C+1 Loss: Learn to Classify C Classes of Interest and the Background Class Differentially
Authors: Changhuai Chen
Xile Shen
Mengyu Ye
Yi Lu
Jun Che
Shiliang Pu
Venue: ICLR 2022 Submitted (2022)
Keywords: C+1 loss
classes of interest
background class

Abstract: There is one kind of problem all around the classification area, where we want to classify C+1 classes of samples, including C semantically deterministic classes which we call classes of interest and the (C+1)th semantically undeterministic class which we call background class. In spite of most classification algorithm use softmax-based cross-entropy loss to supervise the classifier training process without differentiating the background class from the classes of interest, it is unreasonable as each of the classes of interest has its own inherent characteristics, but the background class dosen’t. We figure out that the background class should be treated differently from the classes of interest during training. Motivated by this, firstly we define the C+1 classification problem. Then, we propose three properties that a good C+1 classifier should have: basic discriminability, compactness and background margin. Based on them we define a uniform general C+1 loss, composed of three parts, driving the C+1 classifier to satisfy those properties. Finally, we instantialize a C+1 loss and experiment it in semantic segmentation, human parsing and object detection tasks. The proposed approach shows its superiority over the traditional cross-entropy loss.

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C' + LOSS: LEARN TO CLASSIFY C CLASSES OF INTEREST AND THE BACKGROUND CLASS DIFFERENTIALLY
Anonymous authors
Paper under double-blind review
ABSTRACT
There one kind of problem all around the classification area, where we want to classify C' + I classes of samples, including C' semantically deterministic classes which we call Classes of Interest (Cols) and the (C' + 1)dh semantically unde- terministic class which we call background class. In spite of most classifier use softmax-base -baed cross- cross-yntropy loss to supervise the training process without differ- entiating the background class from the Cols, it is unreasonable Cols has its inherent characteristics, but the background class dosen't. We figure out that the background class should be treated differently from the Cols during training. Motivated by this, firstly we define the C + classification problem. Then, we propose three properties that a good C' 1 classifier should have: sepa- rability, compactness and background margin. Based on these we define a uniform general C'+1 1 loss, composed of three parts, driving the C+1 1 classifier to satisfy those properties. Finally, we instantialize C ++1 1 loss and practice it in semantic segmentation, human parsing and object detection tasks. The proposed approach shows its superiority over the traditional cross-entropy loss.
each of the
INTRODUCTION
In machine learning, Softmax one of the most widely used classifiers for classification, especially in CV tasks. During training, the Softmax classifier is often supervised by cross-entropy loss which treats each class without difference. However, there is a type of problem present all around the classification area, for which it is unreasonable to treat each class the same. We called this type of problem as C'+ I classification. C+1 classífication means classifying samples from C semantically deterministic classes and the (C + 1)th semantically underterministic class. We can semantically uniquely define each of the C classes by its inherent characteristics, so we can say they are seman- tically deterministic. Generally, we interested in the C' classes, of them as a class of interest (Col) hereafter. The (C + 11th class includes all the other stuff beyond C' classes. Because it doesn't have uniform inherent characteristics and can't an't be described uniquely in semantics. That is why we say it is semantically undeterministic. In most cases, we regard things belonging the (C + 1)th class background, and we will call it background class hereinafter.
call them C' Cols and one
Based on the above description, we consider that it is reasonable to treat the C Cols and the back- ground class differentially during training. On one hand, for the C Cols, it's reasonable drive
C' + 1 classifier to lear a compact and independent representation space for each of them because of their inherent characteristics. Then the C + 1 classifier can embed samples from each Col into its own representation space. On the other hand, it's also reasonable to drive the C' + classifier to map any samples from the background class into somewhere feature space far away from all representation spaces of the C' classes, considering that samples from background class doesn' 't have any inherent characteristics different from C Cols. For example in figure 1, if we are interested in cat, we can recognize a cat from an image at the first glance by the knowledge in the subconscious which uniquely defines cat. On the contrary, we can also recognize a not-cat instantly because doesn't 't have any inherent characteristics of cat.
According to the inherent characteristics of C +1 classification, we figure out that a C + classifier will be preferable if it has compact and independent representation space for each of the C' Cols

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Cat
Background class (Not Cat)
Figure 1: C++ classification cases(the source images are from ImageNet Russaakvssks et al. (2015))
in addition its separability for all classes. This can guarantee it behaves well while encountering sample which have different styles from the samples of corresponding Col in the training set. Furthermore, will be much better if there is large enough margin between the background class and the C' Cols. This will make the classifier more robust and generalizable while encountering sample from any new classes belonging to the super background class, especially those that never appear in the training set. Above these, conclude three properties which a good C + classifier should separabbaabillty. compactness and background margin. Based on the three properties, we define uniform general C loss which includes three parts corresponding the three properties, driving the C+1 classifier to satisfy those properties. At last, considering semantic segmentation and object detection are IWo the most typical C classification problems, and widely used in AI systems, we instantialize a C + 1 loss and practice in semantic segmentation and object detection tasks, proving its superiority over the traditional cross-entropy loss.
Specifically, in semantic segmentation, Softmax is widely used to classify each pixel of an image to one label of predefined class set. Typically the predefnned class set includes C' Cols and back- ground class. For instance, PASCAL VOC 2012 segmentation Everingham et al. (2010) contains 20 Cols and a background class. The background class contains all other stuff. In object detection, Softmax is usually used to classify proposal boxes of an image to one of predefined class set. For example, MS COCO Lin et al. (2014) contains Cols. A detector trained on should classify all background class. In these two typical tasks, the C + classifiers need to recognize all the Cols, and classify a variety of other things as background. It's difficult for cross-entropy loss drive the classifiers learn well, which treats all samples without difference during training.
proposal boxes as one of the 80 Cols
This paper contains three contributions summarized follows:
1. We define the + classification problem present all around the classification area.
2. We propose three properties that good C + 1 classifier should have, and define uniform C + loss, which includes three parts driving the classifier to satisfy these properties.
3. We instantialize C' 1 loss consisting of three terms, and practice it semantic segmentation and object detection tasks, proving its superiority over the popular cross-entropy loss.
RELATED WORK
2.1 SOFTMAX
Softmax is one of the most widely used classifier for a variety of pattern recognition tasks. Nowa- days there are plenty of variants for Softmax, such 1.2-Softmax Ranjan et al. (2017). Large-
margin Softmax Liu et al. (2017). Angular Softmax Liu et al. (2016), Normface Wang et al. (017).
AM-Softmax Wang al. (2018)). CosFace Wang al. (b) and ArcFace Deng al.
2019
Large-margin Softmax is the first attempt to add parameter m into the original Softmax to con- trol the margin and the larger m is, the larger the decision margin between the classes. Angular Softmax also known as SphereFace an improvement to Large-margin Softmax with additional constraints W and b, introducing the hypersphere manifold which makes the features suitable for
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open-set FR problem. L2- 12-Softmax and Normface share similar ideas where L2-Softmax normalizes only the features and Normface normalizes both classifier weights and features and applys a scale parameter after that. The normaling and scaling steps push the learning progress focusing op- timizing angles among the classes, making the features not only separable but also discriminable. AM-Softmax(additive margin Softmax loss) and CosFace's works inspired from SphereFace by moving the parameter m that controls the margin from angular space to cosine space by addition. This also makes the implementation easier. ArcFace(additive angular margin loss) moves the pa- rameter m from scaling to addition to expand the optimization boundary. To sum up, thse variants of Softmax improve Softmax from these aspects: normalization of weights or features, margin in angular space or cosine space, setting of margin m. They use the parameter in different ways resulting in different decision boundary. However, they treat all classes equally during training as Softmax. And we propose to give some special care for the background class. So Softmax and its variants are not the best choice for C' + classification problem.
2.2 METRIC LEARNING
Metric learning aims to maximize inter-class variation and minimize the intra-class variations. Con- strastive loss Chopra et al. (2005); Hadsell et al. (2006); [Sun et al. (2014) drives the distances be- tween positive pairs close to 0, and the distances between negative pairs to fall within an absolute range. Triplet loss and its variants Weinberger & Saul (2009): Hoffer & Ailon (2015): Wang et al. 22014; Schroff et al. (2015); Ding et al. (2015); Cheng et al. (2016); Oh Song et al. (2016); Sohn 2016 drive the relative distances between positive pairs and negative pairs to fall lower than pre- set threshold. Center loss Wen et al. (2016) drives model to learn a center for features of each class and penalizes the distances between features and their corresponding class center. Metric learning also treats each class equally, just from a metric perspective. They could not take care of the par- ticularity of background class and the inherent characteristics of every semantic class. In addition, it's not appropriate to learn a center for background class because it has no deterministic and unique definition.
2.3 OPEN-SEI SET RECOGNITION
Open-set recognition Bendale & Boult (2016); Ge et al. (2017); Shu et al. y0 Neal et al. (2018); Liu et al. (2019); Yoshihashi et al. (2019); Oza & Patel (2019); Chen et al. (2019g) Qian et al. (2019); Yu & Tao (2019); (Sun et al. (2020) is the
closest our proposed C classification, wherein there are no training samples for the background class. However, the classifier needs to detect new classes while inferring. The C classification deals with another type of problem, wherein there are both training samples for C Cols and the background class. In practice, it's impossible contain all other semantic classes except the Cols into the background class. Many samples of new semantic classes are likely yo be encountered and should be identified as background class while inferring. So we could call the C' + classification as semi-open-se set recognition.
METHOD
3.1 PROBLEM DEFINITION
Firstly, we define some terminologies as follows.
Semantic Class: a set of samples which could be described uniquely and deterministically.
Cols: set of semantic classes that we are interested in and need to be recognized.
Background Class: other classes beyond C' Cols, including those semantic classes we are not interested and all other stuff.
C+1 Classification Problem: categorize each item of a set into one the C++ 1 classes. Therein, C'11 classes comprise C' Cols and the (C++1)th class of not interested, also called background class. The Cols are deterministic and unique, but the background class is underterministic and includes all stuff beyond those belonging to the C' Cols. The training set comprises many samples from each of the Cols and diverse samples from the background class. Being semantically deterministic means can give deterministic and unique definition for each of the C Cols according to its
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inherent characteristics. Being underministic means the background class has deterministic and unique definition, because it lacks uniform inherent characteristics.
3.2 C LOss
For each of the C' Cols, the C classifier should extract the inherent characteristics, and differen- tiate the background class from In order to achieve this, we consider that a C. + classifier should satisfy the following three key properties.
I.Separaiility: should be able to separate all classes.
2. Compactness: The representation space of C' Cols should be compact enough.
Background margin: There should be large enough space which we call background margin between the background class and each of the C Cols.
The property one guarantees that a C C+1 1 classifier has basic categorization ability for those samples that have similar distribution with the training set. The property two makes sure that the classifier has good generalizability for those samples belonging to the Cols but with different distribution. And the property three gives the classifier good robustness and generalizability for samples of the background class, especially those whose styles are never present at the training set.
In order drive C'+ classifier learn to satisfy the three key properties, argue that the C++1 loss should include at least three parts: Iiseperabilityy Leompact and Lbackgrounds corresponding to the three properties respectively.
LC+1 = separrbbilit + aLcompact + 3 BLbackground
(I)
Herein, Useperability drives the classifier learn discriminate all classes without difference, Leompact drives the classifier to try to grasp the inherent characteristics and to learn compact representation space for each of the C Cols, and Lbackground drives the classifier to differentiate the background class from the C' Cols well.
In practice, could adopt cross-entropy loss as an instantialized instance for Lseparability and center loss Wen et al. (2016) for Leompact- As for Lbackground- we design a novel loss according to the property three as follows.
Lbackground sign 1y==+11
1 N
Σ Σ ms (z.) cx)l
(2)
Herein, sign (expression) = only when the expression is true, otherwise 0. N is the number of background class sample. m, is the background margin between background class and each of the C' Cols. 2; is a sample, and yi is its class label index. C2 is the center of kth Col. f(x) is mapping function for extracting feature of sample æ. J...(ee (xx followed by softmax composes the + classifier. Without losing generality, f(x) is deep neural network.
As centers for center loss and the instantialized Lbackgrounds we define three types of center repre- sentation.
R.perreentt each center of Cols as a learnable weight vector.
2. Reperesent each center of C Cols as moving average of sample features of the corresponding class.
3. Reperesent each center of C' Cols the classifier weight vector of each class from the logit FC layer.
Specifically the third center representation means that we share the center vector parameters with the softmax layer of the C' Cols, and ignore the weight vector of background. We define center for every Col, but not the background class. For every Col, there which can uniquely and deterministically define semantically, however there are no unique and deterministic inherent characteristies for the background class. However, we can calculate the loss
bunch of inherent characteristics
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term Leompact based the distance between every sample of each Col and its center. Further- more, we can calculate the loss term Louckground based on the distance between every sample of background class and the center of each Col.
3.3 APPLICATION
The C' + 1 classifier described in the previous section can be applied to many tasks, including se- mantic segmentation, object detection, human pose estimation and any other classification problem which include the background class. In semantic segmentation, we label each foreground pixel with semantic label, and all other pixels with background label. In object detection, area of object of interest as one of the Cols, such as pedestrian, car and so on, and all other ar- background. In human pose estimation, we label the position of each human keypoint with proper semantic label and the other position with the background label. As for other cases, the recognition problem needs recognize certain number of semantically deterministic classes and the other stuff, the C + classifier can also apply to it. In this paper, we just use some CV tasks as the experimental field, because they are the most common tasks in Al system. Besides the application scenarios presented above, it can also be applied to many other tasks, such as attribute recognition, web text classification, speech recognition and on.
classify the
3.4 DISCUSSIONS
We think C' + 1 classifier is rational because it has sufficient prerequisites. Because every Col has semantically deterministic definition based on a of inherent characteristics, it's rational and reachable to embed all samples of every Col into an independent hypersphere. For example, the cat in the figure has some type of fur, innate shape and contour, so we can define it uniquely and recognize it by the first glance. As for the background class, it has no deterministic definition, so there are no definite and uniform features for it. Then it's not rational to embed all samples of background class into an hypersphere. But it may be reasonable to map it to the outer space of all hyperspheres of the C' Cols. Because the C Cols are separable from the background class based on the uniqueness of every CoL.
3.5 THEORETICAL ANALYSIS
After training. if the mapping function can embed all samples of the C' Cols into their own hyper- sphere, it's almost impossible to map novel sample belonging to the background class into any hypersphere of the Cols, even though the classifier has no any knowledge about the novel sample. Assume that novel sample belonging to the background class is new-brand and there style of samples present at the training set, then we can treat it as a random sample from the nature. From the perspective of statistics, the probability of recognizing it the background class is close to 1. Formally, we assume that the full d-dimension feature representation space is a super ball with R2 as the radius, and the sample features of each Col are distributed inside small super ball with R as the radius. Then the probability of mapping the random sample to the outer space of the C' Col super balls is
similar
(Frandom) ) = C Rd R
(3)
Therein, R < Ry is reasonable assumption, C is a constant (number of Cols), and d is the dimension of feature space, usually very large, such as hundreds, even thousands. C Rd is proxy for union of volumes of all Col super balls, and R&, for the full feature space. Then C-R. is the ratio RØ
between union volumes all Col super balls and the full full feature space, which represents the probability that the mapping function embeds random sample of background class into any of C' Col super balls. In practice, because the high dimension of feature space, which means d is a large integer, such as 1024, p (Frandom is close to 1.
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Table I: Effectiveness validation experiment PASCAL VOC
Loss function
mloU
mAce
aAcc
lsspparbiiisty
75.93
85.47
94.59
Lisepavabilitty + Leompaat
76.25
86.1
94.61
Lspporchiiity Leompact Lbackground
77.35
86.37
94.58
EXPERIMENT
We comprehensively evaluate the effectiveness of + 1 classifier on semantic segmentation, and then transfer to object detection with some minor adjustments. During inference use the output of softmax layer for classification.
4.1 SETTINGS
Semantic Segmentation. Semantic segmentation aims to label each pixel an image with one semantic class label or background label. We evaluate methods
popular semantic seg- mentation dataset: PASCAL VOC and PASCAL Context and human parsing dataset LIP. To make fair comparison, for PASCAL VOC 2012 and PASCAL Context adopt MMSegmentation Con- tributors (2020) as a unified framework for the experiments on semantic segmentation.
PASCAL VOC 2012 contains 20 foreground object classes and one background class. The original dataset contains 1,464 (train), 1,449 (val), and 1,456 (test) pixel-level annotated images. Following the settings in Chen et al. (2018b), we the augmented dataset by the extra annotations provided by EEvernghhmm et al. (2013), which contains 10,582 (trainaug) training images. Following the setting MMSegmmentation Contributors (020), we resize the images into 512x 512 and the output stride is 8. We adopt "SGD" as the optimize and "poly" policy as the learning rate schedule. In addition, we set the initial learning rate 0.01 and weight decay as 0.0005. Furthermore, the batch size 16 and the number of iterations is 20K. We evaluate the performance of our method and other methods using single scale and without flipping.
PASCAL Context Mottaghi et al. (2014) contains 459 labeled categories, including 10, 103 images, of which 4,998 are used for training and 5,105 for validation. The most widely adopted setting is to the most frequent 59 categories the semantic object classes and all the remaining categories as background. Following the setting in MMSegmmentation, we resize the images to 480 x 480. The initial learning rate is 0.004 and weight decay to 0.0001. The batch size is 16 and the number of iterations is 40K. We evaluate the performance using single scale and without flipping.
LIP Gong et al. (2017) ) human part segmentation dataset, with 50,462 images in total, including 30,462 images for traiiing 10,000 images for validation and 10,000 images for testing. In addition, contains 19 semantic classes and 1 background class. We resize the images to 473 x 473. The initial learning rate set to 0.0028 and weight decay to 0.0005. The batch size is 16 and the number of iterations is 110K. We evaluate the performance using single scale and flipping.
Table 2: Effect of three different center representations
Center representation
mloU
m/cee
aAcc
Learnable
76.68
86.29
94.71
Moving average
77.35
86.70
94.87
Shared 76.99
86.57
94.79
4.2 SEMANTIC SEGMENTATION
4.2.1 ABLATION STUDY
For ablation study, we use VOC+Aug as the training set. All images are resized to 512x512 as input. Iteration number is 20K. The initial learning rate 0.01, and then decayed by "poly" policy with

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Table 3: Weights' effect of commpcc
Weights for compact
mloU
mAAcc
aAcc
0.01
76.82
86.43
94.63
0.1
77.35
86.70
94.87
75.22
85.25
94.39
Table 4: Weights' effect of Lbackground
Weights for Lbbckgrouud
mioU
mAcc
aAcc
0.001
75.93
86.04
94.51
0.0001
77.35
86.70
94,87
0.00001
76.47
85.91
94.71
power being 0.9. Batch size is set to 16. We use the same setting for the all ablation study unless specified otherwise.
At first, validate the effectiveness of C + 1 classifier PASCAL VOC by D3 Chen jet al.] (2018a) with ResNet50 He et al.] (2016) as backbone. As for the C Cols, we use moving averages of La-normalized features centers. We set the weights of Leompact and Lbackground as 0.1 and 0.0001 respectively if each of them is used.
observe that Leoopact and Tbackground both boost the performance significantly. When Leompact is used with Lseparabilityy we can improve mIoU by 0.32. If Lbeckground added, we can get positive improvement 1.10 furthermore, and C loss in total can improve the mloU by 1.42. For semantic segmentation task, this is a significant improvement.
From the experiment performance table
Then, we validate the effect of three different center representations on the performance. In this group experiments, we set the weighs of Trompact and Lbbckkrrundd as 0.1 and 0.0001 respectively. We use the same hyper-parameters as above. From the experiment performance on table 2, we could find that moving average achieves the best performance.
Next we analyze the effect of weights of Leompact and Loackground- According to the above exper- iments, moving average is the best center representation, so we adopt moving average this and following experiments. First, we observe the weights' effect of Leompact while set the weight of Libackground as 0.0001. From table we can observe that 0.1 is a reasonable weight for Leompact- Then test the weight's effect of Lbackground while set the weight of Leompact 0.1. From table we find that 0.0001 is reasonable weight for Lhackground. From experiment performance, we conclude that setting the weights of Leompact and Lsbackground as 0.1 and 0.0001 respectively is a proper choice.
Finally, we list the performance details of all classes PASCAL VOC with and without C + loss in table 5. We can observe our method get superior performance over baseline on 13 classes which highlighed by boldface.
4.2.2 BACKBONE
To prove the generality of C' + classifier, experiment PASCAL VOC by DeepLab with ResNet101 as the backbone, displayed in table 6. Considering the larger capacity of ResNet101, we set the iteration 40K and other hyper-parameter the same with ResNet50 the backbone. We can observe that C'+1 classifier is also better than the baseline. Moving average is used as the center representation. The weights of Leompact and Lbackground are set 0.01 and 0.0001 respectively.
4.2.3 COMPARISON WITH SOTA
To prove the generality of C classifier, further experiment PASCAL VOC by other SOTA semantic segmentation algorithms, i.e. HRNet [Sun et al. (2019) and OCRNet Yuan et al. (2020). Both of them take HRNetW48 backbone. We set the hyper-parameters the same Deeplab

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Table 5: The performance details of all classes PASCAL VOC with and without C loss
Lseparability mloU
LC+1
Lseparobiisty mlo
Lo+1
Category
Category
mAcc
mloU
mAce
mAcc
mloU
mAcc
acroplane
90.13
96.01
92.03
95.38
diningtable
57.14
60.24
54.87
57.38
bicycle
41.75
91.74
41.56
95.38
dog
84.18
93.75
86.26
94.38
bird
86.62
92.32
87.71
94.17
horse
84.86
88.88
84.74
92.98
boat
70.92
87.90
72.43
87.27
motorbike
84.51
91.09
83.90
92.30
bottle
76.63
87.79
78.37
89.66
person
84.99
91.61
85.08
91.08
bus
94.68
97.49
95.05
96.99
pottedplant
60.82
70.29
59.70
70.70
car 86.40
93.06
86.03
93.85
sheep
83,93
92.37
88.47
91.98
cat
90.50
94.84
93.10
96.94
sofa
46.29
53.87
55.80
65.52
chair 36.36
55.11
37.44
54.77
train
90.21
94.10
89.40
93.97
cow 86.65
90.30
87.68
90.18
tv/monitor
62.69
75.31
70.45
80.79
background
94.21
97.33
94.35
97.32
Table Experiment results on PASCAL VOC by Deeplab V3+ with ResNet101 as the backbone
Loss
mloU
mAcc
aAcc
DeepLabV34 Chen et (2018a)
78.62
86.55
95.22
DecpLabY3++our
80.00
87.99
95.50
with ResNet101 as the backbone, including center representation and iteration. For OCRNet+ours, set the weights of Lcompact and Lbackground set to 0.1 and 0.0001 respectively, and HR- Net+FCN+ours with 0.01 and 0.0001 respectively. Results in table 7 shows that our C+1 classifier is also applicable to other semantic segmentation algorithms. Especially the OCRNet, method can improve the baseline with 0.99 mloU,
4.2.4 EXPERIMENTS ON PASCAL CONTEXT
To prove the generalization ability of our classifier to other scenarios, also experiment D3+plabV3+ with ResNet50 as backbone on other semantic segmentation dataset, i.c. PASCAL Context. We the moving average as the center representation. All images resized to 480x480. Iteration number is 40K. Initial learning rate set to 0.004. Batch size is set to 16. From table 8, can observe our classifier can also improve the performance PASCAL Context too.
4.3 HUMAN PARSING
For LIP, all images are resized to 473x473, The initial learning rate and weight decay are set to 0.0028 and 0.0005 respectively. The batch size is 16 and the number of iterations is 110K. Experi- mental results are shown in Table
There also other datasets, i.c. Cityscapes Cordts et al. (2016). KITTI Geiger et al. (2013) and ADE20K Zhou et al. (2017 2201)). However these datasets almost have no background anno- tations, it cannot be defined C' + classification problem. Thus we don't experiment them.
Table 7: Experiment results on different SOTA semantic segmentation algorithms
Method
mloU
mAcc
aAcc
HRNee48+FCN Sun et al. (2019)
76.23
84.95
94.66
HRNot48+FCN+Our
76.96
85.38
94.81
OCRNet Yuan et al. 2020
77.14
85.92
94.94
OCRNet+ours
78.13
86.92
95.09
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Table 8: Experiment results PASCAL Context
Method
mloU
mAcc
aAcc
DeepLab V3+ Chen et al. 20188)
47.34
57.40
74.18
DeepL.bb
47.81
58.29
74.68
Table 9: Experiment results on LIP
Method
Flip-test
mloU
m/cc
aAcc
N
53.42
65.20
86.80
HRNet Sun al. (2019)
Y
54.53
65.77
87.30
N
53.76
65.63
86.81
HRNet+ours
Y
54.78
66.19
87.32
4.4 OBJECT DETECTION
Object detection. In this section, we migrated our approach the object detection task. Nowadays, existing methods for object detection can be divided into anchor-based and inchor-free according to whether anchors are needed. Among them, the anchor-based methods are quite different from the segmentation task in the classification head. Specifically, semantic segmentation is the classification of pixels. The target to be classified corresponds to the feature map position one-by-one, while the anchor-based methods needs classify the anchor boxes, which is multiple to the feature map position. Therefore, we choose to verify our approach on the FCOS Tian et al.) (2019) model which the most similar method in object detection to the FCN-based segmentation network.
To make a fair comparison, we adopted MMDetection Chen et al. (211b)) as a unified framework for all the experiments object detection. We use COOC2017 as the evaluation dataset for object detection. COOC2017 contains 80 annotated targets, with 118K training images, 5K validation images and 20K testing images. The standard COO-style evaluation adopted. compare fairly, we use the public MMDetection platform with the provided training setup and learning rate schedule for 2x. The batch size set as 16.
The experimental results in table 10 show that our method can improve the detection performance of small objects.
CONCLUSION
In this paper, firstly we define the C + classification problem. Then we propose a uniform abstract C' + 1 loss for training the C' + 1 classifier. Furthermore design instantialized C' + loss and prove its superiority over popular cross-entropy loss on some CV tasks, including semantic segmentation and object detection. In the future, will explore more instantialized object for the C' + 1 loss and experiment them on more problems, proving its generalizability on common + classification.
Table 10: Experiment results on COCO
Method
AP
AP 50
AP1s
APg
APM
AP1
FCOS(R50) Tian et al. 2019)
38.5
57.7
41.0
21.9
42.8
48.6
FCOS(R50)HourS
39.0
58.5
41.6
23.1
43.0
49.5
FCOS(X101-64x44) Tian et al. 2019
42,6
62.3
45.6
25.7
46.3
54.6
FCOS(X101
1DSSXX101-6xxd)oouu -64x4d)+ours
43.0
62.9
46.1
27.2
46.8
54.5

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Under review as a conference paper at ICLR 2022
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baseline
ours
Figure 2: Feature visualization for foreground classes and the background class in PASCAL
VOC. 0 represents background class, 9 represent the selected 10 Cols. View best in color.
A FEATURE VISUALIZATION
We visualized the features of 10 foreground classes and the background class in PASCAL VOC as displayed in Figure The features are extracted by the DeepLabV3++ours method. We take each pixel of the feature map before classification layer feature vector. By adopting our method, the feature space of every Col became more compact, and further away from background class. That is, there is large enough margin between background class and every Col.
13


Reviews:
[{"review_id": "qZvCHpK16VH", "reviewer": "Reviewer_74g9", "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": "Strengths\n- The introduced C+1 loss is widely applicable to many kinds of tasks that require classification.\n- The experiments are done extensively on multiple tasks to demonstrate the effectiveness of C+1 loss: object detection, semantic segmentation, human parsing.\n\nWeaknesses\n- C+1 loss is a simple and straightforward combination of existing loss functions already explored in previous papers `Wen et al. (2016)`. The background margin loss is almost identical to the conventional margin ranking loss. If you take things that are working really well and combine them in a simple way, it is likely that the combination will work better than any of the individual things.\n- The naming of \"basic discriminability\" is so arbitrary and not supported by anything. Why does it have to be \"basic\"?\n- When the paper mentions it uses center loss for L_compact, it does not cite the any papers about center loss.\n- The proposed properties of C+1 loss are not backed by any theoretical foundations or insights.\n- Except for DeepLabV3 on Pascal VOC, the performance gains are not so significant (most are less than 1%) in the evaluated tasks.\n", "summary_of_the_paper": "This work is motivated by the different nature of the \"other\"/background class in many vision tasks such as object detection and semantic segmentation. It introduces C+1 loss which consists of 3 individual loss terms that focus on the basic discriminability, intra-class compactness, and background margin. Basic discriminability loss is the conventional classification loss for C+1 classes, intra-class compactness uses center loss, and background margin loss is a margin loss acted on the center representation of all C classes and the features of background samples.", "summary_of_the_review": "This paper absolutely feels like a simple repackaging of old methods with a new name (C+1 loss) and there are almost no good enough contributions to make a case for acceptance.", "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": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "S6xHOVCu2QL", "reviewer": "Reviewer_dnQ2", "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:\n+ The employed additional loss functions improved the original methods without these additional loss terms.\n\nWeaknesses:\n- Lack of novelty. The C+1 classification is a straightforward and widely adopted setting, which is the default for segmentation task, while the paper claims that \"We define the C + 1 classification problem ...\"; The method itself is basically adding two additional regularization terms using the center loss, which is employed from existing methods.\n- With the claim being handling C+1 classification problem, methods from the OSR literature should be compared. \n- Though an improvement on overall classification performance is shown, however, no evidence is provided showing that the representation is more compact and the margin has been full filled.\n- No evidence is shown to support the conclusion of equation (3). The radii of the small and large balls should be demonstrated (e.g., by feature visualization).\n- The writing is unsatisfactory, with grammatical errors and typos even in the abstract. For example, CoI is never mentioned before the short form appears; \"In spite of ... use\" ->  \"In spite of ... using\". The main context contains more issues...", "summary_of_the_paper": "This paper aims at dealing with the C+1 classification problem, where C foreground classes and a background class, which could consist of other classes that do not overlap with the C foreground classes. The paper additionally includes center loss for foreground classes and a modified center loss for background class(es), on top of the standard cross-entropy loss. Results are reported on PASCAL VOC, PASCAL Context and LIP datasets.", "summary_of_the_review": "Overall, the paper severely lacks novelty. The method simply adopts a loss function introduced in the existing method and a slightly modified version of it to improve the performance. The claims are not well supported by the experiments. The writing is unsatisfactory.", "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": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "C6VUZSVWgI1", "reviewer": "Reviewer_ZXUD", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "* Significance. The problem addressed by the author is important (the background class is present in most of the vision benchmarks) but few work (to my knowledge) attempted to tackle it in a rigorous way. \n\n* Novelty. The solution proposed by the authors (decompose the loss function into three terms, to enforce some constraints of the last layer feature space) is original, easy to implement and has the potential to inspire others. The properties identified by the authors (which translate into these loss terms) are well discussed and intuitive. \n It might however be surprising  to maintain the basic loss (cross entropy preceded by a softmax) as such (since it probably acts against the compactness and background margin properties enforced by the two other terms). \n\n* Results. The authors report convincing results on four different datasets and two different tasks. The experiments (ablation study) validate the claims of the introduction. While the quantitative analysis consistently show improvement wrt to baseline or the sota, I believe that more challenging experiments could have\nbeen performed for binary classification tasks (eg, human detection/classification, road sign detection), for which the background is often very diverse. \n\n* Clarity. The paper is fluid, a pleasure to read.", "summary_of_the_paper": "The paper addresses the problem of semantic segmentation/classification, in situations where one has C+1 classes at hand, including  C deterministic classes and a background class. The authors identifies the weakness of the classical softmax classification layer in this context, and propose a novel loss, that can better account for the particularity of the non-deterministic background class. Experiments are performed on VOC-2012, Pascal context, LIP and COCO2017. Quantitative results, ablation study and comparison with related work are reported. \n", "summary_of_the_review": "I enjoyed reading the paper because it tackles a well identified problem with clarity and concision.\nThe problem is well defined, the solution is simple and explained with clarity. \nI believe that it belongs to the category of papers that I read once, keep it in memory, and come back to it regularly. \n\n---------------------------------------------------\nUpdates: Thanks for the authors' response, which partially addresses my concerns.  I appreciate the fact that the authors specifically point out in their paper that the background class should be treated in a differentiated way wrt other classes. This observation, in itself, in my view, constitutes the originality of the work --even though the technical solution is surprisingly simple. I encourage the authors to re-submit to an other venue.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "9h01HZfT8O_", "reviewer": "Reviewer_NYF4", "summary": "", "questions": "", "limitations": "", "rating": 1, "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": "The paper tackles an interesting and fair aspect in the field of multiclass classification. However, the neither the idea nor the kind of solution are new. In addition, the experimental results are not promising and show just slightly different results compared to arbitrarily selected baselines. From this points of view, there is neither a novel contribution nor provides the paper thrilling new insights to the tackled problem. In addition, the paper is not written and structured very well. For instance, the mathematical writing and the bibliography need to be seriously checked!", "summary_of_the_paper": "The paper on hands tackles the problem of multi-class classification in the presence of a general  background class. This is illustrated by a specific loss function covering this aspect and demonstrated for a well known, but very old benchmark,", "summary_of_the_review": "To summarize, the paper covers an interesting aspect, however, the overall novelty of the paper is very slim and the quality needs to be seriously improved. Thus, there is the clear recommendation not to accept the paper for ICLR!", "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": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper presents work on classification with a background class.  The reviewers appreciated the important, standard problem the paper considers.  However, concerns were raised regarding presentation, empirical evaluation, clarity, novelty, and signficance of the work.  The reviewers considered the authors' response in their subsequent discussions but felt the concerns were not adequately addressed.  Based on this feedback the paper is not yet ready for publication in ICLR.
Decision: Reject