Assessing two novel distance-based loss functions for few-shot image classification
Authors: Mauricio Mendez Ruiz
Gilberto Ochoa Ruiz
Andres Mendez Vazquez
Jorge Gonzalez-Zapata
Venue: ICLR 2022 Submitted (2022)
Keywords: Metric learning
few-shot learning
image classification

Abstract: Few-shot learning is a challenging area of research which aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches benefit from the meta-learning process in which we have episodic tasks conformed by support set (training) and query set (test), and the objective is to learn a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function is based on an inter and intra class nearest neighbors score, which help us to know the quality of embeddings obtained from the trained network. Extensive experimental results on the miniImagenNet benchmark increase the accuracy performance from other metric-based few-shot learning methods by a margin of $2\%$, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes.

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ASSESSING TWO NOVEL DISTANCE-BASED LOSS FUNCTIONS FOR FEW-SHOT IMAGE CLASSIFICATION
Anonymous authors Paper under double-blind review
ABSTRACT
Few-shot learning is a challenging area of research which aims learn new con- cepts with only a few labeled samples of data. Recent works based on metric- learning approaches benefit from the meta-learning process in which we have episodic tasks conformed by support set (training) and query set (test), and the objective is to learn a similarity comparison metric between those sets. Due the lack of data, the learning process of the embedding network becomes an im- portant part of the few-shot task. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking the intra-class and inter-class distance between the few data. The first loss func- tion is the Proto-Triplet Loss, which is based the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss func- tion is based an inter and intra class nearest neighbors score, which help us to know the quality of embeddings obtained from the trained network. Exten- sive experimental results on the minilmagenNet benchmark increase the accuracy performance from other metric-basee based few-shot learning methods by margin of 2%, demonstrating the capability of these loss functions allow the network generalize better to previously unseen classes.
INTRODUCTION
Despite the advances in deep learning research, remains a challenge for the standard supervised learning to achieve satisfactory results when learning from just a small amount of labeled data. Current deep learning algorithms tend to overfit when they are given a small dataset for training, reducing their generalization capabilities. Moreover, there are many problem domains where ob- taining labeled data can be very difficult or imply a lot of manual work to get the data with its ground truth, representing problem for real world applications as it is time consuming and costly.
Few-shot learning (FSL. methods has been proposed (Koch et al. (2015); y) Snell et al. (2017): 20i7):(Vinyalls Vinyals) et (2016)) [Sung et al. (201)); Finn et al. (201)); Nichol et al. (20 (2018) to classify previously unseen data into set of new classes, given only small amount of labeled instances per class. The main challenge for FSL is to apply fine-tuning process to existing embedding network adapt to new classes, with the problem that this could easily lead to overfitting due to the few labeled samples available for each class. There are two main FSL approaches: The first one is Meta-learning based methods (Finn et al. (2017); Andrychowicz et al. (2016); Li & Malik (2066); Chen et al. (2017) ). where the basic idea is learn from diverse tasks and datasets and adapt the learned algorithm to novel datasets. The second are Metric-learning based methods (Xing er al. (2033;; Koch et al. (2015),, where the objective to learn a pairwise similarity metric such that the score is high for similar samples and dissimilar samples get low score. Later on, these metric learning methods started to adopt the meta learning policy to learn across tasks (Snell al. 2017); Vinyals et al. (2016): (Sung et al.] (2017)). The main objective of these methods is to learn an effective embedding network in order to extract useful features of the task and discriminate on the classes which we trying to predict. From this basic learning setting, many extensions have been proposed to improve the performance of metric learning methods. Some of these works focus on pre-training the embedding network (Chen et al. (2019a)), others introduce task attention modules (Chen et al. (2020); Li et al. (2019a); Zheng et al. (2019)), whereas other try to optimize the embeddings (Lee al.F 2019)) and yet others try
variety of loss functions (Zheng et al. (209)))

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Emtodding Space
Feeture Exracter
Similarity Motri
ICNN Loss
Quiry Data
Figure 1: We propose two loss functions that works well for metric meta-lcarning approaches for few-shot classification. We optimize an embedding network based on the error calculated by the ICNN Loss or the proto-triplet loss, which aims to increase the inter-class distance and decrease the intra-class distance.
Inter-ciass distance Support data Prototypes
Intra-closs distance
Batch
Intra-ciass distance
(a) The ICNN Loss is based on score given by the intra and inter class distance from the batch points. Inter and Intra Class Nearest Neighbors score and optimize the em- hedding network based on the quality of features.
(b) The Proto-Triplet Loss is based the triplet loss. This loss takes as anchor a query point, the prototype from the same class as positive point and the nearest prototype of different class as the nega- tive point.
each data point, we measure
In this work, propose two different loss functions based on the concepts of inter-class and intra- class distance. As showed in Figure [ these loss functions allow us to optimize the embedding network and learn more discriminative features across tasks. For one of the proposed loss functions, we take as inspiration one of the most widely used losses metric-learning: the triplet loss. For the second one, we adopt algorithm based nearest neighbors distance. We demonstrate the effectiveness of our loss functions and show our competitive results compared with state-of-the-art methods.
The rest of the paper is organized as follows: In Section 2, we describe the related work in the few-shot learning problem. In Section Proto-triplet loss function, and then we explain the ICNN Loss function. Then we discuss some of the design choices we needed take for the ICNN loss. In Section we detail the experimental setup used for the implementation of the models. In Section we show the results obtained and discuss about its performance. Finally, in Section 5 we present our conclusions and discuss the future work.
described the proposed model. We first explain the
MOTIVATION AND RELATED WORK
2.1 DEEP METRIC LEARNING
The goal of metric learning to learn a similarity function from the data. More specifically, aims to learn feature embeddings in way that reduce the distance between embeddings corresponding to instances the same class (intra-class) and increase the distance between embeddings corre- sponding instances of different class. Deep metric learning uses embedding network to learn
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the discriminative features that will be used to compute the similarity metrie. Below review the more relevant deep metric learning methods.
One of the fundamental methods for metric learning is the Siamese Networks (Koch et al. (0155) which is a symmetric neural network architecture that consists on two subnetworks both having the same parameters. These networks learn its parameters by calculating distance metric between the feature embeddings of each subnetwork each with a different input. The loss function used in Siamese Networks is the contrastive loss or pairwise ranking loss, which seeks for the distance of samples from the same class to be small and from different class to be large.
The second important metric learning method is the Triplet Network (Schroff et al. 2015 ) which is also a symmetric neural network architecture but this method consist of three identical subnetworks sharing the same parameters. The input of the three subnetworks consist on three different images: The first one is the anchor (the baseline image), the second is the positive sample (an instance that belongs to the same class as the anchor), and the third is the negative sample (an instance that belongs to different class than the anchor). This network use the triplet loss to learn discriminative feature embeddings, and it works by ensuring that the anchor image is close to the positive images and far away from the negative images.
These metric learning methods have been widely used for different purposes as image retrieval (Wang al. (2014)), face recognition (Schroff et al. (2015); Taigman et al. (2014); (Hu et al. 20144), person re-identification (Xiao et al. (2017)), video surveillance (Huang et al. (2018)), three- dimensional modelling (Dai et al. (2017)) signature verification (Bromley al. (1993). medical im- age analysis (Annarumma & Montana (2017) 7)), text understanding (Mueller & Thyagarajan (2016);
Benajiba et al. (2018)), among other problems.
2.2 META-LEARNING FOR FEW-SHOT LEARNING
As deep learning started to produce good results in many machine learning problems, some works proposed to use the meta-learning policy in order to optimize deep models /Andrychowicz et al. (216)) Li & Malik (2016); Chen et al. (2017). The meta-learning policy refers to learn across tasks and then adapt to new tasks, instead learning to the level of samples. The meta-learning objective is to learn the parameters 9 that minimize the loss across all tasks. Few-shot learning is the perfect process in which we can test meta- meta-learning algorithms, because of the few-labeled data given to each task.
The meta leaanieg approach to tackle a fhw-shot learning problem is divided into two stages: meta- train and meta-test. The meta- meta-learning setup consists of episodic tasks, which can be seen batches in traditional deep learning. A few-shot K K-way C-shot image classification task is given K classes and C images per class. The task-specific dataset can be formulated D = (Dirains D where Dirain {(X,, 31) ) denotes the classes reserved for the training phase and Dreat 9::) {(x,,):) )= denotes the classes reserved for the testing phase. For each meta-train task T, K class labels are randomly chosen from Dtrain to form a support set and a query set. The support set, denoted by S, contains K x C' samples (K-way C-shot) and the query set, denoted by Q. contains number of randomly chosen samples from the K classes. The training phase use an episodic mechanism, where each episode F is loaded with a new random task taken from the training data. For the meta-test, the model is tested with a new task T constructed with classes that weren't seen during the meta-train.
We can summarize the few-shot learning methods based on what the model seeks meta-learn. Some approaches consists on having base-learner and a meta-learner, where meta-learner param- eters are optimized by gradual learn across tasks facilitate the fast learning of the base-learner for each specific task. MAML (Finn et al. (2017)), is one of these methods and have the idea to search for a good parameter initialization such that the base learner can rapidly generalize with this initial- ization. Then, REPTILE (Nichol et al. (2018)) incorporates an Lz loss to simplify the computation of MAML. Further on, LEO (ussu et al. (2018)) is proposed as a network to learn low dimension latent embedding of the model. Meta-SGD (Li et al. (2017)) also learns the base learner update direction and learning rate on the meta-learning process. Meta-Leearner LSTM (Ravi & Larochelle (017)) propose to finetune the base learner by LSTM-based meta-learner, which takes input the loss and gradient of base learner with respect to each support sample. Other approaches seek to learn the similarity metric that is expected to be transferrable across different tasks.
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2.3 METRIC META-LEARNING FOR FEW-SHOT LEARNING
There is a whole branch of meta-learning approaches to solve the few-shot learning problem by inheriting the main idea of metric learning. These approaches adopts the meta-learning setup to learn the similarity metric expected to generalize across different tasks. There are baseline methods which achieved important milestones for few-shot learning, such as Prototypical Networks (Snell et al. (217)), Matching Networks (Vinyals et al. (201)) and Relation Networks (Sung et al. (217)) Prototypical Networks the model which we are using as a basis, and works by taking the center of support samples' embeddings from each class to create the class prototypes. Then, the model use a distance metric (typically the euclidean distance) to predict the probabilities for each query sample. The Matching Networks predicts the probability of query samples by measuring the cosine similarity between the query embedding and each support sample embedding. The Relation Networks adopts learnable CNN the pairwse similarity metric, which takes the concatenation of feature maps of support sample and query sample as input and outputs the relation score. These three methods can be considered the base metric learning approaches for few-shot learning.
Further on, some recent works focus on introducing task attention modules (Chen et al. (2020); Li al. (2019)); Zheng al. (2019)) whereas others try to optimize the embeddings (Lee et al. (2019)) and others add a second term to the loss function (Zheng et al. (2019)). Up until now, there lack of research for loss functions which work for the problem of few-shot learning tackled from a metric-lcarning perspective. Our proposed model take part of these meta- meta-learning approaches based on metric learning, by adopting the idea of the intra-class and inter-class variance into two different loss functions, which will help us to better optimize an embedding network to obtain more discriminant feature vectors.
PROPOSED MODEL
We propose two different loss functions for training Convolutional Neural Network (CNN) as an embedding function. These loss functions optimize the embedding space across the meta-learning tasks.
3.1 TROTO-TRIPLETTO LOss
The traditional Triplet Loss (Schroff et al. (2015)) is widely used for metric learning, where the objective is to train a learner by using similarity comparison metric between the sampled data. The loss function aims at pulling similar samples close to each other, while pushing away the samples of different classes far away. The objective of building the triplets consists on creating reference points for query (anchor), and obtain the distance between the query and the embedding of an instance in the same class (positive), and the distance between the query and the embedding of an instance in different class (negative).
The Proto-Triplet Loss based on the original Triplet Loss with the difference that we are using the data points obtained as prototypes for calculating the loss, making it more suitable for the few-shot learning setting. The formula for the proto-triplet loss similar to the original triplet loss:
I(Xa, X Xn) [IL.a - 5n11 1 +a))
(1)
where I is the max between 0 and the result, also known as hinge loss. fa is the embedding from the query, fp is the prototype from the same class as the query and fn is the nearest prototype of different class as the query. is margin hyper parameter to be enforced between the negative and positive pairs. The goal of this function is to keep the distance between the query and the prototype of same class smaller than the distance between the query and the prototype from different class.
Furthermore, inspired in (Li et al. (2019b)), we propose to use the Proto-Triplet Loss with K ref- erence points to not only use negative sample. In the meta-learning setting, we compare an instance with multiple classes, so our loss function should be more effective by performing a com- parison with more prototypes of different classes.
For the negative samples, we take the K nearest prototypes of different class to form the triplets. The modified function is formulated as:
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a( Xp, Xn.)
1 K
[
Σ fpll
-
-fall + a)
(2)
iEU
where U is the set of triplets made by the K negative prototypes. The rest of the terms the formula are the same stated in the previous equation.
3.2 ICNN LOSS
The Inter and Intra Class Nearest Neighbors Score (ICNN Score) GGarcia Ramírez 2021 was proposed measure remove noisy features and improve the performance of manifold-based algorithms for supervised dimensionality reduction, aiding the feature selection by a subset evalu- ation. The ICNN is based on two main concepts: the inter-class and the intra-class distances. The former describes the distance between data points of different classes, while the latter refers to the distance between data points of the same class.
The ICNN assigns score by measuring the distance and variance of the inter and intra k-nearest neighbors each instance in the data. The equation to measure the data points and assign them score is represented by three different terms: X, w and 7. The ICNN formula is given as follows:
ICNN(X)
Σ (x))))())))(()))) 2EX
X
where p. y and r are control constants.
function that penalizes the neighbors of X; with the same class based on how distant they are, and the neighbors of different classes based on how close they are. If the neighbors of different classes are very distant, and the neighbors with same class are very close, the score will be close to
1. The formula for À was modified from the original ICNN proposal (García Ramírez (2021)) to better estimate the score with a few data points scenario. À is calculated as follows:
A(X,) EpeKa. 1
d(X..)) a(x.)
ΣYEKE, B(X.)
d(X..g)
(4)
Kr.
K
where Kg, KNN(2,) Yi are the set of k-nearest neighbors of x; that have the same class. K5,- = KNN((;;) E yı yı are the set of k-nearest neighbors of æ; that has different class. d(a. b) distance function, which in this case the euclidean distance. a(X,) is the distance from X; to the nearest neighbor of different class. 3 is the maximum distance from X, to the neighbors of different class. the ideal scenario, the neighbor's 's distance of the same class are close and the distance with different classes close to 1.
The second function w penalizes the distance variance of neighbors (Eq. 5 The distance is cal- culated as in the À function. A high variance is not desirable as it inereases the chance of class overlaps.
1
= 1100=---arr
Σ
d(X,,p) - 0(X.) -(xx)))((Xx.)
a(Xi) 0(X.)
PEKs;
(5)
d(Xi, 9) -
8(X,)
Var Σ
a(X,) 0(x.)
GE K
Lastly, the function (7) describes the ratio of the neighbor's classes. The optimal situation is when all the neighbors of X; are the same class X,. The formula for y is the following:
K
(x)) = K
Kg,
where |K,, is the number of nearest neighbors in the same class as X,. and [K,, is the number of nearest neighbors in different class X,. Each instance is penalized based the neighbors in the
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same class of rę- Each of the three functions (A, w and y) have output that ranges between 0 and 1.
The idea of the ICNN Loss is use this measure to increase the inter-class distance and reduce the intra-class distance, in order to learn better representations across the meta-tasks. The formula for the ICNN loss is the following:
ICNNLOs = log((CNN(X));
where we apply negative log to the ICNN Score obtain a value close to when the score is close to and high value when the score is close to O.
3.2.1 DESIGN CHOICES IN ICNN LOSS
Having defined the equation for the ICNN Loss function, we test different scenarios by varying the data points given to the algorithm and combining it with cross entropy loss and proto-triplet loss. For training the network, we know which class the support data and the query data belongs to, so we can use both sets to assign score to the current batch. The different options were tested by assigning different score to the support data, the query data and both the support and query data. For the support data, calculating the ICNN Score is straightforward, as each data point has an assigned score based its nearest neighbors and averaged across the set. For the query data, each query is given score based on the nearest neighbors of the support data points. When using both the support and query data, the data points combined and considered for calculating the score for each instance. The options for the algorithm are the following:
1. Score only on support data
2. Score on support data and score in query data
3. Score of support and query data together
We can also opt to make different choice of data given the ICNN algorithm when working with the query set. As our method aims at classifying the queries based on the prototypes, we added the option to give score the query set by using the prototypes neighbors. Each query instance is given a score by using the nearest prototypes.
4 EXPERIMENTAL SETUP
The experiments made on this work designed answer the following questions: (1) Is the Proto-Triplet Loss competitive with other metric-learning state-of-the-art models? (2) Is the ICNN Loss competitive with other metric-learning state-of-the-art models? (3) How does loss func- tions optimize the feature space to make the features more discriminating?
4.1 DATASET
We evaluate experiments using the MinilmageNet dataset (Vinyals al. (016 which is version the ImageNet Large Scale Visual Recognition Competition 2012 (Russakovsyy et al. (0144). Following the split proposed by Ravi & Larochelle (2017), this version of ImageNet is divided into 64 classes for training, 16 classes for validation and 20 classes for testing. making a total of 100 classes for the meta-learning. Each class contains 600 images to have total of 60,000 images. This dataset is used as a benchmark to evaluate most of the state-of-the- few-shot learning methods.
4.2 EVALUATION METRICS
We follow the same method as other metric learning methods four evaluating our results (Snell al. (2017); Vinyals al. (2016); Sung et al. (2017)). reporting the mean accuracy (%) of 1,000 randomly constructed tasks taken from the testing set along with the 95% confidence interval. Each task of the testing phase contains 15 query images per class.

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Model
Feature Extractor
1-shot
5-shot
Matching Networks
ConvNet
43.56 0.84%
55,31 0.73%
Prototypical Networks
ConvNet
49.42 + 0.78%
68.20 + 0.66%
Relation Networks
ConvNet
50.44 + 0.82%
65.32 0.70%
ConvNet
41.08 + 0.70%
54.50 0.66%
MAML
ConvNet
48.70 + 1.84%
63.11 + 0.92%
Reptile
ConvNet
49.97 + 0.32%
65.99 0.58%
Ours-Proto-Trippee Triplet
ConvNet
49.82 1 0.73%
68.76 0.46 %
OCrS_ICNN
ConvNet
49.71 + 0.78%
68.66 + 0.58% %
SNAIL
ResNet-12
55.71 + 0.99%
68.88 0.92%
DN4
ResNet-12
54.37 + 0.36%
74.44 0.29%
TADAM
ResNet-12
58.50%
76.70%
K-tuplet Net
ResNet-12
58.30 + 0.84%
72.37 = 0.63%
ProtoNets + CTM
ResNet-12
59.34 + 0.55%
77.95 0.06%
Principal Characteristic Net
ResNet-12
63.29 + 0.76%
77.08 + 0.68%
O Proto-Triplet
ResNet-12
61.32 + 0.52%
79.93 + 0.76%
OCNN
ResNet-12
60.79 + 0.62%
80.41 = 0.47
Table 1: Test accuracies minilmagenet in the 5-way setting for both 1-shot and 5-shot
4.3 IMPLEMENTATION DETAILS
We follow the same setting other few-shot learning models (Vinyals et al. (2016); Snell et al. (207)); [Sung et al. (201)), making the experiments under the setting of 5-way 1-shot and 5-way 5-shot, and using 15 query images for each class in the task. The input images are resized to 84 x 84 and normalized. We construct 100 random tasks for the training phase over 200 epochs. We validate each epoch with another 500 randomly constructed tasks using images from the validation set. In the testing phase we construct 1000 tasks with images from the testing set. We use the same random seed over all the experiments.
We test two different networks for the feature extractor: a ConvNet and a ResNet- The ConvNet follows the same architecture setting as previous works (Vinyals al. (2016), [nell et al.) (2017). ). This network is composed of 4 layers of convolutional blocks, with each block having 3 x 3 convolution with 64 filters, followed by a batch normalization and a ReLU layer. For this network, use the Adam Optimizer,
used in previous works, with initial learning rate of x 10-3 and a step size of 20. The ResNet follows the same architecture as other recent works (Li et al. (2019)). Lee et al. (2019)). This network is pre-trained with images from the training set, using the Stochastic Gradient Descent (SGD) optimizer with a momentum of 0.9 and learning rate of 0. over 100 epochs with batch size of 128. After the pre-training, we meta-train the network using the SGD optimizer with a learning rate of x 10-1, momentum of 0.9 and step size of 20.
RESULTS AND DISCUSSION
5.1 STANDARD FEW-SHOT LEARNING EVALUATION
For the MinilmageNet dataset, we evaluate our method under the two most common few-shot learn- ing settings: 5-way 1-shot and 5-way 5-shot. The results are compared against base metric learning methods for few-shot classification (Snell et al.
(2017); Vinyals et al.) (2016): [ung al. (201)).
and against recently proposed methods (Li et al.
2019b a): Zheng al. (2019))
As detailed in Table our method outperforms most the baselines in the 5-way 1-shot setting, getting only lower accuracy than Reptile (Nichol et al. (2018)) and Relation Networks Sung et al. (017)) when using a ConvNet as Feature extractor, and lower accuracy than Principal Characteris- ties Net (Zheng et al. (2019)) when using ResNet- 12. For the 5-way 5-shot setting, method outperforms all the baseline methods and the recent ones using ConvNet and ResNet- as feature extractors.

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Model
Backbone
1-shot
5-shot
(i) ICNN in Support
ConvNet
41.82
55.52
ICNN in Support Query
ConvNet
42.81
55.93
( ErossEn + ICNN in Support
ConvNet
49.28
68.33
(iv) CrossEntropy ICNN in Support Query
ConvNet
49.71
68.66
(v) ICNN in Support & Query(Prototypes, (vi) CrossEntropy + ICNN in Sueport&uurry (Protos)
ConvNet
41.81
55.93
ConvNet
48.86
67.74
(vii) Full ICNN
ConvNet
45.42
65.86
(vitt) Cross Entropy + Full ICNN
ConvNet
48.62
68.12
(i) ICNN in Support
ResNet-12 12 56.07
77.44
(ii) ICNN in Support & Query
ResNet-12
58.93
78.42
(iii) CrossEn + ICNN in Support
ResNet-12 60.55
79.11
(tv) CrossEntropy ICNN in Support & Query
ResNet-12
60.50
79.58
(v) ICNN in Support + Query(Prototypes, vi) CrossEntropy ICNN in Ceopport&QuryyPPeoet (vii) Full ICNN
ResNet-12
59.07
79.18
ResNet-12
60.79
80.41
ResNet-12
60.37
78.79
(utti) Cross Entropy + Full ICNN
ResNet-12
60.32
79.30
Table 2: Design choinces for the ICNN Loss function using a ConvNet and ResNet- 12 as feature extractors and 5-way tasks on both 1-shot and 5-shot settings
Model
Backbone
1-shot
5-shot
Proto-Triplet
ConvNet
48.85
67.79
Cross Entropy Proto-Trip Triplet
ConvNet
41.66
66.09
Proto-Triplet + Full ICNN
ConvNet
46.00
62.72
Cross-Entropy Proto-Triplet Full ICNN
ConvNet
49.82
68.76
Proto-Triplet
ResNet-12 12
60.87
78.78
Cross Entropy + Proto-Triplet Proto- Proto-Triplet-1 Full ICNN
ResNet-13
60.09
79.33
ResNet-
59.58
78.53
Cross-Entropy + Proto-Trrillt + Full ICNN
ResNet-12 61.32
79.93
Table 3: Design choinces for the Proto- Priolerripeet Loss function using a ConvNet and ResNet- as feature extractors and 5-way tasks on both 1-shot and 5-shot settings
When using ConvNet as the feature extractor, method achieves improvement of 8.8% over the baseline (Chen et al. (2019b)) 5.3% over the Matching Networks (Vinyals al. (2016) and 0.4% over the base prototypical Networks for the 5-way 1-shot setting. For the setting of 5-way 5-shot, we achieve an improvement 13.4% over the Matching Networks, 3.4% over the Relation Networks and 0.5% over the prototypical networks.
When using a ResNet- 12 as the feature extractor, our method achieves an improvement 5.6% over SNAIL MMshhaa al. (2018) 3% over the K-tuplet Net (Li et al. (2019b) and 2% over the Category Traversal Module (Li et al. (2099)) for the few-shot setting of 5-way 1-shot. On the setting of 5- way 5-shot, we obtained an improvement of 11.6% over SNAIL, 8. over the K-tuplets Net and 3.4% over the Principal Characteristics Net (Zheng et al. (019)).
5.2 ABLATION STUDIES
The ablation studies split into three parts: the proto-triplets loss experiments, the ICNN loss experiments and experiments with the networks used as feature extractor (ConvNet and ResNet-12), For all the experiments, we repeated the design choices using both networks compare against base- lines and recent methods in few-shot image classification. The models using a ResNet-12 greatly improve the accuracy performance compared those using ConvNet.
The results for the design choices for the ICNN loss are reported in table 2 Our baseline is the simplest form of using the ICNN loss, by applying the score only to the support data. This gives us
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ProtoNet
Ours
Figure 3: Umap visualization of the improved feature embeddings obtained from the test set. The feature embeddings were computed in a 5-way 5-shot setting by constructing 1,000 tasks from the test data. When creating the tasks for the feature visualization, we kept fix the 5 classes sampled and randomly draw samples to construct the support and query sets
the worst results from the experiments made, and are not competitive with state-of-the. models. Then, we test loss function by applying the score different sets of data. For (ii) and (ir), we test using ICNN on support data and query data separately, with the difference that (iv) uses the additional loss of the cross-entropy. When using a ConvNet, using the cross entropy and ICNN in support and query (iv), improving the baseline performance by around 8%. For (v) and (vi) modify the ICNN score on the query by comparing distances from each query to the prototypes instead of the comparing the distances from each query to the support data. For the case of using a ResNet-12 as the feature extractor, this combination (vi) gave us the best results, improving the baseline by around 4% for the 1-shot setting and 3% for the 5-shot setting. The last experiments, (vii) and (wii)), apply the ICNN score to the combined set of support data and query data. These last experiments didn't 't lead us to the best results, but they are also quite competitive.
obtained the best results by
The results for the design choices for the proto-triplet loss are reported in table 3 We evaluate the combination of three loss functions: the cross-entropy, proto-triplet and full version of the ICNN loss. First test the proto-triplet loss alone to optimize the network, and obtain already good accuracy performance compared with state-of-the-at results. Then, we start combining the loss functions and we can observe that combining cross entropy with proto-triplet and ICNN loss with proto-triplet we get a worse performance than the obtained using only the proto-triplet loss. The last design choice is the combination of cross entropy, ICNN loss and proto-triplet loss, which is the one with the best accuracy performance by improving the result by 1% using both feature extractors.
6 CONCLUSION
In this paper, we proposed two different loss functions to train an embedding network for few-shot image classification. These loss functions based the concepts of intra-class and inter-class distance, and have as the main objective to pull together instances of the same class and push further away the instances of different class. The proposed model improves the accuracy performance when compared with bascline models which make use of metric learning approaches to solve the few-shot classification problem on the public benchmark dataset. The proposed model also obtaín competitive results when compared with more recent methods which make use of more robust embedding network, as we improve the accuracy for the 5-way 5-shot setting. Our current framework can be extended in several ways. For instance, we could make the hyper-parameters of the ICNN algorithm to be learnable instead of making them of a fixed value. Another direction is to test these loss functions with different metric meta-learning methods to see if they allowing the network to leam better feature representations for few-shot tasks.
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Under review as a conference paper at ICLR 2022
ICNN Score: 0.74
ICNN Score: 0.87
ICNN Score: 0.96
Figure 4: ICNN score behaviour on different 5-way 1-shot scenarios.
ICNN Score: 0.44
Score: 0.65
ICNN Score: 0.95
Figure 5: ICNN score behaviour on different 5-way 5-shot scenarios.
A APPENDIX
In figure and we can visualize how some few-shot tasks scenarios would be rated using the ICNN score.
12


Reviews:
[{"review_id": "uTspjTkKZP7", "reviewer": "Reviewer_TCLP", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths: \n1.\tThe motivation of this paper is clear. It is important for few-shot learning based on metric learning to increase the inter-class distance between sample representations of different classes and decrease the intra-class distance between sample representations of the same class as much as possible.\n2.\tFrom the experimental values and visualization results, the loss function terms introduced by the authors do what they claim to do, i.e., samples of different categories move away and samples of the same category are clustered.\nWeaknesses:\nNovelty: The degree of innovation in this paper is limited, and the two loss terms proposed by the authors can be seen as an application and combination of Triplet Loss and (ICNNS).\n\nPerformance:\nThe method proposed by the authors is not significant in terms of performance, for example, it lags behind in comparison with “Principal Characteristic Net” in Table 1. Also, some comparisons with newer metric-based learning models are missing, such as DeepEMDv2[1].\nWriting:\nSome typing errors also need to be corrected, such as the $K_{x_i}$ in Equation 4", "summary_of_the_paper": "This paper discusses the few-shot learning based on metric learning. In order to better measure the distance between samples of different classes, the authors propose two new metric loss terms considering both inter-class and intra-class distances of samples. The first metric loss is called Proto-Triplet Loss, which improves on the traditional Triplet Loss. The second metric loss is called ICNN loss, which is based on the Inter and Intra Class Nearest Neighbors Score (ICNNS). And the purpose of these two loss is to make the distances between samples of the same class as small as possible and the distances between samples of different classes as large as possible in few-shot learning learning.", "summary_of_the_review": "The paper is well organized and clearly written. And it clearly described the design of Proto-Triplet Loss and ICNN Loss. Though there seems a lot of overlap between Proto-Triplet Loss and classic triplet loss I still recommend this paper be accepted. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "OqIT8V48igZ", "reviewer": "Reviewer_noXn", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths\n1. This is a well-written paper and it is easy to read.\n2. The loss functions proposed in this paper can improve the performance of few shot learning models.\n\nWeakness\n1. In recent two years, many few shot learning methods have been proposed and they need to be introduced and compared. This paper lacks comparisons with the methods after 2019.\n2. The results of the experiment are not sufficient. This paper only provides the results on the mini ImageNet. Experiments should be carried out on more datasets to prove the effectiveness of the method.\n3. The novelty of ICCN Loss may be minor. It seems that this paper directly adopts ICCN Score which has already been proposed previously. \n4. Since the motivations of proposed loss functions are the same, this article should further analyze the applicable conditions of Proto-Triplet Loss and ICNN Loss.\n\n", "summary_of_the_paper": "This paper proposes a new model that takes part of the meta-learning approaches based on metric learning. More specifically, this paper modifies triplet loss to make it more suitable for few shot learning task and proposes ICNN Loss to increase the inter-class distance and reduce the intra-class distance.", "summary_of_the_review": "This  lacks the introduction and comparison of the methods in the last two years, and experiments on more datasets are needed to illustrate the effectiveness of the methods. In addition, the applicable conditions of the two losses should be further analyzed.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "AuzDAmuczN8", "reviewer": "Reviewer_6rdQ", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Pros:\n* few-shot learning is an important problem to focus, miniImageNet is still a tough benchmark\n\nCons:\n* novelty, ICNN is not novel, taken from the cited work with some minor modification, simply using it for few-shot learning would need very strong sota improvement to make the paper interesting; proto-triplet-loss is a hybrid between triplet loss and standard PN loss, and in fact PN loss contains it in a way as it takes into account not only two class prototypes but all of them simultaneously, and there was an old paper extending triplet loss to entire batch and it was shown it is better.\n\n* experiments, (1) miniImageNet only is not enough; (2) the baselines are not sota, please go to the PapersWithCode website and see real sota methods for miniImageNet - the reported results for the proposed methods are far below real sota on miniImageNet", "summary_of_the_paper": "The paper proposes two losses for meta-learning-based few-shot learning. The first loss is a triplet loss where the positive and negative anchors are replaced by class prototypes (averages of class members from the train set of each episode). The second loss is ICNN proposed in Garcıa and Ramırez (2021) for a different task. Experiments show improvement of up to 2% on miniImageNet compared to some (non-state of the art) baselines.", "summary_of_the_review": "The paper as it stands has major drawbacks in novelty and experimental validation, unfortunately in current form it will probably not be interesting to the general audience. Please see my notes above.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "9ko9bvoB_G3", "reviewer": "Reviewer_dCJD", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "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": "Strength\n1.\tThis paper is well written and easy to understand.\n\nWeaknesses\n\n1.\tThe novelty of this paper is incremental. It seems that the authors only apply two existing losses to the existing prototype network. Furthermore, the authors did not provide any in-depth analysis to explain why we need to use these two losses. The previous work [ref1] also used intra- and inter-class distances for few-shot learning, but it provided in-depth theory and experimental analysis. The authors should refer to [1] to add more analysis. Besides, the performance of [ref1] seems to be better than these two proposed methods.\n2.\tThe proposed methods achieve a slight performance improvement, especially for the comparison with the similar work ProtoNet. The gains are only 0.4% and 0.5%, while the ProtoNet uses a more simple loss. These slight improvements may come from random errors. Thus, the results cannot demonstrate the effectiveness of the proposed losses.\n3.\tThe experimental results on only one dataset are not enough to demonstrate the generalization. The authors should evaluate their methods on at least two different datasets.\n4.\tThe compared methods are out-of-the-date. The newest work was published in 2019. The authors should compare more recent state-of-the-art methods.\n\n[ref1] Unraveling Meta-Learning: Understanding Feature Representations for Few-Shot Tasks, ICML2020\n", "summary_of_the_paper": "This paper applies two losses to the few-shot learning model based on metric learning (similar to ProtoNet), which aims to utilize the intra- and inter-class distances. The first one is based on the original triplet loss and adjusted for the prototype network. The second one is based on the recently proposed Inter and Intra Class Nearest Neighbors Score (ICNN Score) (Garc´ıa Ram´ırez (2021)). The experimental results on miniImageNet show the proposed models achieve better performance than several previous metric-based approaches.", "summary_of_the_review": "Since the novelty of this paper is incremental and the experimental results are insufficient. The reviewer recommends rejecting this paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper is proposed to address the few-shot image classification with the help of two newly designed losses. The first loss function is the Proto-Triplet Loss based on the revision of conventional triplet loss. Another loss function is based on an inter- and intra-class nearest neighbors score to estimate the quality of embeddings. The proposed method has shown its superiority over the baselines on the miniImagenNet benchmark. The major concern of this paper is the novelty that both proposed techniques are not new. Moreover, the baselines are not the SOTAs, and the evaluations on miniImagenNet only are not comprehensive enough. In addition, the authors have not provided any rebuttal to address the reviewers' concerns.
Decision: Reject