
50.44 0.82
65.32 = 0.70
62.45
76.11
55.0
69.3
R2D2 2]
CONV
51.2
68.8 1: 0.1
65.3 1 0.2
79.4 0.1
SNAIL 261
ResNet
55.71 1: 0.99
68.88 +: 0.92
TADAM 24]
ResNet
58.50 0.30
76.70 + 0.30
MetaOpeNattSWM 19
ResNet
62.64 0.61
78.63 = 0.46
72.0
84.2 0.5
Meta-Fun
ResNet
62.12 0.30
78.20
LEO 31
WRN
61.76 1: 0.08
77.59 1 0.12
S2M2
64.93
83.18
80.68
+-044
0.19
FreeLunch
5k]
WRN
68.57 1 0.55
82.88 1 0.42
79.56
0.87
90.67 0.35
Transductive Methods
TPN 231
FEAT [5]
CONY
57.04 + 0.20
72.89 + 0.16
TEAM A
CONV
56.57
72.04
75.71
86.04
TPN (1
ResNet
$9.46
75.65
TEAM AG1
ResNet
60.07
75:90
80.16
87.17
SIB [3
WRN
70.0
79.2 0.4
80.0
85.3
ADV-SVM
WRN
72.18 + 0.48
84.38 = 0,30
83,25 = 0.44
91.23 +: 0,23
81.12 0.46
87.41 0.33
ADV-CE
WRN
74.63 +: 0.48
86.12 =: 0.29
84.20
0.43
91.54
0.22
82.02 0.48
88.25 0.31
mean and variance of 2 and {u,} 1/=1 with the weight being v/. averaged over T + steps, where in step 0 it visits only 2,. That is:
1
M4 T+1 1
24
uijuy
1=1
T N₂
Jty( - pi)(us -Mo 11)T )
Σ, = T+1
(z (z- -4i TT++
t=1 ==1
4 Experiments
In this section, we verify the effectiveness of the proposed approach improving the generalization of the few-shot learning. We first introduce the implementation details. Then present the results on the benchmarks, followed by a detailed study of the proposed approach.
We use three benchmarks for performance evaluation: minilmageNet [39, CUB 400 and CIFAR-
FS For all datasets, we construct 5- 5-way 1-shot and 5-way 5-shot tasks by randomly sampling classes. For performance evaluation, we construct 10, 000 meta-testing tasks and report the average classification accuracy with 95% confidence interval.
Implementation details:
we focus on meta-testing phase and directly use the WideRessNet28--10
(WRN) 46 feature extractors pre-trained following the previous work (22. We use ADV-CE to denote the application of ADV in the linear classifier with vicinal cross-entropy loss and ADV-SVM denote the application of ADV in SVM. For ADV-CE, we initialize the weights of the classifier by class prototypes and optimize the vicinal loss in (5) by gradient descent for 100 steps. The learning on the tasks constructed by the meta-vas validation set. For ADV-SVM, we solve the QP in (9) by using differentiable GPU-based QP solver (.. The regularization parameter is set 0.1 and the parameter for RBF kernel is obtained via grid search from 0.1 to 10. In the lazy random walk algorithm, the number of steps T, the lazy stay probability 3 and the temperature are obtained via grid search in 21, 3, 4, 5). 10.1, 0.5). (0.01, 0.1, 1, 10). respectively. Notably, ADV accesses the whole query set as unlabeled data to perform lazy random walk, Thus, ADV is a transductive method. The number of query samples per class is 15.
rate determined by performing grid search from 0.001
7

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Table 2: Comparision with baselines using the same fixed pre-trained WRN feature extractor 5-way 1-shot and 5-way 5-shot classification accuracy (%) on minilmageNet with 95% confidence interval.
Method
1-shot
5-shot
TIM B
74,36 + 0.26
84,58 = 0.15
LaplacianShot 3
69.10 = 0.23
80.86 + 0.15
OM 25 TIM ADV-CE
68.67 0.23
83.42 0.15
74.92 0.25
84.53 + 0.16
Table 3: Comparision with baselines on 5-way 1-shot and 5-way 5-shot classification accuracy (%) on minilmageNet with 95% confidence interval.
Method
1-shot
5-shot
TIM 3
77.8
87,4
LaplacianShot 49
74.86 + 0.19
84. 13 + 0.14
+ TIM
80.04
87.64
18
76.84
84.36
OM 25 TIM
80.64 + 0.34
89.39 + 0.39
ADV-CE TIM
80.75 1: 0.25
88.97 +: 0.14
4.1 Comparison with Baselines
We present the performance of ADV-CE, ADV-SVM with a WRN feature extractor and compare them with existing works in Table D The results of baselines are from 19. 26 and [3 We observe in Table that, in all datasets, ADV achieves the best performance in both 1-shot and 5-shot tasks. Notable, ADV outperforms the best competitor by least 2% in 1-shot tasks. The extraordinary performance of ADV in 1-shot tasks indicates its effectiveness to exploit the information of the unlabeled data from the query set to provide more accurate distribution estimate the true distribution of each class, addressing the issue that the empirical distribution estimated from the support set may deviate significantly from the true distribution.
We also present the experimental results regarding comparison with more SOTA algorithms, includ- ing Transductive Information Maximation (TIM) B] LaplacianShot 4 and Obliquer Manifold (OM) 25.. We compare with these 3 methods because they are all independent of the pre-training of the base model and do require training any extra module the meta-training phase. Note that the performance of few-shot learning is affected by both the base model obtained in the meta-traing prainin phase and the fine-tuning strategy in the meta-testing phase. For a fair comparison in the meta-testing phase, the base model should be the same for different methods. We feed all 4 methods the same fixed WRN feature extractor and the same 10,000 meta-testing tasks. As TIM and LaplacianShot use the same pre-trained weights of feature extractor, we use these pre-trained weights for all of the 4 methods. No data augmentation is applied images meta-testing tasks. From the results in Table 2 observe that ADV-CE outperforms all baselines in 1 1-shot learning and obtains the second best performance in 5-shot learning, which slightly lower than TIM.
The major contributions of TIM lie in regularization on query sets, while ours can be deemed as regularization on support sets, which means its contributions are orthogonal to our contributions. We are more interested in integrating TIM to further boost the proposed method. When integrating TIM with ADV-CE CE and upplying ADV-CE+ TIM achieves competitive performance to the SOTA methods as presented in Table 3 where the performances of the SOTA methods are reported in the original paper.
the WRN feature extractor pre-trained by (22) on minilmageNet.
4.2 Visualization of Vicinal Distributions
The vicinal risk minimization principle the proposed method is built on the vicinal distributions obtained by a lazy random walk. Therefore, the performance of ADV depends on the exactness of the vicinal distribution estimation. Here, we visualize the vicinal distributions to evaluate their exactness. We run the proposed lazy random walk algorithm on two 5-way 1-shot tasks randomly constructed on the meta-testing set of minilmageNet, generate 500 samples from each vicinal distribution, and perform t-SNE algorithm all data. The visualization results are presented in Figure
8

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Figure 2: t-SNE visualization of the vicinal distribution and the true distribution. The first and second subfigures show the original data and the vicinal distributions for task. The third and fourth subfigures show the results for another task. Different colors represent different classes. The 'o' represents the support samples; 'x' represents the query samples; *t' represents the mean of the vicinal distributions; and represents the samples generated from the vicinal distribution.
Table 4: Performance with different backbones on 5-way 1-shot and 5-way 5-shot classification accuracy (%) on minilmageNet with 95% confidence intervals.
Backbone Methods
CONV
ResNet
WRN
1-shot
5-shot
I-shot
5-shot
1-shot
5-shot
Kernel SVM
55.14 + 0.62
68.37 + 0.51
57.85
0.63
73.47
+ 0.51
64.77 + 0.44
80.79 1 0.32
ADV-SVM
59.02 + 0.70
72.13 + 0.53
64.27
0.74
76.37
+ 0.54
72.18 + 0.48
84.38 + 0.30
CE
54.41 0.61
70.74
0.52
56.87 0.65
76.73
1 0.49
65.38
+ 0.52
83.33 1 0.30
ADV-CE
59.22 0.68
72.07 + 0.51
65.03 0.74
77.12
0.52
74.63
0.48
86.12 0.29
We can observe from Figure 2 that the vicinal distribution generated by ADV covers most of the query samples of the same class. This verifies that the lazy random walk module in ADV can provide good estimate of the vicinal distribution, which overlaps with the ground truth distribution. By optimizing the expected loss over the vicinal distributions, the model trained by ADV has smaller probability of overfitting the support samples and provides better generalization to the query set.
4.3 Effect of the Network Architecture of the Feature Extractor
The proposed algorithm ADV is compatible with any pre-trained feature extractor. Here, we validate the effectiveness of ADV on three feature extractors with different backbones, which are trained by different meta-learning methods. We consider WideResNet (WRN) 4d.. ResNet-12 [11 and shallow network of 4 convolutional blocks (CONV) 2 We meta-train the WRN, ResNet, CONV
following [22]
19 and [2). respectively.
We report the performance of kernel SVM classifier and linear classifier trained by cross- entropy (denoted by CE) with and without ADV. The results in
that the performance improvement of ADV is consistent for three feature extractors. This verifies that the effectiveness of ADV is independent of the feature extractor. It is worth noting that the larger performance gains are observed on the better feature extractors. For example, the overall performance of WRN outperforms CONV, and the performance boost of ADV-CE over CE with WRN in 1-shot tasks is 10.5%, which larger than the boost with CONV (4.8%). This observation suggests that 1) even with a superior feature extractor that well preserves the similarity between data in feature space, the classifier trained from limited number of high-quality support data still overfits the data; 2) for a better feature extractor, ADV can exploit more information from the similarity between data to estimate the vicinal distribution support data and alleviate the overfitting.
4.4 Ablation Study
We perform an ablation study on ADV regarding the gain of the VRM principle. To this, we train vanilla linear classifier with cross-entropy loss (denoted by CE), linear classifier with Mixup vicinal distribution 4 (denoted by CE-Mixup), linear classifier with Delta vicinal distribution (denoted by ADV-CE--Man) whose mean locates the same mean estimate by our lazy random walk module and whose variance zero, i.e., Pz, = (2), and compare them with ADV-CE. We also train multi-class SVM classifier, multi-class kernel SVM classifier, and kemel SVM classifier with

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Table 5: Ablation Study of the proposed ADV-CE algorithm on 5-way 1-shot and 5-way 5-shot
classification accuracy (%) on minilmageNet, CUB and CIFAR-FS with 95% confidence intervals.
minilmageNet 5-way
CUB 5-way
CIFAR-FS 5-way
Methods
1-shot
5-shot
1-shot
5-shot
1-shot
5-shot
CE
65.38 + 0.52
83.33
0.30
79.40
0.46
90.36 + 0.24
74.06
0.47
87.74 = 0.32
CE-Mixup
65.53 + 0.43
82.77
0.30
79.02 + 0.45
90.14 1 0.25
74.99 0.47
87.45 1 0.32
ADV-CE- ME-Mean
72.37 + 0.49
84.79 1 0.31
83.04 - 0,46
90.61 + 0.25
80.56 0.47
88.11 + 0.31
ADV-CR
74.63 + 0.48
0.29 86.12
84.20 + 0.43
91.54 + 0.22
82.02 0.48
88.25 + 0.31
SVM
64.33 + 0.44
83.57 + 0.30
78.46 = 0.45
90.93 + 0.23
74.29 0.46
87.31 + 0.32
Kemel SVM
64.77 + 0.44
80.79 0.32
77.69 = 0.45
88.96 + 0.27
74.03
0.46
86.28 + 0.34
ADV-SVM-Mcan
65.33 + 0.43
81.36 0.32
80.97 + 0.48
90.94 + 0.23
80.21
0.48
87.37 + 0.33
ADV-SVM
72.18 + 0.48
84.38 0.30
83.25 0.44
91.23 + 0.23
81.12 0.46
87.41 = 0.33
Delta vicinal distribution (denoted by ADV-SVM-Mean). The training of multi-class SVM classifiers all follows
We report the performance on three benchmarks in Table 5
The results in Table 5) show that the performance of CF-Mixup only competes with CE in minilma- geNet and CIFAR-FS, and is even inferior to CE on the CUB dataset. This suggests that the Mixup vicinal distribution fails improve the generalization given limited number of data. In contrast, the vicinal distribution obtained by the lazy random walk algorithm is more accurate estimate of the true distribution, as evidenced by the fact that the performance of ADV-CE-Mean and ADV-CE is better than CE and CE-Mixup. To be concrete, the performance boost of ADV-CE-Mean over CE demonstrates that the mean of the vicinal distribution, which lies not on the original sample but on a weighted average of the data passed through by the lazy random walk, is closer to the ground-truth distribution. The performance improvement of ADV-CE over ADV-CE-Mead demonstrates that the variance of the vicinal distribution helps to alleviate the overfitting problem.
As shown in Table the performance of Kernel SVM worse than SVM in most cases. The reason may be that the features extracted by WRN are linearly separable and the non-linear kernel technique does not help to further improve the separability. Although the performance of Kernel SVM is inferior to SVM, observe performance boost of ADV-SVM, which is built Kernel SVM. This indicates that learning from the vicinal distributions that are close to the true distribution would sufficiently improve the performance. We also observe the performance gain of ADV-SVM over ADV-SVM-DE again evidencing the importance of the variance of vicinal distributions in alleviating the overfitting.
5 Conclusion and Limitations
In this paper, we discuss the overfitting issue in few-shot learning, which is caused by the deviation of the empirical distribution from the ground-truth distribution. To alleviate the overfitting, we revisit the Vicinal Risk Minimization principle in deep few-shot learning and propose to harness unlabeled data and lazy random walk algorithm to generate adaptive statistical parameters for the vicinal distribution of each training sample. Following the VRM principle, we learn the model by optimizing the resulting expected vicinal loss. We derive the vicinal loss for linear classifiers trained with cross-entropy loss and for SVM classifier and develop the resulting Adaptive Vicinal classifiers as ADV-CE and ADV-SVM, respectively. We evaluate the performance of ADV-CE and ADV-SVM on three benchmarks and validate the effectiveness of ADV in mitigating overfitting and improving the generalization of classifiers learned from a limited number of samples. Currently, our proposed ADC is compatible with CE and SVM only. We will extend it to other loss functions. For the vicinal Cross-EEtrropy loss, we optimize an approximation obtained by second-order Taylor expansion. However, the approximation error can be large. Thus, the performance of ADV-CE may be suboptimal and we can further improve it by deriving a better approximation for the vicinal Cross-Enttrppy loss.
10

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References
[1] Brandon Amos and J Zico Kolter. Opinet: Differentiable optimization as a layer in neural networks. In International Conference Machine Learning, pages 135-145. PMLR, 2017.
[2] Luca Bertinetto, Joao Henriques, Philip HS Torr, and Andrea Vedaldi. Meta-learning with differentiable closed-form solvers. ICLR, 2019.
[3] Malik Boudiaf, Imtiaz Ziko, Jérôme Rony, José Dolz, Pablo Piantanida, and Ismail Ben Ayed. Information maximization for few-shot learning. Advances in Neural Information Processing Systems, pages 2445-2457, 2020.
[4] Olivier Chapelle, Jason Weston, Léon Bottou, and Vladimir Vapnik. Vicinal risk minimization. Advances in neural information processing systems, pages 416-422, 2000.
[5] Wei-Yu Chen, Yen-Cheng Liu, Zsolt Kira, Yu-Chiang Frank Wang, and Jia-Bin Huang. A closer look at few-shot classification. arXiv preprint arXiv:1904.044 04232, 2019.
[6] Yangbin Chen, Yun Ma, Tom Ko, Jianping Wang, and Qing Li. Metamix: improved meta- learning with interpolation consistency regularization. In 2020 25th International Confer- ence on Puttern Recognition (ICPR), pages 407-414. IEEE, 2021.
[7] Koby Crammer and Yoram Singer. On the algorithmic implementation of multiclass kemel- based vector machines. Journal of machine learning research, 2(Dec):265-292, 2001.
[8] Wentao Cui and Yuhong Guo. Parameterless transductive feature re-representation for few-shot learning. In International Conference on Machine Learning, pages 2212-22211 2221. PMLR, 2021,
[9] Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adap- tation of deep networks. In Proceedings of the 34th International Conference on Machine Learning Volume 70, pages 1126-1135. JMLR. org, 2017.
[10] Alex Graves, Abdel-rahman Mohamed, and Geoffrey Hinton. Speech recognition with deep recurrent neural networks. In 2013 IEEE international conference acoustics, speech and signal processing, pages 6645-6649, IEEE, 2013.
[11] Kaiming He, Xiangyu Zhang, Shaoging Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016.
[12] Ruibing Hou, Hong Chang, Bingpeng Ma, Shiguang Shan, and Xilin Chen. Cross attention network for few-shot classification. arXiv preprint arXiv:1910.07677 2019.
[13] Shell Xu Hu, Pablo G Moreno, Yang Xiao, Xi Shen, Guillaume Obozinski, Neil D Lawrence, and Andreas Damianou. Empirical bayes transductive meta-learning with synthetic gradients. arXiv preprint wXX::2004.12666, 2020.
[14] Jongmin Kim, Taesup Kim, Sungwoong Kim, and Chang D Yoo. Edge-labeling graph neural network for few-shot learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11 11-20, 2019.
[15] Gregory Koch, Richard Zemel, and Ruslan Salakhutdinov. Siamese neural networks for one-shot image recognition. In ICML deep learning workshop, volume 2. Lille, 2015.
[16] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pages 1097-1105, 2012.
[17] Seong Min Kye, Hae Beom Lee, Hoirin Kim, and Sung Ju Hwang. Meta-leamed confidence for transductive few-shot learning. 2020.
[18] Dong Hoon Lee and Young Chung. Unsupervised embedding adaptation via early-stage feature reconstruction for few-shot classification. In International Conference on Machine Learning, pages 6098-6108. PMLR, 2021.

---

[19] Kwonjoon Lee, Subhransu Maji, Avinash Ravichandran, and Stefano Soatto. Meta-learning with differentiable convex optimization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pages 10657-10665, 2019.
[20] Zhenguo Li, Fengwei Zhou, Fei Chen, and Hang Li. Meta-sgd: Learning learn quickly for few-shot learning. arXiv preprini arXiv: hatp::/7770033333 2017.
[21] 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. arXiv preprint arXiv: 10002, 2018
[22] Puneet Mangla, Nupur Kumari, Abhishek Sinha, Mayank Singh, Balaji Krishnamurthy, and Vineeth N Balasubramanian. Charting the right manifold: Manifold mixup for few-shot learning. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 2218 1128-2222,22 2020.
[23] Nikhil Mishra, Mostafa Rohaninejad, Xi Chen, and Pieter Abbeel. A simple neural attentive meta-learner. arXiv preprint arXiv: (.Xiv:1707.000 1707003141 2017.
[24] Boris N Oreshkin, Pau Rodriguez, and Alexandre Lacoste. Tadam: Task dependent adaptive metric for improved few-shot learning. arXiv preprint arXiv: 10123, 2018.
[25] Guodong Qi, Huimin Yu, Zhaohui Lu, and Shuzhao Li. Transductive few-shot classification on the oblique manifold. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 8412-8423 8422, 2021.
[26] Limeng Qiao, Yemin Shi, Jia Li, Yaowei Wang, Tiejun Huang, and Yonghong Tian. Trans- ductive episodic-wiss wise adaptive metric for few-shot learning. In Proceedings of the IEEE/CVF International Conference Computer Vision, pages 3603-3612, 2019.
[27] Aniruddh Raghu, Maithra Raghu, Samy Bengio, and Oriol Vinyals. Rapid learning or feature reuse? towards understanding the effectiveness of maml. arXiv preprint 1900::999000957 2019.
[28] Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. 2016.
[29] Mengye Ren, Eleni Triantafillou, Sachin Ravi, Jake Snell, Kevin Swersky, Joshua B Tenen- baum, Hugo Larochelle, and Richard S Zemel. Meta-learning for semi-supervised few-shot classification. arXiv preprint arXiv:1803.006 2018.
[30] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma. Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International jounatiooanoouuuaa journal of computer vision, 115(3):211-252 2015.
[31] Andrei A Rusu, Dushyant Rao, Jakub Sygnowski, Oriol Vinyals, Razvan Pascanu, Simon Osindero, and Raia Hadsell. Meta-learning with latent embedding optimization. arXiv preprint arXiv:1807.05561/ 2018
[32] Sahil Singla, Eric Wallace, Shi Feng, and Soheil Feizi. Understanding impacts of high-order loss approximations and features in deep learning interpretation. In International Conference on Machine Learning, pages 5848-5856. PMLR, 2019.
[33] Jake Snell, Kevin Swersky, and Richard Zemel. Prototypical networks for few-shot learning. In Advances in neural information processing systems, pages 4077-4087, 2017.
[34] 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 Conference Computer Vision and Pattern Recognition, pages 1199-1208, 2018.
[35] Eleni Triantafillou, Tyler Zhu, Vincent Dumoulin, Pascal Lamblin, Utku Evci, Kelvin Xu, Ross Goroshin, Carles Gelada, Kevin Swersky, Pierre-Antoine Manzagol, et al. Meta-dataset: A dataset of datasets for learning to learn from few examples. arXiv preprint arXiv: 1903, 003009 2019.
12

---

[36] Vladimir N Vapnik. The vicinal risk minimization principle and the svms. In The nature of statistical learning theory, pages 267-290. Springer, 2000.
[37] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Advances in neural information processing systems, pages 5998-609000 2017.
[38] Vikas Verma, Alex Lamb, Christopher Beckham, Amir Najafi, Ioannis Mitliagkas, David Lopez- Paz, and Yoshua Bengio. Manifold mixup: Better representations by interpolating hidden states. In International Conference on Machine Learning, pages
PMLR, 2019.
[39] Oriol Vinyals, Charles Blundell, Timothy Lillicrap. Daan Wierstra, et al. Matching networks for one shot learning, In Advances in neural information processing systems, pages 3630-3638, 2016.
[40] Catherine Wah, Steve Branson, Peter Welinder, Pietro Perona, and Serge Belongie. The caltech-uesd birds-200-2011 dataset. 2011.
[41] Jin Xu, Jean-Francois Ton, Hyunjik Kim, Adam R Kosiorek, and Yee Whye Teh. Metafun: Meta-learning with iterative functional updates. arXiv preprint arXiv:1912.02755 2019.
[42] Ling Yang, Liangliang Li, Zilun Zhang, Xinyu Zhou, Erjin Zhou, and Yu Liu. Dpgn: Distribution propagation graph network for few-shot learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13390-13399, 2020.
[43] Shuo Yang, Lu Liu, and Min Xu. Free lunch for few-shot learning: Distribution calibration. ICLR, 2021.
[44] Huaxiu Yao. Long-Kai Huang, Linjun Zhang, Ying Wei, Li Tian, James Zou, Junzhou Huang, Improving generalization meta-learning via task augmentation. International Conference Machine Learning, pages 1187--18997 PMLR, 2021.
[45] Han-Jia Ye, Hexiang Hu, De-Chuan Zhan, and Fei Sha. Few-shot learning via embedding adaptation with set-to-set functions. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, 2020.
[46] Sergey Zagoruyko and Nikos Komodakis. arXiv:1605.07146. 2016.
Wide residual networks. arXiv preprint
[47] Hongyi Zhang, Moustapha Cisse, Yann Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. ICLR, 2018.
[48] Dengyong Zhou and Bernhard Schölkopf. Learning from labeled and unlabeled data using random walks. In Joint Pattern Recognition Symposium, pages 237-244. Springer, 2004.
[49] Imtiaz Ziko, Jose Dolz, Eric Granger, and Ismail Ben Ayed. Laplacian regularized few-shot learning. In International conference machine learning, pages 1 11660-11670. PMLR, 2020.
Checklist
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Did you include the license the code and datasets? [Yes] See Section ??.
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
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14


Reviews:
[{"review_id": "Qj2WXCIddvB", "reviewer": "Reviewer_b8EE", "summary": "The goal of the paper is to improve the robustness of classifier for task-specific generalisation in the meta-testing stage.  The work introduces Vicinal Risk Minimization in which a Gaussian distribution is fitted on the unlabeled data samples and the probabilities of the labeled samples are obtained using lazy random walk. The work proved the expected vicinal loss functions for cross-entropy loss and SVM. Experiments on miniImageNet, CUB, CIFAR-FS for few-shot learning demonstrate the effectiveness of the proposed approach.", "questions": "* \"Our approach also considers Gaussian vicinities but estimates the mean by the unlabeled data, which is generally not on the training samples\". How is this a better formulation?\n\n* What is the dimensionality of the Gaussians being considered here? How realistic is the approach as the dataset scales both in terms of number of samples and size of each image.\n", "limitations": "The limitations have been adequately addressed. ", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths and Weaknesses:\n\n* The paper is well-motivated and easy to follow. The overall idea of constructing vicinal distribution of the training samples using unlabeled training data is novel\n\n* The experimental set-up is sound and demonstrates the usefulness of the approach. The results show the improvement in the generalization performance of the models with the proposed method. The experiments are extensive and outline the set-up clearly.  \n\n* Thorough ablations in Table 3 clearly show the advantage of using the VRM principle over the CE-Mixup principle. \n\n\n\nThere are no major weaknesses in the paper, however, certain claims in the manuscript can be supported with citations. There are a few typos and can be corrected in the revision.\n\n\n\n - Minor line 36: “the significant deviation of the empirical distribution..”  Add citation here?\n\n - Line 81: benchmars-> benchmarks\n\n - Line 99: It [37] -> In\n\n - Lime 110: . Besides, (author?)\n\n - Line 126: tge -> the\n\n - Line 133: expect loss -> expected loss\n\n - Line 177 it replace->replaces", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "QEGng-PHjpC", "reviewer": "Reviewer_WJab", "summary": "In this paper, the distribution of support data is estimated using transition probability between all samples within a meta-test task (including labeled support data and unlabeled query data). A logistic regression or an SVM model is learned via vicinity risk minimizing based on the estimated distribution of support data. The expected vicinity loss is derived in the paper. The experiments indicate that the proposed method outperforms some few-shot learning methods.", "questions": "Typos in line 110. \n\nWhat is \"tge\" in line 126? \n\nAccording to line 210 and 211, it is not clear how to compute $u_i$ and $\\Sigma_i$. The definition of $V_i$ is not given in line 211. Is it a typo? Is it $v_i$ or $V_i$? It is better to give equations about how to compute $u_i$ and $\\Sigma_i$.\n\nWhat is the value of $N_u$?", "limitations": "The author discussed limitations in the paper.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The expected vicinity loss is derived.\n\nEstimate the distribution of support data using weighed unlabeled data, where the weight is based on the transition probability in lazy random walk.\n\n\nWeaknesses:\n\nSome typos in the manuscript. Some technical details are missing. See the next section for details.\n\nThe proposed method is a transductive few-shot learning method as it uses unlabeled data in meta-test tasks. Therefore, it is important to compare to transductive few-shot learning methods with the same backbone. However, the comparison to transductive methods in Table 1 is not fair. For example, the reported results of some methods (e.g. FEAT) are based on shallow backbones (4-layer CNN). It is better to reproduce those methods with the same backbone (WRN), especially since the code is available online for those methods.\n\nIn addition, some recent transductive few-shot methods [1, 2, 3, 4, 5] achieve stronger performance using the same backbone (WRN). The proposed method should be compared with those methods to show the effectiveness of adaptive vicinity risk minimization. Since the authors claim that the proposed method outperforms SOTA few-shot learning methods, it is necessary to compare the true SOTA methods in a fair manner.\n\n[1] Boudiaf, Malik, et al. \"Information maximization for few-shot learning.\" Advances in Neural Information Processing Systems 33 (2020): 2445-2457.\n\n[2] Ziko, Imtiaz, et al. \"Laplacian regularized few-shot learning.\" International Conference on Machine Learning. PMLR, 2020.\n\n[3] Cui, Wentao, and Yuhong Guo. \"Parameterless transductive feature re-representation for few-shot learning.\" International Conference on Machine Learning. PMLR, 2021.\n\n[4] Lee, Dong Hoon, and Sae-Young Chung. \"Unsupervised Embedding Adaptation via Early-Stage Feature Reconstruction for Few-Shot Classification.\" International Conference on Machine Learning. PMLR, 2021.\n\n[5] Qi, Guodong, et al. \"Transductive Few-Shot Classification on the Oblique Manifold.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "G2beXFko_sn", "reviewer": "Reviewer_oXzN", "summary": "The paper proposes to use vicinal loss function in few shot classification to increase the generalization capability.  The vicinal loss is associated with  some prior distributions over the features, which is adaptively obtained via random walk algorithm with the assistance of a set of unlabeled examples.  ", "questions": "* The reviewer believe the statement in L133-L135 is technically not correct, can the authors address this concern?\n* The reviewer believe the vicinal loss is the same as using prior distribution on the features, can the authors clarify?\n* The details of the ablation study is not very clearly presented in the paper.  For example, it is not clear to the reviewer what the delta vicinal distribution is and how it is different from the distribution used in ADV-CE.\n* Unlabeled data.\n    * The paper does not provide any information on the size of unlabeled data used in the experiment.\n    * Does the proposed method give higher classification accuracy with more unlabeled data? This should be shown in the ablation study.  ", "limitations": "Some limitations of the work has been briefly mentioned by the authors. The limitations and questions of the paper the reviewer had is given in Questions section.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "* Originality: The task of few shot learning and the techniques of vicinal loss and random walk algorithms are not new. To the best of the reviewer’s knowledge, the use of these techniques in few shot learning is novel. However, there is a lack of comparison with other methods（eg [15]）use additional unlabeled data. \n* Quality: All claims are supported by the experimental results and the work is complete. The reviewer do not agree with the statement that the proposed method can beat SOTA. \n* Clarity: The idea of the paper is presented clearly. However, there are many typos, especially in the equations.\n\t* typos (an incomplete list): \n\t\t* L110: citation is not right\n\t\t* L126: should be “the” not “tge”\n\t\t* L130: model is $F(x;\\theta)$ not $f_{\\theta}(x)$\n\t\t* L140: model parameter is $\\theta$ not $w$\n\t\t* L146: the density function is a function of $\\tilde z$ on the LHS but does not depend on $\\tilde z$ on the RHS\n\t\t* L71: the expectation is with respect to z not $\\bar z_i$\n\t* technical error: \n\t\t* L133-L135: Although the form of $dP_{\\delta}(x,y)$ is given in the original paper, this is technically not right. The decomposition is saying that x and y are independent. The vicinal loss from a Bayesian point of view can be seen as adding a prior on the predictor x\n* Significance: The paper proposes to use a loss function that is different from the conventional empirical loss under few shot learning setting. The motivation for this approach may be insightful for developing  new methods in few shot learning. The results, while not earthshaking, may be of practical use.", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "1sei90iqGc", "reviewer": "Reviewer_kfYN", "summary": "This submission points out that, in few-shot learning, a limited number of support data can hardly represent the true distribution, which results in poor generalization performance of the empirical risk minimization based methods. To tackle this problem, the authors propose to minimize the vicinal risk and estimate parameters of vicinal distribution of each sample by a random walk algorithm with additional unlabeled data. They demonstrate that their algorithm outperforms baseline methods on three datasets.", "questions": "Methods:\n1. The pre-training phase is the meta-training phase? if not, the authors should detail the learning process of ADV in the meta-training and meta-testing phases.\n2. The main problem is the difference between ADV-CE and ADV-SVM methods. They seem to be two separate branches, and ADV-CE significantly outperforms ADV-SVM. Therefore why provides AVD-SVM?\n3. If i=j, the D_{ij}^{UU} = 0 in equation (11)?\n\nExperiments:\n1. How many query samples are used as unlabeled data to estimate the distribution parameters in experiments?  In general, the commonly used sample size is 15, and the more samples, the better the performance.\n2. In lines 238-239, the authors propose that the support set can deviate from the true distribution. If there is a visualization to support this claim? \n3. In the meta-testing phase, the meta-learning methods (e.g., MAML) are optimized by using 5-10 steps in the fine-tuning phase and the more steps have good performance [1]. However, ADV has 100 steps in the fine-tuning phases. if ADV also uses the same steps (5-10), how does it perform?   \n4. Only four transductive algorithms (TPN, FEAT, TEAM, SIB) are tested with the proposed method, it would be more convincing if more recent state-of-the-art algorithms can be considered.\n5. The performance gain of the proposed method seems to diminish quickly from 1-shot to 5-shot settings. Does this mean in the case of 5 (or more)-shot setting, considering unlabeled test data with the proposed method could even adversely affect the performance?\n\nTypos:\n1. imporving --- imporve in the title\n2. author? in the 110 line \n3. 4.0.1 in the 222 line\n4. ishas in the 254 line\n\n[1] How to Train Your MAML to Excel in Few-Shot Classification", "limitations": "Yes, they discuss the limitations in Section 5. ", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. This paper points out an interesting problem for few-shot image classification.\n2. The experimental evaluation is adequate, and the results convincingly support the main claims.\n\nWeaknesses:\n1. The paper is not very clear, and many aspects make the reviewer's understanding of the entire paper very confusing. Moreover, many typos should be carefully checked before submission. \n2. The main concern is that the core idea is not innovative, similar to the incremental superposition of multiple algorithms. \n3. Some experimental settings are unfair, making it impossible to measure the effectiveness of the method in terms of performance gains.\n4. See questions for more details.", "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": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept