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+        "type": "text",
+        "text": "A Novel Jamming Attacks Detection Approach Based on Machine Learning for Wireless Communication",
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+        "text": "Youness Arjoune, Fatima Salahdine, Md. Shoriful Islam, Elias Ghribi, Naima Kaabouch",
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+        "text": "School of Electrical Engineering and Computer Science  \nUniversity of North Dakota, Grand Forks, United States",
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+        "text": "Abstract—Jamming attacks target a wireless network creating an unwanted denial of service. 5G is vulnerable to these attacks despite its resilience prompted by the use of millimeter wave bands. Over the last decade, several types of jamming detection techniques have been proposed, including fuzzy logic, game theory, channel surfing, and time series. Most of these techniques are inefficient in detecting smart jammers. Thus, there is a great need for efficient and fast jamming detection techniques with high accuracy. In this paper, we compare the efficiency of several machine learning models in detecting jamming signals. We investigated the types of signal features that identify jamming signals, and generated a large dataset using these parameters. Using this dataset, the machine learning algorithms were trained, evaluated, and tested. These algorithms are random forest, support vector machine, and neural network. The performance of these algorithms was evaluated and compared using the probability of detection, probability of false alarm, probability of miss detection, and accuracy. The simulation results show that jamming detection based random forest algorithm can detect jammers with a high accuracy, high detection probability and low probability of false alarm.",
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+        "text": "Keywords—Jamming Attacks; Machine Learning; Random Fores; Neural Network; Support Vector Machine, 5G.",
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+        "text": "I. INTRODUCTION",
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+        "text": "5G is expected to substitute previous generations of cellular networks in the near future, promising higher throughput and lower latency [1] thereby enabling applications such as \"self-driving\" cars, Internet of Things, E-health services, augmented reality, and smart cities. As a result, billions of wireless devices are expected to be connected to the internet. Like the existing networks, 5G is vulnerable to the cyber security attacks, including jamming [2] and GPS spoofing [3, 4]. It will be enabled by cognitive radio, making these networks open to new attacks, including primary user emulation attacks [5] and spectrum sensing data falsification [6]. Thus, it is important to explore the cybersecurity implications of 5G systems [7, 8]. Jammers create an unwanted denial of service by transmitting radio signals that flood the communication channels aiming at decreasing SNR of legitimate users thereby interrupting their communication. The attacks can be easily launched using software defined radio units such as the GNU radio and universal software radio peripherals, which are cheap and easily accessible. Jammers can target any particular frequency channel with low cost [9]. Jamming attacks can be divided into four main types: constant jammers, random jammers, deceptive",
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+        "text": "jammers, and reactive jammers. Constant jammers launch an attack by transmitting a continuous high-power noise sweeping from a channel to another following a fixed strategy and repeating this process over time. Random jammers operate randomly and do not follow any specific strategy jumping from a channel to another. Deceptive jammers send illegitimate packets through the wireless channels to keep them busy. Reactive jammers continuously monitor the state of the frequency channels and target only the channels used for communication [10]. In addition, jammers can be classified as: regular or smart. Regular jammers cannot sense the ongoing transmitted signals and they all play simultaneously. Smart jammers can learn quickly, sense and determine how the legitimate users are transmitting their signals and they can update their attacks' strategies or adjust the transmission power to more damage the legitimate transmission.",
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+        "text": "A number of jamming detection techniques have been proposed [11-19]. These techniques can be categorized into two main classes: non-machine learning [11-17] and machine learning based [18,19]. Non-machine learning methods perform using some parameters and strategies including threshold, fuzzy logic, game theory, channel surfing, mapping jammed region, and timing channel. In [12], the authors developed a time series model in which they measured the state of the link over series of time and compared it with the past link data to detect the state of the communication link. In [13], the authors developed a threshold based model using the packet loss, throughput, and message invalidation ratio to evaluate the performance of the wireless channels in time-critical applications. In [14], the authors proposed two timing channel based models for jamming detection. One model computes the poor packet delivery ratio based on the received signal strength while the second model computes the throughput. Based on these two parameters, they were able to detect whether the link is attacked or not. In [15], the author proposed a fuzzy logic centralized jamming detection technique based on the received signal strength, packet delivery ratio, bad packet ratio, and channel clear assessment parameters. This model also developed a base station to run the detection algorithm which computes the packet delivery to packet received ratio and the signal to noise ratio from the received data to determine the duration of this attack [16, 17].",
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+        "text": "Machine learning methods are based on classifiers like neural networks and support vector machine with different features to detect jamming attacks. For instance, the authors of [18] proposed an artificial neural network based algorithm for cyclic spectral analysis and wideband spectrum sensing. Based on the signal quality and the modulation, the algorithm distinguishes the jamming signals from the narrowband signals. In [19], the authors designed a machine learning based jamming detection system via support vector machine, adaptive boosting, and expectation maximization algorithms. Noise, busy channel ratio, packet delivery ratio, and maximum inactive time were used to detect jamming attacks. Most of the previously mentioned techniques [11-19] require more resources and ultimately serve only as a stopgap. They can detect the state of the link as down, but often they cannot identify the source of the outage of the service. In addition, these techniques have relatively high probability of false alarm. They need accurate algorithms for training and testing the classification models. Features selection and learning curves are often neglected while they are one of the most important processes in designing detection techniques with machine learning. Thus, there is a great need for efficient and fast detection techniques able to detect jamming attacks more accurately.",
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+        "text": "In this paper, we propose using machine learning to detect the transmission link state between a transmitter and a receiver to verify if it is attacked. Machine learning based models can achieve high detection accuracy if the following steps are carefully considered: selecting appropriate input features, measuring, collecting, building a large dataset, and using accurate methodology to train, validate, and test the model. Features and parameters used to detect jamming attacks are: bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. We investigated techniques of selecting appropriate features and assessing the communication link status. We built a large dataset to train, validate, and test machine learning models. Randomization and normalization of the dataset and cross-validation techniques were performed to avoid the problem of underfitting. The rest of the paper is organized as follows. Section II describes the jamming attack model and its classification features. Section III discusses the simulation results. Finally, a conclusion is given at the end.",
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+        "text": "II. METHODOLOGY",
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+        "text": "The jamming attacks detection in this paper is formulated as a classification problem in which the classifier has to choose between two states: the link is lost because of a jammer or the link is lost because of another reason. The reason behind using machine learning theory to solve this problem is the success of this theory to deal with complex problems within an acceptable time and using reasonable resources. Designing a successful machine learning algorithm requires the selection of appropriate features. In this work, several features were selected to identify the presence of jamming attacks. Using one parameter only is not enough to detect if there is a jamming attack. In addition, it can be complicated to find analytic relations between these parameters and the status of the link. For these reasons, machine learning theory is used to find",
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+        "text": "an empiric relation among these four metrics in order to detect jamming attacks.",
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+        "text": "In this section, we describe the jamming attack model used, the feature selection and the four parameters used to detect jamming attacks. Next, we describe the machine learning techniques used, which are random forest, support vector machine with different kernels, and neural networks.",
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+        "text": "A. Jamming attacks model",
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+        "text": "Jamming attacks target both physical layer and cross-layer of the wireless networks [20]. Under these attacks, the desired communication between a transmitter at location A and a receiver at location B is interrupted by the jamming signals which keep the channel busy. When the jamming signals occupy the channel for a longer period of time, they can create a denial of service [21]. If the desired signal, at location A, is denoted by  $x(t)$  and the received signal, at location B, is denoted by  $y(t)$ , then this received signal at the location B, in the absence of the jammer signal, is given by",
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+        "type": "equation",
+        "text": "\n$$\ny (t) = x (t) + n (t) \\tag {1}\n$$\n",
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+        "text": "where  $x(t)$  is the desired signal,  $y(t)$  is the received signal, and  $n(t)$  is an additive white Gaussian noise present within the path between the transmitter and the receiver. The jammers can counterfeit the desired signals creating a signal denoted  $x_{j}(t)$  to flood the channel. The receive signal at location B, in the presence of the jammer signal, is then given as:",
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+        "type": "equation",
+        "text": "\n$$\ny (t) = x (t) + x _ {j} (t) + n (t) + n _ {1} (t) \\tag {2}\n$$\n",
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+        "text": "where  $x_{j}(t)$  is the jammer signal and  $n_1(t)$  is the noise within the path between the receiver and the jammer's location. Thus, the jamming detection problem can be stated as a hypothesis, in which the receiver has to choose between two states,  $H_{0}$  and  $H_{a}$ .  $H_{0}$  is the state where the received signal is not jammed, while  $H_{a}$  is the state where the received signal is jammed. This problem thus can be expressed as a classification problem, in which the machine learning classifier has to attribute the incoming signal into one of the two classes: the received signal is the desired signal, class A, or the received signal is a jamming signal, class B.",
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+        "text": "B. Feature selection",
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+        "text": "Parameters used to detect jamming attacks are bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. The reason behind using these four parameters is that all communication systems are equipped with network interface cards that possess diagnostic mechanisms which allow the estimation of these metrics [22-26].",
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+        "text": "Bad packet ratio is one of the most important parameters to detect jamming attacks. It refers to the percentage of incorrect packages received [23]. It can be measured at the receiver end and is expressed as",
+        "bbox": [
+            504,
+            736,
+            942,
+            792
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP R = \\frac {\\text {N u m b e r o f e r r o n e o u s r e c e i v e d p a c k a g e s}}{\\text {T o t a l n u m b e r o f r e c e i v e d p a c k a g e s}} \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            586,
+            797,
+            939,
+            825
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The receivers compute this bad packet ratio by verifying the frame check sequence of the incoming packets at the medium access control level. If the channel is under any kind of attack, the bad packet ratio increases while it is very low when the link status is good for transmission. The packet delivery ratio refers to the percentage of correctly delivered packages. It is measured at the transmitter end and expressed as",
+        "bbox": [
+            53,
+            66,
+            491,
+            165
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP D R = \\frac {\\text {N u m b e r o f p a c k a g e d e l e v i r e y c o r r e c t l y}}{\\text {T o t a l n u m b e r o f t r a n s m i t t e d p a c k a g e s}} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            120,
+            170,
+            485,
+            196
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The receiver sends back an acknowledgment packet to the transmitter each time it receives a correct packet. The packet delivery ratio is very high when the link status is good while its value decreases exponentially if the link is under any attack. The clear channel assessment can be used to measure the number of transmitter's attempts to send a package and the channel is found to be occupied. The value of this parameter increases if the channel is under jamming attacks.",
+        "bbox": [
+            53,
+            210,
+            491,
+            324
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The received signal strength, RSS, measures the surrounding power of the receiver. It is high when there is no attack; however, it decreases if the channel is under any kind of attack. RSS at the receiver can be expressed as",
+        "bbox": [
+            53,
+            337,
+            490,
+            393
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR S S = \\frac {P _ {t} * G _ {t} * G _ {r} * \\left(h t ^ {2} * h r ^ {2}\\right)}{d ^ {4}} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            398,
+            486,
+            424
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $P_{t}$  is the transmitter signal power,  $G_{t}$  and  $G_{r}$  is the gain of the antenna at transmitter and receiver respectively,  $ht$  and  $hr$  are the height of antenna at transmitter and receiver, and  $d$  is the distance between transmitter and receiver. Equation (20) is expressed as",
+        "bbox": [
+            53,
+            430,
+            490,
+            500
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR S S = K \\frac {P _ {t}}{d ^ {4}} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            223,
+            500,
+            483,
+            522
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $k$  is a constant such that  $k = G_{t} * G_{r} * (ht^{2} * hr^{2})$ .",
+        "bbox": [
+            53,
+            527,
+            444,
+            544
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "C. Machine Learning Algorithms",
+        "text_level": 1,
+        "bbox": [
+            53,
+            558,
+            285,
+            571
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "A description of each of the machine learning algorithms is given below.",
+        "bbox": [
+            53,
+            575,
+            488,
+            603
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "1) Random forest",
+        "text_level": 1,
+        "bbox": [
+            55,
+            611,
+            181,
+            626
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Random forest is a hierarchical classifier method composed of a large number of decision trees. In this approach, the test data is classified by sorting trees based on their feature values. Each decision tree consists of one node and several branches. The decision node is the feature of the test data to be classified, and the branches represent a value that the node can predict. The reason behind using a large number of trees is to avoid the problem of overfitting. System variance is reduced, which eventually increases the performance of the final model. Basic parameters to random forest classifier can be the total number of trees to be generated and decision tree related parameters like minimum split, and split criteria. Random forest is a predictor that collects the information from each tree  $\\{r_n(x,\\theta_m,D_n,m\\geq 1)\\}$ , where  $\\theta_{1},\\theta_{2}\\ldots \\theta_{m}$  are the",
+        "bbox": [
+            53,
+            638,
+            490,
+            821
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "output of each random trees. These trees are combined to form the aggregated estimation to train the forest using:",
+        "bbox": [
+            504,
+            66,
+            939,
+            95
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {r _ {n}} (X, D _ {n}) = E _ {\\theta} \\left[ r _ {n} (X, \\theta , D _ {n}) \\right] \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            620,
+            102,
+            928,
+            119
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $E_{\\theta}$  is the expectation with respect to the random parameter, conditionally, on  $X$  and the data set  $D_{n}$ . Once the forest is trained, each tree can predict independently to output values using the following equation:",
+        "bbox": [
+            504,
+            125,
+            942,
+            184
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {f} _ {n} ^ {j} (x) = \\frac {1}{N ^ {e} (A _ {n} (x))} \\sum_ {\\substack {Y _ {i} \\in A _ {n} (x) \\\\ I _ {i} = e}} Y _ {i} \\tag{8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            638,
+            190,
+            939,
+            220
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $x$  is the query point of each tree. The forest averages the predictions of each tree to get the final value:",
+        "bbox": [
+            504,
+            226,
+            941,
+            255
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {f} _ {n} ^ {(M)} (x) = \\frac {1}{M} \\sum_ {j = 1} ^ {M} f _ {n} ^ {j} (x) \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            653,
+            261,
+            928,
+            284
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $A_{n}(x)$  is the leaf containing  $x$  and  $N^{e}(A_{n}(x))$  is the number of estimation points it contains. For the binary classification using random forest, random response  $Y$  takes only two values in  $\\{0,1\\}$ . Given  $X$ , random forest has to attribute 0 or 1 to  $Y$ . Random forest is based on Borel classification measurable rule  $m_{n}$ , which is used to estimate the label of  $Y$  from  $x$  and  $D_{n}$  where the classifier  $m_{n}$  is consistent if its conditional probability of error is low which can be expressed as follow",
+        "bbox": [
+            504,
+            289,
+            942,
+            402
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL \\left(m _ {n}\\right) = P \\left[ m _ {n} (X) \\neq Y \\left[ D _ {n} \\right] \\right] \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            407,
+            939,
+            426
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL \\left(m _ {n}\\right) = P \\left[ m _ {n} (X) \\neq Y \\left[ D _ {n} \\right] \\right] \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            622,
+            431,
+            939,
+            450
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $L^{*}$  is the error of the optimal but unknown and  $E$  is the expectations with respect to the random parameter  $\\theta$ . After that Bayes classifier is used to get the output for both 0 and 1.",
+        "bbox": [
+            504,
+            454,
+            941,
+            498
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm ^ {*} (x) = \\left\\{ \\begin{array}{l} 1, \\text {i f} P [ Y = 1, X = x ] > [ Y = 0, X = x <   0 ] \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            503,
+            939,
+            534
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In the classification situation where the dataset is divided into several classes based on the input parameters threshold values, the random forest classifier is obtained via a majority vote among the classification trees, that is",
+        "bbox": [
+            504,
+            542,
+            941,
+            607
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm _ {M, n} \\left(x; \\theta_ {1} \\dots . \\theta_ {m}, D _ {n}\\right) = \\left\\{ \\begin{array}{l l} 1, & i f \\frac {1}{M} \\sum_ {j = 1} ^ {M} m _ {n} \\left(x; \\theta_ {j}, D _ {n}\\right) > 1 / 2 \\\\ 0, & o t h e r w i s e. \\end{array} \\right] \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            609,
+            937,
+            648
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $n$  is the number of trees and  $M$  tends to infinity number of trees. Based on the majority votes, the output is classified as 1 or 0. If more than  $50\\%$  of the total trees vote for 1 then the final prediction of random forest is 1 and if more than  $50\\%$  of the total trees vote for 0 then the final prediction of random forest is considered as 0.",
+        "bbox": [
+            504,
+            656,
+            942,
+            753
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2) Support vector machine",
+        "text_level": 1,
+        "bbox": [
+            506,
+            763,
+            687,
+            777
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Support vector machine creates a hyperplane to separate data into two classes. The choice of the kernel determines the separation boundary between the two classes. Different kernels can be used",
+        "bbox": [
+            504,
+            780,
+            941,
+            823
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "with this model such as linear kernel, radial basis function, quadratic, and cubic kernels. The linear kernel is defined as:",
+        "bbox": [
+            53,
+            66,
+            488,
+            95
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nK (x) = \\mathrm {w} ^ {T} x + b \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            204,
+            101,
+            488,
+            119
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Linear support vector machine is formulated as solving an optimization problem as:",
+        "bbox": [
+            53,
+            123,
+            488,
+            152
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\min  _ {w \\in R ^ {d}} \\| w \\| ^ {2} + C \\sum_ {i} ^ {N} \\max  \\left(0, 1 - y _ {i} K \\left(x _ {i}\\right)\\right) \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            137,
+            157,
+            488,
+            181
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Quadratic and cubic kernels are polynomial kernels with degrees of 2 and 3, respectively. Polynomials kernels are defined as:",
+        "bbox": [
+            53,
+            186,
+            488,
+            215
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nK (x, y) = (x. y + 1) ^ {d} \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            222,
+            486,
+            239
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $x$  and  $y$  are vectors of features and  $d$  is the degree of the polynomial. Radial basis function kernel is defined as:",
+        "bbox": [
+            53,
+            244,
+            488,
+            273
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {K} (\\mathrm {x}, \\mathrm {y}) = \\exp (- \\gamma \\| \\mathrm {x} - \\mathrm {y} \\| ^ {2}) \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
+            279,
+            488,
+            296
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3) Neural Network",
+        "text_level": 1,
+        "bbox": [
+            55,
+            300,
+            191,
+            314
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A neural network is a biological-inspired programming paradigm, which enables a machine to learn from observational data. This network has shown a great ability to learn and solve various problems in different research areas such as image processing, signal processing, and wireless communication. A neural network consists of one input layer, one or several hidden layers, and an output layer. Each layer consists of either one or several neurons. A neuron consists of an activation function and several links connecting them to other neurons in different layers. An initial weight is associated with each link and the neural network in the learning phase try to find the set of optimal weight that minimizes the error between the hypothesis function and the given dataset labels. Each neural network consists of two main concepts, which are the forward propagation and backpropagation. Forward propagation is the simplest type of artificial neural networks where the information moves in only one direction, from input to the output through hidden layers. Input features can be denoted as  $x_{1}, x_{2} \\ldots x_{n}$  and the input layer can be summarized by the following equations:",
+        "bbox": [
+            53,
+            316,
+            488,
+            580
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\na _ {(j)} ^ {(i)} = x _ {i} \\tag {18}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            218,
+            585,
+            483,
+            608
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $a_{(j)}^{(i)}$  is the input layer and  $x_{i}$  is the input features. Input layer is connected with the hidden layers which can be denoted as follows: In the  $i^{\\text{th}}$  hidden layer, we have",
+        "bbox": [
+            53,
+            614,
+            488,
+            662
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nz ^ {(i)} = \\theta^ {(i)} a ^ {(i)} \\tag {19}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            212,
+            667,
+            483,
+            685
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $z^{(i)}$  is the hidden neuron,  $\\theta^{(i)}$  is each layer matrix weight, and  $a^{(i)}$  is the hidden layer for the  $i^{\\text{th}}$  hidden layer. The final layer is the output layer which can be denoted as:",
+        "bbox": [
+            53,
+            691,
+            488,
+            734
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\na ^ {(i)} = g \\left(z ^ {(i)}\\right) \\tag {20}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            236,
+            741,
+            486,
+            758
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Neural network cost function is used to find out the optimal output based on different number of layers and neurons. It is expressed by:",
+        "bbox": [
+            53,
+            770,
+            488,
+            814
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nJ (\\theta) = - \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\sum_ {k = 1} ^ {k} \\left[ y _ {k} ^ {(i)} \\log \\left(\\left(h _ {\\theta} (x ^ {(i)})\\right) _ {k}\\right) + \\left(1 - \\right. \\right.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            532,
+            66,
+            880,
+            88
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left. y _ {k} ^ {(i)}\\right) \\log \\left(1 - \\left(h _ {\\theta} \\left(x ^ {(i)}\\right)\\right) _ {k}\\right) ] + \\frac {\\lambda}{2 m} \\sum_ {l = 1} ^ {L - 1} \\sum_ {i = 1} ^ {s _ {l}} \\sum_ {j = 1} ^ {s _ {l + 1}} \\left(\\theta_ {j, i} ^ {(l)}\\right) ^ {2} \\tag {21}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            89,
+            939,
+            109
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $J(\\theta)$  is the cost function,  $h_\\theta$  is the hypothesis function, and  $\\lambda$  is the regularization factor. Regularization cost function is used to reduce the effect of over bias and under bias by regularization factor  $(\\lambda)$",
+        "bbox": [
+            504,
+            114,
+            941,
+            172
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nJ (\\theta) = \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\sum_ {k = 1} ^ {k} \\left[ - y _ {k} ^ {(i)} \\log \\left(\\left(h _ {\\theta} (x ^ {(i)})\\right) _ {k}\\right) - (1 - \\right.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            526,
+            172,
+            877,
+            193
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left. y _ {k} ^ {(i)}\\right) \\log \\left(1 - \\left(h _ {\\theta} (x ^ {(i)})) _ {k}\\right) \\right] + \\frac {\\lambda}{2 m} \\left[ \\sum_ {l = 1} ^ {L - 1} \\sum_ {i = 1} ^ {s _ {l}} \\left(\\theta_ {j, k} ^ {(1)}\\right) ^ {2} + \\right.\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            529,
+            194,
+            890,
+            214
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left. \\sum_ {j = 1} ^ {L} \\sum_ {k = 1} ^ {s l} \\left(\\theta_ {j, k} ^ {(2)}\\right) ^ {2} \\right] \\tag {22}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            529,
+            214,
+            937,
+            234
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where the regularization factor  $\\lambda$  is used to reduce the effect of the over bias and under bias. Neural networks use different optimization techniques such as Adam, gradient descent, and stochastic gradient descent to minimize the cost function. At the output layer, neural network uses a sigmoid function to attribute the new dataset into one of the two classes, in the case of binary classification, by calculating the hypothesis using the weights determined in the leaning parts. If this hypothesis is greater than 0.5, then it concludes that \"y=1\"; otherwise \"y=0\".",
+        "bbox": [
+            504,
+            239,
+            941,
+            367
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "III. RESULTS AND DISCUSSION",
+        "text_level": 1,
+        "bbox": [
+            617,
+            376,
+            828,
+            388
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To validate the machine learning models, four different parameters were used as features to detect jamming attacks. A real environment simulation was performed to collect measurements of these parameters in the two scenarios: link is under attack and link under no attack. To train and test the models, the dataset was divided into  $N$  folds using the cross-validation technique.  $N$ -fold cross-validation was used to divide the dataset into  $N$  number of subsamples with equal size. In this work, machines learning algorithms were trained with a different number of fold sizes such as 2, 5, 10, and 20 to evaluate the performance of these machines for the given dataset. For instance, if the number of folds is 10, then the total data is divided into 10 folds and randomly the algorithm selects 9 folds to train the model and 1 fold is used to test the machine. This process is repeated until the dataset is tested on the 10 folds. To evaluate the performance of the classifiers, several metrics were used, namely probabilities of detection, false alarm, miss detection, and accuracy.  $P_{d}$  refers to the likelihood that the detection technique attributes signals coming from a jammer to the class of jamming signals meaning that it correctly detects that the link is under a jamming attack",
+        "bbox": [
+            504,
+            393,
+            941,
+            672
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {d} = \\frac {\\text {N u m b e r o f t r u l y d e t e c t e d a t t a c k s}}{\\text {T o t a l n u m b e r o f a t t a c k s}} \\tag {23}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            580,
+            676,
+            937,
+            702
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$P_{md}$  is the percentage of attacks that the algorithm miss detected. It is given by:",
+        "bbox": [
+            506,
+            708,
+            939,
+            739
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {m} = \\frac {\\text {N u m b e r o f m i s s d e t e c t e d a t t a c k s}}{\\text {T o t a l n u m b e r o f a t t a c k s}} \\tag {24}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            589,
+            747,
+            937,
+            771
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$P_{fa}$  is the percentage of non-attacks that the algorithm detected as attacks",
+        "bbox": [
+            504,
+            780,
+            939,
+            810
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP _ {f a} = \\frac {\\text {N u m b e r o f n o n - a t t a c k s d e t e c t e d a s a n a t t a c k}}{\\text {T o t a l n u m b e r o f n o n - a t t a c k s}} \\tag {25}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            555,
+            820,
+            939,
+            845
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Accuracy gives the total number of attacks and non-attacks that are detected accurately compared to the total number of trials. It is given by:",
+        "bbox": [
+            53,
+            66,
+            491,
+            109
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA c c u r a c y = \\frac {\\text {T o t a l n u m b e r o f c o r r e c t l y d e t e c t e d a t t a c k a n d n o n - a t t a c k t r i a l s}}{\\text {T o t a l n u m b e r o f t r i a l s}} \\tag {26}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            53,
+            114,
+            488,
+            136
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conducted several experiments and examples of results are given from Fig. 1 to Fig. 4. Fig. 1 shows the accuracy of the classification using random forest versus the number of estimators for a different number of folds in the cross-validation. It can be seen from this figure that for all values of K-folds, 5, 10, and 20, the accuracy of the classification is exponentially increasing as a function of the number of estimators, for numbers of estimators less than 60. However, this accuracy remains slightly constant for numbers higher than 60 and in some cases, it drops. This figure also shows the impact of the number of folds on the accuracy. One can see that with 20 folds, the accuracy is higher than the one with 10 and 5 folds.",
+        "bbox": [
+            53,
+            141,
+            490,
+            308
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/14b0f21385e40bf7c4a16cc0a4e2b0ed2be7d2013645eedf5d894805978768f2.jpg",
+        "image_caption": [
+            "Fig. 1. Accuracy versus the number of estimators for random forest using different number of k-folds cross validation  $\\mathrm{CV} = 5$ , 10, and 20."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            148,
+            315,
+            395,
+            459
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To select the best support vector model, we investigated how the accuracy varies for different kernels and regularization parameter  $C$  in order to select the best combination for this given dataset. Fig. 2 shows the accuracy of the classification function of the regularization factor \"C\" for linear, quadratic, cubic, radial basis function, and sigmoid kernels. From this figure, it can be seen that the impact of the regularization factor \"C\" does not change the accuracy very much. However, as one can see the choice of the kernel impacts the accuracy. The accuracy is high for radial basis function kernel, followed by linear, cubic, sigmoid, and then quadratic kernels. Support vector machine with radial basis function and regularization factor equal to 3 has the highest accuracy of  $94\\%$ .",
+        "bbox": [
+            53,
+            496,
+            490,
+            675
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/536e47eef3fd4534e0041eccfea26036bdfd3e881aac85331f05e2a8a7a0027e.jpg",
+        "image_caption": [
+            "Fig. 2. Accuracy Vs regularization factor for support vector machine."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            169,
+            676,
+            401,
+            830
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fig. 3 shows the accuracy of the classification function of the number of hidden neurons in one hidden layer of neural network for a different number of k-folds cross-validation. One can observe that the impact of the number of hidden neurons and the number of cross-validation technique is not significant as the accuracy of the classification remains around  $94\\%$ , but the highest one is achieved with 1 neuron with 5-folds cross-validation and with 100 neurons with 10-folds cross-validation.",
+        "bbox": [
+            504,
+            66,
+            944,
+            178
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/b124737788a16547cc0998a0f374719c287b79944bc5f9c37b8d9633102dd2d3.jpg",
+        "image_caption": [
+            "Fig. 3. Accuracy of neural network Vs number of neurons in one hidden layer."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            583,
+            186,
+            864,
+            369
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fig. 4 shows  $Pd$  Vs  $Pfa$  using linear, polynomial with degree 2, radial basis function SVM, neural network with two hidden layers of 2 neurons each, and random forest with 100 estimators. One can see that  $P_{d}$  increases as  $P_{fa}$  increases. In addition, it can be observed that random forest has the higher ROC followed by radial basis function SVM, cubic SVM, linear SVM, and then the neural network which means that random forest outperforms other algorithms regarding the ROC curve.",
+        "bbox": [
+            504,
+            392,
+            941,
+            503
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/57c833d3be351bb3dd894d81effd5ede680b133d54b2fd3db1639e217c4c3832.jpg",
+        "image_caption": [
+            "Fig. 4. Probability of detection Vs the probability of false alarm."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            599,
+            506,
+            846,
+            669
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table I compares the performance of the jamming detection techniques based on machine learning classifiers for the four evaluation metrics. Random forest achieves the highest probability of detection with  $97.5\\%$  followed by cubic SVM with  $97.1\\%$  neural network with  $96.4\\%$  linear SVM with  $86.9\\%$  RBF SVM with  $86.2\\%$  sigmoid SVM with  $73.8\\%$  and quadratic SVM with  $72\\%$ . It can also be seen that random forest has the lowest probabilities of false alarm of  $5.6\\%$  followed by neural network with  $11.1\\%$  RBF SVM with  $27.2\\%$  linear SVM with  $27.25\\%$  sigmoid SVM with  $40.1\\%$  cubic SVM with  $54\\%$  and quadratic SVM with  $65.2\\%$ . This table shows also that random forest has the",
+        "bbox": [
+            504,
+            693,
+            944,
+            845
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "lowest miss detection with  $2.5\\%$ , followed by cubic SVM with  $2.9\\%$ , neural network with  $3.6\\%$ , linear SVM with  $13.1\\%$ , RBF SVM with  $13.8\\%$ , sigmoid SVM with  $26.22\\%$ , and quadratic SVM with  $28\\%$ . In terms of accuracy, random forest has an accuracy as high as  $96.6\\%$  followed by neural network with  $94.4\\%$ , RBF SVM with  $84.7\\%$ , linear SVM with  $83\\%$ , sigmoid SVM with  $82.6\\%$ , cubic SVM  $70.1\\%$ , quadratic SVM with  $62\\%$ .",
+        "bbox": [
+            53,
+            66,
+            488,
+            165
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/836df78541c48006600e02bfbdaf4abb8988953fc07d6ab8e9df07d603c3faa9.jpg",
+        "table_caption": [
+            "TABLE I. PERFORMANCE COMPARISON"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Classification technique</td><td>Pd(%)</td><td>Pfa(%)</td><td>Pmd(%)</td><td>Accuracy (%)</td></tr><tr><td>Linear SVM</td><td>86.9</td><td>27.25</td><td>13.1</td><td>83</td></tr><tr><td>Quadratic SVM</td><td>72</td><td>65.2</td><td>28</td><td>62</td></tr><tr><td>Cubic SVM</td><td>97.1</td><td>54</td><td>2.9</td><td>70.1</td></tr><tr><td>RBF SVM</td><td>86.2</td><td>27.2</td><td>13.8</td><td>84.7</td></tr><tr><td>Sigmoid SVM</td><td>73.8</td><td>40.1</td><td>26.22</td><td>82.6</td></tr><tr><td>Neural network</td><td>96.4</td><td>11.1</td><td>3.6</td><td>94.4</td></tr><tr><td>Random Forest estimators = 100</td><td>97.5</td><td>5.6</td><td>2.5</td><td>96.6</td></tr></table>",
+        "bbox": [
+            57,
+            194,
+            486,
+            390
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "CONCLUSION",
+        "text_level": 1,
+        "bbox": [
+            225,
+            398,
+            318,
+            412
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5G technology is designed to be resilient to jamming attacks by using millimeter wave band. However, it is also designed to use frequencies below 6 GHz, which are easy to target by jammers. Smart jamming detection techniques are required to prevent these attacks. In this paper, we reviewed the existing jamming detection techniques. We investigated and compared the performance of several machine learning models to detect jamming attacks. Feature extraction and feature selection were performed and a large dataset was constructed to train, validate, and test random forest, support vector machine, and neural network algorithms. We used a cross-validation technique and provided learning curves to evaluate the performance of these models based on a number of metrics. The results show that random forest based technique detects jamming attacks with a very high accuracy and a low cost.  $P_{d}$  of random forest based detection is as high as  $97.5\\%$  whereas  $P_{fa}$  of the neural network and cubic support vector machine is around  $96.4\\%$  and  $97.1\\%$ .  $P_{md}$  and  $P_{fa}$  of random forest are also very low compared to neural network and cubic support vector machine which are  $5.6\\%$  and  $2.5\\%$ . High  $P_{d}$  and low  $P_{fa}$  make this proposed model suitable for jamming attack detection. These trained machines are able to process a huge number of data within a very short time, which helps increase efficiency and reduce the processing time. Future work includes investigating the efficiency of deep learning in detecting all types of jamming attacks.",
+        "bbox": [
+            53,
+            417,
+            490,
+            751
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES",
+        "text_level": 1,
+        "bbox": [
+            679,
+            68,
+            767,
+            80
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Y. Wu, A. Khisti, C. Xiao, G. Caire, K. Wong, X. Gao, “A survey of physical layer security technique for 5G wireless networks and challenges ahead,” IEEE J. Selected Areas Commun., vol. 36, no. 4, pp. 679-695, 2018.",
+            "[2] D. Karas, G. Karagiannidis, R. Schober, \"Neural network based PHY-layer key exchange for wireless communication,\" IEEE Int. Symposium Personal, Indoor and Mobile Radio Commun., pp. 1233-1238, 2011.",
+            "[3] P. Sinha, V. Jha, A. Rai, B. Bhushan, \"Security vulnerabilities, attacks and countermeasures in wireless sensor networks at various layers of OSI reference model: A Survey,\" Int. Conf. Signal Proc. Commun., pp. 288-293, 2017.",
+            "[4] J. Heo, J. Kim, J. Paek, S. Bahn, “Mitigating stealthy jamming attacks in low-power and lossy wireless networks,” J. Commun. Netw., pp. 219-230, 2018.",
+            "[5] M. Bouabdellah, E. Ghribi, and N. Kaabouch. \"RSS-Based Localization with Maximum Likelihood Estimation for PUE Attacker Detection in Cognitive Radio Networks.\" IEEE International Conference on Electro Information Technology (EIT), pp. 1-6, 2019.",
+            "[6] I. Ngomane, M. Velempini, S. Dlamini, \"The detection of the spectrum sensing data falsification attack in cognitive radio ad hoc networks,\" Info. Commun. Techn. Society Conf., pp. 1-5, 2018.",
+            "[7] F. Salahdine, N. Kaabouch, \"Social Engineering Attacks: A Survey,\" Future Internet J., Vol. 11, No. 89, pp. 1-17, 2019.",
+            "[8] D. Fang, Y. Qian, R. Hu, \"Security for 5G mobile wireless networks,\" IEEE Access, vol-6, pp. 4850-4874, 2017.",
+            "[9] W. Alhakami, A. Mansour, G. Safdar, \"Spectrum sharing security and attacks in CRNs: A review,\" Int. J. Advanced Comput. Sci., vol. 5, no. 1, pp. 76-87, 2014.",
+            "[10] R. Pietro, G. Oligeri, “Jamming mitigation in cognitive radio networks,” IEEE Netw., vol. 27, no. 3, pp. 10–15, 2013.",
+            "[11] Z. Lu, W. Wang, C. Wang, \"Modeling, evaluation, and detection of jamming attacks in time-critical wireless applications,\" IEEE Trans. Mobile Comput., vol.13, no.8, pp-1746-1759, 2014.",
+            "[12] H. Yang, M. Shi, Y. Xia, \"Security research on wireless networked control systems subject to jamming attacks,\" IEEE Trans. Cybernetics, , pp-1-10, 2018.",
+            "[13] M. Cheng, Y. Ling, W. Wu, \"Time series analysis for jamming attack detection in wireless networks,\" IEEE global Commun. Conf., pp. 1-7, 2017.",
+            "[14] H. Reyes, N. Kaabouch, \"Jamming and lost link detection in wireless networks with fuzzy logic,\" Int. J. Sentic Eng. research, vol. 4, pp. 1-7, 2013.",
+            "[15] S. Khattab, D. Mosse, R. Melhem, \"Modeling of the channel-hopping anti-jamming defense in multi-radio wireless networks,\" Int. Conf. mobile ubiquitous syst., pp. 1-10, 2008.",
+            "[16] Y. Lin, M. Li, \"Distributed detection of jamming and defense in wireless sensor networks,\" Ann. Conf. Info. science and systems, pp. 829-834, 2009.",
+            "[17] T. Nawaz, et all. \"Jammer detection algorithm for wideband radios using spectral correlation and neural networks,\" Int. Wireless Commun. Mobile Comput. Conf., pp. 112-118, 2017.",
+            "[18] O. Punal, I. Aktas, C. J. Schnelke, G. Abidin, K. Wehrle, and J. Gross, \"Machine learning-based jamming detection for IEEE 802.11: design and experimental evaluation,\" IEEE Int. Symposium Wireless, Mobile and Multimedia Networks, pp. 1-10, 2014.",
+            "[19] K. Grover; A. Lim; Q. Yang, “Jamming and anti-jamming techniques in wireless networks: A survey,” Int. J. Ad Hoc Ubiquitous., pp. 197-215, 2014.",
+            "[20] N. Sufyan, N. Saqib, M. Zia, “Detection of jamming attacks in 802.11b wireless networks,” J. Wireless Commun. Netw., pp. 1-18, 2013.",
+            "[21] A. Vakili, J. Gregoire, \"Real-time packet loss probability estimates from IP traffic parameters,\" Int. J. Advance Netw. services, vol. 5, no. 1, pp. 34-42, 2012.",
+            "[22] R. Hernandez, C. Cardenas, D. Munoz, \"Epidemic routing in vehicular delay-tolerant networks: the use of heterogeneous conditions to increase packet delivery ratio,\" IEEE Int. Smart Cities Conf., pp. 1-7, 2015.",
+            "[23] K. Son, S. Hong, S. Moon, T. Chang, H. Cho, \"Segmentized clear channel assessment for IEEE 802.15.4 networks,\" IEEE Sensors J., vol. 16, pp. 1-16, 2016."
+        ],
+        "bbox": [
+            506,
+            85,
+            941,
+            766
+        ],
+        "page_idx": 5
+    }
+]

2003.07xxx/2003.07308/bc01c5f7-f295-4135-8673-99f17db5b9f1_model.json

@@ -0,0 +1,1422 @@
+[
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.073,
+                0.069,
+                0.928,
+                0.145
+            ],
+            "angle": 0,
+            "content": "A Novel Jamming Attacks Detection Approach Based on Machine Learning for Wireless Communication"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.181,
+                0.162,
+                0.82,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Youness Arjoune, Fatima Salahdine, Md. Shoriful Islam, Elias Ghribi, Naima Kaabouch"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.315,
+                0.195,
+                0.684,
+                0.224
+            ],
+            "angle": 0,
+            "content": "School of Electrical Engineering and Computer Science  \nUniversity of North Dakota, Grand Forks, United States"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.058,
+                0.253,
+                0.488,
+                0.501
+            ],
+            "angle": 0,
+            "content": "Abstract—Jamming attacks target a wireless network creating an unwanted denial of service. 5G is vulnerable to these attacks despite its resilience prompted by the use of millimeter wave bands. Over the last decade, several types of jamming detection techniques have been proposed, including fuzzy logic, game theory, channel surfing, and time series. Most of these techniques are inefficient in detecting smart jammers. Thus, there is a great need for efficient and fast jamming detection techniques with high accuracy. In this paper, we compare the efficiency of several machine learning models in detecting jamming signals. We investigated the types of signal features that identify jamming signals, and generated a large dataset using these parameters. Using this dataset, the machine learning algorithms were trained, evaluated, and tested. These algorithms are random forest, support vector machine, and neural network. The performance of these algorithms was evaluated and compared using the probability of detection, probability of false alarm, probability of miss detection, and accuracy. The simulation results show that jamming detection based random forest algorithm can detect jammers with a high accuracy, high detection probability and low probability of false alarm."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.058,
+                0.514,
+                0.488,
+                0.541
+            ],
+            "angle": 0,
+            "content": "Keywords—Jamming Attacks; Machine Learning; Random Fores; Neural Network; Support Vector Machine, 5G."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.209,
+                0.551,
+                0.336,
+                0.564
+            ],
+            "angle": 0,
+            "content": "I. INTRODUCTION"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.058,
+                0.57,
+                0.488,
+                0.846
+            ],
+            "angle": 0,
+            "content": "5G is expected to substitute previous generations of cellular networks in the near future, promising higher throughput and lower latency [1] thereby enabling applications such as \"self-driving\" cars, Internet of Things, E-health services, augmented reality, and smart cities. As a result, billions of wireless devices are expected to be connected to the internet. Like the existing networks, 5G is vulnerable to the cyber security attacks, including jamming [2] and GPS spoofing [3, 4]. It will be enabled by cognitive radio, making these networks open to new attacks, including primary user emulation attacks [5] and spectrum sensing data falsification [6]. Thus, it is important to explore the cybersecurity implications of 5G systems [7, 8]. Jammers create an unwanted denial of service by transmitting radio signals that flood the communication channels aiming at decreasing SNR of legitimate users thereby interrupting their communication. The attacks can be easily launched using software defined radio units such as the GNU radio and universal software radio peripherals, which are cheap and easily accessible. Jammers can target any particular frequency channel with low cost [9]. Jamming attacks can be divided into four main types: constant jammers, random jammers, deceptive"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.253,
+                0.94,
+                0.46
+            ],
+            "angle": 0,
+            "content": "jammers, and reactive jammers. Constant jammers launch an attack by transmitting a continuous high-power noise sweeping from a channel to another following a fixed strategy and repeating this process over time. Random jammers operate randomly and do not follow any specific strategy jumping from a channel to another. Deceptive jammers send illegitimate packets through the wireless channels to keep them busy. Reactive jammers continuously monitor the state of the frequency channels and target only the channels used for communication [10]. In addition, jammers can be classified as: regular or smart. Regular jammers cannot sense the ongoing transmitted signals and they all play simultaneously. Smart jammers can learn quickly, sense and determine how the legitimate users are transmitting their signals and they can update their attacks' strategies or adjust the transmission power to more damage the legitimate transmission."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.51,
+                0.468,
+                0.94,
+                0.813
+            ],
+            "angle": 0,
+            "content": "A number of jamming detection techniques have been proposed [11-19]. These techniques can be categorized into two main classes: non-machine learning [11-17] and machine learning based [18,19]. Non-machine learning methods perform using some parameters and strategies including threshold, fuzzy logic, game theory, channel surfing, mapping jammed region, and timing channel. In [12], the authors developed a time series model in which they measured the state of the link over series of time and compared it with the past link data to detect the state of the communication link. In [13], the authors developed a threshold based model using the packet loss, throughput, and message invalidation ratio to evaluate the performance of the wireless channels in time-critical applications. In [14], the authors proposed two timing channel based models for jamming detection. One model computes the poor packet delivery ratio based on the received signal strength while the second model computes the throughput. Based on these two parameters, they were able to detect whether the link is attacked or not. In [15], the author proposed a fuzzy logic centralized jamming detection technique based on the received signal strength, packet delivery ratio, bad packet ratio, and channel clear assessment parameters. This model also developed a base station to run the detection algorithm which computes the packet delivery to packet received ratio and the signal to noise ratio from the received data to determine the duration of this attack [16, 17]."
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.067,
+                0.493,
+                0.375
+            ],
+            "angle": 0,
+            "content": "Machine learning methods are based on classifiers like neural networks and support vector machine with different features to detect jamming attacks. For instance, the authors of [18] proposed an artificial neural network based algorithm for cyclic spectral analysis and wideband spectrum sensing. Based on the signal quality and the modulation, the algorithm distinguishes the jamming signals from the narrowband signals. In [19], the authors designed a machine learning based jamming detection system via support vector machine, adaptive boosting, and expectation maximization algorithms. Noise, busy channel ratio, packet delivery ratio, and maximum inactive time were used to detect jamming attacks. Most of the previously mentioned techniques [11-19] require more resources and ultimately serve only as a stopgap. They can detect the state of the link as down, but often they cannot identify the source of the outage of the service. In addition, these techniques have relatively high probability of false alarm. They need accurate algorithms for training and testing the classification models. Features selection and learning curves are often neglected while they are one of the most important processes in designing detection techniques with machine learning. Thus, there is a great need for efficient and fast detection techniques able to detect jamming attacks more accurately."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.379,
+                0.492,
+                0.629
+            ],
+            "angle": 0,
+            "content": "In this paper, we propose using machine learning to detect the transmission link state between a transmitter and a receiver to verify if it is attacked. Machine learning based models can achieve high detection accuracy if the following steps are carefully considered: selecting appropriate input features, measuring, collecting, building a large dataset, and using accurate methodology to train, validate, and test the model. Features and parameters used to detect jamming attacks are: bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. We investigated techniques of selecting appropriate features and assessing the communication link status. We built a large dataset to train, validate, and test machine learning models. Randomization and normalization of the dataset and cross-validation techniques were performed to avoid the problem of underfitting. The rest of the paper is organized as follows. Section II describes the jamming attack model and its classification features. Section III discusses the simulation results. Finally, a conclusion is given at the end."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.204,
+                0.638,
+                0.342,
+                0.652
+            ],
+            "angle": 0,
+            "content": "II. METHODOLOGY"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.657,
+                0.493,
+                0.839
+            ],
+            "angle": 0,
+            "content": "The jamming attacks detection in this paper is formulated as a classification problem in which the classifier has to choose between two states: the link is lost because of a jammer or the link is lost because of another reason. The reason behind using machine learning theory to solve this problem is the success of this theory to deal with complex problems within an acceptable time and using reasonable resources. Designing a successful machine learning algorithm requires the selection of appropriate features. In this work, several features were selected to identify the presence of jamming attacks. Using one parameter only is not enough to detect if there is a jamming attack. In addition, it can be complicated to find analytic relations between these parameters and the status of the link. For these reasons, machine learning theory is used to find"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.068,
+                0.943,
+                0.097
+            ],
+            "angle": 0,
+            "content": "an empiric relation among these four metrics in order to detect jamming attacks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.102,
+                0.943,
+                0.173
+            ],
+            "angle": 0,
+            "content": "In this section, we describe the jamming attack model used, the feature selection and the four parameters used to detect jamming attacks. Next, we describe the machine learning techniques used, which are random forest, support vector machine with different kernels, and neural networks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.507,
+                0.18,
+                0.695,
+                0.195
+            ],
+            "angle": 0,
+            "content": "A. Jamming attacks model"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.197,
+                0.944,
+                0.337
+            ],
+            "angle": 0,
+            "content": "Jamming attacks target both physical layer and cross-layer of the wireless networks [20]. Under these attacks, the desired communication between a transmitter at location A and a receiver at location B is interrupted by the jamming signals which keep the channel busy. When the jamming signals occupy the channel for a longer period of time, they can create a denial of service [21]. If the desired signal, at location A, is denoted by \\( x(t) \\) and the received signal, at location B, is denoted by \\( y(t) \\), then this received signal at the location B, in the absence of the jammer signal, is given by"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.671,
+                0.344,
+                0.941,
+                0.361
+            ],
+            "angle": 0,
+            "content": "\\[\ny (t) = x (t) + n (t) \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.365,
+                0.943,
+                0.452
+            ],
+            "angle": 0,
+            "content": "where \\( x(t) \\) is the desired signal, \\( y(t) \\) is the received signal, and \\( n(t) \\) is an additive white Gaussian noise present within the path between the transmitter and the receiver. The jammers can counterfeit the desired signals creating a signal denoted \\( x_{j}(t) \\) to flood the channel. The receive signal at location B, in the presence of the jammer signal, is then given as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.593,
+                0.457,
+                0.937,
+                0.475
+            ],
+            "angle": 0,
+            "content": "\\[\ny (t) = x (t) + x _ {j} (t) + n (t) + n _ {1} (t) \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.481,
+                0.944,
+                0.624
+            ],
+            "angle": 0,
+            "content": "where \\( x_{j}(t) \\) is the jammer signal and \\( n_1(t) \\) is the noise within the path between the receiver and the jammer's location. Thus, the jamming detection problem can be stated as a hypothesis, in which the receiver has to choose between two states, \\( H_{0} \\) and \\( H_{a} \\). \\( H_{0} \\) is the state where the received signal is not jammed, while \\( H_{a} \\) is the state where the received signal is jammed. This problem thus can be expressed as a classification problem, in which the machine learning classifier has to attribute the incoming signal into one of the two classes: the received signal is the desired signal, class A, or the received signal is a jamming signal, class B."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.507,
+                0.63,
+                0.654,
+                0.643
+            ],
+            "angle": 0,
+            "content": "B. Feature selection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.647,
+                0.943,
+                0.732
+            ],
+            "angle": 0,
+            "content": "Parameters used to detect jamming attacks are bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. The reason behind using these four parameters is that all communication systems are equipped with network interface cards that possess diagnostic mechanisms which allow the estimation of these metrics [22-26]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.737,
+                0.943,
+                0.794
+            ],
+            "angle": 0,
+            "content": "Bad packet ratio is one of the most important parameters to detect jamming attacks. It refers to the percentage of incorrect packages received [23]. It can be measured at the receiver end and is expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.588,
+                0.799,
+                0.941,
+                0.826
+            ],
+            "angle": 0,
+            "content": "\\[\nP R = \\frac {\\text {N u m b e r o f e r r o n e o u s r e c e i v e d p a c k a g e s}}{\\text {T o t a l n u m b e r o f r e c e i v e d p a c k a g e s}} \\tag {3}\n\\]"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.068,
+                0.493,
+                0.166
+            ],
+            "angle": 0,
+            "content": "The receivers compute this bad packet ratio by verifying the frame check sequence of the incoming packets at the medium access control level. If the channel is under any kind of attack, the bad packet ratio increases while it is very low when the link status is good for transmission. The packet delivery ratio refers to the percentage of correctly delivered packages. It is measured at the transmitter end and expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.121,
+                0.171,
+                0.486,
+                0.198
+            ],
+            "angle": 0,
+            "content": "\\[\nP D R = \\frac {\\text {N u m b e r o f p a c k a g e d e l e v i r e y c o r r e c t l y}}{\\text {T o t a l n u m b e r o f t r a n s m i t t e d p a c k a g e s}} \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.212,
+                0.492,
+                0.325
+            ],
+            "angle": 0,
+            "content": "The receiver sends back an acknowledgment packet to the transmitter each time it receives a correct packet. The packet delivery ratio is very high when the link status is good while its value decreases exponentially if the link is under any attack. The clear channel assessment can be used to measure the number of transmitter's attempts to send a package and the channel is found to be occupied. The value of this parameter increases if the channel is under jamming attacks."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.338,
+                0.491,
+                0.395
+            ],
+            "angle": 0,
+            "content": "The received signal strength, RSS, measures the surrounding power of the receiver. It is high when there is no attack; however, it decreases if the channel is under any kind of attack. RSS at the receiver can be expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.4,
+                0.488,
+                0.425
+            ],
+            "angle": 0,
+            "content": "\\[\nR S S = \\frac {P _ {t} * G _ {t} * G _ {r} * \\left(h t ^ {2} * h r ^ {2}\\right)}{d ^ {4}} \\tag {5}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.431,
+                0.491,
+                0.501
+            ],
+            "angle": 0,
+            "content": "where \\( P_{t} \\) is the transmitter signal power, \\( G_{t} \\) and \\( G_{r} \\) is the gain of the antenna at transmitter and receiver respectively, \\( ht \\) and \\( hr \\) are the height of antenna at transmitter and receiver, and \\( d \\) is the distance between transmitter and receiver. Equation (20) is expressed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.225,
+                0.501,
+                0.485,
+                0.523
+            ],
+            "angle": 0,
+            "content": "\\[\nR S S = K \\frac {P _ {t}}{d ^ {4}} \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.528,
+                0.445,
+                0.545
+            ],
+            "angle": 0,
+            "content": "where \\( k \\) is a constant such that \\( k = G_{t} * G_{r} * (ht^{2} * hr^{2}) \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.055,
+                0.559,
+                0.287,
+                0.573
+            ],
+            "angle": 0,
+            "content": "C. Machine Learning Algorithms"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.576,
+                0.489,
+                0.604
+            ],
+            "angle": 0,
+            "content": "A description of each of the machine learning algorithms is given below."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.057,
+                0.612,
+                0.182,
+                0.627
+            ],
+            "angle": 0,
+            "content": "1) Random forest"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.64,
+                0.491,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Random forest is a hierarchical classifier method composed of a large number of decision trees. In this approach, the test data is classified by sorting trees based on their feature values. Each decision tree consists of one node and several branches. The decision node is the feature of the test data to be classified, and the branches represent a value that the node can predict. The reason behind using a large number of trees is to avoid the problem of overfitting. System variance is reduced, which eventually increases the performance of the final model. Basic parameters to random forest classifier can be the total number of trees to be generated and decision tree related parameters like minimum split, and split criteria. Random forest is a predictor that collects the information from each tree \\(\\{r_n(x,\\theta_m,D_n,m\\geq 1)\\}\\), where \\(\\theta_{1},\\theta_{2}\\ldots \\theta_{m}\\) are the"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.068,
+                0.941,
+                0.096
+            ],
+            "angle": 0,
+            "content": "output of each random trees. These trees are combined to form the aggregated estimation to train the forest using:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.622,
+                0.103,
+                0.929,
+                0.12
+            ],
+            "angle": 0,
+            "content": "\\[\n\\bar {r _ {n}} (X, D _ {n}) = E _ {\\theta} \\left[ r _ {n} (X, \\theta , D _ {n}) \\right] \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.125,
+                0.943,
+                0.185
+            ],
+            "angle": 0,
+            "content": "where \\( E_{\\theta} \\) is the expectation with respect to the random parameter, conditionally, on \\( X \\) and the data set \\( D_{n} \\). Once the forest is trained, each tree can predict independently to output values using the following equation:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.639,
+                0.191,
+                0.941,
+                0.221
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {f} _ {n} ^ {j} (x) = \\frac {1}{N ^ {e} (A _ {n} (x))} \\sum_ {\\substack {Y _ {i} \\in A _ {n} (x) \\\\ I _ {i} = e}} Y _ {i} \\tag{8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.227,
+                0.942,
+                0.256
+            ],
+            "angle": 0,
+            "content": "where \\( x \\) is the query point of each tree. The forest averages the predictions of each tree to get the final value:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.655,
+                0.262,
+                0.929,
+                0.285
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {f} _ {n} ^ {(M)} (x) = \\frac {1}{M} \\sum_ {j = 1} ^ {M} f _ {n} ^ {j} (x) \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.29,
+                0.943,
+                0.403
+            ],
+            "angle": 0,
+            "content": "where \\( A_{n}(x) \\) is the leaf containing \\( x \\) and \\( N^{e}(A_{n}(x)) \\) is the number of estimation points it contains. For the binary classification using random forest, random response \\( Y \\) takes only two values in \\( \\{0,1\\} \\). Given \\( X \\), random forest has to attribute 0 or 1 to \\( Y \\). Random forest is based on Borel classification measurable rule \\( m_{n} \\), which is used to estimate the label of \\( Y \\) from \\( x \\) and \\( D_{n} \\) where the classifier \\( m_{n} \\) is consistent if its conditional probability of error is low which can be expressed as follow"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.606,
+                0.409,
+                0.941,
+                0.428
+            ],
+            "angle": 0,
+            "content": "\\[\nL \\left(m _ {n}\\right) = P \\left[ m _ {n} (X) \\neq Y \\left[ D _ {n} \\right] \\right] \\tag {10}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.623,
+                0.433,
+                0.941,
+                0.451
+            ],
+            "angle": 0,
+            "content": "\\[\nL \\left(m _ {n}\\right) = P \\left[ m _ {n} (X) \\neq Y \\left[ D _ {n} \\right] \\right] \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.455,
+                0.942,
+                0.499
+            ],
+            "angle": 0,
+            "content": "where \\( L^{*} \\) is the error of the optimal but unknown and \\( E \\) is the expectations with respect to the random parameter \\( \\theta \\). After that Bayes classifier is used to get the output for both 0 and 1."
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.507,
+                0.504,
+                0.941,
+                0.535
+            ],
+            "angle": 0,
+            "content": "\\[\nm ^ {*} (x) = \\left\\{ \\begin{array}{l} 1, \\text {i f} P [ Y = 1, X = x ] > [ Y = 0, X = x <   0 ] \\\\ 0, \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.543,
+                0.942,
+                0.608
+            ],
+            "angle": 0,
+            "content": "In the classification situation where the dataset is divided into several classes based on the input parameters threshold values, the random forest classifier is obtained via a majority vote among the classification trees, that is"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.507,
+                0.61,
+                0.938,
+                0.65
+            ],
+            "angle": 0,
+            "content": "\\[\nm _ {M, n} \\left(x; \\theta_ {1} \\dots . \\theta_ {m}, D _ {n}\\right) = \\left\\{ \\begin{array}{l l} 1, & i f \\frac {1}{M} \\sum_ {j = 1} ^ {M} m _ {n} \\left(x; \\theta_ {j}, D _ {n}\\right) > 1 / 2 \\\\ 0, & o t h e r w i s e. \\end{array} \\right] \\tag {13}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.657,
+                0.943,
+                0.755
+            ],
+            "angle": 0,
+            "content": "where \\( n \\) is the number of trees and \\( M \\) tends to infinity number of trees. Based on the majority votes, the output is classified as 1 or 0. If more than \\( 50\\% \\) of the total trees vote for 1 then the final prediction of random forest is 1 and if more than \\( 50\\% \\) of the total trees vote for 0 then the final prediction of random forest is considered as 0."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.507,
+                0.765,
+                0.688,
+                0.779
+            ],
+            "angle": 0,
+            "content": "2) Support vector machine"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.781,
+                0.942,
+                0.824
+            ],
+            "angle": 0,
+            "content": "Support vector machine creates a hyperplane to separate data into two classes. The choice of the kernel determines the separation boundary between the two classes. Different kernels can be used"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.068,
+                0.49,
+                0.096
+            ],
+            "angle": 0,
+            "content": "with this model such as linear kernel, radial basis function, quadratic, and cubic kernels. The linear kernel is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.205,
+                0.102,
+                0.489,
+                0.12
+            ],
+            "angle": 0,
+            "content": "\\[\nK (x) = \\mathrm {w} ^ {T} x + b \\tag {14}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.124,
+                0.489,
+                0.154
+            ],
+            "angle": 0,
+            "content": "Linear support vector machine is formulated as solving an optimization problem as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.138,
+                0.159,
+                0.489,
+                0.183
+            ],
+            "angle": 0,
+            "content": "\\[\n\\min  _ {w \\in R ^ {d}} \\| w \\| ^ {2} + C \\sum_ {i} ^ {N} \\max  \\left(0, 1 - y _ {i} K \\left(x _ {i}\\right)\\right) \\tag {15}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.187,
+                0.489,
+                0.217
+            ],
+            "angle": 0,
+            "content": "Quadratic and cubic kernels are polynomial kernels with degrees of 2 and 3, respectively. Polynomials kernels are defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.204,
+                0.223,
+                0.488,
+                0.24
+            ],
+            "angle": 0,
+            "content": "\\[\nK (x, y) = (x. y + 1) ^ {d} \\tag {16}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.245,
+                0.489,
+                0.274
+            ],
+            "angle": 0,
+            "content": "where \\( x \\) and \\( y \\) are vectors of features and \\( d \\) is the degree of the polynomial. Radial basis function kernel is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.28,
+                0.489,
+                0.297
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathrm {K} (\\mathrm {x}, \\mathrm {y}) = \\exp (- \\gamma \\| \\mathrm {x} - \\mathrm {y} \\| ^ {2}) \\tag {17}\n\\]"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.056,
+                0.301,
+                0.192,
+                0.315
+            ],
+            "angle": 0,
+            "content": "3) Neural Network"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.317,
+                0.49,
+                0.581
+            ],
+            "angle": 0,
+            "content": "A neural network is a biological-inspired programming paradigm, which enables a machine to learn from observational data. This network has shown a great ability to learn and solve various problems in different research areas such as image processing, signal processing, and wireless communication. A neural network consists of one input layer, one or several hidden layers, and an output layer. Each layer consists of either one or several neurons. A neuron consists of an activation function and several links connecting them to other neurons in different layers. An initial weight is associated with each link and the neural network in the learning phase try to find the set of optimal weight that minimizes the error between the hypothesis function and the given dataset labels. Each neural network consists of two main concepts, which are the forward propagation and backpropagation. Forward propagation is the simplest type of artificial neural networks where the information moves in only one direction, from input to the output through hidden layers. Input features can be denoted as \\( x_{1}, x_{2} \\ldots x_{n} \\) and the input layer can be summarized by the following equations:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.22,
+                0.586,
+                0.484,
+                0.609
+            ],
+            "angle": 0,
+            "content": "\\[\na _ {(j)} ^ {(i)} = x _ {i} \\tag {18}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.615,
+                0.489,
+                0.663
+            ],
+            "angle": 0,
+            "content": "where \\( a_{(j)}^{(i)} \\) is the input layer and \\( x_{i} \\) is the input features. Input layer is connected with the hidden layers which can be denoted as follows: In the \\( i^{\\text{th}} \\) hidden layer, we have"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.214,
+                0.669,
+                0.484,
+                0.686
+            ],
+            "angle": 0,
+            "content": "\\[\nz ^ {(i)} = \\theta^ {(i)} a ^ {(i)} \\tag {19}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.692,
+                0.489,
+                0.736
+            ],
+            "angle": 0,
+            "content": "where \\( z^{(i)} \\) is the hidden neuron, \\( \\theta^{(i)} \\) is each layer matrix weight, and \\( a^{(i)} \\) is the hidden layer for the \\( i^{\\text{th}} \\) hidden layer. The final layer is the output layer which can be denoted as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.237,
+                0.742,
+                0.488,
+                0.76
+            ],
+            "angle": 0,
+            "content": "\\[\na ^ {(i)} = g \\left(z ^ {(i)}\\right) \\tag {20}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.055,
+                0.771,
+                0.489,
+                0.815
+            ],
+            "angle": 0,
+            "content": "Neural network cost function is used to find out the optimal output based on different number of layers and neurons. It is expressed by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.533,
+                0.068,
+                0.882,
+                0.089
+            ],
+            "angle": 0,
+            "content": "\\[\nJ (\\theta) = - \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\sum_ {k = 1} ^ {k} \\left[ y _ {k} ^ {(i)} \\log \\left(\\left(h _ {\\theta} (x ^ {(i)})\\right) _ {k}\\right) + \\left(1 - \\right. \\right.\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.508,
+                0.09,
+                0.94,
+                0.111
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left. y _ {k} ^ {(i)}\\right) \\log \\left(1 - \\left(h _ {\\theta} \\left(x ^ {(i)}\\right)\\right) _ {k}\\right) ] + \\frac {\\lambda}{2 m} \\sum_ {l = 1} ^ {L - 1} \\sum_ {i = 1} ^ {s _ {l}} \\sum_ {j = 1} ^ {s _ {l + 1}} \\left(\\theta_ {j, i} ^ {(l)}\\right) ^ {2} \\tag {21}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.116,
+                0.942,
+                0.173
+            ],
+            "angle": 0,
+            "content": "where \\( J(\\theta) \\) is the cost function, \\( h_\\theta \\) is the hypothesis function, and \\( \\lambda \\) is the regularization factor. Regularization cost function is used to reduce the effect of over bias and under bias by regularization factor \\( (\\lambda) \\)"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.527,
+                0.173,
+                0.878,
+                0.194
+            ],
+            "angle": 0,
+            "content": "\\[\nJ (\\theta) = \\frac {1}{m} \\sum_ {i = 1} ^ {m} \\sum_ {k = 1} ^ {k} \\left[ - y _ {k} ^ {(i)} \\log \\left(\\left(h _ {\\theta} (x ^ {(i)})\\right) _ {k}\\right) - (1 - \\right.\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.53,
+                0.195,
+                0.892,
+                0.215
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left. y _ {k} ^ {(i)}\\right) \\log \\left(1 - \\left(h _ {\\theta} (x ^ {(i)})) _ {k}\\right) \\right] + \\frac {\\lambda}{2 m} \\left[ \\sum_ {l = 1} ^ {L - 1} \\sum_ {i = 1} ^ {s _ {l}} \\left(\\theta_ {j, k} ^ {(1)}\\right) ^ {2} + \\right.\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.53,
+                0.215,
+                0.938,
+                0.236
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left. \\sum_ {j = 1} ^ {L} \\sum_ {k = 1} ^ {s l} \\left(\\theta_ {j, k} ^ {(2)}\\right) ^ {2} \\right] \\tag {22}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.241,
+                0.942,
+                0.368
+            ],
+            "angle": 0,
+            "content": "where the regularization factor \\(\\lambda\\) is used to reduce the effect of the over bias and under bias. Neural networks use different optimization techniques such as Adam, gradient descent, and stochastic gradient descent to minimize the cost function. At the output layer, neural network uses a sigmoid function to attribute the new dataset into one of the two classes, in the case of binary classification, by calculating the hypothesis using the weights determined in the leaning parts. If this hypothesis is greater than 0.5, then it concludes that \"y=1\"; otherwise \"y=0\"."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.619,
+                0.377,
+                0.83,
+                0.39
+            ],
+            "angle": 0,
+            "content": "III. RESULTS AND DISCUSSION"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.395,
+                0.942,
+                0.673
+            ],
+            "angle": 0,
+            "content": "To validate the machine learning models, four different parameters were used as features to detect jamming attacks. A real environment simulation was performed to collect measurements of these parameters in the two scenarios: link is under attack and link under no attack. To train and test the models, the dataset was divided into \\(N\\) folds using the cross-validation technique. \\(N\\)-fold cross-validation was used to divide the dataset into \\(N\\) number of subsamples with equal size. In this work, machines learning algorithms were trained with a different number of fold sizes such as 2, 5, 10, and 20 to evaluate the performance of these machines for the given dataset. For instance, if the number of folds is 10, then the total data is divided into 10 folds and randomly the algorithm selects 9 folds to train the model and 1 fold is used to test the machine. This process is repeated until the dataset is tested on the 10 folds. To evaluate the performance of the classifiers, several metrics were used, namely probabilities of detection, false alarm, miss detection, and accuracy. \\(P_{d}\\) refers to the likelihood that the detection technique attributes signals coming from a jammer to the class of jamming signals meaning that it correctly detects that the link is under a jamming attack"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.581,
+                0.678,
+                0.938,
+                0.703
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {d} = \\frac {\\text {N u m b e r o f t r u l y d e t e c t e d a t t a c k s}}{\\text {T o t a l n u m b e r o f a t t a c k s}} \\tag {23}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.507,
+                0.709,
+                0.941,
+                0.74
+            ],
+            "angle": 0,
+            "content": "\\(P_{md}\\) is the percentage of attacks that the algorithm miss detected. It is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.59,
+                0.748,
+                0.938,
+                0.772
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {m} = \\frac {\\text {N u m b e r o f m i s s d e t e c t e d a t t a c k s}}{\\text {T o t a l n u m b e r o f a t t a c k s}} \\tag {24}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.781,
+                0.941,
+                0.811
+            ],
+            "angle": 0,
+            "content": "\\(P_{fa}\\) is the percentage of non-attacks that the algorithm detected as attacks"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.556,
+                0.821,
+                0.94,
+                0.846
+            ],
+            "angle": 0,
+            "content": "\\[\nP _ {f a} = \\frac {\\text {N u m b e r o f n o n - a t t a c k s d e t e c t e d a s a n a t t a c k}}{\\text {T o t a l n u m b e r o f n o n - a t t a c k s}} \\tag {25}\n\\]"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.068,
+                0.492,
+                0.111
+            ],
+            "angle": 0,
+            "content": "Accuracy gives the total number of attacks and non-attacks that are detected accurately compared to the total number of trials. It is given by:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.055,
+                0.115,
+                0.49,
+                0.137
+            ],
+            "angle": 0,
+            "content": "\\[\nA c c u r a c y = \\frac {\\text {T o t a l n u m b e r o f c o r r e c t l y d e t e c t e d a t t a c k a n d n o n - a t t a c k t r i a l s}}{\\text {T o t a l n u m b e r o f t r i a l s}} \\tag {26}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.142,
+                0.491,
+                0.309
+            ],
+            "angle": 0,
+            "content": "We conducted several experiments and examples of results are given from Fig. 1 to Fig. 4. Fig. 1 shows the accuracy of the classification using random forest versus the number of estimators for a different number of folds in the cross-validation. It can be seen from this figure that for all values of K-folds, 5, 10, and 20, the accuracy of the classification is exponentially increasing as a function of the number of estimators, for numbers of estimators less than 60. However, this accuracy remains slightly constant for numbers higher than 60 and in some cases, it drops. This figure also shows the impact of the number of folds on the accuracy. One can see that with 20 folds, the accuracy is higher than the one with 10 and 5 folds."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.149,
+                0.316,
+                0.396,
+                0.46
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.055,
+                0.463,
+                0.445,
+                0.489
+            ],
+            "angle": 0,
+            "content": "Fig. 1. Accuracy versus the number of estimators for random forest using different number of k-folds cross validation \\(\\mathrm{CV} = 5\\), 10, and 20."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.497,
+                0.491,
+                0.676
+            ],
+            "angle": 0,
+            "content": "To select the best support vector model, we investigated how the accuracy varies for different kernels and regularization parameter \\( C \\) in order to select the best combination for this given dataset. Fig. 2 shows the accuracy of the classification function of the regularization factor \"C\" for linear, quadratic, cubic, radial basis function, and sigmoid kernels. From this figure, it can be seen that the impact of the regularization factor \"C\" does not change the accuracy very much. However, as one can see the choice of the kernel impacts the accuracy. The accuracy is high for radial basis function kernel, followed by linear, cubic, sigmoid, and then quadratic kernels. Support vector machine with radial basis function and regularization factor equal to 3 has the highest accuracy of \\( 94\\% \\)."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.171,
+                0.677,
+                0.402,
+                0.831
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.055,
+                0.831,
+                0.418,
+                0.845
+            ],
+            "angle": 0,
+            "content": "Fig. 2. Accuracy Vs regularization factor for support vector machine."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.068,
+                0.946,
+                0.179
+            ],
+            "angle": 0,
+            "content": "Fig. 3 shows the accuracy of the classification function of the number of hidden neurons in one hidden layer of neural network for a different number of k-folds cross-validation. One can observe that the impact of the number of hidden neurons and the number of cross-validation technique is not significant as the accuracy of the classification remains around \\(94\\%\\), but the highest one is achieved with 1 neuron with 5-folds cross-validation and with 100 neurons with 10-folds cross-validation."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.584,
+                0.187,
+                0.865,
+                0.37
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.507,
+                0.372,
+                0.922,
+                0.386
+            ],
+            "angle": 0,
+            "content": "Fig. 3. Accuracy of neural network Vs number of neurons in one hidden layer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.393,
+                0.942,
+                0.505
+            ],
+            "angle": 0,
+            "content": "Fig. 4 shows \\( Pd \\) Vs \\( Pfa \\) using linear, polynomial with degree 2, radial basis function SVM, neural network with two hidden layers of 2 neurons each, and random forest with 100 estimators. One can see that \\( P_{d} \\) increases as \\( P_{fa} \\) increases. In addition, it can be observed that random forest has the higher ROC followed by radial basis function SVM, cubic SVM, linear SVM, and then the neural network which means that random forest outperforms other algorithms regarding the ROC curve."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.601,
+                0.507,
+                0.847,
+                0.67
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.507,
+                0.673,
+                0.848,
+                0.687
+            ],
+            "angle": 0,
+            "content": "Fig. 4. Probability of detection Vs the probability of false alarm."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.694,
+                0.945,
+                0.847
+            ],
+            "angle": 0,
+            "content": "Table I compares the performance of the jamming detection techniques based on machine learning classifiers for the four evaluation metrics. Random forest achieves the highest probability of detection with \\(97.5\\%\\) followed by cubic SVM with \\(97.1\\%\\) neural network with \\(96.4\\%\\) linear SVM with \\(86.9\\%\\) RBF SVM with \\(86.2\\%\\) sigmoid SVM with \\(73.8\\%\\) and quadratic SVM with \\(72\\%\\). It can also be seen that random forest has the lowest probabilities of false alarm of \\(5.6\\%\\) followed by neural network with \\(11.1\\%\\) RBF SVM with \\(27.2\\%\\) linear SVM with \\(27.25\\%\\) sigmoid SVM with \\(40.1\\%\\) cubic SVM with \\(54\\%\\) and quadratic SVM with \\(65.2\\%\\). This table shows also that random forest has the"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.067,
+                0.49,
+                0.166
+            ],
+            "angle": 0,
+            "content": "lowest miss detection with \\(2.5\\%\\), followed by cubic SVM with \\(2.9\\%\\), neural network with \\(3.6\\%\\), linear SVM with \\(13.1\\%\\), RBF SVM with \\(13.8\\%\\), sigmoid SVM with \\(26.22\\%\\), and quadratic SVM with \\(28\\%\\). In terms of accuracy, random forest has an accuracy as high as \\(96.6\\%\\) followed by neural network with \\(94.4\\%\\), RBF SVM with \\(84.7\\%\\), linear SVM with \\(83\\%\\), sigmoid SVM with \\(82.6\\%\\), cubic SVM \\(70.1\\%\\), quadratic SVM with \\(62\\%\\)."
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.15,
+                0.179,
+                0.396,
+                0.19
+            ],
+            "angle": 0,
+            "content": "TABLE I. PERFORMANCE COMPARISON"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.058,
+                0.195,
+                0.487,
+                0.391
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Classification technique</td><td>Pd(%)</td><td>Pfa(%)</td><td>Pmd(%)</td><td>Accuracy (%)</td></tr><tr><td>Linear SVM</td><td>86.9</td><td>27.25</td><td>13.1</td><td>83</td></tr><tr><td>Quadratic SVM</td><td>72</td><td>65.2</td><td>28</td><td>62</td></tr><tr><td>Cubic SVM</td><td>97.1</td><td>54</td><td>2.9</td><td>70.1</td></tr><tr><td>RBF SVM</td><td>86.2</td><td>27.2</td><td>13.8</td><td>84.7</td></tr><tr><td>Sigmoid SVM</td><td>73.8</td><td>40.1</td><td>26.22</td><td>82.6</td></tr><tr><td>Neural network</td><td>96.4</td><td>11.1</td><td>3.6</td><td>94.4</td></tr><tr><td>Random Forest estimators = 100</td><td>97.5</td><td>5.6</td><td>2.5</td><td>96.6</td></tr></table>"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.227,
+                0.4,
+                0.319,
+                0.413
+            ],
+            "angle": 0,
+            "content": "CONCLUSION"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.054,
+                0.419,
+                0.491,
+                0.752
+            ],
+            "angle": 0,
+            "content": "5G technology is designed to be resilient to jamming attacks by using millimeter wave band. However, it is also designed to use frequencies below 6 GHz, which are easy to target by jammers. Smart jamming detection techniques are required to prevent these attacks. In this paper, we reviewed the existing jamming detection techniques. We investigated and compared the performance of several machine learning models to detect jamming attacks. Feature extraction and feature selection were performed and a large dataset was constructed to train, validate, and test random forest, support vector machine, and neural network algorithms. We used a cross-validation technique and provided learning curves to evaluate the performance of these models based on a number of metrics. The results show that random forest based technique detects jamming attacks with a very high accuracy and a low cost. \\( P_{d} \\) of random forest based detection is as high as \\( 97.5\\% \\) whereas \\( P_{fa} \\) of the neural network and cubic support vector machine is around \\( 96.4\\% \\) and \\( 97.1\\% \\). \\( P_{md} \\) and \\( P_{fa} \\) of random forest are also very low compared to neural network and cubic support vector machine which are \\( 5.6\\% \\) and \\( 2.5\\% \\). High \\( P_{d} \\) and low \\( P_{fa} \\) make this proposed model suitable for jamming attack detection. These trained machines are able to process a huge number of data within a very short time, which helps increase efficiency and reduce the processing time. Future work includes investigating the efficiency of deep learning in detecting all types of jamming attacks."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.68,
+                0.069,
+                0.769,
+                0.081
+            ],
+            "angle": 0,
+            "content": "REFERENCES"
+        },
+        {
+            "type": "ref_text",
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+            ],
+            "angle": 0,
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+            "content": "[15] S. Khattab, D. Mosse, R. Melhem, \"Modeling of the channel-hopping anti-jamming defense in multi-radio wireless networks,\" Int. Conf. mobile ubiquitous syst., pp. 1-10, 2008."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.509,
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+                0.532
+            ],
+            "angle": 0,
+            "content": "[16] Y. Lin, M. Li, \"Distributed detection of jamming and defense in wireless sensor networks,\" Ann. Conf. Info. science and systems, pp. 829-834, 2009."
+        },
+        {
+            "type": "ref_text",
+            "bbox": [
+                0.509,
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+                0.941,
+                0.567
+            ],
+            "angle": 0,
+            "content": "[17] T. Nawaz, et all. \"Jammer detection algorithm for wideband radios using spectral correlation and neural networks,\" Int. Wireless Commun. Mobile Comput. Conf., pp. 112-118, 2017."
+        },
+        {
+            "type": "ref_text",
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+                0.509,
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+            ],
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+            "content": "[18] O. Punal, I. Aktas, C. J. Schnelke, G. Abidin, K. Wehrle, and J. Gross, \"Machine learning-based jamming detection for IEEE 802.11: design and experimental evaluation,\" IEEE Int. Symposium Wireless, Mobile and Multimedia Networks, pp. 1-10, 2014."
+        },
+        {
+            "type": "ref_text",
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+            ],
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+            "content": "[19] K. Grover; A. Lim; Q. Yang, “Jamming and anti-jamming techniques in wireless networks: A survey,” Int. J. Ad Hoc Ubiquitous., pp. 197-215, 2014."
+        },
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+        },
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+]

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+# A Novel Jamming Attacks Detection Approach Based on Machine Learning for Wireless Communication
+
+Youness Arjoune, Fatima Salahdine, Md. Shoriful Islam, Elias Ghribi, Naima Kaabouch
+
+School of Electrical Engineering and Computer Science  
+University of North Dakota, Grand Forks, United States
+
+Abstract—Jamming attacks target a wireless network creating an unwanted denial of service. 5G is vulnerable to these attacks despite its resilience prompted by the use of millimeter wave bands. Over the last decade, several types of jamming detection techniques have been proposed, including fuzzy logic, game theory, channel surfing, and time series. Most of these techniques are inefficient in detecting smart jammers. Thus, there is a great need for efficient and fast jamming detection techniques with high accuracy. In this paper, we compare the efficiency of several machine learning models in detecting jamming signals. We investigated the types of signal features that identify jamming signals, and generated a large dataset using these parameters. Using this dataset, the machine learning algorithms were trained, evaluated, and tested. These algorithms are random forest, support vector machine, and neural network. The performance of these algorithms was evaluated and compared using the probability of detection, probability of false alarm, probability of miss detection, and accuracy. The simulation results show that jamming detection based random forest algorithm can detect jammers with a high accuracy, high detection probability and low probability of false alarm.
+
+Keywords—Jamming Attacks; Machine Learning; Random Fores; Neural Network; Support Vector Machine, 5G.
+
+# I. INTRODUCTION
+
+5G is expected to substitute previous generations of cellular networks in the near future, promising higher throughput and lower latency [1] thereby enabling applications such as "self-driving" cars, Internet of Things, E-health services, augmented reality, and smart cities. As a result, billions of wireless devices are expected to be connected to the internet. Like the existing networks, 5G is vulnerable to the cyber security attacks, including jamming [2] and GPS spoofing [3, 4]. It will be enabled by cognitive radio, making these networks open to new attacks, including primary user emulation attacks [5] and spectrum sensing data falsification [6]. Thus, it is important to explore the cybersecurity implications of 5G systems [7, 8]. Jammers create an unwanted denial of service by transmitting radio signals that flood the communication channels aiming at decreasing SNR of legitimate users thereby interrupting their communication. The attacks can be easily launched using software defined radio units such as the GNU radio and universal software radio peripherals, which are cheap and easily accessible. Jammers can target any particular frequency channel with low cost [9]. Jamming attacks can be divided into four main types: constant jammers, random jammers, deceptive
+
+jammers, and reactive jammers. Constant jammers launch an attack by transmitting a continuous high-power noise sweeping from a channel to another following a fixed strategy and repeating this process over time. Random jammers operate randomly and do not follow any specific strategy jumping from a channel to another. Deceptive jammers send illegitimate packets through the wireless channels to keep them busy. Reactive jammers continuously monitor the state of the frequency channels and target only the channels used for communication [10]. In addition, jammers can be classified as: regular or smart. Regular jammers cannot sense the ongoing transmitted signals and they all play simultaneously. Smart jammers can learn quickly, sense and determine how the legitimate users are transmitting their signals and they can update their attacks' strategies or adjust the transmission power to more damage the legitimate transmission.
+
+A number of jamming detection techniques have been proposed [11-19]. These techniques can be categorized into two main classes: non-machine learning [11-17] and machine learning based [18,19]. Non-machine learning methods perform using some parameters and strategies including threshold, fuzzy logic, game theory, channel surfing, mapping jammed region, and timing channel. In [12], the authors developed a time series model in which they measured the state of the link over series of time and compared it with the past link data to detect the state of the communication link. In [13], the authors developed a threshold based model using the packet loss, throughput, and message invalidation ratio to evaluate the performance of the wireless channels in time-critical applications. In [14], the authors proposed two timing channel based models for jamming detection. One model computes the poor packet delivery ratio based on the received signal strength while the second model computes the throughput. Based on these two parameters, they were able to detect whether the link is attacked or not. In [15], the author proposed a fuzzy logic centralized jamming detection technique based on the received signal strength, packet delivery ratio, bad packet ratio, and channel clear assessment parameters. This model also developed a base station to run the detection algorithm which computes the packet delivery to packet received ratio and the signal to noise ratio from the received data to determine the duration of this attack [16, 17].
+
+Machine learning methods are based on classifiers like neural networks and support vector machine with different features to detect jamming attacks. For instance, the authors of [18] proposed an artificial neural network based algorithm for cyclic spectral analysis and wideband spectrum sensing. Based on the signal quality and the modulation, the algorithm distinguishes the jamming signals from the narrowband signals. In [19], the authors designed a machine learning based jamming detection system via support vector machine, adaptive boosting, and expectation maximization algorithms. Noise, busy channel ratio, packet delivery ratio, and maximum inactive time were used to detect jamming attacks. Most of the previously mentioned techniques [11-19] require more resources and ultimately serve only as a stopgap. They can detect the state of the link as down, but often they cannot identify the source of the outage of the service. In addition, these techniques have relatively high probability of false alarm. They need accurate algorithms for training and testing the classification models. Features selection and learning curves are often neglected while they are one of the most important processes in designing detection techniques with machine learning. Thus, there is a great need for efficient and fast detection techniques able to detect jamming attacks more accurately.
+
+In this paper, we propose using machine learning to detect the transmission link state between a transmitter and a receiver to verify if it is attacked. Machine learning based models can achieve high detection accuracy if the following steps are carefully considered: selecting appropriate input features, measuring, collecting, building a large dataset, and using accurate methodology to train, validate, and test the model. Features and parameters used to detect jamming attacks are: bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. We investigated techniques of selecting appropriate features and assessing the communication link status. We built a large dataset to train, validate, and test machine learning models. Randomization and normalization of the dataset and cross-validation techniques were performed to avoid the problem of underfitting. The rest of the paper is organized as follows. Section II describes the jamming attack model and its classification features. Section III discusses the simulation results. Finally, a conclusion is given at the end.
+
+# II. METHODOLOGY
+
+The jamming attacks detection in this paper is formulated as a classification problem in which the classifier has to choose between two states: the link is lost because of a jammer or the link is lost because of another reason. The reason behind using machine learning theory to solve this problem is the success of this theory to deal with complex problems within an acceptable time and using reasonable resources. Designing a successful machine learning algorithm requires the selection of appropriate features. In this work, several features were selected to identify the presence of jamming attacks. Using one parameter only is not enough to detect if there is a jamming attack. In addition, it can be complicated to find analytic relations between these parameters and the status of the link. For these reasons, machine learning theory is used to find
+
+an empiric relation among these four metrics in order to detect jamming attacks.
+
+In this section, we describe the jamming attack model used, the feature selection and the four parameters used to detect jamming attacks. Next, we describe the machine learning techniques used, which are random forest, support vector machine with different kernels, and neural networks.
+
+# A. Jamming attacks model
+
+Jamming attacks target both physical layer and cross-layer of the wireless networks [20]. Under these attacks, the desired communication between a transmitter at location A and a receiver at location B is interrupted by the jamming signals which keep the channel busy. When the jamming signals occupy the channel for a longer period of time, they can create a denial of service [21]. If the desired signal, at location A, is denoted by  $x(t)$  and the received signal, at location B, is denoted by  $y(t)$ , then this received signal at the location B, in the absence of the jammer signal, is given by
+
+$$
+y (t) = x (t) + n (t) \tag {1}
+$$
+
+where  $x(t)$  is the desired signal,  $y(t)$  is the received signal, and  $n(t)$  is an additive white Gaussian noise present within the path between the transmitter and the receiver. The jammers can counterfeit the desired signals creating a signal denoted  $x_{j}(t)$  to flood the channel. The receive signal at location B, in the presence of the jammer signal, is then given as:
+
+$$
+y (t) = x (t) + x _ {j} (t) + n (t) + n _ {1} (t) \tag {2}
+$$
+
+where  $x_{j}(t)$  is the jammer signal and  $n_1(t)$  is the noise within the path between the receiver and the jammer's location. Thus, the jamming detection problem can be stated as a hypothesis, in which the receiver has to choose between two states,  $H_{0}$  and  $H_{a}$ .  $H_{0}$  is the state where the received signal is not jammed, while  $H_{a}$  is the state where the received signal is jammed. This problem thus can be expressed as a classification problem, in which the machine learning classifier has to attribute the incoming signal into one of the two classes: the received signal is the desired signal, class A, or the received signal is a jamming signal, class B.
+
+# B. Feature selection
+
+Parameters used to detect jamming attacks are bad packet ratio, packet delivery ratio, received signal strength, and clear channel assessment. The reason behind using these four parameters is that all communication systems are equipped with network interface cards that possess diagnostic mechanisms which allow the estimation of these metrics [22-26].
+
+Bad packet ratio is one of the most important parameters to detect jamming attacks. It refers to the percentage of incorrect packages received [23]. It can be measured at the receiver end and is expressed as
+
+$$
+P R = \frac {\text {N u m b e r o f e r r o n e o u s r e c e i v e d p a c k a g e s}}{\text {T o t a l n u m b e r o f r e c e i v e d p a c k a g e s}} \tag {3}
+$$
+
+The receivers compute this bad packet ratio by verifying the frame check sequence of the incoming packets at the medium access control level. If the channel is under any kind of attack, the bad packet ratio increases while it is very low when the link status is good for transmission. The packet delivery ratio refers to the percentage of correctly delivered packages. It is measured at the transmitter end and expressed as
+
+$$
+P D R = \frac {\text {N u m b e r o f p a c k a g e d e l e v i r e y c o r r e c t l y}}{\text {T o t a l n u m b e r o f t r a n s m i t t e d p a c k a g e s}} \tag {4}
+$$
+
+The receiver sends back an acknowledgment packet to the transmitter each time it receives a correct packet. The packet delivery ratio is very high when the link status is good while its value decreases exponentially if the link is under any attack. The clear channel assessment can be used to measure the number of transmitter's attempts to send a package and the channel is found to be occupied. The value of this parameter increases if the channel is under jamming attacks.
+
+The received signal strength, RSS, measures the surrounding power of the receiver. It is high when there is no attack; however, it decreases if the channel is under any kind of attack. RSS at the receiver can be expressed as
+
+$$
+R S S = \frac {P _ {t} * G _ {t} * G _ {r} * \left(h t ^ {2} * h r ^ {2}\right)}{d ^ {4}} \tag {5}
+$$
+
+where  $P_{t}$  is the transmitter signal power,  $G_{t}$  and  $G_{r}$  is the gain of the antenna at transmitter and receiver respectively,  $ht$  and  $hr$  are the height of antenna at transmitter and receiver, and  $d$  is the distance between transmitter and receiver. Equation (20) is expressed as
+
+$$
+R S S = K \frac {P _ {t}}{d ^ {4}} \tag {6}
+$$
+
+where  $k$  is a constant such that  $k = G_{t} * G_{r} * (ht^{2} * hr^{2})$ .
+
+# C. Machine Learning Algorithms
+
+A description of each of the machine learning algorithms is given below.
+
+# 1) Random forest
+
+Random forest is a hierarchical classifier method composed of a large number of decision trees. In this approach, the test data is classified by sorting trees based on their feature values. Each decision tree consists of one node and several branches. The decision node is the feature of the test data to be classified, and the branches represent a value that the node can predict. The reason behind using a large number of trees is to avoid the problem of overfitting. System variance is reduced, which eventually increases the performance of the final model. Basic parameters to random forest classifier can be the total number of trees to be generated and decision tree related parameters like minimum split, and split criteria. Random forest is a predictor that collects the information from each tree  $\{r_n(x,\theta_m,D_n,m\geq 1)\}$ , where  $\theta_{1},\theta_{2}\ldots \theta_{m}$  are the
+
+output of each random trees. These trees are combined to form the aggregated estimation to train the forest using:
+
+$$
+\bar {r _ {n}} (X, D _ {n}) = E _ {\theta} \left[ r _ {n} (X, \theta , D _ {n}) \right] \tag {7}
+$$
+
+where  $E_{\theta}$  is the expectation with respect to the random parameter, conditionally, on  $X$  and the data set  $D_{n}$ . Once the forest is trained, each tree can predict independently to output values using the following equation:
+
+$$
+\mathrm {f} _ {n} ^ {j} (x) = \frac {1}{N ^ {e} (A _ {n} (x))} \sum_ {\substack {Y _ {i} \in A _ {n} (x) \\ I _ {i} = e}} Y _ {i} \tag{8}
+$$
+
+where  $x$  is the query point of each tree. The forest averages the predictions of each tree to get the final value:
+
+$$
+\mathrm {f} _ {n} ^ {(M)} (x) = \frac {1}{M} \sum_ {j = 1} ^ {M} f _ {n} ^ {j} (x) \tag {9}
+$$
+
+where  $A_{n}(x)$  is the leaf containing  $x$  and  $N^{e}(A_{n}(x))$  is the number of estimation points it contains. For the binary classification using random forest, random response  $Y$  takes only two values in  $\{0,1\}$ . Given  $X$ , random forest has to attribute 0 or 1 to  $Y$ . Random forest is based on Borel classification measurable rule  $m_{n}$ , which is used to estimate the label of  $Y$  from  $x$  and  $D_{n}$  where the classifier  $m_{n}$  is consistent if its conditional probability of error is low which can be expressed as follow
+
+$$
+L \left(m _ {n}\right) = P \left[ m _ {n} (X) \neq Y \left[ D _ {n} \right] \right] \tag {10}
+$$
+
+$$
+L \left(m _ {n}\right) = P \left[ m _ {n} (X) \neq Y \left[ D _ {n} \right] \right] \tag {11}
+$$
+
+where  $L^{*}$  is the error of the optimal but unknown and  $E$  is the expectations with respect to the random parameter  $\theta$ . After that Bayes classifier is used to get the output for both 0 and 1.
+
+$$
+m ^ {*} (x) = \left\{ \begin{array}{l} 1, \text {i f} P [ Y = 1, X = x ] > [ Y = 0, X = x <   0 ] \\ 0, \text {o t h e r w i s e .} \end{array} \right. \tag {12}
+$$
+
+In the classification situation where the dataset is divided into several classes based on the input parameters threshold values, the random forest classifier is obtained via a majority vote among the classification trees, that is
+
+$$
+m _ {M, n} \left(x; \theta_ {1} \dots . \theta_ {m}, D _ {n}\right) = \left\{ \begin{array}{l l} 1, & i f \frac {1}{M} \sum_ {j = 1} ^ {M} m _ {n} \left(x; \theta_ {j}, D _ {n}\right) > 1 / 2 \\ 0, & o t h e r w i s e. \end{array} \right] \tag {13}
+$$
+
+where  $n$  is the number of trees and  $M$  tends to infinity number of trees. Based on the majority votes, the output is classified as 1 or 0. If more than  $50\%$  of the total trees vote for 1 then the final prediction of random forest is 1 and if more than  $50\%$  of the total trees vote for 0 then the final prediction of random forest is considered as 0.
+
+# 2) Support vector machine
+
+Support vector machine creates a hyperplane to separate data into two classes. The choice of the kernel determines the separation boundary between the two classes. Different kernels can be used
+
+with this model such as linear kernel, radial basis function, quadratic, and cubic kernels. The linear kernel is defined as:
+
+$$
+K (x) = \mathrm {w} ^ {T} x + b \tag {14}
+$$
+
+Linear support vector machine is formulated as solving an optimization problem as:
+
+$$
+\min  _ {w \in R ^ {d}} \| w \| ^ {2} + C \sum_ {i} ^ {N} \max  \left(0, 1 - y _ {i} K \left(x _ {i}\right)\right) \tag {15}
+$$
+
+Quadratic and cubic kernels are polynomial kernels with degrees of 2 and 3, respectively. Polynomials kernels are defined as:
+
+$$
+K (x, y) = (x. y + 1) ^ {d} \tag {16}
+$$
+
+where  $x$  and  $y$  are vectors of features and  $d$  is the degree of the polynomial. Radial basis function kernel is defined as:
+
+$$
+\mathrm {K} (\mathrm {x}, \mathrm {y}) = \exp (- \gamma \| \mathrm {x} - \mathrm {y} \| ^ {2}) \tag {17}
+$$
+
+# 3) Neural Network
+
+A neural network is a biological-inspired programming paradigm, which enables a machine to learn from observational data. This network has shown a great ability to learn and solve various problems in different research areas such as image processing, signal processing, and wireless communication. A neural network consists of one input layer, one or several hidden layers, and an output layer. Each layer consists of either one or several neurons. A neuron consists of an activation function and several links connecting them to other neurons in different layers. An initial weight is associated with each link and the neural network in the learning phase try to find the set of optimal weight that minimizes the error between the hypothesis function and the given dataset labels. Each neural network consists of two main concepts, which are the forward propagation and backpropagation. Forward propagation is the simplest type of artificial neural networks where the information moves in only one direction, from input to the output through hidden layers. Input features can be denoted as  $x_{1}, x_{2} \ldots x_{n}$  and the input layer can be summarized by the following equations:
+
+$$
+a _ {(j)} ^ {(i)} = x _ {i} \tag {18}
+$$
+
+where  $a_{(j)}^{(i)}$  is the input layer and  $x_{i}$  is the input features. Input layer is connected with the hidden layers which can be denoted as follows: In the  $i^{\text{th}}$  hidden layer, we have
+
+$$
+z ^ {(i)} = \theta^ {(i)} a ^ {(i)} \tag {19}
+$$
+
+where  $z^{(i)}$  is the hidden neuron,  $\theta^{(i)}$  is each layer matrix weight, and  $a^{(i)}$  is the hidden layer for the  $i^{\text{th}}$  hidden layer. The final layer is the output layer which can be denoted as:
+
+$$
+a ^ {(i)} = g \left(z ^ {(i)}\right) \tag {20}
+$$
+
+Neural network cost function is used to find out the optimal output based on different number of layers and neurons. It is expressed by:
+
+$$
+J (\theta) = - \frac {1}{m} \sum_ {i = 1} ^ {m} \sum_ {k = 1} ^ {k} \left[ y _ {k} ^ {(i)} \log \left(\left(h _ {\theta} (x ^ {(i)})\right) _ {k}\right) + \left(1 - \right. \right.
+$$
+
+$$
+\left. y _ {k} ^ {(i)}\right) \log \left(1 - \left(h _ {\theta} \left(x ^ {(i)}\right)\right) _ {k}\right) ] + \frac {\lambda}{2 m} \sum_ {l = 1} ^ {L - 1} \sum_ {i = 1} ^ {s _ {l}} \sum_ {j = 1} ^ {s _ {l + 1}} \left(\theta_ {j, i} ^ {(l)}\right) ^ {2} \tag {21}
+$$
+
+where  $J(\theta)$  is the cost function,  $h_\theta$  is the hypothesis function, and  $\lambda$  is the regularization factor. Regularization cost function is used to reduce the effect of over bias and under bias by regularization factor  $(\lambda)$
+
+$$
+J (\theta) = \frac {1}{m} \sum_ {i = 1} ^ {m} \sum_ {k = 1} ^ {k} \left[ - y _ {k} ^ {(i)} \log \left(\left(h _ {\theta} (x ^ {(i)})\right) _ {k}\right) - (1 - \right.
+$$
+
+$$
+\left. y _ {k} ^ {(i)}\right) \log \left(1 - \left(h _ {\theta} (x ^ {(i)})) _ {k}\right) \right] + \frac {\lambda}{2 m} \left[ \sum_ {l = 1} ^ {L - 1} \sum_ {i = 1} ^ {s _ {l}} \left(\theta_ {j, k} ^ {(1)}\right) ^ {2} + \right.
+$$
+
+$$
+\left. \sum_ {j = 1} ^ {L} \sum_ {k = 1} ^ {s l} \left(\theta_ {j, k} ^ {(2)}\right) ^ {2} \right] \tag {22}
+$$
+
+where the regularization factor  $\lambda$  is used to reduce the effect of the over bias and under bias. Neural networks use different optimization techniques such as Adam, gradient descent, and stochastic gradient descent to minimize the cost function. At the output layer, neural network uses a sigmoid function to attribute the new dataset into one of the two classes, in the case of binary classification, by calculating the hypothesis using the weights determined in the leaning parts. If this hypothesis is greater than 0.5, then it concludes that "y=1"; otherwise "y=0".
+
+# III. RESULTS AND DISCUSSION
+
+To validate the machine learning models, four different parameters were used as features to detect jamming attacks. A real environment simulation was performed to collect measurements of these parameters in the two scenarios: link is under attack and link under no attack. To train and test the models, the dataset was divided into  $N$  folds using the cross-validation technique.  $N$ -fold cross-validation was used to divide the dataset into  $N$  number of subsamples with equal size. In this work, machines learning algorithms were trained with a different number of fold sizes such as 2, 5, 10, and 20 to evaluate the performance of these machines for the given dataset. For instance, if the number of folds is 10, then the total data is divided into 10 folds and randomly the algorithm selects 9 folds to train the model and 1 fold is used to test the machine. This process is repeated until the dataset is tested on the 10 folds. To evaluate the performance of the classifiers, several metrics were used, namely probabilities of detection, false alarm, miss detection, and accuracy.  $P_{d}$  refers to the likelihood that the detection technique attributes signals coming from a jammer to the class of jamming signals meaning that it correctly detects that the link is under a jamming attack
+
+$$
+P _ {d} = \frac {\text {N u m b e r o f t r u l y d e t e c t e d a t t a c k s}}{\text {T o t a l n u m b e r o f a t t a c k s}} \tag {23}
+$$
+
+$P_{md}$  is the percentage of attacks that the algorithm miss detected. It is given by:
+
+$$
+P _ {m} = \frac {\text {N u m b e r o f m i s s d e t e c t e d a t t a c k s}}{\text {T o t a l n u m b e r o f a t t a c k s}} \tag {24}
+$$
+
+$P_{fa}$  is the percentage of non-attacks that the algorithm detected as attacks
+
+$$
+P _ {f a} = \frac {\text {N u m b e r o f n o n - a t t a c k s d e t e c t e d a s a n a t t a c k}}{\text {T o t a l n u m b e r o f n o n - a t t a c k s}} \tag {25}
+$$
+
+Accuracy gives the total number of attacks and non-attacks that are detected accurately compared to the total number of trials. It is given by:
+
+$$
+A c c u r a c y = \frac {\text {T o t a l n u m b e r o f c o r r e c t l y d e t e c t e d a t t a c k a n d n o n - a t t a c k t r i a l s}}{\text {T o t a l n u m b e r o f t r i a l s}} \tag {26}
+$$
+
+We conducted several experiments and examples of results are given from Fig. 1 to Fig. 4. Fig. 1 shows the accuracy of the classification using random forest versus the number of estimators for a different number of folds in the cross-validation. It can be seen from this figure that for all values of K-folds, 5, 10, and 20, the accuracy of the classification is exponentially increasing as a function of the number of estimators, for numbers of estimators less than 60. However, this accuracy remains slightly constant for numbers higher than 60 and in some cases, it drops. This figure also shows the impact of the number of folds on the accuracy. One can see that with 20 folds, the accuracy is higher than the one with 10 and 5 folds.
+
+![](images/14b0f21385e40bf7c4a16cc0a4e2b0ed2be7d2013645eedf5d894805978768f2.jpg)  
+Fig. 1. Accuracy versus the number of estimators for random forest using different number of k-folds cross validation  $\mathrm{CV} = 5$ , 10, and 20.
+
+To select the best support vector model, we investigated how the accuracy varies for different kernels and regularization parameter  $C$  in order to select the best combination for this given dataset. Fig. 2 shows the accuracy of the classification function of the regularization factor "C" for linear, quadratic, cubic, radial basis function, and sigmoid kernels. From this figure, it can be seen that the impact of the regularization factor "C" does not change the accuracy very much. However, as one can see the choice of the kernel impacts the accuracy. The accuracy is high for radial basis function kernel, followed by linear, cubic, sigmoid, and then quadratic kernels. Support vector machine with radial basis function and regularization factor equal to 3 has the highest accuracy of  $94\%$ .
+
+![](images/536e47eef3fd4534e0041eccfea26036bdfd3e881aac85331f05e2a8a7a0027e.jpg)  
+Fig. 2. Accuracy Vs regularization factor for support vector machine.
+
+Fig. 3 shows the accuracy of the classification function of the number of hidden neurons in one hidden layer of neural network for a different number of k-folds cross-validation. One can observe that the impact of the number of hidden neurons and the number of cross-validation technique is not significant as the accuracy of the classification remains around  $94\%$ , but the highest one is achieved with 1 neuron with 5-folds cross-validation and with 100 neurons with 10-folds cross-validation.
+
+![](images/b124737788a16547cc0998a0f374719c287b79944bc5f9c37b8d9633102dd2d3.jpg)  
+Fig. 3. Accuracy of neural network Vs number of neurons in one hidden layer.
+
+Fig. 4 shows  $Pd$  Vs  $Pfa$  using linear, polynomial with degree 2, radial basis function SVM, neural network with two hidden layers of 2 neurons each, and random forest with 100 estimators. One can see that  $P_{d}$  increases as  $P_{fa}$  increases. In addition, it can be observed that random forest has the higher ROC followed by radial basis function SVM, cubic SVM, linear SVM, and then the neural network which means that random forest outperforms other algorithms regarding the ROC curve.
+
+![](images/57c833d3be351bb3dd894d81effd5ede680b133d54b2fd3db1639e217c4c3832.jpg)  
+Fig. 4. Probability of detection Vs the probability of false alarm.
+
+Table I compares the performance of the jamming detection techniques based on machine learning classifiers for the four evaluation metrics. Random forest achieves the highest probability of detection with  $97.5\%$  followed by cubic SVM with  $97.1\%$  neural network with  $96.4\%$  linear SVM with  $86.9\%$  RBF SVM with  $86.2\%$  sigmoid SVM with  $73.8\%$  and quadratic SVM with  $72\%$ . It can also be seen that random forest has the lowest probabilities of false alarm of  $5.6\%$  followed by neural network with  $11.1\%$  RBF SVM with  $27.2\%$  linear SVM with  $27.25\%$  sigmoid SVM with  $40.1\%$  cubic SVM with  $54\%$  and quadratic SVM with  $65.2\%$ . This table shows also that random forest has the
+
+lowest miss detection with  $2.5\%$ , followed by cubic SVM with  $2.9\%$ , neural network with  $3.6\%$ , linear SVM with  $13.1\%$ , RBF SVM with  $13.8\%$ , sigmoid SVM with  $26.22\%$ , and quadratic SVM with  $28\%$ . In terms of accuracy, random forest has an accuracy as high as  $96.6\%$  followed by neural network with  $94.4\%$ , RBF SVM with  $84.7\%$ , linear SVM with  $83\%$ , sigmoid SVM with  $82.6\%$ , cubic SVM  $70.1\%$ , quadratic SVM with  $62\%$ .
+
+TABLE I. PERFORMANCE COMPARISON  
+
+<table><tr><td>Classification technique</td><td>Pd(%)</td><td>Pfa(%)</td><td>Pmd(%)</td><td>Accuracy (%)</td></tr><tr><td>Linear SVM</td><td>86.9</td><td>27.25</td><td>13.1</td><td>83</td></tr><tr><td>Quadratic SVM</td><td>72</td><td>65.2</td><td>28</td><td>62</td></tr><tr><td>Cubic SVM</td><td>97.1</td><td>54</td><td>2.9</td><td>70.1</td></tr><tr><td>RBF SVM</td><td>86.2</td><td>27.2</td><td>13.8</td><td>84.7</td></tr><tr><td>Sigmoid SVM</td><td>73.8</td><td>40.1</td><td>26.22</td><td>82.6</td></tr><tr><td>Neural network</td><td>96.4</td><td>11.1</td><td>3.6</td><td>94.4</td></tr><tr><td>Random Forest estimators = 100</td><td>97.5</td><td>5.6</td><td>2.5</td><td>96.6</td></tr></table>
+
+# CONCLUSION
+
+5G technology is designed to be resilient to jamming attacks by using millimeter wave band. However, it is also designed to use frequencies below 6 GHz, which are easy to target by jammers. Smart jamming detection techniques are required to prevent these attacks. In this paper, we reviewed the existing jamming detection techniques. We investigated and compared the performance of several machine learning models to detect jamming attacks. Feature extraction and feature selection were performed and a large dataset was constructed to train, validate, and test random forest, support vector machine, and neural network algorithms. We used a cross-validation technique and provided learning curves to evaluate the performance of these models based on a number of metrics. The results show that random forest based technique detects jamming attacks with a very high accuracy and a low cost.  $P_{d}$  of random forest based detection is as high as  $97.5\%$  whereas  $P_{fa}$  of the neural network and cubic support vector machine is around  $96.4\%$  and  $97.1\%$ .  $P_{md}$  and  $P_{fa}$  of random forest are also very low compared to neural network and cubic support vector machine which are  $5.6\%$  and  $2.5\%$ . High  $P_{d}$  and low  $P_{fa}$  make this proposed model suitable for jamming attack detection. These trained machines are able to process a huge number of data within a very short time, which helps increase efficiency and reduce the processing time. Future work includes investigating the efficiency of deep learning in detecting all types of jamming attacks.
+
+# REFERENCES
+
+[1] Y. Wu, A. Khisti, C. Xiao, G. Caire, K. Wong, X. Gao, “A survey of physical layer security technique for 5G wireless networks and challenges ahead,” IEEE J. Selected Areas Commun., vol. 36, no. 4, pp. 679-695, 2018.  
+[2] D. Karas, G. Karagiannidis, R. Schober, "Neural network based PHY-layer key exchange for wireless communication," IEEE Int. Symposium Personal, Indoor and Mobile Radio Commun., pp. 1233-1238, 2011.  
+[3] P. Sinha, V. Jha, A. Rai, B. Bhushan, "Security vulnerabilities, attacks and countermeasures in wireless sensor networks at various layers of OSI reference model: A Survey," Int. Conf. Signal Proc. Commun., pp. 288-293, 2017.  
+[4] J. Heo, J. Kim, J. Paek, S. Bahn, “Mitigating stealthy jamming attacks in low-power and lossy wireless networks,” J. Commun. Netw., pp. 219-230, 2018.  
+[5] M. Bouabdellah, E. Ghribi, and N. Kaabouch. "RSS-Based Localization with Maximum Likelihood Estimation for PUE Attacker Detection in Cognitive Radio Networks." IEEE International Conference on Electro Information Technology (EIT), pp. 1-6, 2019.  
+[6] I. Ngomane, M. Velempini, S. Dlamini, "The detection of the spectrum sensing data falsification attack in cognitive radio ad hoc networks," Info. Commun. Techn. Society Conf., pp. 1-5, 2018.  
+[7] F. Salahdine, N. Kaabouch, "Social Engineering Attacks: A Survey," Future Internet J., Vol. 11, No. 89, pp. 1-17, 2019.  
+[8] D. Fang, Y. Qian, R. Hu, "Security for 5G mobile wireless networks," IEEE Access, vol-6, pp. 4850-4874, 2017.  
+[9] W. Alhakami, A. Mansour, G. Safdar, "Spectrum sharing security and attacks in CRNs: A review," Int. J. Advanced Comput. Sci., vol. 5, no. 1, pp. 76-87, 2014.  
+[10] R. Pietro, G. Oligeri, “Jamming mitigation in cognitive radio networks,” IEEE Netw., vol. 27, no. 3, pp. 10–15, 2013.  
+[11] Z. Lu, W. Wang, C. Wang, "Modeling, evaluation, and detection of jamming attacks in time-critical wireless applications," IEEE Trans. Mobile Comput., vol.13, no.8, pp-1746-1759, 2014.  
+[12] H. Yang, M. Shi, Y. Xia, "Security research on wireless networked control systems subject to jamming attacks," IEEE Trans. Cybernetics, , pp-1-10, 2018.  
+[13] M. Cheng, Y. Ling, W. Wu, "Time series analysis for jamming attack detection in wireless networks," IEEE global Commun. Conf., pp. 1-7, 2017.  
+[14] H. Reyes, N. Kaabouch, "Jamming and lost link detection in wireless networks with fuzzy logic," Int. J. Sentic Eng. research, vol. 4, pp. 1-7, 2013.  
+[15] S. Khattab, D. Mosse, R. Melhem, "Modeling of the channel-hopping anti-jamming defense in multi-radio wireless networks," Int. Conf. mobile ubiquitous syst., pp. 1-10, 2008.  
+[16] Y. Lin, M. Li, "Distributed detection of jamming and defense in wireless sensor networks," Ann. Conf. Info. science and systems, pp. 829-834, 2009.  
+[17] T. Nawaz, et all. "Jammer detection algorithm for wideband radios using spectral correlation and neural networks," Int. Wireless Commun. Mobile Comput. Conf., pp. 112-118, 2017.  
+[18] O. Punal, I. Aktas, C. J. Schnelke, G. Abidin, K. Wehrle, and J. Gross, "Machine learning-based jamming detection for IEEE 802.11: design and experimental evaluation," IEEE Int. Symposium Wireless, Mobile and Multimedia Networks, pp. 1-10, 2014.  
+[19] K. Grover; A. Lim; Q. Yang, “Jamming and anti-jamming techniques in wireless networks: A survey,” Int. J. Ad Hoc Ubiquitous., pp. 197-215, 2014.  
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+# clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation
+
+Suprosanna Shit *¹ Johannes C. Paetzold *¹ Anjany Sekuboyina¹ Ivan Ezhov¹ Alexander Unger¹ Andrey Zhylka² Josien P. W. Pluim² Ulrich Bauer¹ Bjoern H. Menze¹  
+¹Technical University of Munich ² Eindhoven University of Technology
+
+# Abstract
+
+Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.
+
+# 1. Introduction
+
+Segmentation of tubular and curvilinear structures is an essential problem in numerous domains, such as clinical and biological applications (blood vessel and neuron segmentation from microscopic, optoacoustic, or radiology images), remote sensing applications (road network segmentation from satellite images) and industrial quality control, etc. In the aforementioned domains, a topologically accurate segmentation is necessary to guarantee error-free downstream tasks, such as computational hemodynamics, route planning, Alzheimer's disease prediction [18], or stroke modeling [20]. When optimizing computational algorithms for segmenting curvilinear structures, the two most commonly used categories of quantitative performance measures for evaluating segmentation accuracy of tubular struc
+
+![](images/a3b7d710f565e85268c20c8ff6642287abb961743b5007d719b43cdfc9aaf65f.jpg)
+
+![](images/ff4d7175b83fa57dab0cf362010335451e5982ab5e8650d875083765d635d8db.jpg)  
+Figure 1. Motivation: The figure shows a 3D rendering of a complex, whole brain vascular dataset [50], where an exemplary 2D slice of the data is chosen and segmented by two different models, see purple (middle) and red (right), respectively. The two segmentation results achieve identical quality in terms of the traditional Dice score. Note that the purple segmentation does not capture the small vessels while segmenting the large vessel very accurately; on the other side, the red segmentation captures all vessels in the image while being less accurate on the radius of the large vessel. Skeleton are drawn in yellow. From a topology or network perspective, the red segmentation is evidently preferred.
+
+tures, are 1) overlap based measures such as Dice, precision, recall, and Jaccard index; and 2) volumetric distance measures such as the Hausdorff and Mahalanobis distance [21, 42, 37, 16].
+
+However, in most segmentation problems, where the object of interest is 1) locally a tubular structure and 2) globally forms a network, the most important characteristic is the connectivity of the global network topology. Note that network in this context implies a physically connected structure, such as a vessel network, a road network, etc., which is also the primary structure of interest for the given image data. As an example, one can refer to brain vascula
+
+ture analysis, where a missed vessel segment in the segmentation mask can pathologically be interpreted as a stroke or may lead to dramatic changes in a global simulation of blood flow. On the other hand, limited over- or under-segmentation of vessel radius can be tolerated, because it does not affect clinical diagnosis.
+
+For evaluating segmentations in such tubular-network structures, traditional volume-based performance indices are sub-optimal. For example, Dice and Jaccard rely on the average voxel-wise hit or miss prediction [48]. In a task like network-topology extraction, a spatially contiguous sequence of correct voxel prediction is more meaningful than a spurious correct prediction. This ambiguity is relevant for objects of interest, which are of the same thickness as the resolution of the signal. For them, it is evident that a single-voxel shift in the prediction can change the topology of the whole network. Further, a globally averaged metric does not equally weight tubular-structures with large, medium, and small radii (cf. Fig 1). In real vessel datasets, where vessels of wide radius ranges exist, e.g.  $30~\mu \mathrm{m}$  for arterioles and  $5\mu \mathrm{m}$  for capillaries [50, 9], training on a globally averaged loss induces a strong bias towards the volumetric segmentation of large vessels. Both scenarios are pronounced in imaging modalities, such as fluorescence microscopy [50, 60] and optoacoustics, which focus on mapping small capillary structures.
+
+To this end, we are interested in a topology-aware image segmentation, eventually enabling a correct network extraction. Therefore, we ask the following research questions:
+
+Q1. What is a good pixelwise measure to benchmark segmentation algorithms for tubular, and related linear and curvilinear structure segmentation while guaranteeing the preservation of the network-topology?  
+Q2. Can we use this improved measure as a loss function for neural networks, which is a void in existing literature?
+
+# 1.1. Related Literature
+
+Achieving topology preservation can be crucial to obtain meaningful segmentation, particularly for elongated and connected shapes, e.g. vascular structures or roads. However, analyzing preservation of topology while simplifying geometries is a difficult analytical and computational problem [11, 10].
+
+For binary geometries, various algorithms based on thinning and medial surfaces have been proven to be topology-preserving according to varying definitions of topology [23, 25, 26, 36]. For non-binary geometries, existing methods applied topology and connectivity constraints onto variational and Markov random field-based methods: tree shape priors for vessel segmentation [46], graph representation
+
+prriors to natural images [2], higher-order cliques which connect superpixels [55] and adversarial learning for road segmentation [53], integer programming to general curvilinear structures [51], and proposed a tree-structured convolutional gated recurrent unit [22], morphological optimization [14], among others [3, 15, 32, 31, 34, 38, 43, 54, 59, 58]. Further, topological priors of containment were applied to histology scans [5], a 3D CNN with graph refinement was used to improve airway connectivity [19], and recently, Mosinska et al. trained networks which perform segmentation and path classification simultaneously [30]. Another approach enables the predefinition of Betti numbers and enforces them on the training[8].
+
+The aforementioned literature has advanced the communities understanding of topology-preservation, but critically, they do not possess end-to-end loss functions that optimize topology-preservation. In this context, the literature remains sparse. Recently, Mosinska et al. suggested that pixel-wise loss-functions are unsuitable and used selected filter responses from a VGG19 network as an additional penalty [29]. Nonetheless, their approach does not prove topology preservation. Importantly, Hu et al. proposed the first continuous-valued loss function based on the Betti number and persistent homology [17]. However, this method is based on matching critical points, which, according to the authors makes the training very expensive and error-prone for real image-sized patches [17]. While this is already limiting for a translation to large real world data set, we find that none of these approaches have been extended to three dimensional (3D) data.
+
+# 1.2. Our Contributions
+
+The objective of this paper is to identify an efficient, general, and intuitive loss function that enables topology preservation while segmenting tubular objects. We introduce a novel connectivity-aware similarity measure named clDice for benchmarking tubular-segmentation algorithms. Importantly, we provide theoretical guarantees for the topological correctness of the clDice for binary 2D and 3D segmentation. As a consequence of its formulation based on morphological skeletons, our measure pronounces the network's topology instead of equally weighting every voxel. Using a differentiable soft-skeletonization, we show that the clDice measure can be used to train neural networks. We show experimental results for various 2D and 3D network segmentation tasks to demonstrate the practical applicability of our proposed similarity measure and loss function.
+
+# 2. Let's Emphasize Connectivity
+
+We propose a novel connectivity-preserving metric to evaluate tubular and linear structure segmentation based on intersecting skeletons with masks. We call this metric centerlineDice or cLDice.
+
+![](images/8ddee8760162a919ab2b3e9d62dd92ce6606cfc1f4a281b3397606859b4b62d7.jpg)  
+Figure 2. Schematic overview of our proposed method: Our proposed clDice loss can be applied to any arbitrary segmentation network. The soft-skeletonization can be easily implemented using pooling functions from any standard deep-learning toolbox.
+
+We consider two binary masks: the ground truth mask  $(V_{L})$  and the predicted segmentation masks  $(V_{P})$ . First, the skeletons  $S_{P}$  and  $S_{L}$  are extracted from  $V_{P}$  and  $V_{L}$  respectively. Subsequently, we compute the fraction of  $S_{P}$  that lies within  $V_{L}$ , which we call Topology Precision or Tprec  $(S_{P}, V_{L})$ , and vice-a-versa we obtain Topology Sensitivity or Tsens  $(S_{L}, V_{P})$  as defined below;
+
+$$
+\operatorname {T p r e c} \left(S _ {P}, V _ {L}\right) = \frac {\left| S _ {P} \cap V _ {L} \right|}{\left| S _ {P} \right|}; \quad \operatorname {T s e n s} \left(S _ {L}, V _ {P}\right) = \frac {\left| S _ {L} \cap V _ {P} \right|}{\left| S _ {L} \right|} \tag {1}
+$$
+
+We observe that the measure  $\mathrm{Tprec}(S_P, V_L)$  is susceptible to false positives in the prediction while the measure  $\mathrm{Tsen}(S_L, V_P)$  is susceptible to false negatives. This explains our rationale behind referring to the  $\mathrm{Tprec}(S_P, V_L)$  as topology's precision and to the  $\mathrm{Tsen}(S_L, V_P)$  as its sensitivity. Since we want to maximize both precision and sensitivity (recall), we define  $clDice$  to be the harmonic mean (also known as F1 or Dice) of both the measures:
+
+$$
+\operatorname {c l D i c e} \left(V _ {P}, V _ {L}\right) = 2 \times \frac {\operatorname {T p r e c} \left(S _ {P} , V _ {L}\right) \times \operatorname {T s e n s} \left(S _ {L} , V _ {P}\right)}{\operatorname {T p r e c} \left(S _ {P} , V _ {L}\right) + \operatorname {T s e n s} \left(S _ {L} , V _ {P}\right)} \tag {2}
+$$
+
+Note that our clDice formulation is not defined for Tprec = 0 and Tsens = 0, but can easily be extended continuously with the value 0.
+
+# 3. Topological Guarantees for clDice
+
+The following section provides general theoretical guarantees for the preservation of topological properties
+
+achieved by optimizing clDice under mild conditions on the input. Roughly, these conditions state that the object of interest is embedded in  $S^3$  in a non-knotted way, as is typically the case for blood vessel and road structures.
+
+Specifically, we assume that both ground truth and prediction admit foreground and background skeleta, which means that both foreground and background are homotopy-equivalent to topological graphs, which we assume to be embedded as skeleta. Here, the voxel grid is considered as a cubical complex, consisting of elementary cubes of dimensions 0, 1, 2, and 3. This is a special case of a cell complex (specifically, a CW complex), which is a space constructed inductively, starting with isolated points (0-cells), and gluing a collection of topological balls of dimension  $k$  (called  $k$ -cells) along their boundary spheres to a  $k - 1$ -dimensional complex. The voxel grid, seen as a cell complex in this sense, can be completed to an ambient complex that is homeomorphic to the 3-sphere  $S^3$  by attaching a single exterior cell to the boundary. In order to consider foreground and background of a binary image as complementary subspaces, the foreground is now assumed to be the union of closed unit cubes in the voxel grid, corresponding to voxels with value 1; and the background is the complement in the ambient complex. This convention is commonly used in digital topology [24, 23]. The assumption on the background can then be replaced by a convenient equivalent condition, stating that the foreground is also homotopy equivalent to a subcomplex obtained from the ambient complex by only removing 3-cells and 2-cells. Such a subcomplex is then clearly homotopy-equivalent to the complement of a 1-complex.
+
+We will now observe that the above assumptions imply that the foreground and the background are connected and have a free fundamental group and vanishing higher fundamental groups. In particular, the homotopy type is already determined by the first Betti number  ${}^{1}$ ; moreover, a map inducing an isomorphism in homology is already a homotopy equivalence. To see this, first note that both foreground and background are assumed to have the homology of a graph, in particular, homology is trivial in degree 2. By Alexander duality [1], then, both foreground and background have trivial reduced cohomology in degree 0, meaning that they are connected. This implies that both have a free fundamental group (as any connected graph) and vanishing higher homotopy groups. In particular, since homology in degree 1 is the Abelianization of the fundamental group, these two groups are isomorphic. This in turn implies that in our setting a map that induces isomorphisms in homology already induces isomorphisms between all homotopy groups. By Whitehead's theorem [56], such a map is then a homotopy equivalence.
+
+The following theorem shows that under our assumptions on the images admitting foreground and background skeleta, the existence of certain nested inclusions already implies the homotopy-equivalence of foreground and background, which we refer to as topology preservation.
+
+Theorem 1. Let  $L_{A} \subseteq A \subseteq K_{A}$  and  $L_{B} \subseteq B \subseteq K_{B}$  be connected subcomplexes of some cell complex. Assume that the above inclusions are homotopy equivalences. If the subcomplexes also are related by inclusions  $L_{A} \subseteq B \subseteq K_{A}$  and  $L_{B} \subseteq A \subseteq K_{B}$ , then these inclusions must be homotopy equivalences as well. In particular,  $A$  and  $B$  are homotopy-equivalent.
+
+Proof. An inclusion of connected cell complexes is a homotopy equivalence if and only if it induces isomorphisms on all homotopy groups. Since the inclusion  $L_A \subseteq B \subseteq K_A$  induces an isomorphism, the inclusion  $L_A \subseteq B$  induces a monomorphism, and since  $B \subseteq K_B$  induces an isomorphism, the inclusion  $L_A \subseteq K_B$  also induces a monomorphism. At the same time, since the inclusion  $L_B \subseteq A \subseteq K_B$  induces an isomorphism, the inclusion  $A \subseteq K_B$  induces an epimorphism, and since  $L_A \subseteq A$  induces an isomorphism, the inclusion  $L_A \subseteq K_B$  also induces an epimorphism. Together, this implies that the inclusion  $L_A \subseteq K_B$  induces an isomorphism.
+
+Together with the isomorphisms induced by  $L_{A} \subseteq A$  and  $B \subseteq K_{B}$ , we obtain isomorphisms induced by  $L_{A} \subseteq B$  and
+
+by  $A \subseteq K_B$ , which compose to an isomorphism between the homotopy groups of  $A$  and  $B$ .
+
+Corollary 1.1. Let  $V_{L}$  and  $V_{P}$  be two binary masks admitting foreground and background skeleta, such that the foreground skeleton of  $V_{L}$  is included in the foreground of  $V_{P}$  and vice versa, and similarly for the background. Then the foregrounds of  $V_{L}$  and  $V_{P}$  are homotopy equivalent, and the same is true for their backgrounds.
+
+Note that the inclusion condition in this corollary is satisfied if and only if  $clDice$  evaluates to 1 on both foreground and background of  $(V_L, V_P)$ .
+
+This proof lays the ground for a general interpretation of  $clDice$  as a topology preserving metric. Additionally, we provide an elaborate explanation of  $clDice$  topological properties, using concepts of applied digital topology in the theory section of the Supplementary material [24, 23].
+
+# 4. Training Neural Networks with clDice
+
+In the previous section we provided general theoretic guarantees how  $clDice$  has topology preserving properties. The following chapter shows how we applied our theory to efficiently train topology preserving networks using the  $clDice$  formulation. $^2$
+
+# 4.1. Soft-clDice using Soft-skeletonization:
+
+Extracting accurate skeletons is essential to our method. For this task, a multitude of approaches has been proposed. However, most of them are not fully differentiable and therefore unsuited to be used in a loss function. Popular approaches use the Euclidean distance transform or utilize repeated morphological thinning. Euclidean distance transform has been used on multiple occasions [44, 57], but remains a discrete operation and, to the best of our knowledge, an end-to-end differentiable approximation remains to be developed, preventing the use in a loss function for training neural networks. On the contrary, morphological thinning is a sequence of dilation and erosion operations [c.f. Fig. 3].
+
+Importantly, thinning using morphological operations (skeletonization) on curvilinear structures can be topology-preserving [36]. Min- and max filters are commonly used as the grey-scale alternative of morphological dilation and erosion. Motivated by this, we propose 'soft-skeletonization', where an iterative min- and max-pooling is applied as a proxy for morphological erosion and dilation. The Algorithm 1 describes the iterative processes involved in its computation. The hyper-parameter  $k$  involved in its computation represents the iterations and has to be greater than or equal to the maximum observed radius. In our experiments, this parameter depends on the dataset. For example, it is
+
+![](images/517761b6ead1565f573b780327709380fca0f85a8926e534e324360fb9bd81c7.jpg)  
+Figure 3. Based on the initial vessel structure (purple), sequential bagging of skeleton voxels (red) via iterative skeletonization leads to a complete skeletonization, where  $d$  denotes the diameter and  $k > j > i$  iterations.  
+Figure 4. Algorithm 1 calculates the proposed soft-skeleton, here  $I$  is the mask to be soft-skeletonized and  $k$  is the number of iterations for skeletonization. Algorithm 2, calculates the soft-clDice loss, where  $V_{P}$  is a real-valued probabilistic prediction from a segmentation network and  $V_{L}$  is the true mask. We denote Hadamard product using  $\circ$ .
+
+Algorithm 1: soft-skeleton  
+Input:  $I,k$ $I^{\prime}\gets \mathrm{maxpool(minpool(I))}$ $S\gets \mathsf{ReLU}(I - I^{\prime})$    
+for  $i\gets 0$  to  $k$  do  
+ $I\gets \mathrm{minpool}(I)$ $I^{\prime}\gets \mathrm{maxpool(minpool(I))}$ $S\gets S + (1 - S)\circ \mathsf{ReLU}(I - I^{\prime})$    
+end  
+Output:  $S$
+
+Algorithm 2: soft-clDice  
+Output: clDice  
+Input:  $V_{P},V_{L}$ $S_P\gets$  soft-skeleton  $(V_{P})$ $S_L\gets$  soft-skeleton  $(V_L)$  Tprec  $(S_P,V_L)\gets \frac{|S_P\circ V_L| + \epsilon}{|S_P| + \epsilon}$  Tsens  $(S_L,V_P)\gets \frac{|S_L\circ V_P| + \epsilon}{|S_L| + \epsilon}$  clDice  $\leftarrow$ $2\times \frac{T_{prec}(S_P,V_L)\times T_{sens}(S_L,V_P)}{T_{prec}(S_P,V_L) + T_{sens}(S_L,V_P)}$
+
+$k = 5\dots 25$  in our experiments, matching the pixel radius of the largest observed tubular structures. Choosing a larger  $k$  does not reduce performance but increases computation time. On the other hand, a too low  $k$  leads to incomplete skeletonization.
+
+In Figure 3, the successive steps of our skeletonization are intuitively represented. In the early iterations, the structures with a small radius are skeletonized and preserved until the later iterations when the thicker structures become
+
+skeletonized. This enables the extraction of a parameter-free, morphologically motivated soft-skeleton. The aforementioned soft-skeletonization enables us to use  $clDice$  as a fully differentiable, real-valued, estimizable measure. The Algorithm 2 describes its implementation. We refer to this as the soft-clDice.
+
+For a single connected foreground component and in the absence of knots, the homotopy type is specified by the number of linked loops. Hence, if the reference and the predicted volumes are not homotopy equivalent, they do not have pairwise linked loops. To include these missing loops or exclude the extra loops, one has to add or discard deformation retracted skeleta of the solid foreground. This implies adding new correctly predicted voxels. In contrast to other volumetric losses such as Dice, cross-entropy, etc., clDice only considers the deformation-retracted graphs of the solid foreground structure. Thus, we claim that clDice requires the least amount of new correctly predicted voxels to guarantee the homotopy equivalence. Along these lines, Dice or cross-entropy can only guarantee homotopy equivalence if every single voxel is segmented correctly. On the other hand, clDice can guarantee homotopy equivalence for a broader combinations of connected-voxels. Intuitively, this is a very much desirable property as it makes clDice robust towards outliers and noisy segmentation labels.
+
+# 4.2. Cost Function
+
+Since our objective here is to preserve topology while achieving accurate segmentations, and not to learn skeleta, we combine our proposed soft-clDice with soft-Dice in the following manner:
+
+$$
+\mathcal {L} _ {c} = (1 - \alpha) (1 - \text {s o f t D i c e}) + \alpha (1 - \text {s o f t c l D i c e}) \tag {3}
+$$
+
+where  $\alpha \in [0,0.5]$ . In stark contrast to previous works, where segmentation and centerline prediction has been learned jointly as multi-task learning [52, 49], we are not
+
+interested in learning the centerline. We are interested in learning a topology-preserving segmentation. Therefore, we restrict our experimental choice of alpha to  $\alpha \in [0, 0.5]$ . We test  $clDice$  on two state-of-the-art network architectures: i) a 2D and 3D U-Net[39, 6], and ii) a 2D and 3D fully connected networks (FCN) [49, 13]. As baselines, we use the same architectures trained using soft-Dice [27, 47].
+
+# 4.3. Adaption for Highly Imbalanced Data
+
+Our theory (Section 3), describes a two-class problem where clDice should be computed on both the foreground and the background channels. In our experiments, we show that for complex and highly imbalanced dataset it is sufficient to calculate the clDice loss on the underrepresented foreground class. We attribute this to the distinct properties of tubulerness, sparsity of foreground and the lack of cavities (Betti number 2) in our data. An intuitive interpretation how these assumptions are valid in terms of digital topology can be found in the supplementary material.
+
+# 5. Experiments
+
+# 5.1. Datasets
+
+We employ five public datasets for validating clDice and soft-clDice as a measure and an objective function, respectively. In 2D, we evaluate on the DRIVE retina dataset [45], the Massachusetts Roads dataset [28] and the CREMI neuron dataset [12]. In 3D, a synthetic vessel dataset with an added Gaussian noise term [41] and the Vessap dataset of multi-channel volumetric scans of brain vessels is used [50, 35]. For the Vessap dataset we train different models for one and two input channels. For all of the datasets, we perform three fold cross-validation and test on held-out, large, and highly-variant test sets. Details concerning the experimental setup can be found in the supplementary.
+
+# 5.2. Evaluation Metrics
+
+We compare the performance of various experimental setups using three types of metrics: volumetric, topology-based, and graph-based.
+
+1. Volumetric: We compute volumetric scores such as Dice coefficient, Accuracy, and the proposed clDice.  
+2. Topology-based: We calculate the mean of absolute Betti Errors for the Betti Numbers  $\beta_0$  and  $\beta_{1}$  and the mean absolute error of Euler characteristic,  $\chi = V - E + F$ , where  $V, E$ , and  $F$  denotes number of vertices, edges, and faces.  
+3. Graph-based: we extract random patch-wise graphs for the 2D/3D images. We uniformly sample fixed number of points from the graph and compute the StreetmoverDistance (SMD) [4]. SMD captures a Wasserstein distance between two graphs. Additionally we compute the F1 score of junction-based metric [7].
+
+# 5.3. Results and Discussion
+
+We trained two segmentation architectures, a U-Net and an FCN, for the various loss functions in our experimental setup. As a baseline, we trained the networks using soft-dice and compared it with the ones trained using the proposed loss (Eq. 3), by varying  $\alpha$  from (0.1 to 0.5).
+
+Quantitative: We observe that including soft-clDice in any proportion  $(\alpha > 0)$  leads to improved topological, volumetric and graph similarity for all 2D and 3D datasets, see Table 1. We conclude that  $\alpha$  can be interpreted as a hyper parameter which can be tuned per-dataset. Intuitively, increasing the  $\alpha$  improves the clDice measure for most experiments. Most often, clDice is high or highest when the graph and topology based measures are high or highest, particularly the  $\beta_{1}$  Error, Streetmover distance and Opt-J F1 score; quantitatively indicating that topological properties are indeed represented in the clDice measure.
+
+In spite of not optimizing for a high soft-clDice on the background class, all of our networks converge to superior segmentation results. This not only reinforces our assumptions on dataset-specific necessary conditions but also validates the practical applicability of our loss. Our findings hold for the different network architectures, for 2D or 3D, and for tubular or curvilinear structures, strongly indicating its generalizability to analogous binary segmentation tasks.
+
+Observe that CREMI and the synthetic vessel dataset (see Supplementary material) appear to have the smallest increase in scores over the baseline. We attribute this to them being the least complex datasets in the collection, with CREMI having an almost uniform thickness of radii and the synthetic data having a high signal-to-noise ratio and insignificant illumination variation. More importantly, we observe larger improvements for all measures in case of the more complex Vessap and Roads data see Figure 5. In direct comparison to performance measures reported in two recent publications by Hu et al. and Mosinska et al. [17, 29], we find that our approach is on par or better in terms of Accuracy and Betti Error for the Roads and CREMI dataset. It is important to note that we used a smaller subset of training data for the Road dataset compared to both while using the same test set.
+
+Hu et al. reported a Betti error for the DRIVE data, which exceeds ours; however, it is important to consider that their approach explicitly minimizes the mismatch of the persistence diagram, which has significantly higher computational complexity during training, see the section below. We find that our proposed loss performs superior to the baseline in almost every scenario. The improvement appears to be pronounced when evaluating the highly relevant graph and topology based measures, including the recently
+
+Table 1. Quantitative experimental results for the Massachusetts road dataset (Roads), the CREMI dataset, the DRIVE retina dataset and the Vessap dataset (3D). Bold numbers indicate the best performance. The performance according to the  $clDice$  measure is highlighted in rose. For all experiments we observe that using soft-clDice in  $\mathcal{L}_c$  results in improved scores compared to soft-Dice. This improvement holds for almost  $\alpha > 0$ ;  $\alpha$  can be interpreted as a dataset specific hyper-parameter.  
+
+<table><tr><td>Dataset</td><td>Network</td><td>Loss</td><td>Dice</td><td>Accuracy</td><td>clDice</td><td>β0Error</td><td>β1Error</td><td>SMD [4]</td><td>χerror</td><td>Opt-J F1 [7]</td></tr><tr><td rowspan="14">Roads</td><td rowspan="6">FCN</td><td>soft-dice</td><td>64.84</td><td>95.16</td><td>70.79</td><td>1.474</td><td>1.408</td><td>0.1216</td><td>2.634</td><td>0.766</td></tr><tr><td>Lc,α=0.1</td><td>66.52</td><td>95.70</td><td>74.80</td><td>0.987</td><td>1.227</td><td>0.1002</td><td>2.625</td><td>0.768</td></tr><tr><td>Lc,α=0.2</td><td>67.42</td><td>95.80</td><td>76.25</td><td>0.920</td><td>1.280</td><td>0.0954</td><td>2.526</td><td>0.770</td></tr><tr><td>Lc,α=0.3</td><td>65.90</td><td>95.35</td><td>74.86</td><td>0.974</td><td>1.197</td><td>0.1003</td><td>2.448</td><td>0.775</td></tr><tr><td>Lc,α=0.4</td><td>67.18</td><td>95.46</td><td>76.92</td><td>0.934</td><td>1.092</td><td>0.0991</td><td>2.183</td><td>0.803</td></tr><tr><td>Lc,α=0.5</td><td>65.77</td><td>95.09</td><td>75.22</td><td>0.947</td><td>1.184</td><td>0.0991</td><td>2.361</td><td>0.782</td></tr><tr><td rowspan="6">U-NET</td><td>soft-dice</td><td>76.23</td><td>96.75</td><td>86.83</td><td>0.491</td><td>1.256</td><td>0.0589</td><td>1.120</td><td>0.881</td></tr><tr><td>Lc,α=0.1</td><td>76.66</td><td>96.77</td><td>87.35</td><td>0.359</td><td>0.938</td><td>0.0457</td><td>0.980</td><td>0.878</td></tr><tr><td>Lc,α=0.2</td><td>76.25</td><td>96.76</td><td>87.29</td><td>0.312</td><td>1.031</td><td>0.0415</td><td>0.865</td><td>0.900</td></tr><tr><td>Lc,α=0.3</td><td>74.85</td><td>96.57</td><td>86.10</td><td>0.322</td><td>1.062</td><td>0.0504</td><td>0.827</td><td>0.913</td></tr><tr><td>Lc,α=0.4</td><td>75.38</td><td>96.60</td><td>86.16</td><td>0.344</td><td>1.016</td><td>0.0483</td><td>0.755</td><td>0.916</td></tr><tr><td>Lc,α=0.5</td><td>76.45</td><td>96.64</td><td>88.17</td><td>0.375</td><td>0.953</td><td>0.0527</td><td>1.080</td><td>0.894</td></tr><tr><td>Mosinska et al.</td><td>[29, 17]</td><td>-</td><td>97.54</td><td>-</td><td>-</td><td>2.781</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Hu et al.</td><td>[17]</td><td>-</td><td>97.28</td><td>-</td><td>-</td><td>1.275</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="8">CREMI</td><td rowspan="6">U-NET</td><td>soft-dice</td><td>91.54</td><td>97.11</td><td>95.86</td><td>0.259</td><td>0.657</td><td>0.0461</td><td>1.087</td><td>0.904</td></tr><tr><td>Lc,α=0.1</td><td>91.76</td><td>97.21</td><td>96.05</td><td>0.222</td><td>0.556</td><td>0.0395</td><td>1.000</td><td>0.900</td></tr><tr><td>Lc,α=0.2</td><td>91.66</td><td>97.15</td><td>96.01</td><td>0.231</td><td>0.630</td><td>0.0419</td><td>0.991</td><td>0.902</td></tr><tr><td>Lc,α=0.3</td><td>91.78</td><td>97.18</td><td>96.21</td><td>0.204</td><td>0.537</td><td>0.0437</td><td>0.919</td><td>0.913</td></tr><tr><td>Lc,α=0.4</td><td>91.56</td><td>97.12</td><td>96.09</td><td>0.250</td><td>0.630</td><td>0.0444</td><td>0.995</td><td>0.902</td></tr><tr><td>Lc,α=0.5</td><td>91.66</td><td>97.16</td><td>96.16</td><td>0.231</td><td>0.620</td><td>0.0455</td><td>0.991</td><td>0.907</td></tr><tr><td>Mosinska et al.</td><td>[29, 17]</td><td>82.30</td><td>94.67</td><td>-</td><td>-</td><td>1.973</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Hu et al.</td><td>[17]</td><td>-</td><td>94.56</td><td>-</td><td>-</td><td>1.113</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="10">DRIVE retina</td><td rowspan="6">FCN</td><td>soft-Dice</td><td>78.23</td><td>96.27</td><td>78.02</td><td>2.187</td><td>1.860</td><td>0.0429</td><td>3.275</td><td>0.773</td></tr><tr><td>Lc,α=0.1</td><td>78.36</td><td>96.25</td><td>79.02</td><td>2.100</td><td>1.610</td><td>0.0393</td><td>3.203</td><td>0.777</td></tr><tr><td>Lc,α=0.2</td><td>78.75</td><td>96.29</td><td>80.22</td><td>1.892</td><td>1.382</td><td>0.0383</td><td>2.895</td><td>0.793</td></tr><tr><td>Lc,α=0.3</td><td>78.29</td><td>96.20</td><td>80.28</td><td>1.888</td><td>1.332</td><td>0.0318</td><td>2.918</td><td>0.798</td></tr><tr><td>Lc,α=0.4</td><td>78.00</td><td>96.11</td><td>80.43</td><td>2.036</td><td>1.602</td><td>0.0423</td><td>3.141</td><td>0.764</td></tr><tr><td>Lc,α=0.5</td><td>77.76</td><td>96.04</td><td>80.95</td><td>1.836</td><td>1.408</td><td>0.0394</td><td>2.848</td><td>0.794</td></tr><tr><td rowspan="2">U-Net</td><td>soft-Dice</td><td>74.25</td><td>95.63</td><td>75.71</td><td>1.745</td><td>1.455</td><td>0.0649</td><td>2.997</td><td>0.760</td></tr><tr><td>Lc,α=0.5</td><td>75.21</td><td>95.82</td><td>76.86</td><td>1.538</td><td>1.389</td><td>0.0586</td><td>2.737</td><td>0.767</td></tr><tr><td>Mosinska et al.</td><td>[29, 17]</td><td>-</td><td>95.43</td><td>-</td><td>-</td><td>2.784</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Hu et al.</td><td>[17]</td><td>-</td><td>95.21</td><td>-</td><td>-</td><td>1.076</td><td>-</td><td>-</td><td>-</td></tr><tr><td rowspan="16">Vessap data</td><td rowspan="2">FCN, 1 ch</td><td>soft-dice</td><td>85.21</td><td>96.03</td><td>90.88</td><td>3.385</td><td>4.458</td><td>0.00459</td><td>5.850</td><td>0.862</td></tr><tr><td>Lc,α=0.5</td><td>85.44</td><td>95.91</td><td>91.32</td><td>2.292</td><td>3.677</td><td>0.00417</td><td>5.620</td><td>0.864</td></tr><tr><td rowspan="6">FCN, 2 ch</td><td>soft-dice</td><td>85.31</td><td>95.82</td><td>90.10</td><td>2.833</td><td>4.771</td><td>0.00629</td><td>6.080</td><td>0.849</td></tr><tr><td>Lc,α=0.1</td><td>85.96</td><td>95.99</td><td>91.02</td><td>2.896</td><td>4.156</td><td>0.00447</td><td>5.980</td><td>0.860</td></tr><tr><td>Lc,α=0.2</td><td>86.45</td><td>96.11</td><td>91.22</td><td>2.656</td><td>4.385</td><td>0.00466</td><td>5.530</td><td>0.869</td></tr><tr><td>Lc,α=0.3</td><td>85.72</td><td>95.93</td><td>91.20</td><td>2.719</td><td>4.469</td><td>0.00423</td><td>5.470</td><td>0.866</td></tr><tr><td>Lc,α=0.4</td><td>85.65</td><td>95.95</td><td>91.65</td><td>2.719</td><td>4.469</td><td>0.00423</td><td>5.670</td><td>0.869</td></tr><tr><td>Lc,α=0.5</td><td>85.28</td><td>95.76</td><td>91.22</td><td>2.615</td><td>4.615</td><td>0.00433</td><td>5.320</td><td>0.870</td></tr><tr><td rowspan="2">U-Net, 1 ch</td><td>soft-dice</td><td>87.46</td><td>96.35</td><td>91.18</td><td>3.094</td><td>5.042</td><td>0.00549</td><td>5.300</td><td>0.863</td></tr><tr><td>Lc,α=0.5</td><td>87.82</td><td>96.52</td><td>93.03</td><td>2.656</td><td>4.615</td><td>0.00533</td><td>4.910</td><td>0.872</td></tr><tr><td rowspan="6">U-Net, 2 ch</td><td>soft-dice</td><td>87.98</td><td>96.56</td><td>90.16</td><td>2.344</td><td>4.323</td><td>0.00507</td><td>5.550</td><td>0.855</td></tr><tr><td>Lc,α=0.1</td><td>88.13</td><td>96.59</td><td>91.12</td><td>2.302</td><td>4.490</td><td>0.00465</td><td>5.180</td><td>0.872</td></tr><tr><td>Lc,α=0.2</td><td>87.96</td><td>96.74</td><td>92.52</td><td>2.208</td><td>3.979</td><td>0.00342</td><td>4.830</td><td>0.861</td></tr><tr><td>Lc,α=0.3</td><td>87.70</td><td>96.71</td><td>92.56</td><td>2.115</td><td>4.521</td><td>0.00309</td><td>5.260</td><td>0.858</td></tr><tr><td>Lc,α=0.4</td><td>88.57</td><td>96.87</td><td>93.25</td><td>2.281</td><td>4.302</td><td>0.00327</td><td>5.370</td><td>0.868</td></tr><tr><td>Lc,α=0.5</td><td>88.14</td><td>96.74</td><td>92.75</td><td>2.135</td><td>4.125</td><td>0.00328</td><td>5.390</td><td>0.864</td></tr></table>
+
+introduced OPT-Junction F1 by Citraro et al. [7]. Our results are consistent across different network architectures, indicating that soft-clDice can be deployed to any network architecture.
+
+Qualitative: In Figure 5, typical results for our datasets are depicted. Our networks trained on the proposed loss term recover connections, which were false negatives when trained with the soft-Dice loss. These missed connections appear to be particularly frequent in the complex road and
+
+DRIVE dataset. For the CREMI dataset, we observe these situations less frequently, which is in line with the very high quantitative scores on the CREMI data. Interestingly, in the real 3D vessel dataset, the soft-Dice loss oversegments vessels, leading to false positive connections. This is not the case when using our proposed loss function, which we attribute to its topology-preserving nature. Additional qualitative results can be inspected in the supplementary.
+
+Computational Efficiency: Naturally, inference times of CNNs with the same architecture but different training losses are identical. However, during training, our soft-skeleton algorithm requires  $O(kn^2)$  complexity for an  $n \times n$  2D image where  $k$  is the number of iterations. As a comparison, [17] needs  $O(c^2 m \log(m))$  (see [15]) complexity to compute the 1d persistent homology where  $d$  is the number of points with zero gradients in the prediction and  $m$  is the number of simplices. Roughly,  $c$  is proportional to  $n^2$ , and  $m$  is of  $O(n^2)$  for a 2D Euclidean grid. Thus, the worst complexity of [17] is  $O(n^6 \log(n))$ . Additionally, their approach requires an  $O(c \log(c))$  complexity to find an optimal matching of the birth-death pairs. We note that the total run-time overhead for soft-clDice compared to soft-Dice is marginal, i.e., for batch-size of 4 and 1024x1024 image resolution, the former takes 1.35s while the latter takes 1.24s on average (<10% increase) on an RTX-8000.
+
+Future Work: Although our proposed soft-skeleton approximation works well in practice, a better differentiable skeletonization can only improve performance, which we reserve for future research. Any such skeletonization can be readily plugged into our approach. Furthermore, theoretical and experimental multi-class studies would sensibly extend our study.
+
+# 6. Conclusive Remarks
+
+We introduce clDice, a novel topology-preserving similarity measure for tubular structure segmentation. Importantly, we present a theoretical guarantee that clDice enforces topology preservation up to homotopy equivalence. Next, we use a differentiable version of the clDice, soft-clDice, in a loss function, to train state-of-the-art 2D and 3D neural networks. We use clDice to benchmark segmentation quality from a topology-preserving perspective along with multiple volumetric, topological, and graph-based measures. We find that training on soft-clDice leads to segmentations with more accurate connectivity information, better graph-similarity, better Euler characteristics, and improved Dice and Accuracy. Our soft-clDice is computationally efficient and can be readily deployed to any other deep learning-based segmentation tasks such as neuron segmentation in biomedical imaging, crack detection in industrial quality control, or remote sensing.
+
+Acknowledgement: J. C. Paetzold. and S. Shit. are supported by the GCB and Translatum, TU Munich. S.Shit., A. Zhylka. and I. Ezhov. are supported by TRABIT (EU Grant: 765148). We thank Ali Ertuerk, Mihail I. Todorov, Nils Borner and Giles Tetteh.
+
+![](images/20e69f06f3c11e4f9084fd9378cf0a463f6e32b6d134accfb0217a9ce472b11d.jpg)  
+Image Label Soft-Dice Ours  
+Figure 5. Qualitative results: from top to bottom we show two rows of results for: the Massachusetts road dataset, the DRIVE retina dataset, the CREMI neuron data and 2D slices from the 3D Vessap dataset. From left to right, the real image, the label, the prediction using soft-Dice and the U-Net predictions using  $\mathcal{L}_c(\alpha = 0.5)$  are shown, respectively. The images indicate that clDice segments road, retina vessel connections and neuron connections which the soft-Dice loss misses, but also does not segment false-positive vessels in 3D. Some, but not all, missed connections are indicated with solid red arrows, false positives are indicated with red-yellow arrows. More qualitative results can be found in the Supplementary material.
+
+# References
+
+[1] Pavel S Aleksandrov. Combinatorial topology, volume 1. Courier Corporation, 1998. 4  
+[2] Bjoern Andres et al. Probabilistic image segmentation with closedness constraints. In ICCV, pages 2611-2618. IEEE, 2011. 2  
+[3] Ricardo J Araújo, Jaime S Cardoso, and Hélder P Oliveira. A deep learning design for improving topology coherence in blood vessel segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 93-101. Springer, 2019. 2  
+[4] Davide Belli and Thomas Kipf. Image-conditioned graph generation for road network extraction. arXiv preprint arXiv:1910.14388, 2019. 6, 7, 16  
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+
+# A. Theory - clDice in Digital Topology
+
+In addition to our Theorem 1 in the main paper, we are providing intuitive interpretations of  $clDice$  from the digital topology perspective. Betti numbers describe and quantify topological differences in algebraic topology. The first three Betti numbers  $(\beta_0, \beta_1,$  and  $\beta_{2}$ ) comprehensively capture the manifolds appearing in 2D and 3D topological space. Specifically,
+
+-  $\beta_0$  represents the number of connected-components,  
+-  $\beta_{1}$  represents the number of circular holes, and  
+-  $\beta_{2}$  represents the number of cavities (Only in 3D)
+
+![](images/7e032cfbb39c10f766879f7199363444469e056e66657b00b96b1ae9dc05a8d9.jpg)  
+Figure 6. Examples of the topology properties. Left, a hole in 2D, in the middle a hole in 3D and right a cavity inside a sphere in 3D.
+
+Using the concepts of Betti numbers and digital topology by Kong et al. [23, 40], we formulate the effect of topological changes between a true binary mask  $(V_{L})$  and a predicted binary mask  $(V_{P})$  in Fig. 7. We will use the following definition of ghosts and misses, see Figure 7.
+
+1. Ghosts in skeleton: We define ghosts in the predicted skeleton  $(S_P)$  when  $S_P \not\subset V_L$ . This means the predicted skeleton is not completely included in the true mask. In other words, there exist false-positives in the prediction, which survive after skeletonization.  
+2. Misses in skeleton: We define misses in the predicted skeleton  $(S_P)$  when  $S_L \not\subset V_P$ . This means the true skeleton is not completely included in the predicted mask. In other words, there are false-negatives in the prediction, which survive after skeletonization.
+
+The false positives and false negatives are denoted by  $V_{P} \backslash V_{L}$  and  $V_{L} \backslash V_{P}$ , respectively, where  $\backslash$  denotes a set difference operation. The loss function aims to minimize both errors. We call an error correction to happen when the value of a previously false-negative or false-positive voxel flips to a correct value. Commonly used voxel-wise loss functions, such as Dice-loss, treat every false-positive and false-negative equally, irrespective of the improvement in regards to topological differences upon their individual error correction. Thus, they cannot guarantee homotopy equivalence until and unless every single voxel is correctly classified. In stark contrast, we show in the following proposition that clDice guarantees homotopy equivalence under a minimum error correction.
+
+Proposition 2. For any topological differences between  $V_P$  and  $V_L$ , achieving optimal clDice to guarantee homotopy equivalence requires a minimum error correction of  $V_P$ .
+
+Proof. From Fig 7, any topological differences between  $V_{P}$  and  $V_{L}$  will result in ghosts or misses in the foreground or background skeleton. Therefore, removing ghosts and misses are sufficient conditions to remove topological differences. Without the loss of generalizability, we consider the case of ghosts and misses separately:
+
+For a ghost  $g \subset S_P$ ,  $\exists$  a set of predicted voxels  $E1 \subset \{V_P \setminus V_L\}$  such that  $V_P \setminus E1$  does not create any misses and removes  $g$ . Without the loss of generalizability, let's assume that there is only one ghost  $g$ . Now, to remove  $g$ , under a minimum error correction of  $V_P$ , we have to minimize  $|E1|$ . Let's say an optimum solution  $E1_{min}$  exists. By construction, this implies that  $V_P \setminus E1_{min}$  removes  $g$ .
+
+For a miss  $m \subset V_P^6$ ,  $\exists$  a set of predicted voxels  $E2 \subset \{V_L \setminus V_P\}$  such that  $V_P \cup E2$  does not create any ghosts and removes  $m$ . Without the loss of generalizability, let's assume that there is only one miss  $m$ . Now, to remove  $m$ , under a minimum error correction of  $V_P$ , we have to minimize  $|E2|$ . Let's say an optimum solution  $E2_{min}$  exists. By construction, this implies that  $V_P \cup E2_{min}$  removes  $m$ .
+
+Thus, in the absence of any ghosts and misses, from Lemma 2.1,  $clDice = 1$  for both foreground and background. Finally, Therefore, Theorem 1 (from the main paper) guarantees homotopy equivalence.
+
+Lemma 2.1. In the absence of any ghosts and misses  $\text{clDice} = 1$ .
+
+Proof. The absence of any ghosts  $S_P \in V_L$  implies  $T\text{prec} = 1$ ; and the absence of any misses  $S_L \in V_P$  implies  $T\text{sens} = 1$ . Hence,  $\text{clDice} = 1$ .
+
+# A.1. Interpretation of the Adaption to Highly Unbalanced Data According to Digital Topology:
+
+Considering the adaptions we described in the main text, the following provides analysis on how these assumptions and adaptations are funded in the concept of ghosts and misses, described in the previous proofs. Importantly, the described adaptations are not detrimental to the performance of  $clDice$  for our datasets. We attribute this to the non-applicability of the necessary conditions specific to the background (i.e. II, IV, VI, VII, and IX in Figure A), as explained below:
+
+- II.  $\rightarrow$  In tubular structures, all foreground objects are eccentric (or anisotropic). Therefore isotropic skeletonization will highly likely produce a ghost in the foreground.
+
+![](images/2b1cf057ad965608a126450a66cc6582576eb9082504e48744edb222f33268a7.jpg)  
+Figure 7. Upper part, left, taxonomy of the  $iff$  conditions to preserve topology in 3D using the concept of Betti numbers [23, 24]; interpreted as the necessary violation of skeleton properties for any possible topological change in the terminology of ghosts and misses (upper part right). Lower part, intuitive depictions of ghosts and misses in the prediction; for the skeleton of the foreground (left) and the skeleton of the background (right).
+
+- IV.  $\rightarrow$  Creating a hole outside the labeled mask means adding a ghost in the foreground. Creating a hole inside the labeled mask is extremely unlikely because no such holes exist in our training data.  
+- VI.  $\rightarrow$  The deletion of a hole without creating a miss is extremely unlikely because of the sparsity of the data.  
+- VII.and IX. (only for 3D)  $\rightarrow$  Creating or removing a cavity is very unlikely because no cavities exist in our training data.
+
+# B. Additional Qualitative Results
+
+![](images/72abdabb516c5758b71e2b3473453dd49974765ea0e1b203d6170b2355281cfd.jpg)  
+Image
+
+![](images/3098e098d5fd6ada2cd8564a0490ad22e8c1234ade641e4f3b533eb0d1c6aaf5.jpg)  
+Label
+
+![](images/eb33cf0de8ebff677fff89b272dcaa70a88226e6eec1a6bb2c922614639e969f.jpg)  
+Soft-Dice
+
+![](images/2630255f59e3611947791c683aa573f3d675695cda41c2e1afae40514696d6ad.jpg)  
+Ours
+
+![](images/1fb3c1355f4c332a0196dcd3c12ebc97e9c6501070a6ff4ce9686e99ababc539.jpg)
+
+![](images/5fb378c27a181e096b3afbb50480f27ee61456b2a6c404b41a2f2ac4d7f11bf2.jpg)
+
+![](images/2143d637288f8e69f26ffb8559bf61a5426e5fa09834915db139088b6d464594.jpg)
+
+![](images/ccc2ec2059af4eb1e176b030b63cfc9af51310646ef5276e74512bd1c166f1f8.jpg)
+
+![](images/c60d9da1940c81ad4ab257b1dbc27734c600b317a65a6f9fb43fba43fbfa5645.jpg)
+
+![](images/5063ffade092420efe4064dd9431f5b9389aeed2b599b714c6a12c39e001038a.jpg)
+
+![](images/c61a0fe1a848cf8d4e8b90b1b3dfb9378ea2883897e1a1f2b026c7becb251b51.jpg)
+
+![](images/6ffdf362a4ec9eb7d840e9b6f6a9d09b43ff5b4791a9db4b49d43ead7ef051bf.jpg)
+
+![](images/a818b0f71b12d2704d8f85278b03eadbbc09b7c05356c3bb5c70600c30e7dadb.jpg)
+
+![](images/c46e270de195173ac2b01d16cd3a16fbcb6241d4d761ad27ac043d71672c7cbc.jpg)
+
+![](images/fe3d0e28f38320bd25ed1b3e7d04590ebbf0502319042dad73ec7b24c2dfafa9.jpg)
+
+![](images/42ff41fdd9eeb4b6d510ab03a28c94069183a0d142e12fbf9ac2e06897d5b1ef.jpg)
+
+![](images/ecc98da76392a82a61c17049519d1af5653f042f32ba42e92f347110f7c27175.jpg)  
+Figure 8. Qualitative results: for the Massachusetts Road dataset and for the DRIVE retina dataset (last row). From left to right, the real image, the label, the prediction using soft-dice and the predictions using the proposed  $\mathcal{L}_c(\alpha = 0.5)$ , respectively. The first three rows are U-Net results and the fourth row is an FCN result. This indicates that soft-clDice segments road connections which the soft-dice loss misses. Some, but not all, missed connections are indicated with solid red arrows, false positives are indicated with red-yellow arrows.
+
+![](images/ea308e515c13113f5ab4ce2466a4ed7e62ede6898f8ba036e2d0fe4febe8e474.jpg)
+
+![](images/dcb50894913094adeb7bc4f1bd364cf1808185d8970f3966d8ed82771ad87a62.jpg)
+
+![](images/095f8e1816b571425c64893d4a9b727a3d74e1afe394fab74afabc991d4306ac.jpg)
+
+![](images/779515620fbfded20a1716f74e5676bbf478eed5ac00121d11b7d844f40212f2.jpg)  
+Image
+
+![](images/d62e203b7ce0288cf96d0af54273f3d0e481b89315508f6decd2a57e0b319b36.jpg)  
+Label
+
+![](images/ee187234b4329f7d2748fa2b3608eeedd654fe1b9ca51c0b26e97d0aee95eef6.jpg)  
+Soft-Dice
+
+![](images/105fa37e49793f5f55ba00d3c0fcdc26a86c93a4c35d88c25f1df6bd02008fdf.jpg)  
+Ours
+
+![](images/3cdb5bf9bffd7613e8487b505d1eedc633d1660d525f2a9af95d384baddd7052.jpg)
+
+![](images/4d65aaee5f2f5c6d63832cd6330afdf8135c54068ed84971c750d27e5a17ec8d.jpg)
+
+![](images/e09c8f3a5171e1db2aacc3d2880c16cb0ad83b55553edaf058a16f4030cdf962.jpg)
+
+![](images/52cf436d1429508923454c4c6256337acf8e229d3ffd1685520a2ffa790ebdaa.jpg)
+
+![](images/d6ef12acb25ad96d99e5b472e0439d827dc8d3ab5a6b940d081c600c29f579a3.jpg)
+
+![](images/e2f407266287a4faeb6735c114d47046006b6adb9ba17136e0605d5926046a95.jpg)
+
+![](images/d67df652b74af90d9fb40b8776da2f3dda6914caef9789bd8eec926705d8ed30.jpg)
+
+![](images/fa78ad9a5f103c3b8a304f5d2a6f09d0d9885890b7f2a831b2bd9cebe092f5a2.jpg)
+
+![](images/8a9f6bd095457ec7baf71ed306425c17ee6fa1745076a7d38cc6ba2838bdb1a7.jpg)  
+Figure 9. Qualitative results: 2D slices of the 3D vessel dataset for different sized field of views. From left to right, the real image, the label, the prediction using soft-dice and the U-Net predictions using  $\mathcal{L}_c(\alpha = 0.4)$ , respectively. These images show that soft-clDice helps to better segment the vessel connections. Importantly the networks trained using soft-dice over-segment the vessel radius and segments incorrect connections. Both of these errors are not present when we train including soft-clDice in the loss. Some, but not all, false positive connections are indicated with red-yellow arrows.
+
+![](images/989d1905d00e313d2ea00e396bb349f8b96209273eb11b15b42d957927600f51.jpg)
+
+![](images/47379f649c6cfabb3b4ece30b0832dcbf57e320de5c44d33a45097eb5d887a8b.jpg)
+
+![](images/7e371bf8f92655b3f8c480a840010573ebf92979b409b5c2887cdbd80887fe87.jpg)
+
+# C. Comparison to Other Literature:
+
+A recent pre-print proposed a region-separation approach, which aims to tackle the issue by analysing disconnected foreground elements [33]. Starting with the predicted distance map, a network learns to close ambiguous gaps by referring to a ground truth map which is dilated by a five-pixel kernel, which is used to cover the ambiguity. However, this does not generalize to scenarios with
+
+a close or highly varying proximity of the foreground elements (as is the case for e.g. capillary vessels, synaptic gaps or irregular road intersections). Any two foreground objects which are placed at a twice-of-kernel-size distance or closer to each other will potentially be connected by the trained network. This is facilitated by the loss function considering the gap as a foreground due to performing dilation in the training stage. Generalizing their approach to smaller kernels has been described as infeasible in their paper [33].
+
+# D. Datasets and Training Routine
+
+For the DRIVE vessel segmentation dataset, we perform three-fold cross-validation with 30 images and deploy the best performing model on the test set with 10 images. For the Massachusetts Roads dataset, we choose a subset of 120 images (ignoring imaged without a network of roads) for three-fold cross-validation and test the models on the 13 official test images. For CREMI, we perform three-fold cross-validation on 324 images and test on 51 images. For the 3D synthetic dataset, we perform experiments using 15 volumes for training, 2 for validation, and 5 for testing. For the Vessap dataset, we use 11 volumes for training, 2 for validation and 4 for testing. In each of these cases, we report the performance of the model with the highest clDice score on the validation set.
+
+# E. Network Architectures
+
+We use the following notation:  $\text{In(input channels)}$ ,  $\text{Out(output channels)}$ ,
+
+$B(\text{output channels})$  present input, output, and bottleneck information (for U-Net);  $C(\text{filter size}, \text{output channels})$  denote a convolutional layer followed by ReLU and batch-normalization;  $U(\text{filter size}, \text{output channels})$  denote a transposed convolutional layer followed by ReLU and batch-normalization;  $\downarrow 2$  denotes maxpooling;  $\oplus$  indicates concatenation of information from an encoder block. We had to choose a different FCN architecture for the Massachusetts road dataset because we realize that a larger model is needed to learn useful features for this complex task.
+
+# E.1. Drive Dataset
+
+# E.1.1 FCN:
+
+$$
+\begin{array}{l} I N (3 \operatorname {c h}) \to C (3, 5) \to C (5, 1 0) \to C (5, 2 0) \to \\ C (3, 5 0) \to C (1, 1) \to O u t (1) \end{array}
+$$
+
+# E.1.2 Unet :
+
+$$
+\begin{array}{l} \text {C o n v B l o c k}: C _ {B} (3, \text {o u t s i z e}) \equiv C (3, \text {o u t s i z e}) \to \\ C (3, \text {o u t s i z e}) \to \downarrow 2 \end{array}
+$$
+
+$$
+\begin{array}{l} \textbf {U p C o n v B l o c k :} U _ {B} (3, \text {o u t s i z e}) \equiv U (3, \text {o u t s i z e}) \to \\ \oplus \to C (3, \text {o u t s i z e}) \end{array}
+$$
+
+$$
+\begin{array}{l} \text {E n c o d e r :} I N (3 \operatorname {c h}) \to C _ {B} (3, 6 4) \to C _ {B} (3, 1 2 8) \to \\ C _ {B} (3, 2 5 6) \to C _ {B} (3, 5 1 2) \to C _ {B} (3, 1 0 2 4) \to B (1 0 2 4) \end{array}
+$$
+
+$$
+\begin{array}{l} \text {D e c o d e r :} B (1 0 2 4) \to U _ {B} (3, 1 0 2 4) \to U _ {B} (3, 5 1 2) \to \\ U _ {B} (3, 2 5 6) \to U _ {B} (3, 1 2 8) \to U _ {B} (3, 6 4) \to O u t (1) \end{array}
+$$
+
+# E.2. Road Dataset
+
+# E.2.1 FCN:
+
+$$
+\begin{array}{l l l l l l l} I N (3 \operatorname {c h}) & \to & C (3, 1 0) & \to & C (5, 2 0) & \to & C (7, 3 0) & \to \\ C (1 1, 3 0) & \to & C (7, 4 0) & \to & C (5, 5 0) & \to & C (3, 6 0) & \to \\ C (1, 1) & \to & O u t (1) \end{array}
+$$
+
+# E.2.2 Unet :
+
+Same as Drive Dataset, except we used 2x2 up-convolutions instead of bilinear up-sampling followed by a 2D convolution with kernel size 1.
+
+# E.3. Cremi Dataset
+
+# E.3.1 Unet :
+
+Same as Road Dataset.
+
+# E.4. 3D Dataset
+
+# E.4.1 3D FCN:
+
+$$
+\begin{array}{l} I N (1 \text {o r} 2 \operatorname {c h}) \to C (3, 5) \to C (5, 1 0) \to C (5, 2 0) \to \\ C (3, 5 0) \to C (1, 1) \to O u t (1) \end{array}
+$$
+
+# E.4.2 3D Unet :
+
+$$
+\begin{array}{l} \text {C o n v B l o c k}: C _ {B} (3, \text {o u t s i z e}) \equiv C (3, \text {o u t s i z e}) \to \\ C (3, \text {o u t s i z e}) \to \downarrow 2 \end{array}
+$$
+
+$$
+\begin{array}{l} \textbf {U p C o n v B l o c k :} U _ {B} (3, o u t s i z e) \equiv U (3, o u t s i z e) \to \\ \oplus \to C (3, o u t s i z e) \end{array}
+$$
+
+$$
+\begin{array}{l} \text {E n c o d e r :} I N (1 \text {o r} 2 \operatorname {c h}) \to C _ {B} (3, 3 2) \to C _ {B} (3, 6 4) \to \\ C _ {B} (3, 1 2 8) \to C _ {B} (5, 2 5 6) \to C _ {B} (5, 5 1 2) \to B (5 1 2) \end{array}
+$$
+
+$$
+\begin{array}{l} \text {D e c o d e r :} B (5 1 2) \to U _ {B} (3, 5 1 2) \to U _ {B} (3, 2 5 6) \to \\ U _ {B} (3, 1 2 8) \to U _ {B} (3, 6 4) \to U _ {B} (3, 3 2) \to O u t (1) \end{array}
+$$
+
+Table 2. Total number of parameters for each of the architectures used in our experiment.  
+
+<table><tr><td>Dataset</td><td>Network</td><td>Number of parameters</td></tr><tr><td rowspan="2">Drive</td><td>FCN</td><td>15.52K</td></tr><tr><td>UNet</td><td>28.94M</td></tr><tr><td>Road</td><td>FCN</td><td>279.67K</td></tr><tr><td>Cremi</td><td>UNet</td><td>31.03M</td></tr><tr><td rowspan="2">3D</td><td>FCN 2ch</td><td>58.66K</td></tr><tr><td>Unet 2ch</td><td>19.21M</td></tr></table>
+
+# F. Soft Skeletonization Algorithm
+
+![](images/de13059f57c687de90620ef945cb50fbb64aa6a3f66f7fce6d9277340ea17bbb.jpg)  
+Figure 10. Scheme of our proposed differentiable skeletonization. On the top left the mask input is fed. Next, the input is treatedly eroded and dilated. The resulting erosions and dilations are compared to the image before dilation. The difference between these images is part of the skeleton and will be added iteratively to obtain a full skeletonization. The ReLu operation eliminates pixels that were generated by the dilation but are not part of the original or eroded image.
+
+# G. Code for the clDice similarity measure and the soft-clDice loss (PyTorch):
+
+# G.1. clDice measure
+
+fromskimage.morphologyimportskeletonize
+
+import numpy as np
+
+def cl_score(v, s):
+
+return np.sum(v*s)/np.sum(s)
+
+def clDice(v_p, v_l):
+
+tprec  $=$  cl_score(v_p,skeletonize(v_1))
+
+tsens  $=$  cl_score(v_l,skeletonize(v_p))
+
+return 2*tprec*tsens/(tprec+tsens)
+
+# G.2. soft-skeletonization in 2D
+
+import torch.nn.Functional as F
+
+def soft_erule (img):
+
+$\mathrm{p1} = -\mathrm{F}$  .max_pool2d(-img，(3,1)，(1,1)，(1,0))
+
+$\mathrm{p2} = -\mathrm{F}$  .max_pool2d(-img，(1,3)，(1,1)，(0,1))
+
+return torch.min(p1, p2)
+
+def soft_dilate (img):
+
+return F.max_pool2d(img, (3,3), (1,1), (1,1))
+
+def soft_open (img):
+
+return soft_dilate(soft_erode(img))
+
+def soft_skel (img, iter):
+
+img1 = soft_open (img)
+
+$\mathrm{skel} = \mathrm{F. relu}(\mathrm{img - img1})$
+
+for j in range (iter):
+
+img = soft_ erode (img)
+
+img1 = soft_open (img)
+
+```txt
+delta = F.relu(img - img1)  
+skel = skel + F.relu(delta - skel * delta)  
+return skel
+```
+
+# G.3. soft-skeletonization in 3D
+
+import torch.nn.Functional as F
+
+```txt
+def soft_ erode (img):
+p1  $=$  -F.max_pool13d(-img,(3,1,1),(1,1,1),(1,0,0))
+p2  $=$  -F.max_pool13d(-img,(1,3,1),(1,1,1),(0,1,0))
+p3  $=$  -F.max_pool13d(-img,(1,1,3),(1,1,1),(0,0,1))
+```
+
+```lua
+return torch.min(torch.min(p1, p2), p3)
+```
+
+```python
+def soft_dilate (img):
+    return F.max_pool3d(img, (3, 3, 3), (1, 1, 1), (1, 1, 1))
+```
+
+```python
+def soft_open(img):
+    return soft_dilate(soft_ERode(img))
+```
+
+```python
+def soft_skel(img, iter_):
+    img1 = soft_open(img)
+    skel = F.relu(img - img1)
+    for j in range(img):
+        img = soft(erode(img))
+        img1 = soft_open(img)
+        delta = F.relu(img - img1)
+        skel = skel + F.relu(delta - skel * delta)
+    return skel
+```
+
+# H. Evaluation Metrics
+
+As discussed in the text, we compare the performance of various experimental setups using three types of metrics: volumetric, graph-based and topology-based.
+
+# H.1. Overlap-based:
+
+Dice coefficient, Accuracy and clDice, we calculate these scores on the whole 2D/3D volumes. clDice is calculated using a morphological skeleton (skeletonize3D from the skimage library).
+
+# H.2. Graph-based:
+
+We extract graphs from random patches of  $64 \times 64$  pixels in 2D and  $48 \times 48 \times 48$  in 3D images.
+
+For the StreetmoverDistance (SMD) [4] we uniformly sample a fixed number of points from the graph of the prediction and label, match them and calculate the Wasserstein distance between these graphs. For the junction-based metric (Opt-J) we compute the F1 score of junction-based metrics, recently proposed by [7]. According to their paper this metric is advantageous over all previous junction-based metrics as it can account for nodes with an arbitrary number of incident edges, making this metric more sensitive to endpoints and missed connections in predicted networks. For more information please refer to their paper.
+
+# H.3. Topology-based:
+
+For topology-based scores we calculate the Betti Errors for the Betti Numbers  $\beta_0$  and  $\beta_{1}$ . Also, we calculate the Euler characteristic,  $\chi = V - E + F$ , where  $E$  is the number of edges,  $F$  is the number of faces and  $V$  is the number of vertices. We report the relative Euler characteristic error ( $\chi_{ratio}$ ), as the ratio of the  $\chi$  of the predicted mask and that of the ground truth. Note that a  $\chi_{ratio}$  closer to one is preferred. All three topology-based scores are calculated on random patches of  $64 \times 64$  pixels in 2D and  $48 \times 48 \times 48$  in 3D images.
+
+# I. Additional Quantitative Results
+
+Table 3. Quantitative experimental results for the 3D synthetic vessel dataset. Bold numbers indicate the best performance. We trained baseline models of binary-cross-entropy (BCE), softDice and mean-squared-error loss (MSE) and combined them with our soft-clDice and varied the  $\alpha >0$ . For all experiments we observe that using soft-clDice in  $\mathcal{L}_c$  results in improved scores compared to soft-Dice. This improvement holds for almost  $\alpha >0$ . We observe that soft-clDice can be efficiently combined with all three frequently used loss functions.  
+
+<table><tr><td>Loss</td><td>Dice</td><td>clDice</td></tr><tr><td>BCE</td><td>99.81</td><td>98.24</td></tr><tr><td>Lc, α = 0.5</td><td>99.76</td><td>98.25</td></tr><tr><td>Lc, α = 0.4</td><td>99.77</td><td>98.29</td></tr><tr><td>Lc, α = 0.3</td><td>99.76</td><td>98.20</td></tr><tr><td>Lc, α = 0.2</td><td>99.78</td><td>98.29</td></tr><tr><td>Lc, α = 0.1</td><td>99.82</td><td>98.39</td></tr><tr><td>Lc, α = 0.01</td><td>99.83</td><td>98.46</td></tr><tr><td>Lc, α = 0.001</td><td>99.85</td><td>98.42</td></tr><tr><td>soft-Dice</td><td>99.74</td><td>97.07</td></tr><tr><td>Lc, α = 0.5</td><td>99.74</td><td>97.53</td></tr><tr><td>Lc, α = 0.4</td><td>99.74</td><td>97.07</td></tr><tr><td>Lc, α = 0.3</td><td>99.80</td><td>98.13</td></tr><tr><td>Lc, α = 0.2</td><td>99.74</td><td>97.08</td></tr><tr><td>Lc, α = 0.1</td><td>99.74</td><td>97.08</td></tr><tr><td>Lc, α = 0.01</td><td>99.74</td><td>97.07</td></tr><tr><td>Lc, α = 0.001</td><td>99.74</td><td>97.12</td></tr><tr><td>MSE</td><td>99.71</td><td>97.03</td></tr><tr><td>Lc, α = 0.5</td><td>99.62</td><td>98.22</td></tr><tr><td>Lc, α = 0.4</td><td>99.65</td><td>97.04</td></tr><tr><td>Lc, α = 0.3</td><td>99.67</td><td>98.16</td></tr><tr><td>Lc, α = 0.2</td><td>99.70</td><td>97.10</td></tr><tr><td>Lc, α = 0.1</td><td>99.74</td><td>98.21</td></tr><tr><td>Lc, α = 0.01</td><td>99.82</td><td>98.32</td></tr><tr><td>Lc, α = 0.001</td><td>99.84</td><td>98.37</td></tr></table>

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+# Characterizing Cryptocurrency Exchange Scams
+
+Pengcheng Xia  
+Beijing University of Posts and Telecommunications, China
+
+Bingyu Gao  
+Beijing University of Posts and Telecommunications, China
+
+Bowen Zhang  
+Beijing University of Posts and Telecommunications, China
+
+Lei Wu  
+Zhejiang University, China
+
+Ru Ji  
+Beijing University of Posts and Telecommunications, China
+
+Xiapu Luo  
+The Hong Kong Polytechnic University
+
+Haoyu Wang*  
+Beijing University of Posts and Telecommunications, China
+
+# ABSTRACT
+
+As the indispensable trading platforms of the ecosystem, hundreds of cryptocurrency exchanges are emerging to facilitate the trading of digital assets. While, it also attracts the attentions of attackers. A number of scam attacks were reported targeting cryptocurrency exchanges, leading to a huge mount of financial loss. However, no previous work in our research community has systematically studied this problem. In this paper, we make the first effort to identify and characterize the cryptocurrency exchange scams. We first identify over 1,500 scam domains and over 300 fake apps, by collecting existing reports and using typosquatting generation techniques. Then we investigate the relationship between them, and identify 94 scam domain families and 30 fake app families. We further characterize the impacts of such scams, and reveal that these scams have incurred financial loss of  $520\mathrm{k}$  US dollars at least. We further observe that the fake apps have been sneaked to major app markets (including Google Play) to infect unsuspanic users. Our findings demonstrate the urgency to identify and prevent cryptocurrency exchange scams. To facilitate future research, we have publicly released all the identified scam domains and fake apps to the community.
+
+# KEYWORDS
+
+Cryptocurrency, Scam, Exchange, Domain Typosquatting, Fake App, Trust-trading
+
+# 1 INTRODUCTION
+
+Since the first Bitcoin block was mined back in 2009, cryptocurrency has seen an explosive growth thanks to the evolvement of blockchain technology and their economic ecosystems. Besides Bitcoin, thousands of unique cryptocurrencies have popped up from time to time. As of the end of 2018, there are over 2,000 different cryptocurrencies, and the total market capitalization is $100bn, which is higher than the GDP of 127 countries [7].
+
+As the indispensable trading platforms of the ecosystem, hundreds of cryptocurrency exchanges are emerging to facilitate the trading of digital assets (e.g., Bitcoin) with both traditional fiat currencies (e.g., US dollars) or other digital assets (e.g., Ether).
+
+Inevitably, the prosperity of cryptocurrency exchanges are great targets for hackers to perform attacks to make a profit. A number of exchanges have been targeted by large-scale hacking attacks. It
+
+# Guoai Xu
+
+Beijing University of Posts and Telecommunications, China
+
+is reported that the cryptocurrency exchanges suffered a total loss of  $882 million due to targeted attacks in 2017 and in the first three quarters of 2018[1]. The number keeps increasing in 2019. For example, as reported in May 2019, attackers have stolen 7,000 bitcoins (which worth$ 41m) from Binance, one of the top leading exchanges all over the world, using a variety of techniques, including phishing, viruses and other attacks[2]. The exchange Coinhouse suffered a phishing attack on September 2019, and attackers gained access to all the user names and email addresses[6]. It is worth noting that, many attacks are relying on the social engineering techniques, i.e., phishing and trust-trading scams.
+
+It is urgent to identify and prevent scam attacks targeting exchanges. The blockchain community has started to pay attention to the scam attacks in the cryptocurrency ecosystem. For example, several open-source databases (e.g., CryptoScamDB and EtherscamDB) have collected malicious domains and their associated addresses that have the intent of deceiving people for the purposes of financial gain by using a crowd-sourcing based approach (e.g., being actively reported by victims), although only a few of them are related to cryptocurrency exchanges. To the best of our knowledge, no previous study in our research community has made efforts to investigate this problem. We are still unaware: 1) to the extent the scams exist in the ecosystem; and 2) who are the attackers behind them; and 3) what are the impacts of the scams.
+
+Our Study. In this paper, we make the first effort to look at the cryptocurrency exchange scams. To cover as much scams as possible, we first use a hybrid approach by first collecting existing known scams and then developing an automated approach, to identify both well-known scams and scams that have not been disclosed to public (see Section 4). We have identified 1,595 scam domains, and over  $60\%$  of them are not publicly known. Besides, we have identified over 300 fake exchange apps. Based on the harvested dataset, we propose to cluster the domains and apps, and further investigate the relationship between them (see Section 5). We have identified 94 scam domain families and 30 fake app families. At last, we have investigated the distribution channels of such scams, and their real-world impacts by analyzing their associated blockchain addresses (see Section 6).
+
+In summary, we make the following main research contributions:
+
+- To the best of our knowledge, this paper is the first systematic study of the cryptocurrency exchange scams.
+
+We collected by far the largest exchange scam dataset, and performed deep analysis of them, including the attackers and impacts. Most of the identified scams have not been known to the community.
+
+- We have revealed that a majority of the scam domains and fake apps were created and controlled by a small number of groups (attackers), which could be useful for us to further identify and track the new scams in the future.  
+- We have revealed over 182 blockchain addresses related to such scams. We also identify 518 addresses associated to them, which are quite possible to be controlled by the same group of people. Such information could be used to track the money flow of the scam attacks. These scams have incurred financial loss of over 520K US dollars (lower-bound).
+
+We have released the scam dataset we collected and all the experiment results to the community at:
+
+https://cryptoexchangescam.github.io/ScamDataset/
+
+# 2 BACKGROUND AND RELATED WORK
+
+# 2.1 Cryptocurrency and Exchange
+
+Cryptocurrency is a kind of digital asset that uses cryptography to ensure its creation security and transaction security. The first and most well-known cryptocurrency, Bitcoin, was released in 2009, and till now there are over 2,500 different kinds of cryptocurrencies. With the rise of cryptocurrencies in 2017, people pay more attention on cryptocurrency exchanges in order to get or trade cryptocurrencies. A cryptocurrency exchange is a marketplace where users can buy and sell cryptocurrencies. Many of them only offer trade services among cryptocurrencies while a few offer fiat (e.g., US Dollar or Euro) to cryptocurrency transactions. Similar to stock market, people flood into cryptocurrency exchanges to invest in order to get the benefit of cryptocurrency price changes. There are three types of cryptocurrency exchanges: centralized exchanges (CEX) which is governed by a company or an organisation, decentralized exchanges (DEX) which provide automated process for peer-to-peer trades, and hybrid exchanges which combine the both of the above.
+
+# 2.2 Related Work
+
+2.2.1 Blockchain Scams and Attacks. Blockchain platforms are always the targets of scams and security attacks. A few studies have characterized the blockchain scams. Most of them were focused on detecting the ponzi schemes [12, 13, 16]. Besides, a large number of studies focused on detecting and analyzing attacks from different levels, including blockchain consensus [14], smart contract [11], abnormal transactions [15, 18], etc. Despite cryptocurrency exchanges are the key infrastructure of the blockchain ecosystem, however, the security-related issues, including the scam problem studied in this work, have not been well-studied yet.
+
+2.2.2 Domain Typosquatting. Typosquatting (URL hijacking) is the act of registering a domain name very similar to an existing legitimate domain, which relies on mistakes such as typos made by Internet users when inputting a website address into a web browser. These typosquatting domains are often exploited by attackers. Many
+
+research studies were focused on detecting and analyzing domain typosquatting. Wang et al. [31] proposed a general and widely adopted approach to generate typosquatting domain names. Szurdi et al. [27] estimated that  $20\%$  of the .com domain registrations are true typo domains and the number is increasing with the expansion of the .com domain space. Agten et al. [9] found that even though  $95\%$  of the popular domains we investigated are actively targeted by typosquatting, only few trademark owners protect themselves against this practice by proactively registering their own typosquatting domains. Besides, a few tools are available to generate possible squatting domains, including URLCrazy [8], dNSTwist [5], etc. In this study, we identify that a number of the exchange scams are in the form of typosquatting. Thus, we take advantage of existing techniques to generate typosquatting domains and further analyze the scams (see Section 4.1).
+
+2.2.3 Fake Apps/App Clones. A fake app masquerades as the legitimate one by mimicking the look or functionality. Fake apps usually have identical app names or package names to the original ones. There have been a number of studies focusing on this topic. Wang et al. [30] proposed a clustering approach on app names to detect potential fake apps. Tang et al. [28] have characterized over 150K fake apps that have same package names or app names with popular apps. Kywe et al. [21] and Li et al. [22] proposed technique to detect fake apps based on the external features of apps, e.g., icons, app names. In this paper, we follow the most traditional method to identify fake apps, i.e., apps share the same app name or app ID (package name) but with different authorship (see Section 4.2).
+
+# 3 STUDY DESIGN
+
+In this paper, we perform a large-scale measurement of cryptocurrency exchange scams in the wild. We therefore take advantage of various sources and approaches to collect a dataset that covers scams targeting the top cryptocurrency exchanges, in the form of both domains and mobile apps.
+
+# 3.1 Target Cryptocurrency Exchange
+
+It is first necessary to compile a list of Cryptocurrency Exchanges, which may be subject to scam attacks. As the volume of each cryptocurrency exchange fluctuates greatly every day, the ranking of exchanges is not stable. Thus, we resort to Google to first retrieve several ranking lists of Cryptocurrency Exchanges, and then merge them to build a list of 70 popular exchanges, as shown in Table  $1^{1}$ .
+
+To cover both domain and mobile apps, we further collected the official domain names of these exchanges (some exchanges have more than one domain), and their corresponding Android apps<sup>2</sup>.
+
+# 3.2 Research Questions
+
+Our measurement study in this paper is driven by the following research questions (RQs):
+
+RQ1 Are scam attacks prevalent in the cryptocurrency exchanges? Although a number of media reports revealed that
+
+Table 1: The target exchanges and the corresponding results.  
+
+<table><tr><td>Name</td><td>Launch Time</td><td>Official Site</td><td>#Mal URLs</td><td>App</td><td># Fake Apps</td></tr><tr><td>Anxpro</td><td>Mar-2014</td><td>anxpro.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>B2bx</td><td>Oct-2017</td><td>b2bx.exchange</td><td>0</td><td>X</td><td>1(0)</td></tr><tr><td>Bcex</td><td>Aug-2017</td><td>bcex.ca</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>Bgogo</td><td>May-2018</td><td>bgogo.com</td><td>5</td><td>✓</td><td>0(0)</td></tr><tr><td>Bibox</td><td>Nov-2017</td><td>bibox.com/bibox365.com</td><td>11</td><td>✓</td><td>1(1)</td></tr><tr><td>Binance</td><td>Jul-2017</td><td>binance.com</td><td>320</td><td>✓</td><td>16(9)</td></tr><tr><td>Bisq</td><td>Dec-2014</td><td>bisq.network</td><td>0</td><td>✓</td><td>0(0)</td></tr><tr><td>Bit-Z</td><td>Jun-2016</td><td>bit-z.com</td><td>3</td><td>✓</td><td>1(0)</td></tr><tr><td>Bitbay</td><td>Feb-2014</td><td>bitbay.net</td><td>20</td><td>✓</td><td>4(0)</td></tr><tr><td>Bitfinex</td><td>Oct-2012</td><td>bitfinex.com</td><td>46</td><td>✓</td><td>8(4)</td></tr><tr><td>bitFlyer</td><td>Jan-2014</td><td>bitflyer.com</td><td>13</td><td>✓</td><td>0(0)</td></tr><tr><td>Bitforex</td><td>Jun-2018</td><td>bitforex.com</td><td>7</td><td>X</td><td>1(0)</td></tr><tr><td>Bithumb</td><td>Jan-2014</td><td>bithumb.com</td><td>5</td><td>✓</td><td>5(4)</td></tr><tr><td>Bitlish</td><td>Jul-2014</td><td>bitlish.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>BitMart</td><td>Mar-2018</td><td>bitmart.com</td><td>9</td><td>✓</td><td>0(0)</td></tr><tr><td>BitMax</td><td>Jul-2018</td><td>bitmax.io</td><td>4</td><td>✓</td><td>0(0)</td></tr><tr><td>BitMEX</td><td>Apr-2014</td><td>bitmex.com</td><td>68</td><td>X</td><td>20(8)</td></tr><tr><td>Bitpanda</td><td>Oct-2014</td><td>bitpanda.com</td><td>44</td><td>✓</td><td>2(1)</td></tr><tr><td>Bitso</td><td>May-2014</td><td>bitso.com</td><td>7</td><td>✓</td><td>1(0)</td></tr><tr><td>Bitstamp</td><td>Jul-2011</td><td>bitstamp.net</td><td>13</td><td>✓</td><td>3(1)</td></tr><tr><td>Bittrex</td><td>Feb-2014</td><td>bittrex.com</td><td>78</td><td>X</td><td>11(5)</td></tr><tr><td>BW.COM</td><td>Jan-2017</td><td>bw.com</td><td>0</td><td>✓</td><td>0(0)</td></tr><tr><td>CEX.IO</td><td>Jan-2013</td><td>cex.io</td><td>1</td><td>✓</td><td>3(0)</td></tr><tr><td>Changelly</td><td>Oct-2015</td><td>changelly.com</td><td>24</td><td>✓</td><td>6(6)</td></tr><tr><td>Cobinhood</td><td>Dec-2017</td><td>cobinhood.com</td><td>18</td><td>✓</td><td>4(0)</td></tr><tr><td>CoinAll</td><td>Aug-2018</td><td>coinall.com</td><td>0</td><td>✓</td><td>0(0)</td></tr><tr><td>Coinbase</td><td>May-2014</td><td>coinbase.com</td><td>120</td><td>✓</td><td>23(15)</td></tr><tr><td>Coinbene</td><td>Sep-2017</td><td>coinbene.com</td><td>13</td><td>✓</td><td>0(0)</td></tr><tr><td>Coincheck</td><td>Nov-2014</td><td>coincheck.com</td><td>31</td><td>✓</td><td>3(3)</td></tr><tr><td>Coineal</td><td>Apr-2018</td><td>coineal.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>CoinEx</td><td>Dec-2017</td><td>coinex.com</td><td>2</td><td>✓</td><td>0(0)</td></tr><tr><td>CoinExchange</td><td>Mar-2016</td><td>coinexchange.io</td><td>0</td><td>X</td><td>12(9)</td></tr><tr><td>Coinfloor</td><td>Mar-2014</td><td>coinfloor.co.uk</td><td>0</td><td>X</td><td>0(0)</td></tr><tr><td>Coinify</td><td>Dec-2017</td><td>coinify.com</td><td>0</td><td>X</td><td>0(0)</td></tr><tr><td>Coinmama</td><td>Apr-2013</td><td>coinmama.com</td><td>25</td><td>X</td><td>7(4)</td></tr><tr><td>Coinone</td><td>Jun-2014</td><td>coinone.co.kr</td><td>0</td><td>✓</td><td>1(0)</td></tr><tr><td>Cryptonex</td><td>Oct-2017</td><td>cryptonex.org</td><td>3</td><td>✓</td><td>0(0)</td></tr><tr><td>Cryptopia</td><td>May-2014</td><td>cryptopopia.co.nz</td><td>3</td><td>X</td><td>23(8)</td></tr><tr><td>Deribit</td><td>Mar-2015</td><td>deribit.com</td><td>27</td><td>✓</td><td>0(0)</td></tr><tr><td>DigiFinex</td><td>Apr-2018</td><td>digifinex.com</td><td>20</td><td>✓</td><td>0(0)</td></tr><tr><td>Erisx</td><td>Oct-2018</td><td>erisx.com</td><td>9</td><td>X</td><td>0(0)</td></tr><tr><td>Etoro</td><td>Jun-2011</td><td>etoro.com</td><td>10</td><td>✓</td><td>13(2)</td></tr><tr><td>EXX</td><td>Oct-2017</td><td>exx.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>FatBTC</td><td>May-2014</td><td>fatbtc.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>FCoin</td><td>May-2018</td><td>fcoin.com</td><td>6</td><td>✓</td><td>1(0)</td></tr><tr><td>Gate.io</td><td>Jan-2013</td><td>gate.io</td><td>1</td><td>✓</td><td>2(0)</td></tr><tr><td>GBX</td><td>Oct-2017</td><td>exchange.gbx.gi</td><td>0</td><td>✓</td><td>0(0)</td></tr><tr><td>Gemini</td><td>Oct-2014</td><td>gemini.com</td><td>10</td><td>✓</td><td>0(0)</td></tr><tr><td>HitBTC</td><td>Dec-2013</td><td>hitbtc.com</td><td>54</td><td>✓</td><td>16(7)</td></tr><tr><td>Huobi</td><td>Sep-2013</td><td>huobi.com/hbg.com</td><td>25</td><td>✓</td><td>0(0)</td></tr><tr><td>IDAX</td><td>Dec-2017</td><td>idax.pro</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>itBit</td><td>Nov-2013</td><td>itbit.com</td><td>6</td><td>X</td><td>0(0)</td></tr><tr><td>Kraken</td><td>Jul-2011</td><td>kraken.com</td><td>35</td><td>X</td><td>11(2)</td></tr><tr><td>KuCoin</td><td>Aug-2017</td><td>kucoin.com/kcs.top</td><td>44</td><td>✓</td><td>14(7)</td></tr><tr><td>LATOKEN</td><td>Jul-2017</td><td>latoken.com</td><td>11</td><td>X</td><td>0(0)</td></tr><tr><td>Lbank</td><td>Oct-2016</td><td>lbank.info</td><td>0</td><td>✓</td><td>2(2)</td></tr><tr><td>Liquid</td><td>Mar-2014</td><td>liquid.com</td><td>0</td><td>X</td><td>0(0)</td></tr><tr><td>Livecoin</td><td>Mar-2014</td><td>livecoin.net</td><td>11</td><td>X</td><td>2(2)</td></tr><tr><td>LocalBitcoins</td><td>Jun-2012</td><td>localbitcoins.com</td><td>211</td><td>X</td><td>32(18)</td></tr><tr><td>Luno</td><td>Feb-2017</td><td>luno.com</td><td>5</td><td>✓</td><td>2(2)</td></tr><tr><td>OKEx</td><td>Jan-2014</td><td>okex.com/okcoin.com</td><td>21</td><td>✓</td><td>2(2)</td></tr><tr><td>OOOBTC</td><td>Nov-2017</td><td>ooobtc.com</td><td>1</td><td>✓</td><td>0(0)</td></tr><tr><td>Paxful</td><td>Jul-2015</td><td>paxful.com</td><td>75</td><td>✓</td><td>13(11)</td></tr><tr><td>Poloniex</td><td>Jan-2014</td><td>poloniex.com</td><td>45</td><td>✓</td><td>35(30)</td></tr><tr><td>ShapeShift</td><td>Jun-2015</td><td>shapeshift.io</td><td>23</td><td>✓</td><td>0(0)</td></tr><tr><td>Wirex</td><td>Dec-2014</td><td>wirexapp.com</td><td>13</td><td>✓</td><td>0(0)</td></tr><tr><td>Xapo</td><td>Mar-2014</td><td>xapo.com</td><td>2</td><td>✓</td><td>2(2)</td></tr><tr><td>xCoins</td><td>Apr-2016</td><td>xcoins.io</td><td>0</td><td>X</td><td>1(1)</td></tr><tr><td>Yorbit</td><td>Aug-2014</td><td>yorbit.net</td><td>22</td><td>X</td><td>19(4)</td></tr><tr><td>ZB.com</td><td>Nov-2017</td><td>zb.com/zbg.com</td><td>8</td><td>✓</td><td>0(0)</td></tr></table>
+
+cryptocurrency exchange scam attacks popped up from time to time, it is still unknown to us to what extent these attacks exist in the ecosystem, and how prevalent are them. Besides, it is also interesting to investigate which cryptocurrency exchanges are their main targets, and how do they perform the scam attacks. We further divide RQ1 into two sub-RQs,
+
+RQ1.1: what is the presence and trend of scam domains? and RQ1.2: what is the presence and trend of scam mobile apps?
+
+RQ2 Who are the attackers behind them? To understand such attacks in a systematic way, we further want to characterize the real attackers behind them. It is interesting to investigate whether such scams were performed by a group of identical hackers.
+
+RQ3 What is the impact of the scams? Although it is known to us the existence of such scams (e.g., squatting websites and fake apps), it is not clear to us the impact of them, e.g., how many users were tricked and got financial loss.
+
+To answer RQ1, we make effort to collect the existing known scams and further identify a large number of unknown scams based on techniques adapted from domain squatting attacks and fake mobile apps. To answer RQ2, we perform the domain relation analysis based on a set of inherent domain features (e.g., passive DNS, whois, etc.), and the app relation analysis based on the developpr signature and code-level similarity comparison. To answer RQ3, we make effort to correlate the scams to blockchain addresses, and collect the transaction information to estimate the number of victims and the amount of financial losses.
+
+# 4 MEASUREMENT OF THE SCAMS
+
+In this section, we measure the presence of exchange scams in the form of both domain scams and app scams. To cover as much scams as possible, we use a hybrid approach here, by collecting the existing known scams first and then develop automated approaches to further identify scams that have not been disclosed to public.
+
+# 4.1 Detecting the Scam Domains
+
+4.1.1 Collecting Scam Domains from Existing Corpus. There are some well-known websites collecting scam cryptocurrency domains in our community, e.g., etherscamdb.info and cryptoscamdb.org are two representative ones. Thus, we first write crawlers to collect the known scam domains, and then filter exchange related ones. To this end, 657 scam exchange domains were collected using this approach by the time of our study.
+
+4.1.2 Generating the Squatting Domains. By manually exploring the collected scam domains, we have identified that a number of them were distributed using the domain typosquatting techniques. They are mainly using these domains to create websites looking exactly similar with the correct one, resulting in the loss of users' credentials or assets.
+
+Thus, we further explore whether there are more scam domains that have not been disclosed to public. As domain squatting has been widely studied in our community and there are many tools available, we take advantage of dnstwist[5], a widely used tool to generate typosquatting domains and identify the scam ones [17, 29]. Dnstwist has embedded 13 generation models to explore the possible squatting domains. Take domain *binance.com* as an example, over 2,000 possible squatting domains would be generated using different transformation methods, such as addition (e.g., *binancer.com*), bitsquatting (e.g., *biance.com*), homoglyph (e.g., *binance.com*), hyphenation (e.g., *bi-nance.com*), insertion (e.g., *binance.com*), omission (e.g., *binace.com*), repetition (e.g., *binance.com*), replacement (e.g., *binancw.com*), subdomain (e.g., *binan.ce.com*), transposition (e.g.,
+
+![](images/1f254a0f2c5fd0dfd1ee513efaa50a3346bf61421bb3f4a5d85550add815a690.jpg)  
+(1) paxfulservice.com(a phishing domain that targets exchange paxful.com).
+
+![](images/8918f98d4b94c523a9204b4a091050913ac22b0285f858fcce17d8d49b1f0a9e.jpg)  
+(3)deriibt.com(a referral fraud domain that targets exchange deribit.com).  
+Figure 1: Examples of Scam Domains.
+
+![](images/b7d9bb5d7692f9bf7eadac930a1afbac923b59554095e4670e2d0b21c78ec1f5.jpg)  
+(2)coinbasegive.com(a trading-scam domain that targets exchange coinbase.com).
+
+![](images/e23265665d8fe3a40b4f484a2c6c0ec577dabb7ea151f460324c9f8565801c74.jpg)  
+(4)okexw.com(a gambling domain that targets exchange okex.com).
+
+binanec.com), vowel-swap (e.g., binonce.com), various (e.g., binancecom.com) and dictionary (e.g., my-binance.com,binancepay.com).
+
+In this way, we feed the domains of the 70 studied exchanges to dnstwist, and we have generated 144,392 squatting candidates in total. Note that, as some domains have not been registered, thus we further filter the domains that have no corresponding IP addresses during our visiting. At last, we have identified 4,457 valid domains by the time of our study (2019-09-23).
+
+4.1.3 Labelling the Domains. Note that, not all the squatting domains deliver the malicious or scam purposes, as some of them are only used for parking services [10, 25]. Thus, we further seek to label the suspicious domains and identify the malicious ones. We collect all the possible information related each domain, including the WHOIS information, DNS information, autonomous system numbers and VirusTotal anti-virus engine scan results<sup>3</sup>. Furthermore, we write crawler to get the screenshots of these websites, the source code of webpage, and record the redirect links. Then, we follow the most widely used approach [26] in our community, to label the domains in an semi-automated way.
+
+First, as some domains display only blank pages during our visiting, thus we remove such domains (labelled as C1: Registered). Then, for each domain, we analyze the landing URL (the page that one URL is finally redirected to), source code and screenshots, by comparing them with the ones of known parking services and their corresponding official websites, to determine whether they are using parking service or redirect users to their referral links (labelled
+
+as C2: Parked and C5: Referral Fraud). After that, we take advantage of OCR techniques to analyze the content similarity and image similarity, between these websites and their corresponding official websites, in order to identify the phishing websites (labelled as C3: Phishing). We also rely on VirusTotal's labelling results to classify if a domain is used for phishing and scamming purposes. For the domains flagged by VirusTotal, we further manually analyze them to classify them into phishing (labelled as C3: Phishing) or trading scam (labelled as C4: Trading Scam). Furthermore, we collect all the image contents listed on the domains to identify whether they are used to perform devious behaviors (e.g., adult and gambling) using Google Cloud Natural Language API and Vision  $\mathrm{API}^4$  (labelled as C6: Adult and Gambling). At last, for the remaining unclassified domains, we perform manually analysis to see whether they belong to the aforementioned categories or not. Note that, some of the generated domains may be false positives, i.e., they are benign and their names are authentic, which will be flagged during the manually verification (labelled as C0: False Positive).
+
+In this way, we are able to classify the scam domains into the following categories:
+
+- C0 False Positive: There are 728 domains (14.30%) belonging to this category, which were flagged during manually verification. Their names are authentic and they are benign websites. For example, the domain name https://bidflyer.com/ looks like bitFlyer's domain, while it is an auction platform for airlines.
+
+- C1 Registered: Although some domains have corresponding resolved IP addresses, while they cannot reached during our experiments or they just display blank pages. Thus, we label such domains as 'Registered'. Roughly  $23.54\%$  (1,198) domains belong to this category.  
+- C2 Parked: The domains using parking services account for  $30.83\%$  of our dataset. People who hold domains usually use parking services to advertise or sale their domains.  
+- C3 Phishing: Phishing domains account for  $8.35\%$  of our generated dataset. They often have similar looks with the official ones, making it easier for users to be tricked into typing in their account credentials or downloading malware the domains provide. In our dataset, Binance exchange has the most number of phishing domains (107 domains).  
+- C4 Trading Scam: These domains tend to directly take users' money or digital assets. Among 249 Trading scam cases, 232 domains are the Trust-Trading scams. A trust-trading occurs when a victim gives a scammer money (e.g., BTC or ETH), trusting that the scammer will then return them with high-level interest rate investment or rich payback. Instead, however, the attackers simply take the victim's money and leave. Other cases of this category include offering fake exchange support channel or Ponzi schemes, etc.  
+- C5 Referral Fraud: The Referral Fraud domains account for  $16.42\%$  of our dataset. This kind of domains often forwards users to the official exchanges' domain while adding attackers' affiliate code in order to earn a reward provided by these exchanges' referral program.  
+- C6 Adult and Gambling: We find 85 domains redirect users to adult or gambling websites. Although these websites have almost no relations with cryptocurrency exchanges, they create these typosquatting domains with the malicious purpose of attracting users.
+
+In this paper, we regard the last four categories (phishing, trading scam, referral fraud, adult and gambling) as scam domains in general, as all of them fulfill either scam or malicious purposes. Figure 1 shows the four representative examples of scam domains.
+
+4.1.4 Overall Result. At last, we have identified 1,595 scam domains, and 58 exchanges (83%) were targeted by them. Note that only 657 domains have been reported on existing scam databases, and over 58.8% of them have not been disclosed to our community.
+
+General Distribution. The distribution of these domains is shown in Figure 2. Referral Fraud is the most popular category, representing  $52.41\%$  of all the scam domains. Phishing is the second largest category, targeting 28 exchanges. Besides, we have identified 249 trading scam domains, targeting 21 exchanges.
+
+Target Exchanges Figure 3 shows the distribution of targeted exchanges, and the relation with the exchanges' volume<sup>5</sup>. Binance, LocalBitcoins, and Coinbase are the exchanges that have the most number of scam domains. It is interesting to see that, in general, scam domains mainly target the exchanges with high volume, while not all popular exchanges have a large number of scam domains. For example, BitMax has the largest trading volume on 2019-08-01, while it only has 4 scam domains. The reason might be that, BitMax
+
+![](images/5253a18aec869888328d24b6a59ea8f60c4ece11377e97167934a46667dd97cf.jpg)  
+Figure 2: The distribution of scam domains.
+
+![](images/232a9fe3c7d7b1cd5a8b3872e7f85011937b1f027493faa6066e5590c4f38568.jpg)  
+Figure 3: The volume of Exchange VS. the number of scan domains.
+
+![](images/e4e5b8bf804d7be5561ec1fa4f1267b196ba2ced99ca64ec21a291c393bea576.jpg)  
+Figure 4: The distribution of creation time of scam domains.
+
+becomes popular since mid 2019, and it has released an incentive plan to attract users<sup>6</sup>. Before that, it is not as popular as other major exchanges. Thus, we find only a few scams of it.
+
+The Evolution of Scam Domain. We further analyzed the evolution of scam domains, as shown in Figure 4. We use the creation date of WHOIS information to represent when a domain was appeared. As expected, the number of scam domains has increased rapidly after 2017, following the explosive growth of blockchain techniques. It is surprising to observe that, the first exchange scam domain was found in 2004-04-08. However, there was no exchange by the time of 2004. Our manually verification suggests that this is not a false positive. The domain name is www.etorro.com, which
+
+Table 2: Top-5 domains ranked by the most number of endings on VirusTotal.  
+
+<table><tr><td>Domain</td><td>Target exchange</td><td># engines reported</td><td>Category</td></tr><tr><td>xn-localitcoins-bh4f.net</td><td>LocalBitcoins</td><td>14</td><td>Phishing</td></tr><tr><td>paxfuyl.com</td><td>paxful</td><td>11</td><td>ReferralFraud</td></tr><tr><td>yobit.tilda.ws</td><td>yobit</td><td>10</td><td>Trading Scam</td></tr><tr><td>binance.eth-win.com</td><td>Binance</td><td>10</td><td>Trading Scam</td></tr><tr><td>bincepromo-now online</td><td>Binance</td><td>10</td><td>Trading Scam</td></tr></table>
+
+is verified to be a Referral Fraud domain targeting Etoro exchange. Thus, we guess that the domain turns to be the referral fraud after Etoro was founded in 2011), before that it might be a domain with other purposes.
+
+How many of them are flagged by anti-virus engines? As shown in Figure 5, it is surprising to see that, over  $60\%$  of the domains in our dataset have not been flagged by any anti-virus engine on VirusTotal and only  $40.56\%$  of the domains are flagged by at least 1 engine. As for each category, over  $90\%$  of ReferralFraud domains and  $90\%$  of Adult and Gambling domains are not detected by anti-virus engines. Although most of the Trading Scam and Phishing domains are labelled by at least 1 engines, only very few of them are labelled by 10 or more engines<sup>7</sup>. Table 2 shows the top-5 domains ranked by the most number of flagged engines.
+
+![](images/6087d19d120a1e912689c222565e84148248624385d1021ed9cbfa389201f69c.jpg)  
+Figure 5: The distribution of the number of flagged VT engines for our collected scam domains.
+
+Answer to RQ1.1: Our experiment results suggested that the scam exchange domains are prevalent in the ecosystem. Over  $83\%$  (58) of our studied exchanges are targeted by 1,595 scam domains, and most of them were used for malicious purposes including phishing, trading scam, referral fraud, adult and gambling. We have identified 938 domains that have not been disclosed to our community. Unfortunately, most of the domains cannot be flagged by existing anti-virus engines on VirusTotal.
+
+# 4.2 Detecting the Fake Apps
+
+4.2.1 Identifying Fake Apps. To identify fake exchange apps, we first make efforts to collect all the most up-to-data apps from
+
+![](images/3c8e4a940a928e1c02787f220cd0ae7db11a5d4dfff4cc733aeaee17aef7eab7.jpg)  
+Figure 6: Top 10 targeted exchanges of Fake Apps.
+
+the official websites for each exchange, and extract the certificate signatures from apps<sup>8</sup>. Then we seek to search all the possible fake apps from app markets. Note that, as app market such as Google Play always removes malicious and fake apps from time to time, it is hard for us to compile a complete list of fake exchange apps. Here, we resort to Koodous<sup>9</sup>, a large Android app repository with over 53 million apps in total by the time of our study, containing apps from various sources including Google Play. We use crawler to search the app names and package names in Koodous, and collect all the related apps with same app names or package names. For the collected apps, we further analyze their developer signatures and compare them with the original ones. If found mismatch, we then regard them as fake apps. Note that, this is the general method used in our community to identify fake apps.
+
+4.2.2 Overall Result. We have collected 2,810 apps from Koodous, and 323 of them are fake apps - have same app name/package name with the official exchange apps but signed by different developer signatures. The other apps are official apps with different versions released by the exchanges.
+
+![](images/c14d7e085dbeae83949a13bd696501a6165269c22f4782478faa1a08e0fc812f.jpg)  
+Figure 7: The volume of exchange vs. the number of fake apps.
+
+Distribution of Fake apps. These fake apps target 38 exchanges (54%) in total. Figure 6 shows the top-10 targeted exchanges. Polonieux
+
+![](images/35c3dd5e8e5b3ad53af8d50db0b118d0f7413549720453c81b9ee432de1beeb5.jpg)  
+Figure 8: The evolution of fake apps.
+
+![](images/b632638255834b2cfe805b7fd8e8299ef4581f6dea21b366ed99979c78b9bdbb.jpg)  
+Figure 9: # of VirusTotal reported engines when scanning fake apps.
+
+exchange has 35 fake apps in total (with 45 scam domains as shown in Figure 2). For the top-10 targets of fake apps, 7 of them are the same with that of scam domains. We further investigate whether the popular exchanges would receive more fake apps. As shown in Figure 7, the general trend is similar with that of scam domains, i.e., fake apps usually target popular exchanges with large trading volume. But there are exceptional cases too. For example, BitMax has no corresponding fake apps in our study, while it has only 4 scam domains. As aforementioned, the reason might be that BitMax becomes popular since mid 2019 due to its incentive mechanism introduced, and it has not received much attention from attackers by the time of our study.
+
+The Evolution of Scam Apps. We refer to the first seen time on VirusTotal to show the evolution of scam apps, and the distribution is shown in Figure 8. The first fake exchange app in our dataset appeared on Nov 16th 2013, targeting at Etoro exchange with a referral link. In our dataset, fake apps began to appear in the second half of 2013 and reached its peak of 85 in the first half of 2018.
+
+How many of them are flagged by anti-virus engines? We further analyze how many of the fake apps are flagged by anti-virus engines. As shown in Figure 9, over  $52.6\%$  (170) of them are flagged at least one engine, and 33 apps are flagged by over 10 engines. Table 3 shows top-5 of them.
+
+4.2.3 Classification of Fake apps. To classify the fake apps, we use two complementary approaches. For the 170 apps that were
+
+Table 3: Top-5 fake apps ranked by the number of flagged engines on VirusTotal.  
+
+<table><tr><td>App name</td><td>Target exchange</td><td>md5</td><td># engines reported</td></tr><tr><td>Bitcoin allot - Coinbase</td><td>Coinbase</td><td>d41d8cd98f00b204e9800998ecf8427e</td><td>32</td></tr><tr><td>Binance Secured</td><td>Binance</td><td>487ad3a4d18c8b2274bf5916c67bee9</td><td>31</td></tr><tr><td>Bithumb update</td><td>Bithumb</td><td>e7f634c53f0f0ddd48503d4efb661824</td><td>29</td></tr><tr><td>Bitcoin allot - Coinbase</td><td>Coinbase</td><td>76c691abacd276642f11041ec2f78355</td><td>29</td></tr><tr><td>Coinbase</td><td>Coinbase</td><td>b9f6d2c42e961330dfed437f068a6bb1</td><td>29</td></tr></table>
+
+![](images/65316cca57721d87e1e246a429b60b9c6ea94543f87d609884fc0edf647b4a2b.jpg)  
+Figure 10: The distribution of malware types.
+
+![](images/a11a05f45508d482a70aa039e1c93bf7b54fad78d8cfffce989310a2e602eeff.jpg)  
+Figure 11: The distribution of malware families.
+
+flagged by VirusTotal, we use Euphony [19], a widely-used tool to analyze the scanned results to label a malware type and malware family for each of them. For the remaining 153 apps that were not flagged by VirusTotal, we either install them on smartphones or decompile them using static analysis tools for manually examination.
+
+Malware Type and Malware Family Distribution. As shown in Figure 10, for the 170 flagged fake apps, roughly  $50\%$  of them are labelled as grayware by VirusTotal. Over  $40\%$  of them are flagged as Trojan, and roughly  $4\%$  of them are labelled as adware. This result suggests that these fake apps may expose great security threats to users. To be specific, we use Euphony to generate a malware family label for each of them, and Figure 11 shows the malware family distribution. As expected, family fakeapp ranks the first, with 23 apps labelled. The labels of the remaining apps vary greatly,
+
+including adware families like inmobi, mobidash, and malicious categories like smmsgpy and slocker. Note that, there are 102 apps that Euphony cannot give them a family label based on the flagged results of engines. This result also suggests that existing anti-virus engines cannot classify these fake apps accurately.
+
+Manually Inspection. For the remaining 153 fake apps, we found that all of them are referral apps with advertisements. Similar with referral fraud domains, most of the referral apps use webview to connect to their referral links, intending to attract new users. In general, they will also embed some ad libraries to increase the income.
+
+Examples. Figure 12 shows examples of the fake apps we identified. Figure 12(1) shows a phishing app<sup>10</sup> that targets Poloniex. It fabricates a fake login screen and tricks users into typing in their Poloniex accounts. After that, it will continue to display a fake 2FA verification screen and ask for full email access to further steal users' email accounts. Once success, attackers will get full access to users' Poloniex accounts and steal their money in a silent way. Figure 12(2) is a Coinbase adware<sup>11</sup> sample. It was repackaged from official Coinbase app, and embedded with aggressive ad libraries. During run-time, it requires users to install recommended apps, otherwise users cannot access to the main functionality of the app. However, most of the recommended apps are considered to be malicious. Furthermore, the app will push mobile ads during its running at background, which could lead to the unintentionally clicking of the advertisement. Figure 12(3) is a referral app<sup>12</sup> that targets Binance. It simply implements a webview and connects to the referral link https://www.binance.com/?ref=20270961. Attackers will benefit from users who register from this links. The benefit is usually a portion of commission fee, depending on the referral rules of different exchanges<sup>13</sup>. Figure 12(4) is a code snippet of a Bithumb trojan app<sup>14</sup>. As highlighted in the decompiled code, it will collect users' text messages, contracts, and call logs secretly, and then upload them to http://bithumbbinback.pro/, which was the attacker's private server. Moreover, it monitors the device's incoming calls and messages at background.
+
+Answer to RQ1.2: Fake exchange apps are also prevalent in the ecosystem. Over 38 exchanges are targeted by 323 fake apps. A number of them show malicious behaviors and pose great security threats to mobile users.
+
+# 5 UNDERSTANDING THE ATTACKERS
+
+Our previous exploration suggests that exchange scams are prevalent in the ecosystem. In this section, we further investigate the relationship between these scams, in order to understand the attackers behind them. We first correlate the scam domains based on the information we collected, then we group fake apps based on code similarity and developer signatures. At last, we further identify the relationship between scam domains and fake apps.
+
+![](images/ccaf1425096a9020cb6c529a1fd6e8eb52646ea6ff89c38ee9f33531d4f4d7ef.jpg)  
+Keeping hackers out.
+
+The vast majority of customer deposits are stored offline in air-gapped cold storage. We only keep enough online to facilitate active trading, which greatly minimizes risk
+
+![](images/1f866250cf112bf500845f1ca30f78447ec1c61f952420837ed5a44791768df2.jpg)
+
+![](images/3c45c075ceb9ad256bf7f63e8da0bbbe470d60b8efa481cd772855290a65d980.jpg)  
+(1)A Poloniex phishing app
+
+![](images/caed950194a5f229b56acb47815dae33cc4f403ae392407d56fd7cc7974491d0.jpg)  
+(3)A Binance referral app
+
+![](images/e8d9ea563a9bf37843cd617578524b7a109b60db53ad6a39aaa7d1c252dabac2.jpg)  
+(2)A Coinbase adware app  
+(4)A Bithumb trojan app  
+Figure 12: Examples of Identified Fake Apps.
+
+# 5.1 The Relation of the Scam Domains
+
+5.1.1 Approach. We use a three-phase clustering approach to characterize their relationship, as shown in Figure 13.
+
+![](images/8843b025bca1cec074ca933c6b5307b1254d2d366c222308a8f0be0280e90759.jpg)  
+Figure 13: A Three-phase Domain Clustering.
+
+IP clustering. For each scam domain, we first resort to urlscan $^{15}$  to collect all the related IP addresses by searching its history resolve IPs (Passive DNS). We have collected 1,348 unique IP addresses that related to the 1,534 scam domains. Note that one domains may correspond to multiple IP addresses, and several domains may share the same IP addresses. In Section 4.1.3, we collected the domains that uses parking services and their IPs. We further remove IPs related to parking service in case they affect the cluster result. Then we group the domains based on IP addresses. During grouping, we also find other IPs related to parking services or domain hosting services due to their uncommon cluster sizes, and we remove them too. At last, we have remained 1,215 IP addresses that we believe were used for malicious purposes. After this step, we have 76 clusters in total, with 580 domains in the clusters. Note that, the remaining 1015 domains are isolated in this step.
+
+Whois Clustering. Whois information usually contains some personal data of the domain holders, which may help identify the domain groups held by each attacker[20, 26]. Only 266 domains (16.7%) in our datasets have corresponding valid Whois information<sup>16</sup>. Among 266 domains, there are 51 unique Whois information and 11 of them are shared by 226 domains. This results in 6 new clusters, and 2 clusters in step 1 are combined. Therefore, after this step, we further cluster the domains to 81 clusters (including 644 domains).
+
+Blockchain Address Clustering. As some identified domains are used for trading scams, and they have embedded the scam blockchain addresses in the corresponding webpages. Thus we further analyzed the crawled HTML webpage, and use regular expressions and checksum to identify blockchain addresses. Table 4 shows examples of regular expressions we used to identify Bitcoin and Ethereum addresses, respectively. We have identified 182 blockchain addresses in total, across 6 kinds of Cryptocurrencies,
+
+Table 4: Examples of regular expressions we use to identify blockchain addresses.  
+
+<table><tr><td>Cryptocurrencies</td><td>Regular expression</td></tr><tr><td>Bitcoin</td><td>(bc1|[13])[a-zA-HJ-NP-Z0-9]{25,39}</td></tr><tr><td>Ethereum</td><td>0x[a-fA-F0-9]{40}</td></tr></table>
+
+Table 5: A summary of blockchain addresses we got from scam domains.  
+
+<table><tr><td>Blockchain</td><td># target exchanges</td><td>Target exchanges</td><td># domains</td><td># addr</td></tr><tr><td>Ethereum</td><td>19</td><td>Binance,Bibox,OKEx,Cobinhood ,Coinbase,BitMEX,...</td><td>138</td><td>111</td></tr><tr><td>Bitcoin</td><td>7</td><td>Binance,Coinbase,Huobi,Kraken, OKEx,BitMEX,Yobit</td><td>85</td><td>66</td></tr><tr><td>XRP</td><td>2</td><td>Binance,Kucoin</td><td>5</td><td>2</td></tr><tr><td>Tron</td><td>2</td><td>Poloniex,Kucoin</td><td>5</td><td>1</td></tr><tr><td>NEO</td><td>2</td><td>Poloniex,Kucoin</td><td>3</td><td>1</td></tr><tr><td>Binance Coin</td><td>1</td><td>Binance</td><td>1</td><td>1</td></tr></table>
+
+including Ethereum, Bitcoin, XRP, Tron, NEO and Binance Coin, as shown in Table 5. More specifically, we have 66 Bitcoin scam addresses and 111 Ethereum scam addresses. Then, we group the domains based on these addresses, and achieve the final clustering results.
+
+5.1.2 Results. At last, we have obtained 94 clusters, with 699 domains  $(43.8\%)$  in total. Note that there are 896 isolated domains. The distribution of cluster size is shown in Figure 14. We can observe that most of the clusters are small clusters with size 2 or 3, and there are only 18 clusters with a size larger than 5. Table 6 lists the top-15 clusters, which we have assigned each cluster a family name. This result suggests that: (1) some attackers have the tendency to create a large number of scam domains. For example, the largest family in our dataset has created 254 scam domains, targeting 11
+
+![](images/ef350ce9e13074d8b938d9e457c7d795f7e46918daec056fa8db1153004c61b4.jpg)  
+Figure 14: The distribution of cluster size.
+
+different exchanges; (2) attackers tend to use the same method to create the scam domains, i.e., the scam category remains the same for most clusters. The reason might be that it is easier for them to reuse one method in creating multiple scam domains.
+
+# 5.2 The Relation of the Fake Apps
+
+5.2.1 Approach. We group fake apps based on both developer signatures and code similarity.
+
+Clustering based on developer signatures. Android system uses developer certificates to identify the authorship of apps. In our dataset, we have extracted 206 unique developer signatures in total. Note that, some fake apps may use the common signatures that widely known in our community. For example, Android framework has provided four common keys. Thus, we further analyze these signatures and remove a common Android framework signature '61ed377e85d386a8dfee6b864bd85b0bfaa5af81' (related to 6 exchanges and 9 fake apps). We thus have 205 unique developer signatures in total.
+
+Clustering based on code similarity. Previous work suggested that malicious developers always reuse the code to generated apps. Thus, we further measure the code-level similarity of these fake apps. Here, we take advantage of SimiDroid [23], a tool that provides comprehensive pairwise comparison to understand the similarity among apps. We perform pair-wise comparison to calculate method-level similarity of all the apps we collected. Apps with similarity higher than  $80\%^{17}$  will be classified into a same cluster.
+
+5.2.2 Results. For the signature-level clustering, we observe that 60 signatures were reused by fake apps, with 169 apps in total. The other remaining 145 signatures only have one corresponding app each<sup>18</sup>. Table 7 shows the result. Fake apps in signature-level clusters account for over  $52\%$  of all the fake apps we identified. As to the code-level clustering, we have clustered 34 groups, including 270 fake apps  $(83.6\%)$ , with only 53 isolated apps. Table 8 shows the top-5 code similarity clustering groups.
+
+Results show that both developer signatures and code similarity can help identify attacker groups. We further study the relations of the signature-same clusters and code-similar clusters. Based on the code similarity clusters, we combine the clusters that contain same signatures and then add signature clusters that are not in the similarity clusters. At last, we combine 9 similarity clusters into 3 clusters and add two signature clusters. We finally have grouped
+
+30 app clusters, with 275 apps  $(85.1\%)$  in total (with only 48 isolated apps).
+
+We further sampled apps from each cluster for manually inspection, and we have the following observations. First, fake apps signed by the same certificate are usually with high code similarity, indicating that they share the similar malicious behaviors and purposes. Second, similar to the scam domains, to reduce development cost, quite a few attackers prefer to use easy-to-use visual programming platforms like App Inventor<sup>19</sup> or AppsGeyser(https://appsgeyser.com/) to develop their forged apps with a specific template.
+
+# 5.3 The Tie between Scam Domains and Apps
+
+To investigate the tie between scam domains and fake apps, we further analyzed the connected URLs and domains of fake apps, to see whether they are overlapped with the scam domains we identified. Therefore, we extract urIs from the fake apps using Apkatshu $^{20}$ , a popular tool for extracting urIs, emails, and IP addresses fromapk files. We seek to investigate whether we could find some clues to link the scam domains and apps. However, from the data we collected, we can only find 1 phishing url (xn-polonix-y8a.com) targeting at Poloniex. This result suggested that, there is no clear evidence to link scam domains and the fake apps. The reason might be that, fake apps usually use the app name and user interface to infect unsuspecting users. As long as users have installed the fake apps, the malicious behaviors can be performed in either foreground (e.g., using the fake UIs) or background (e.g., stealthy behaviors), without the need of further using squatting domains to cheat users.
+
+Answer to RQ2: Our experiment results suggested that a number of the scams are controlled in groups, i.e.,  $43.8\%$  of the scam domains and  $85.1\%$  of fake apps could be clustered into groups. This observation could help us identify and track the new scams in the future. For example, new domains that related to existing scam IP addresses and blockchain addresses are high suspicious to be malicious. The apps released by the known scam signatures should also be paid special attention to.
+
+# 6 CHARACTERIZING THE IMPACTS
+
+In this section, we measure the impacts of cryptocurrency exchange scams from two ways. First, we trace the money flow of scam addresses, in order to quantifying the scale of the scams, i.e., the number of victims and the amount of financial loss. Second, we measure the presence of fake apps on major app markets, to see how many of them have penetrated to popular app markets to infect unsusicious users.
+
+# 6.1 Money flow of scam addresses
+
+As aforementioned in Section 5.1.1, we extract 182 unique wallet addresses contained in the trading scam websites. Thus, we further analyze the transaction information related to these addresses to estimate the impact the scams. Note that, the financial loss we estimated here is a lower-bound of the whole ecosystem, considering that there are many scam domains that we are not able to directly investigate their impacts here.
+
+Table 6: Top-15 clusters ranked by the number of scam domains. Note that we have assigned a family name for each cluster by randomly picking one scam domain name.  
+
+<table><tr><td>Family</td><td>#urls</td><td># exchanges</td><td>Target exchanges</td><td>Category</td><td>Shared IPs</td><td>Shared Whois</td><td>Shared addresses</td></tr><tr><td>olcalbitcoins.com</td><td>254</td><td>11</td><td>Binance,Livecoin,Wirex, Bitbay,LocalBitcoin,...</td><td>Referral Fraud</td><td>136.243.255.0/24</td><td>Vitalii Vselenskiy</td><td></td></tr><tr><td>coincheck.com</td><td>42</td><td>8</td><td>Poloniex,Binance,CoinCheck, Kraken,HitBTC,...</td><td>Referral Fraud</td><td></td><td>xu shuaiwei</td><td></td></tr><tr><td>kralkem.com</td><td>28</td><td>7</td><td>Poloniex,Binance,Bittrex, Kraken,KuCoin,...</td><td>Phishing</td><td>185.110.132.214</td><td></td><td></td></tr><tr><td>coinbasegift.com</td><td>22</td><td>3</td><td>Coinbase,Binance,Kraken</td><td>Trading Scam</td><td>198.187.29.252, 199.33.112.226, 69.77.162.51,...</td><td></td><td>1FZWWiRH5zSwaFY5gUFXVGML6NHsADngRp, 19R9MWW88rZwivGWvz15Ey9G7mpjYesB, 1CdWQJMiQF1uYbwKc7fb5VBb9JBrhykcNf</td></tr><tr><td>bitma.io</td><td>20</td><td>2</td><td>BitMEX,BitMax</td><td>Referral Fraud</td><td>46.166.184.106, 185.206.180.119</td><td>Sun Wukong</td><td></td></tr><tr><td>virexapp.com</td><td>15</td><td>5</td><td>Wirex,BitMEX,Bitfinex, Kraken,HitBTC</td><td>Referral Fraud,Scam</td><td>77.78.104.3</td><td></td><td></td></tr><tr><td>bitbai.net</td><td>15</td><td>3</td><td>Yobit,Bitbay,Bitforex</td><td>Referral Fraud</td><td>212.91.7.33, 185.253.212.22</td><td></td><td></td></tr><tr><td>deribiy.com</td><td>14</td><td>2</td><td>Huobi,Deribit</td><td>Referral Fraud</td><td>185.182.56.12</td><td></td><td></td></tr><tr><td>bitpannda.com</td><td>12</td><td>2</td><td>Bitpanda,Coinmama</td><td>Referral Fraud</td><td>78.109.174.110</td><td></td><td></td></tr><tr><td>yobitr.net</td><td>11</td><td>5</td><td>Yobit,Binance,Kraken, Hitbtc,Bittrex</td><td>Phishing</td><td>185.110.132.216</td><td>Sergei Nesmiyanov</td><td></td></tr><tr><td>kueoin.com</td><td>9</td><td>5</td><td>Poloniex,BitMEX,Bitfinex, KuCoin,Bittrex</td><td>Phishing</td><td>5.45.65.239</td><td></td><td></td></tr><tr><td>paxfulverify.com</td><td>9</td><td>3</td><td>Yobit,LocalBitcoin,Paxful</td><td>Phishing</td><td>204.93.160.0/19, 198.38.82.0/24,...</td><td></td><td></td></tr><tr><td>binance-presents.fund</td><td>7</td><td>1</td><td>Binance</td><td>Trading Scam</td><td>162.144.100.203</td><td></td><td>1Mn386ue8o3mW9866octLNP8HFqYsphJC, 0x11775A106157a283873A81E8Ec58394b8d568E06</td></tr><tr><td>loginviet-binance.com</td><td>6</td><td>1</td><td>Binance</td><td>Phishing</td><td>198.187.29.106, 198.54.116.199,...</td><td>Taraku Apostrof</td><td></td></tr><tr><td>giveaway-coinbase.top</td><td>6</td><td>1</td><td>Coinbase</td><td>Trading Scam</td><td>181.215.237.183</td><td></td><td>0xEF50C2DA0a52f2a3a231eD38fA1B79Ad97ab9563, 0xf5e36B888bc15528b6Bd42fe0B1b2aF62693eB9</td></tr></table>
+
+Table 7: Top-10 fake app clusters (signature-level).  
+
+<table><tr><td>Developer signature(SHA1)</td><td>Target exchanges</td><td># apps</td></tr><tr><td>2CB7E9064D1EC3852191B45F3645A02EF55105B9</td><td>Kraken,Bitstamp, Cryptopia,HitBTC</td><td>4</td></tr><tr><td>21064B6D32EB94D49143FE23F06BD222C116B348</td><td>Paxful,Coinmama, Bitfinex</td><td>3</td></tr><tr><td>7CD76D9FEA4736AEFF636AD02512FFE625702FC6</td><td>Cryptopia,Polonix, Bittrex</td><td>3</td></tr><tr><td>86DA54FDAD362FC78354C987E4337F762D37B702</td><td>Bitfinex,Coinmama, Bitstamp</td><td>3</td></tr><tr><td>E99A56A0F329F243CC2759317F07E94CDF9ACFA8</td><td>Cryptopia,Polonix, Bittrex</td><td>3</td></tr><tr><td>7B927F47E2F99722846F9706E3B1CAD129E17D90</td><td>Cryptopia,Bittrex</td><td>5</td></tr><tr><td>AF49696504D84B6BD15E3B505EC79049F45DCC73</td><td>Bitfinex,Bitstamp</td><td>3</td></tr><tr><td>8DDD7A5D446A3FEAE270DA5BBC6A14186CD4843E</td><td>CoinExchange,LocalCoins</td><td>2</td></tr><tr><td>7238E7D72F225EBCD660B0932E47B3197BCE1EB7</td><td>LocalCoins,Polonix</td><td>2</td></tr><tr><td>F16B1CD5DA076CEEEEE8BB1523B25B63EC6FAA171</td><td>CoinExchange</td><td>9</td></tr></table>
+
+Table 8: Top-5 code similarity clusters which have most apps.  
+
+<table><tr><td>an app&#x27;s SHA256 in fake app families</td><td># of apps in 
+same family 
+(# of apps 
+reported by 
+VirusTotal)</td><td># of 
+Target 
+exchanges</td><td>Target exchanges</td><td>Reported malware types</td></tr><tr><td>96348ed94d796d7c0f3459560ca499d- 
+adfb852c678cc55ba3d3d5ac0df2613d</td><td>86(71)</td><td>18</td><td>Bibbox,Binance,BitMEX, 
+bitstamp,Bittrex,...</td><td>Gray,Trojan</td></tr><tr><td>6cb9ab55b6bd9dc85c585546408de196- 
+2391a4966cc2aeea39b028d29dc94da</td><td>33(11)</td><td>15</td><td>b2bx,Binance,bifinfix, 
+BitMEX,bitslo,...</td><td>Adware,Trojan</td></tr><tr><td>818c1a91d5049adb0d1748a97c8cb2- 
+2a5464f9b7e13c6085e97751670507d</td><td>16(12)</td><td>9</td><td>Binance,bifinfix,BiTMEX, 
+bitstamp,Bittrex,...</td><td>Repmalware,Riskware, 
+Trojan</td></tr><tr><td>7f5db9450bad17ae6d0747b24a4c9- 
+88cb09edecd34277c3b391349f6ca1a1</td><td>15(3)</td><td>7</td><td>Binance,bifinfix,cryptopia, 
+etoro,hitbc,...</td><td>Adware,Gray, 
+Repmalware</td></tr><tr><td>82d8ed60f6d25114280ba2824f34d2- 
+9d86066b0e06275b48fa1a69c48b03</td><td>10(0)</td><td>6</td><td>Bittrex,cryptopia,hitbc, 
+Kraken,Polonix,yorbit</td><td></td></tr></table>
+
+6.1.1 Overall Result. We further retrieved all the transaction data related to these addresses. There are 1,713 income transactions taken place and these scam address received a total number of 28.84
+
+BTC, 1625.29 ETH, and other tokens, which is equivalent to roughly over 520K US dollars $^{21}$ .
+
+Distribution. We analyze the distribution of BTC and ETH addresses' incoming transactions, as shown in Figure 15. For the amount of money loss, over  $41.8\%$  of the transactions are over 100 US Dollars. The largest transaction record took place on 2018-11-22 and the scam address 1MpLjpT44A5yyRbtGG61rtpgwxdJB3onsB received about 15K dollars in total.
+
+As to the transaction time, the first victim was deceived 0.99 Ethereum (167.18$) on Sept 16th 2017 on the cobinhood.io whose target is Cobinhood shortly after the exchange's ICO launch. It is interesting to observe that, ETH is popular before 2019, while BTC turns to be more prevalent after July of 2019.
+
+The most profitable addresses. On average, each scam address has received 9 transactions. While some addresses are more active than we expected, e.g.,  $0x40949225c4a1745a9946f6aaf763241c082c$  b9ac has received over 474 transactions. We further analyzed the amount of incoming transactions for BTC and ETH addresses, and the distribution is shown in Figure 16. On average, each address has received 2941.05 Dollars. Roughly  $75\%$  of the BTC addresses have received less than 918.58 US Dollar equivalent tokens, and  $80.04\%$  of ETH addresses have received less than 167.42 US Dollar equivalent tokens. Table 9 lists the top-5 profitable addresses. The largest one has received roughly 500 ETH, which is roughly equivalent to 83K US Dollars.
+
+Scam Families. We further analyze the scam families we identified in Section 5.1.2. Among the 36 families that have at least one address, 35 of them are trading scams and the remaining one is a phishing family. They have 68 addresses in total, while the other
+
+Table 9: Top-5 profitable addresses.  
+
+<table><tr><td>Target exchange</td><td>Scam domain</td><td>Scam address</td><td># total incoming transactions</td><td>Total received</td><td>Current value($)</td></tr><tr><td>Binance</td><td>binancefree2018.droppages.com</td><td>0x40949225c4a1745a9946F6AAf763241c082cb9ac</td><td>474</td><td>497.39 ETH</td><td>83192.66</td></tr><tr><td>shapeshift</td><td>shapishift.io,xn-hapeshit-ez9c2y.com</td><td>0x3853ba76ec6ae97818e2d0e0839c9eda6c396690</td><td>140</td><td>309.13 ETH</td><td>51702.10</td></tr><tr><td>Coinbase</td><td>coinbase-airdrop.top,coinbase-btc.xyz</td><td>1MpLjpT44A5yyRbtGG61rtpgwxdJB3onsB</td><td>28</td><td>4.93 BTC</td><td>42537.83</td></tr><tr><td>Binance</td><td>dropfinance.com,giftfinance.com</td><td>1CdWQJMiQF1uYbwbKc7fb5VBb9JBbrhykcNf</td><td>13</td><td>4.43 BTC</td><td>38232.70</td></tr><tr><td>Binance</td><td>binanceclaims</td><td>13XzbaQV6k21yfbS5WDkzwSPkAxQ1AsbQ3</td><td>14</td><td>1.96 BTC</td><td>16950.98</td></tr></table>
+
+Table 10: Top-5 profitable families.  
+
+<table><tr><td>Target exchanges</td><td>Family</td><td># domains</td><td># addresses</td><td>Addresses</td><td># total incoming transactions</td><td>Total received</td><td>Current value($)</td></tr><tr><td>Binance, Coinbase, Kraken</td><td>coinbasegift.com</td><td>22</td><td>18</td><td>1FZWWiRH5zSswaFY5gUFXVGML6NHsADnqRp, 19R9MWW88rZwivGWvvy15Ey9G7mpgJYesB, 1CdWQJMiQF1uYbwKc7fb5VBb9JBrhykcNf,...</td><td>65</td><td>8.25 BTC</td><td>71128.11</td></tr><tr><td>Coinbase</td><td>coinbase-btc.xyz</td><td>2</td><td>1</td><td>1MpLjtpT44A5yyRbtGG61rtpgwxdJB3onsB</td><td>28</td><td>4.93 BTC</td><td>42537.83</td></tr><tr><td>Binance</td><td>binance.updog.co</td><td>4</td><td>2</td><td>0x76bb5b6177096b337c79F2f948Aa08b0db5f5211, 13XzbaQV6k21yfbS5WDkzwSPkAxQ1AsbQ3</td><td>56</td><td>35.79 ETH, 1.97 BTC</td><td>23028.14</td></tr><tr><td>Bithumb, Huobi</td><td>huobiglobal.ltd</td><td>3</td><td>1</td><td>0xe2e4B53A1324F5a7368724eA73e532c626517f19</td><td>107</td><td>60.48 ETH</td><td>10411.29</td></tr><tr><td>Binance</td><td>binance-presents.fund</td><td>7</td><td>4</td><td>0x11775A106157a283873A81E8Ec58394b8d568E06, 1Mn386ue8o3mW9866octLNP8HFqcYsphJC,...</td><td>29</td><td>20.70 ETH, 0.62 BTC</td><td>8794.36</td></tr></table>
+
+![](images/716e2fbac298ed62dcafefa8931902d55cbc3392ee4236972ba29d61f02b5ceb.jpg)  
+Figure 15: The scatter diagram of two major cryptocurrencies' 1,659 transactions.
+
+114 addresses are isolated. Note that, 25 families (69.4% of the families that have blockchain addresses) have only one corresponding blockchain address. The top 5 profitable families are listed in Table 10. The family 'coinbasegift.com' is most profitable, and it has received over 70,000 equivalent US dollars in BTC.
+
+6.1.2 Money Flow. We further attempt to identify the relations between scam addresses by sorting out the money flows. We first label the addresses in the money flow into three categories: 1) the scam addresses, the addresses that we extracted from the scam websites. Note that not all the addresses we found have transactions
+
+![](images/33deb1525de7fcc3d6608fc49ce92eb97f4390e2ae9d99b4d6234adf1c9a50fb.jpg)  
+Figure 16: The distribution of incoming transactions for each scam address.
+
+records, thus we remove the silent scam addresses during the money flow analysis. 2) the victim addresses, which have ever transferred money to the scam addresses and did not receive money from scam addresses; 3) the fund transfer addresses, which were used to transfer money originated from the scam addresses. Note that BTC's change addresses[3] are also a part of money flow, we consider them as fund transfer addresses. Figure 17 shows the money flow of two major cryptocurrencies, BTC and ETH, respectively.
+
+Scam analysis. There are 1,320 victim addresses (470 in BTC and 850 in ETH) and 132 scam addresses (53 in BTC and 79 in ETH). In
+
+![](images/eb4e7c542620c2485076b6ad871468f6240c715d66d48e93a23037daa71497dc.jpg)  
+(a) BTC addresses' fund transfer flow.
+
+![](images/139ffa0258060e6c00c8e39be82e9eea6c7b192bfda52a0d22d08f76eee7b5ed.jpg)  
+(b) ETH addresses' fund transfer flow.
+
+victim addresses, we find many of them have transferred money to multiple scam addresses. For example, the address  $0xfbb1b73c4f0bda-4f67dca266ce6ef42f520fbb98$  transferred money to 10 scam addresses with 68 transactions.
+
+On average, each BTC scam address is related to 9 victim addresses while each ETH scam address links to about 11, which may suggests that ETH-based scams have a slightly higher success rate.
+
+Fund transfer analysis. There are 518 fund transfer addresses (165 in BTC and 353 in ETH), which are far more than the scam addresses. We further studied their relations. We found 28 addresses share 13 fund transfer addresses. Table 11 shows the top-5 of them. It is interesting to see that scam family coinbasegift.com accounts for most of the top shared fund transfer addresses. Considering that this family also has multiple scam addresses and transactions among scam addresses[22], this team of attackers is likely to carry out a careful plan to avoid tracking and we found only the tip of the iceberg. Besides, we found most of the fund transfer addresses have transferred all the tokens they received, suggesting that most of the attackers have transfer money through a chain of addresses. To better cover their tracks, attackers may further use the mixing service [4] to achieve the purpose of money laundering.
+
+# 6.2 Scams in Major App Markets
+
+As we have identified over 300 fake apps, we further analyze whether these apps have penetrated into major app markets.
+
+Although we crawled fake apps from Koodous, it does not contain app source information. Thus we resort to Janus $^{23}$  and Andro-zoo $^{24}$ , two major app repositories to track fake apps' evidence in
+
+![](images/b8da5e9241bbb592149ee6fd7f38ccc0c2be8758f160fc2a2d99f56931d73ad4.jpg)  
+Figure 17: Fund transfer diagram of two major cryptocurrencies.  
+Figure 18: The app market distribution of fake apps.
+
+app markets. Among the 323 fake apps, over 66 (20.4%) of them have been found in major app markets, as shown in Figure 18. Obviously, the official market – Google Play, is the first target, with 60 fake apps in total. Other third-party app markets, have hosted one or more fake apps. Note that, as we cannot get the download information of these fake apps[25], we are not able to estimate the overall number of the victims here. Nevertheless, this result suggests that, existing app security check mechanisms deployed on app markets are not able to identify these fake apps effectively, which may affect many unsuspecting users.
+
+Table 11: The top-5 fund transfer addresses ordered by the number of shared scam addresses.  
+
+<table><tr><td>Scam addresses</td><td>Scam family</td><td>Fund transfer address</td><td># related scam addresses</td><td># of related transactions</td><td>Total received($)</td></tr><tr><td>13tsX2zBiPz3P2nt5HgyFKxXTQFWRqXEuj, 1FGZE75bUCHkoEcaoQLRzBuPYB9NA8XRCQ, 1FZWiRH5zSwsaFY5gUFXVGML6NHsADngRp</td><td>2 isolated, 1 in coinbasegift.com</td><td>bc1qq09hzxsprzh3fqdhcf6qtg9kcvcwwp6nuyly</td><td>3</td><td>3</td><td>10162.78</td></tr><tr><td>1CdWQJMiQF1uYbwKc7fb5VBb9JBrhykCnF, 1Lkakee2QGSQ92uNBUCUD1LaL4RKQToTBLG, 1BdencTWBaDrxpVBK7PPDtb9cot5Ns8D1T</td><td>coinbasegift.com</td><td>bc1qfw3660gw5xv0t9p594hlq2xkmlkz0gmzley003</td><td>3</td><td>3</td><td>5458.23</td></tr><tr><td>0x1363077895b20ae90f80794ce4e575559517d033, 0x915c95415d3449212fd0991ccf5eb42864118ec9</td><td>2 isolated</td><td>0x8b03bbe38069a34d1ab6db2f545f6cb8cd2d6a1e</td><td>2</td><td>4</td><td>11481.87</td></tr><tr><td>0x2784574e2405a7d3be1259b5f00412ae652018f4, 0x3e9163816b073c2ce425c99e68ba8ae7caaec067</td><td>1 isolated, 1 in binanceth.net</td><td>0x9dd648a58cb8d2b5fbf937b863c627ba747dbf12</td><td>2</td><td>2</td><td>5763.00</td></tr><tr><td>1NuZ4rxsQPU4izGTKScs793Uxx2c6ADRQo, 16wd9B1LiXmTNf9hxQyb3Q9fbVHzP3NvSV</td><td>1 in coinbasegift.com, 1 in win-binance.com</td><td>bc1qmvpfmglf9wk4wchucjp7gdhk7gv3wny4vm7z37</td><td>2</td><td>2</td><td>3704.43</td></tr></table>
+
+Answer to RQ3: Our experiment results suggested that there are about 1700 victims been deceived, with the amount scammed up to 520k dollars in our dataset. And although attackers' groups can be identified, they used multiple fund transfer addresses and mixing services to hide their tracks. On the other side, attackers have the ability to bypass the security check of the app markets and distribute their fake apps to markets, which exposes great threat to the community.
+
+# 7 IMPLICATIONS AND LIMITATIONS
+
+# 7.1 Implications
+
+Our observations are of key importance to stakeholders in the blockchain community. First, considering the large number of scam domains, fake apps, and blockchain addresses we discovered, the governance of the ecosystem needs to be improved. Second, considering most of the cryptocurrency exchanges are suffering from a growing number of scam attacks, our community should apply detection methods like we used in this paper to identify such scams and prevent users from being cheated by them. A growing and up-to-date scam database is also needed. Third, as we observed in this paper, many scams have strong relations and we could classify them into clusters. This observation could guide us to identify new scams and raise alarms when new related domains found.
+
+# 7.2 Limitations
+
+Our study carries some limitations. In several cases, First, the methods and techniques we used in this paper are old-fashioned, i.e., typosquatting generation and fake app detection, and we also rely on some manually efforts in the study. Nevertheless, we have identify a number of scams and most of them have not been revealed to the community. Some advanced techniques (e.g., machine learning techniques) could be used to identify and classify the scams. Second, in this paper, we are only focused on the exchange scams. However, a number of scams may target cryptocurrency wallets and tokens. Thus, a promising future research direction is to study the scams in the other parts of the blockchain ecosystem. Third, due to the limitation of dataset, we did not study the distribution channels of the scams, i.e., how do they get to users. The future direction might
+
+be investigating the advertisements of scams in social networking platforms (e.g., Facebook and Twitter).
+
+# 8 CONCLUDING REMARKS
+
+In this paper, we present the first systematic study of cryptocurrency exchange scams. We have created a dataset of over 1,500 scam domains and over 300 fake apps, and shared it to the community to boost future related research. We characterized the types and behaviors of scam domains and apps, and revealed that a majority of the scams were controlled by a small group of attackers. We further identified 183 blockchain addresses related to such attackers, and analyzed impacts of them. Our observations are of key importance to stakeholders in the blockchain community, and demonstrate the urgency to identify and prevent blockchain scams.
+
+# ACKNOWLEDGMENT
+
+This work was supported by the National Key Research and Development Program of China (No. 2018YFB0803603) and the National Natural Science Foundation of China (No. 61702045).
+
+# REFERENCES
+
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+    {
+        "type": "text",
+        "text": "Domain Adaptive Ensemble Learning",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Abstract—The problem of generalizing deep neural networks from multiple source domains to a target one is studied under two settings: When unlabeled target data is available, it is a multi-source unsupervised domain adaptation (UDA) problem, otherwise a domain generalization (DG) problem. We propose a unified framework termed domain adaptive ensemble learning (DAEL) to address both problems. A DAEL model is composed of a CNN feature extractor shared across domains and multiple classifier heads each trained to specialize in a particular source domain. Each such classifier is an expert to its own domain but a non-expert to others. DAEL aims to learn these experts collaboratively so that when forming an ensemble, they can leverage complementary information from each other to be more effective for an unseen target domain. To this end, each source domain is used in turn as a pseudo-target-domain with its own expert providing supervisory signal to the ensemble of non-experts learned from the other sources. To deal with unlabeled target data under the UDA setting where real expert does not exist, DAEL uses pseudo labels to supervise the ensemble learning. Extensive experiments on three multi-source UDA datasets and two DG datasets show that DAEL improves the state of the art on both problems, often by significant margins.",
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Index Terms—Domain adaptation, domain generalization, collaborative ensemble learning",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "I. INTRODUCTION",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep neural networks trained with sufficient labeled data typically perform well when the test data follows a similar distribution as the training data. However, when the test data distribution is different, neural networks often suffer from significant performance degradation. Such a problem is common to machine learning models and is often referred to as domain shift [1] (or distribution shift). To overcome the domain shift problem, two related areas have been studied extensively, namely unsupervised domain adaptation (UDA) [2, 3, 4, 5, 6, 7, 8, 9] and domain generalization (DG) [10, 11, 12, 13, 14, 15]. UDA aims to adapt a model from a labeled source domain to an unlabeled target domain. In contrast, DG aims to learn a model only from source data typically gathered from multiple distinct but related domains, and the model is directly deployed in a target domain without any fine-tuning or adaptation steps.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Early UDA work focuses on single-source scenarios. Recently, multi-source UDA [16, 17, 18] has started to attract more attention, thanks to the introduction of large-scale multidomain datasets such as DomainNet [18]. In contrast, having multiple source domains has been the default setting for most DG methods from much early on [11]. This is understandable: without the guidance from target domain data, DG models rely on the diversity of source domain to learn generalizable",
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "knowledge. This paper focuses on the multi-source setting for both problems.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "How can multiple source domains be exploited to help generalization? Many DG methods [19, 20, 21] aim to learn a domain-invariant feature representation or classifier across the source domains, in the hope that it would also be invariant to domain shift brought by the target domain. However, there is an intrinsic flaw in this approach, that is, when the source domains become more diverse, learning a domain-invariant model becomes more difficult. This is because each domain now contains much domain-specific information. Simply removing the information may be detrimental to model generalization because such information could potentially be useful for a target domain, especially when combined across different source domains. An example can be found in Fig. 1(a) where the only thing in common of the five source domains for the airplane class seems to be shape. However, texture information is also useful for object recognition in the target sketch domain, which we want to maintain in the learned classifier. Existing multi-source UDA methods, on the other hand, attempt to align the data distribution of the target domain with each source domain individually [17, 18, 22] or by means of a hard [23] or soft [16] domain selector. Again, Fig. 1(a) suggests that aligning the target domain to each individual source domain is not only difficult but could also be counterproductive due to drastic variations among source domains.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose a novel unified framework for both multi-source DG and UDA based on the idea of collaborative ensemble learning. Our framework, termed domain adaptive ensemble learning (DAEL), takes a very different approach from previous work. Specifically, each domain is used to learn a model that is specialized in that domain (see Fig. 1(a)). We call it a domain expert—a relative term as an expert to a specific source domain would be a non-expert to all other source domains as well as the target domain. The key idea of DAEL is to learn these experts collaboratively so that when forming an ensemble, they can leverage complementary information to better tackle the target domain.",
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+        "type": "text",
+        "text": "To realize the DAEL framework for a UDA or DG model, a number of issues need to be addressed. (1) Scalability: Training an ensemble of models instead of a single model means higher computational cost. To solve this problem, we design a DAEL model as a deep multi-expert network consisting of a shared convolutional neural network (CNN) feature extractor and multiple classifier heads. Each head is trained to classify images from a particular source domain. Therefore, different heads learn different patterns from the shared features for classification. (2) Training: Since the target domain data is either non-existent (for DG) or has no label (for UDA), there is no target domain expert to provide supervisory",
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+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
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+    {
+        "type": "page_footnote",
+        "text": "K. Zhou is with Nanyang Technological University, Singapore.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "Y. Yang and T. Xiang are with the University of Surrey, UK.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "Y. Qiao is with the Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China.",
+        "bbox": [
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+    },
+    {
+        "type": "aside_text",
+        "text": "arXiv:2003.07325v3 [cs.CV] 8 Sep 2021",
+        "bbox": [
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+            272,
+            60,
+            700
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/9b927fbb2faa846ad4a795b968fd567693edefa270da9e89ff3bae6cd6e1cee0.jpg",
+        "image_caption": [
+            "Fig. 1: Overview of domain adaptive ensemble learning (DAEL)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "signal for the source domain expert ensemble. To overcome this, each source domain is used in turn as a pseudo-target-domain with its own expert providing supervisory signal to the ensemble of non-experts learned from the other sources (see Fig. 1(b)). For unlabeled target data under the UDA setting where real expert does not exist, DAEL uses as pseudo-label the most confident estimation among all experts and train the ensemble to fit the pseudo-label (see Fig. 1(c)). (3) How to measure the effectiveness of a non-expert ensemble w.r.t. an expert: Inspired by consistency regularization (CR) [24, 25] used in semi-supervised learning, the ensemble's effectiveness is measured by how close its prediction is to that of an expert when both are fed with a data point from the expert's domain. To amplify the regularization effect brought by CR, we use weak and strong augmentation for input to an expert and a non-expert ensemble respectively. Such a strategy has been shown useful in recent semi-supervised learning methods [26, 27, 28]. Once these three issues are addressed, we have a simple but effective solution to both UDA and DG. By sending supervisory signal to an ensemble rather than each individual, different domain-specific experts are allowed to exploit complementary domain-specific information from each other, resulting in a more domain-generalizable ensemble.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We summarize our contributions as follows. (1) We present a novel framework called domain adaptive ensemble learning (DAEL), which improves the generalization of a multi-expert network by explicitly training the ensemble to solve the target task. (2) A realization of DAEL is formulated which provides a simple yet effective solution for both multi-source UDA and DG, unlike previous methods that only tackle one of them. (3) We define miniDomainNet, a reduced version of DomainNet [18] to allow fast prototyping and experimentation. For benchmarking, a unified implementation and evaluation platform of all compared methods is created, called Dassl.pytorch, which has been made publicly available.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "(4) We demonstrate the effectiveness of DAEL on three multisource UDA datasets and two DG datasets where DAEL outperforms the current state of the art by a large margin (see Table 1 & 2).",
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+    {
+        "type": "text",
+        "text": "II. RELATED WORK",
+        "text_level": 1,
+        "bbox": [
+            638,
+            470,
+            785,
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+    },
+    {
+        "type": "text",
+        "text": "Unsupervised domain adaptation. Motivated by the seminal theory work by Ben-David et al. [29], numerous UDA methods seek to reduce distribution discrepancy between source and target features using some distance metrics, such as maximum mean discrepancy [3, 30, 31], optimal transport [32, 33], and graph matching [34, 35, 36]. Inspired by generative adversarial network (GAN) [37], several methods [2, 38, 39, 40, 41] additionally train a domain discriminator for feature alignment. GAN has also been exploited for pixel-level domain adaptation where target images are synthesized via image translation/generation [42, 43]. Instead of aligning the coarse marginal distribution, recent alignment methods have shown that fine-grained alignment such as aligning class centroids [44, 45, 46, 47] or using task-specific classifiers [6, 48, 49] can give a better adaptation performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The multi-source UDA methods are more related to our work because of the same problem setting. Several works [17, 18, 22] extend the domain alignment idea to multi-source UDA by considering all possible source-target pairs. Kang et al. [47] propose contrastive adaptation network where a contrastive domain discrepancy loss is minimized for samples from the same class but of different domains while maximized for samples from different classes. Relationships between each source and the target are learned by Li et al. [23] and only the target-related sources are kept for model learning. Hoffman et al. [16] compute distribution-based weights for combining source classifiers. Our model architecture—a shared feature extractor and multiple domain-specific classifiers—is similar to  $\\mathbf{M}^3\\mathbf{SDA}$  [18]. However, DAEL is very different in that different domain-specific classifiers are learned collaboratively",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            416,
+            41
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "footer",
+        "text": "$^{1}$ https://github.com/KaiyangZhou/Dassl.pytorch.",
+        "bbox": [
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+            930,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "where each source domain is used in turn as a pseudo-target-domain to train the ensemble.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Domain generalization. Many DG methods follow the idea of distribution alignment originated from the UDA community to learn domain-invariant features through minimizing in-between-source distances [19, 20, 21]. Data augmentation is another popular research direction where the motivation is to avoid overfitting to source data. This can be achieved by, for example, adding adversarial gradients to the input [13, 50], learning data generation networks [10, 14], or mixing instance-level feature statistics [15]. Meta-learning has also been investigated for learning domain-generalizable neural networks [51, 52, 53, 54]. Different from existing DG methods that mostly train a single classifier, our work for the first time introduces collaborative ensemble learning to mine domain-specific information using domain-specific classifiers. Although our pseudo-target-domain idea is related in spirit to meta-learning, no episodic training is required in DAEL, which makes the training procedure much simpler. We refer readers to Zhou et al. [1] for a comprehensive survey in DG.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Ensemble methods have been extensively researched in the machine learning community [55]. The principle is to train multiple learners for the same problem and combine them for inference. Such technique has also been widely used in competitions like ILSVRC [56] where multiple CNNs are trained and combined to improve the test performance [57, 58]. In this work, to prompt the emergence of generalizable features, we learn an ensemble of classifiers (experts) in a collaborative way—using each individual expert to supervise the learning of the non-expert ensemble.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "III. METHODOLOGY",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Problem definition. Given a labeled training dataset collected from  $K$  source domains,  $\\mathcal{D}_S = \\{\\mathcal{D}_1,\\dots ,\\mathcal{D}_K\\}$ , we aim to learn a model that can generalize well to a target domain  $\\mathcal{D}_T$ . If the unlabeled target data is available during training, it is a multi-source unsupervised domain adaptation (UDA) problem [18], otherwise a domain generalization (DG) problem [11]. Our method addresses these two problems in a unified framework.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Model. We aim to learn a multi-expert model, denoted by  $\\{E_i\\}_{i=1}^K$ , with each expert  $E_i$  specializing in a particular source domain  $\\mathcal{D}_i$ . For clarity,  $E_i$  is called an expert to  $\\mathcal{D}_i$  but a non-expert to  $\\{\\mathcal{D}_j\\}_{j \\neq i}$ . The ensemble prediction for an image  $x$  is used at test time, i.e.  $p(y|x) = \\frac{1}{K} \\sum_{i=1}^{K} E_i(x)$ . In implementation, the multi-expert model shares a CNN backbone for feature extraction, followed by domain-specific classification heads. To allow the ensemble to better exploit complementary information between experts, we propose domain adaptive ensemble learning (DAEL). The main idea of DAEL is to strengthen the ensemble's generalizability by simulating how it is tested—using an expert's output to supervise the learning of ensemble of non-experts. This is realized by consistency regularization (CR) training, as shown in Fig. 2. To amplify the regularization effect, we follow Sohn et al. [28] to use weak and strong augmentations, denoted by  $a(\\cdot)$  and  $A(\\cdot)$  respectively. Specifically, weak augmentation,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "which corresponds to simple flip-and-shift transformations, is used for pseudo-label generation; strong augmentation, which induces stronger noises like rotation and shearing, is used for ensemble prediction.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Domain-specific expert learning. Next, we detail the DAEL training procedure, starting with how each expert is trained to be domain-specific. Let  $H(\\cdot, \\cdot)$  denote cross-entropy between two probability distributions, the loss function for domain-specific expert learning is",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {c e} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\mathbb {E} _ {x ^ {i}, y \\left(x ^ {i}\\right) \\sim \\mathcal {D} _ {i}} [ H (y \\left(x ^ {i}\\right), E _ {i} (a \\left(x ^ {i}\\right))) ], \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $y(x^{i})$  is the one-hot label of  $x^{i}$ ; the expectation is implemented by mini-batch sampling (same for the following equations).",
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+    },
+    {
+        "type": "text",
+        "text": "Collaborative ensemble learning using source domain data. Given an image  $x^{i}$  from the  $i$ -th source domain (treated as a pseudo-target-domain), the idea is to use as target the corresponding expert's prediction for the weakly augmented image,  $E_{i}(a(x^{i}))$ , and encourage the ensemble prediction of non-experts from other source domains for the strongly augmented image,  $\\frac{1}{K - 1}\\sum_{j\\neq i}E_{j}(A(x^{i}))$ , to be close to the target. Such a design explicitly teaches the ensemble how to handle data from unseen domains (mimicked by strong augmentation and guided by a pseudo-target-domain expert), thus improving the robustness to domain shift. Formally, the loss is defined as the mean-squared error (MSE) between the two outputs:2",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {c r} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\mathbb {E} _ {x ^ {i} \\sim \\mathcal {D} _ {i}} \\left[ \\| E _ {i} \\left(a \\left(x ^ {i}\\right)\\right) - \\frac {1}{K - 1} \\sum_ {j \\neq i} E _ {j} \\left(A \\left(x ^ {i}\\right)\\right) \\| ^ {2} \\right]. \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Collaborative ensemble learning using unlabeled target data. Given a weakly augmented target domain image  $a(x^t)$ , we first ask each source-expert to produce a class probability distribution,  $p_i(y|a(x^t)) = E_i(a(x^t))$ , and select as pseudolabel the most confident expert's prediction based on their maximum probability,  $\\arg \\max(p_{i*})$ , where  $i^*$  is the index of the most confident expert. This is inspired by the observation that correct predictions are usually confident with peaked value on the predicted class [28]. Then, we force the ensemble prediction of all source-experts for the strongly augmented image,  $\\bar{E}(A(x^t)) = \\frac{1}{K}\\sum_{i=1}^{K}E_i(A(x^t))$ , to fit the one-hot pseudo-label  $\\hat{y}(x^t) = \\arg \\max(p_{i*})$ . The loss is defined as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {u} = \\mathbb {E} _ {x ^ {t} \\sim \\mathcal {D} _ {T}} [ \\mathbb {1} (\\max  (p _ {i ^ {*}}) \\geq \\epsilon) H (\\hat {y} (x ^ {t}), \\bar {E} (A (x ^ {t}))) ], \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "where  $\\epsilon$  is a confidence threshold (fixed to 0.95 in this paper).",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Eq. (3) can be viewed as a combination of CR and entropy minimization [59] because the conversion from soft probability to one-hot encoding essentially reduces the entropy of the class distribution. The confidence threshold provides a curriculum for filtering out less confident (unreliable) pseudo labels in the early training stages [28, 60].",
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+        "list_items": [
+            "2We chose MSE over KL divergence because the former led to a slightly higher performance.",
+            "3For simplicity we assume arg max converts soft probability to one-hot encoding."
+        ],
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+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            75,
+            29,
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
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+        "page_idx": 2
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "$x^{i}$  : data from  $i$  -th source domain",
+            "$x^t$ : data from target domain",
+            "$a(\\cdot)$  : weak augmentation",
+            "$A(\\cdot)$  : strong augmentation"
+        ],
+        "bbox": [
+            158,
+            68,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/8d7573b2902ea306974e35afe91cd5422fd7b4b7b19a06ad713a7af504af7f2d.jpg",
+        "image_caption": [
+            "Fig. 2: Illustration of domain adaptive ensemble learning. Left: collaborative learning using source domains. Right: collaborative learning using unlabeled target domain via pseudo-labeling. The ensemble of all experts is used for testing. Gradients are only back-propagated through the ensemble prediction path."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/d41be18c7c1b4a3f934d284cf58a51593b2a3834a6f135f4342b6a7e3b2f3b31.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The full learning objective is a weighted sum of Eq. (1), (2) and (3),",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {c e} + \\mathcal {L} _ {c r} + \\lambda_ {u} \\mathcal {L} _ {u}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda_{u}$  is a hyper-parameter for balancing the weighting between  $\\mathcal{L}_u$  and the losses for the labeled source domains. For multi-source UDA, DAEL uses Eq. (4). For DG,  $\\mathcal{L}_u$  is removed due to the absence of target domain data. DAEL not only provides a unified solution to the two problems, but is also very easy to implement (see Appendix B for pseudo-code).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Gradient analysis. To understand the benefit of collaborative learning (i.e.,  $\\| \\frac{1}{K}\\sum_{i}p_{i} - p^{*}\\|^{2}$ ) against individual learning (i.e.,  $\\frac{1}{K}\\sum_{i}\\| p_i - p^*\\|^2$ ) where  $p^*$  denotes the target, we analyze their gradients with respect to a single expert's output  $p_i$ . For collaborative learning, we have  $\\Delta p_i = \\frac{2}{K} (\\frac{1}{K} (p_i + \\sum_{j\\neq i}p_j) - p^*)$ . For individual learning, we have  $\\Delta p_i = \\frac{2}{K} (p_i - p^*)$ . It is clear that collaborative learning updates an expert by combining information from other experts, which facilitates the exploitation of complementary information. Table 3a further confirms the advantage of collaborative learning.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Relation to knowledge distillation. DAEL is similar to knowledge distillation (KD) [61] in the sense that the teacher-student training is used. However, in DAEL the boundary between teacher and student is blurred because each student can become a teacher when the input data come from its domain of expertise. Moreover, the collaborative ensemble learning strategy is specifically designed for dealing with multi-domain data—it encourages different experts to learn complementary information such that the ensemble is more generalizable to unseen domains.",
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+    {
+        "type": "text",
+        "text": "IV. EXPERIMENTS",
+        "text_level": 1,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A. Experiments on Domain Adaptation",
+        "text_level": 1,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Datasets. (1) Digit-5 consists of five different digit recognition datasets, which are MNIST [62], MNIST-M [2], USPS, SVHN [63] and SYN [2]. We follow the same setting as",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4The same conclusion can be drawn when using KL divergence as the objective.",
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+    {
+        "type": "text",
+        "text": "in  $\\mathbf{M}^3\\mathbf{SDA}$  [18] for experimentation. See Fig. 3 left for example images. (2) DomainNet [18] is a recently introduced benchmark for large-scale multi-source domain adaptation. It has six domains (Clipart, Infograph, Painting, Quickdraw, Real and Sketch) and 0.6M images of 345 classes. See Fig. 3 right for example images. (3) The full DomainNet requires considerable computing resources for training, preventing wide deployment and extensive ablative studies. Inspired by the miniImageNet dataset [64] that has been widely used in the few-shot learning community, we propose miniDomainNet, which takes a subset of DomainNet and uses a smaller image size ( $96 \\times 96$ ). As noted by Saito et al. [49] that the labels of some domains and classes are very noisy in the original DomainNet, we follow them to select four domains and 126 classes. As a result, miniDomainNet contains 18,703 images of Clipart, 31,202 images of Painting, 65,609 images of Real and 24,492 images of Sketch. In general, miniDomainNet maintains the complexity of the original DomainNet, reduces the requirements for computing resources and allows fast prototyping and experimentation.",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "The implementation details (of all experiments in this paper) are provided in Appendix A. To ensure the results are convincing, we run each experiment three times and report the mean accuracy and standard deviation. The results of baseline models are from either their papers (if reported) or our reimplementation (only when their source code is available).",
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+        "type": "text",
+        "text": "Results. Following the standard test protocol [18], one domain is used as target and the rest as sources, and classification accuracy on the target domain test set is reported. Table 1 shows the results on the multi-source UDA datasets. We summarize our findings as follows. (1) In terms of the overall performance (the rightmost Avg column), DAEL achieves the best results on all three datasets, outperforming the second-best methods by large margins:  $3.51\\%$  on Digit-5,  $2.2\\%$  on",
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+        "list_items": [
+            "<sup>5</sup>We have noticed that the 't-shirt' class (index 327) is excluded from Painting's training set (see the official painting_train.txt file), but is included in the test set, which could affect the performance.",
+            "It usually takes several GPU days for training a deep model on the full DomainNet."
+        ],
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+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            418,
+            41
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/b19fe76cfc2e7b7622b1381c204f98c287c9d5a27bbefb0ff363288aada4f117.jpg",
+        "image_caption": [
+            "Fig. 3: Example images from Digit-5 and DomainNet."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            183,
+            68,
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+            229
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/31aa26f65a43a6baceac5cfefc311890a53861a2afbd44d1af207a2ebe9e9829.jpg",
+        "image_caption": [
+            "Fig. 4: Ablation study for evaluating each component in Eq. (4)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            202,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "DomainNet and  $6.21\\%$  on miniDomainNet.",
+        "bbox": [
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+        "list_items": [
+            "(2) On the small Digit-5 dataset, DAEL achieves near-oracle performance (our  $96.47\\%$  vs. oracle's  $97.00\\%$ ). In particular, MNIST-M and SVHN are the two most difficult domains as can be seen in Fig. 3—MNIST-M has complex backgrounds while SVHN contains blurred and cluttered digits. Those distinctive features make MNIST-M and SVHN drastically different from other domains and thus make the adaptation task harder. Nonetheless, DAEL obtains the highest accuracy which beats  $\\mathrm{M}^3\\mathrm{SDA}$ —the 2nd best method—by  $11.62\\%$  on MNIST-M and  $4.06\\%$  on SVHN.",
+            "(3) On the large-scale DomainNet/miniDomainNet, DAEL achieves the best performance among all methods. Notably, compared with the latest state of the art on DomainNet, i.e. CMSS, DAEL obtains a clear margin of  $2.2\\%$  on average, which demonstrates the advantage of exploiting complementarity between source domains for ensemble prediction.",
+            "(4) Compared with  $\\mathbf{M}^3\\mathbf{SDA}$ , the most related method to ours that also has domain-specific classifiers, DAEL is superior on all three datasets. This is because aligning distributions between the target and each individual source, as in  $\\mathbf{M}^3\\mathbf{SDA}$ , is difficult due to large domain variations between sources."
+        ],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "B. Experiments on Domain Generalization",
+        "text_level": 1,
+        "bbox": [
+            75,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Datasets. (1) PACS [12] is a commonly used DG dataset with four domains: Photo (1,670 images), Art Painting (2,048 images), Cartoon (2,344 images) and Sketch (3,929 images). There are seven object categories: dog, elephant, giraffe, guitar, horse, house and person. (2) Office-Home [69] contains around 15,500 images of 65 categories, which are related to office and home objects. Similar to PACS, there are four",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "domains: Artistic, Clipart, Product and Real World. For evaluation, we follow the prior works [12, 54, 67] to use the leave-one-domain-out protocol, i.e. choosing one domain as the (unseen) test domain and using the remaining three as source domains for model training.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Results. The comparison with the state-of-the-art DG methods is shown in Table 2. Overall, DAEL achieves the best results on both datasets with clear margins against all competitors. We provide a more detailed discussion as follows. (1) DAEL is clearly better than the distribution alignment methods, i.e. CCSA and MMD-AAE, with  $\\geq 4\\%$  improvement on PACS and  $\\geq 1.2\\%$  improvement on Office-Home. This is not surprising because the distribution alignment theory [29] developed for DA does not necessarily work for DG (which does not have access to target data). (2) Compared with the recent self-supervised method JiGen, DAEL obtains a clear improvement of  $2.9\\%$  on PACS. The gap is further increased to  $4.9\\%$  on Office-Home. When it comes to CrossGrad, a state-of-the-art data augmentation method, DAEL achieves clear improvements as well. (3) The recently proposed Epi-FCR shares a similar design choice with DAEL—to simulate domain shift during training. Again, DAEL is clearly superior thanks to the design of collaborative ensemble learning. Further, Epi-FCR requires domain-specific feature extractors, as well as additional domain-agnostic feature extractors and classifiers, incurring much higher computational cost.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "C. Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Ablation study. We start from the baseline ensemble model trained by  $\\mathcal{L}_{ce}$  only and progressively add  $\\mathcal{L}_{cr}$  and  $\\mathcal{L}_u$  (see Eq. (4)). The results are shown in Fig. 4. Each of  $\\mathcal{L}_{cr}$  and  $\\mathcal{L}_u$  contributes positively to the performance. Combining  $\\mathcal{L}_{cr}$",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            416,
+            41
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
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+            30,
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+            40
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/eed9da8d845c28406d483242262c22f6211314a57a73795ffab52f1690324de4.jpg",
+        "table_caption": [
+            "TABLE 1: Comparing DAEL with state of the art on multi-source UDA datasets.",
+            "(a) Digit-5."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>MNIST-M</td><td>MNIST</td><td>USPS</td><td>SVHN</td><td>SYN</td><td>Avg</td></tr><tr><td>Oracle</td><td>95.36±0.15</td><td>99.50±0.08</td><td>99.18±0.09</td><td>92.28±0.14</td><td>98.69±0.04</td><td>97.00</td></tr><tr><td>Source-only</td><td>68.08±0.39</td><td>99.06±0.05</td><td>97.20±0.48</td><td>84.56±0.36</td><td>89.87±0.32</td><td>87.75</td></tr><tr><td>DCTN [17]</td><td>76.20±0.51</td><td>99.38±0.06</td><td>94.39±0.58</td><td>86.37±0.54</td><td>86.78±0.31</td><td>88.63</td></tr><tr><td>DANN [65]</td><td>83.44±0.12</td><td>98.46±0.07</td><td>94.19±0.31</td><td>84.08±0.60</td><td>92.91±0.23</td><td>90.61</td></tr><tr><td>CMSS [66]</td><td>75.30±0.57</td><td>99.00±0.08</td><td>97.70±0.13</td><td>88.40±0.54</td><td>93.70±0.21</td><td>90.80</td></tr><tr><td>MCD [6]</td><td>80.65±0.51</td><td>99.22±0.08</td><td>98.32±0.07</td><td>81.87±0.72</td><td>95.42±0.04</td><td>91.09</td></tr><tr><td>SE [60]</td><td>80.16±0.48</td><td>99.41±0.06</td><td>98.87±0.08</td><td>86.15±0.76</td><td>96.44±0.34</td><td>92.20</td></tr><tr><td>MME [49]</td><td>83.07±0.57</td><td>99.35±0.03</td><td>98.64±0.17</td><td>86.40±0.41</td><td>95.78±0.15</td><td>92.65</td></tr><tr><td>M3SDA [18]</td><td>82.15±0.49</td><td>99.38±0.07</td><td>98.71±0.12</td><td>88.44±0.72</td><td>96.10±0.10</td><td>92.96</td></tr><tr><td>DAEL (ours)</td><td>93.77±0.12</td><td>99.45±0.02</td><td>98.69±0.79</td><td>92.50±0.15</td><td>97.91±0.03</td><td>96.47</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/9a84e4e6f0b7fb51781575d27f29e309ac6de61fa7b831a6e7b0abd639f49a32.jpg",
+        "table_caption": [
+            "(b) DomainNet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Clp</td><td>Inf</td><td>Pnt</td><td>Qdr</td><td>Rel</td><td>Skt</td><td>Avg</td></tr><tr><td>Oracle [18]</td><td>69.3±0.37</td><td>34.5±0.42</td><td>66.3±0.67</td><td>66.8±0.51</td><td>80.1±0.59</td><td>60.7±0.48</td><td>63.0</td></tr><tr><td>Source-only [18]</td><td>47.6±0.52</td><td>13.0±0.41</td><td>38.1±0.45</td><td>13.3±0.39</td><td>51.9±0.85</td><td>33.7±0.54</td><td>32.9</td></tr><tr><td>DANN [65]</td><td>45.5±0.59</td><td>13.1±0.72</td><td>37.0±0.69</td><td>13.2±0.77</td><td>48.9±0.65</td><td>31.8±0.62</td><td>32.6</td></tr><tr><td>DCTN [17]</td><td>48.6±0.73</td><td>23.5±0.59</td><td>48.8±0.63</td><td>7.2±0.46</td><td>53.5±0.56</td><td>47.3±0.47</td><td>38.2</td></tr><tr><td>MCD [6]</td><td>54.3±0.64</td><td>22.1±0.70</td><td>45.7±0.63</td><td>7.6±0.49</td><td>58.4±0.65</td><td>43.5±0.57</td><td>38.5</td></tr><tr><td>\\( M^3 \\)SDA [18]</td><td>58.6±0.53</td><td>26.0±0.89</td><td>52.3±0.55</td><td>6.3±0.58</td><td>62.7±0.51</td><td>49.5±0.76</td><td>42.6</td></tr><tr><td>CMSS [66]</td><td>64.2±0.18</td><td>28.0±0.20</td><td>53.6±0.39</td><td>16.0±0.12</td><td>63.4±0.21</td><td>53.8±0.35</td><td>46.5</td></tr><tr><td>DAEL (ours)</td><td>70.8±0.14</td><td>26.5±0.13</td><td>57.4±0.28</td><td>12.2±0.70</td><td>65.0±0.23</td><td>60.6±0.25</td><td>48.7</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/4ac634ce50be752d0c8d51424ad9aa79bd2a7e4ee2af23e9adc0134b79ff01fc.jpg",
+        "table_caption": [
+            "(c) miniDomainNet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Clipart</td><td>Painting</td><td>Real</td><td>Sketch</td><td>Avg</td></tr><tr><td>Oracle</td><td>72.59±0.30</td><td>60.53±0.74</td><td>80.47±0.34</td><td>63.44±0.15</td><td>69.26</td></tr><tr><td>Source-only</td><td>63.44±0.76</td><td>49.92±0.71</td><td>61.54±0.08</td><td>44.12±0.31</td><td>54.76</td></tr><tr><td>MCD [6]</td><td>62.91±0.67</td><td>45.77±0.45</td><td>57.57±0.33</td><td>45.88±0.67</td><td>53.03</td></tr><tr><td>DCTN [17]</td><td>62.06±0.60</td><td>48.79±0.52</td><td>58.85±0.55</td><td>48.25±0.32</td><td>54.49</td></tr><tr><td>DANN [65]</td><td>65.55±0.34</td><td>46.27±0.71</td><td>58.68±0.64</td><td>47.88±0.54</td><td>54.60</td></tr><tr><td>\\( M^3SDA \\) [18]</td><td>64.18±0.27</td><td>49.05±0.16</td><td>57.70±0.24</td><td>49.21±0.34</td><td>55.03</td></tr><tr><td>MME [49]</td><td>68.09±0.16</td><td>47.14±0.32</td><td>63.33±0.16</td><td>43.50±0.47</td><td>55.52</td></tr><tr><td>DAEL (ours)</td><td>69.95±0.52</td><td>55.13±0.78</td><td>66.11±0.14</td><td>55.72±0.79</td><td>61.73</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/200d2747e53f025f265c760f39cf8058eead6c75f86a90d826d881c8fa1d61f0.jpg",
+        "image_caption": [
+            "Fig. 5: Sensitivity of  $\\lambda_{u}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    {
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+        "img_path": "images/93840d511adba32c453dd56f06f06b3ae1cfe5ce15cf6dec8d65a0bb5f8a59f9.jpg",
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+    {
+        "type": "text",
+        "text": "and  $\\mathcal{L}_u$  gives the best performance, which confirms their complementarity.",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "Sensitivity of  $\\lambda_{u}$ . Fig. 5 shows that the performance soars from  $\\lambda_{u} = 0$  to  $\\lambda_{u} = 0.5$  and remains relatively stable between  $\\lambda_{u} = 0.5$  and  $\\lambda_{u} = 1.0$ . The overall results suggest that the model's performance is in general insensitive to  $\\lambda_{u}$  around 0.5.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Collaborative ensemble or individual expert training? As discussed in the gradient analysis part in Methodology, collaborative learning aggregates gradients from different ex",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "perts, which can better exploit the complementarity between different sources. We justify this design in Table 3a where collaborative learning shows clear improvements over individual learning.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Learning an ensemble of classifiers or a single classifier? The motivation for the former is to enable the model to better handle complicated source data distributions—as discussed before, learning a single classifier forces the model to erase domain-specific knowledge that could otherwise be useful for recognition in the target domain. To justify this design, we switch from the ensemble classifiers to a single classifier while keeping other designs unchanged. Table 3b confirms that learning an ensemble of classifiers is essential.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Using expert's prediction or real label in  $\\mathcal{L}_{cr}$ ? Table 3c shows that using real label  $(Y)$  is slightly worse than using expert's prediction  $(E_i)$ . This is because expert's prediction automatically encodes the relations between classes (reflected in the soft probability distribution [70]), thus providing better supervisory signal.",
+        "bbox": [
+            501,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Most confident expert's prediction vs. ensemble predic",
+        "bbox": [
+            519,
+            929,
+            921,
+            945
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            416,
+            41
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
+        "bbox": [
+            911,
+            31,
+            919,
+            40
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/2c2fbe1761106dfac9530ff8ac9982ac179d42b3d90aef3aa236249c08ba48d2.jpg",
+        "table_caption": [
+            "TABLE 2: Comparing DAEL with state of the art on DG datasets PACS (left) and Office-Home (right)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">PACS</td><td colspan=\"5\">Office-Home</td></tr><tr><td>Art</td><td>Cat</td><td>Pho</td><td>Skt</td><td>Avg</td><td>Art</td><td>Clp</td><td>Prd</td><td>Rel</td><td>Avg</td></tr><tr><td>Vanilla</td><td>77.0</td><td>75.9</td><td>96.0</td><td>69.2</td><td>79.5</td><td>58.9</td><td>49.4</td><td>74.3</td><td>76.2</td><td>64.7</td></tr><tr><td>MMD-AAE [21]</td><td>75.2</td><td>72.7</td><td>96.0</td><td>64.2</td><td>77.0</td><td>56.5</td><td>47.3</td><td>72.1</td><td>74.8</td><td>62.7</td></tr><tr><td>CCSA [19]</td><td>80.5</td><td>76.9</td><td>93.6</td><td>66.8</td><td>79.4</td><td>59.9</td><td>49.9</td><td>74.1</td><td>75.7</td><td>64.9</td></tr><tr><td>JiGen [67]</td><td>79.4</td><td>75.3</td><td>96.0</td><td>71.6</td><td>80.5</td><td>53.0</td><td>47.5</td><td>71.5</td><td>72.8</td><td>61.2</td></tr><tr><td>CrossGrad [13]</td><td>79.8</td><td>76.8</td><td>96.0</td><td>70.2</td><td>80.7</td><td>58.4</td><td>49.4</td><td>73.9</td><td>75.8</td><td>64.4</td></tr><tr><td>Epi-FCR [54]</td><td>82.1</td><td>77.0</td><td>93.9</td><td>73.0</td><td>81.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMG [68]</td><td>76.9</td><td>80.4</td><td>93.4</td><td>75.2</td><td>81.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DAEL (ours)</td><td>84.6</td><td>74.4</td><td>95.6</td><td>78.9</td><td>83.4</td><td>59.4</td><td>55.1</td><td>74.0</td><td>75.7</td><td>66.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/39fc0c72f15b25fbd8beb4136ac7453df29dec2784503a0640d17c1ff2c01013.jpg",
+        "table_caption": [
+            "TABLE 3: Evaluation of design choices in DAEL. D-5: Digit-5. miniDN: miniDomainNet.",
+            "(a) Collaborative ensemble vs. individual expert learning."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Col.</td><td>96.47</td><td>61.73</td></tr><tr><td>Ind.</td><td>93.07</td><td>60.20</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/d0e20408e6162da000ecffb5d93a60313513ce55662e5eb9332b44ac2853091b.jpg",
+        "table_caption": [
+            "(b) Learning an ensemble of classifiers vs. a single classifier."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ensemble</td><td>96.47</td><td>61.73</td></tr><tr><td>Single</td><td>95.02</td><td>60.09</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/6d2c2afec4d2b6d09f8158184adfb02439b42fd59efb234e527a0c0e2ff7f3a5.jpg",
+        "table_caption": [
+            "(c) Expert's prediction vs. real label (see  $\\mathcal{L}_{cr}$ )."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ei</td><td>91.04</td><td>56.35</td></tr><tr><td>Y</td><td>90.84</td><td>56.11</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/726b370f74f6663fe7a81e02250f2c956bed9ae35a5e9ca1ebdbfec735993d25.jpg",
+        "table_caption": [
+            "(d) Expert's prediction vs. ensemble prediction (see  $\\mathcal{L}_u$ )."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ei</td><td>96.47</td><td>61.73</td></tr><tr><td>E</td><td>95.86</td><td>60.16</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "tion for  $\\mathcal{L}_u$ ? Table 3d suggests that using the most confident expert's output  $(E_{i^*})$  is better. A plausible explanation is that assembling smooths out the overall probability distribution when experts have disagreements, which may lead to potentially correct instances discarded due to weak confidence (i.e. probability less than the confidence threshold  $\\epsilon$ ).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Diagnosis into individual experts. Fig. 6 shows the performance of each individual source expert versus the ensemble on miniDomainNet trained with different losses. For  $\\mathcal{L}_{ce}$  (blue bars), the variance between  $E_{1-3}$  is large and each individual's performance is low, indicating that the experts are themselves biased (overfitting). Comparing  $\\mathcal{L}_{ce} + \\mathcal{L}_{cr}$  (orange bars) with  $\\mathcal{L}_{ce}$ , we observe that the variance between  $E_{1-3}$  is reduced and each individual's performance is significantly improved, leading to a much stronger ensemble. By adding  $\\mathcal{L}_u$  (green bars), each individual's performance is further boosted, and hence the ensemble. To better understand how the ensemble helps prediction, we visualize the top-3 classes predicted by each expert and the ensemble in Fig. 7. In Fig. 7(a) top, expert-3 mis-recognizes the bear as dog but the ensemble prediction is dominated by the correct predictions made by expert-1 and -2. A similar pattern can be observed in Fig. 7(a) bottom. Fig. 7(b) provides examples of incorrect predictions where we observe that the model struggles to differentiate between classes of similar features. For example, the kangaroo in Fig. 7(b) top looks indeed similar to a dog due to the similarity in the face and skin texture—without looking at the body structure and the pouch. Such mistakes might be avoided by using neural networks that can extract features at multiple scales [71].",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Augmentation strategy. Recall that we use weak and strong augmentations for pseudo-label generation and prediction respectively. The rationales behind this design are: 1) We need the expert to provide accurate supervision (pseudo labels) to the non-expert ensemble so we feed the expert with weakly augmented data; 2) We apply strong augmentation to the non-expert ensemble in order to reduce overfitting to noisy pseudo",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/18725661c230a9022d8488e7f293a16c97f40e5dfde2f6646b005b7d291e3aa0.jpg",
+        "table_caption": [
+            "TABLE 4: Comparison with baseline models trained using strong augmentation on miniDomainNet."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Clipart</td><td>Painting</td><td>Real</td><td>Sketch</td><td>Avg</td></tr><tr><td>Source-only</td><td>63.44</td><td>49.92</td><td>61.54</td><td>44.12</td><td>54.76</td></tr><tr><td>Source-only+A(·)</td><td>64.34</td><td>49.31</td><td>58.81</td><td>48.02</td><td>55.12</td></tr><tr><td>MSDA</td><td>64.18</td><td>49.05</td><td>57.70</td><td>49.21</td><td>55.03</td></tr><tr><td>MSDA+A(·)</td><td>65.08</td><td>49.68</td><td>57.04</td><td>54.29</td><td>56.52</td></tr><tr><td>MME</td><td>68.09</td><td>47.14</td><td>63.33</td><td>43.50</td><td>55.52</td></tr><tr><td>MME+A(·)</td><td>68.25</td><td>49.21</td><td>60.26</td><td>44.23</td><td>55.49</td></tr><tr><td>DAEL</td><td>69.95</td><td>55.13</td><td>66.11</td><td>55.72</td><td>61.73</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "labels. If we swap these two augmentations, i.e. using weak augmentation for prediction while strong augmentation for pseudo-label generation, the accuracy decreases from  $61.73\\%$  to  $54.32\\%$  on miniDomainNet. In addition, if strong augmentation is applied to both branches, the accuracy declines to  $58.05\\%$ , which suggests the weak-strong augmentation strategy is essential. These observations have also been reported by Sohn et al. [28].",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To justify that using strong augmentation is not the sole contributor to our approach, we compare with top-performing baselines that also use strong augmentation in Table 4. We can see that the improvements brought by strong augmentation for the baselines are rather limited, and the gap with our method remains large. This result confirms that collaborative ensemble learning is the key to our superior performance.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Visualization of features. We use t-SNE [72] to visualize the features learned by Source-only and our DAEL. Figure 8 shows that the target features learned by Source-only are poorly aligned—the model cannot clearly differentiate between “1”, “0”, “5”, “3”, and “8” (zoom-in to see the class labels). In contrast, the target features learned by DAEL have a much smaller domain discrepancy with the source features and exhibit clearer class-based clustering patterns.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            416,
+            41
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/38063cb19f86bd478ac3c877f8a647c9c8bb0765ed3e543e5528abea29bba10a.jpg",
+        "image_caption": [
+            "Fig. 6: Individual experts  $(E_{1-3})$  vs. ensemble  $(\\bar{E})$  on miniDomainNet."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/05243daabaa0a56ecd59e96ccbfc597629f3d6e7f5a7c8df91d560431272dbff.jpg",
+        "image_caption": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/41f8575dde3b48180cfc432fb3d3362e3dad8ed2b03fe6047df0575b6d42df26.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/5eb72f5fc937f5cb40df2da570c25f381420213c60ed7205b04bc7e716ee677d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/a5bc9357ccda348daa5eea6002b991b64190fe9a3b21463a17f883e46a789970.jpg",
+        "image_caption": [
+            "(a) Correct predictions"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
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+            460
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/bb925c10c758620fd020fea53628f0e01f9138a8fa323f49e363feb56f56b4bc.jpg",
+        "image_caption": [
+            "(b) Incorrect predictions"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/b7633cb56449e5192588742fb66716bb9d9f60b9cdbd4c25cfdbf0adb8af81de.jpg",
+        "image_caption": [
+            "Fig. 7: Visualization of predicted classes (top-3) and the corresponding confidence by each expert and the ensemble.",
+            "(a) Source-only",
+            "Fig. 8: Visualization of features from Digit-5 using t-SNE [72]."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/96ac3a79757f41cfdd0ac9a6951ca04b753facd6340a93e34289c57434efee10.jpg",
+        "image_caption": [
+            "(b) DAEL"
+        ],
+        "image_footnote": [],
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "V. CONCLUSION",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our approach, domain adaptive ensemble learning (DAEL), takes the first step toward a general framework for generalizing neural networks from multiple source domains to a target domain. When target data are not provided (the DG problem), DAEL shows promising out-of-distribution generalization performance on PACS and Office-Home. When unlabeled target data are accessible (the UDA problem), DAEL leverages pseudo labels and follows the same collaborative ensemble learning strategy as used in the DG setting to prompt the emergence of domain-generalizable features. Currently, to avoid overfitting to noisy pseudo labels, advanced data augmentation methods are used. However, the design of data augmentation is often task-specific, e.g., for digit recognition we cannot use random flip; for fine-grained recognition, color",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "distortion might be discarded. Future work can focus on new algorithmic designs to mitigate the overfitting problem in a more flexible way.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX A",
+        "text_level": 1,
+        "bbox": [
+            666,
+            594,
+            759,
+            606
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "IMPLEMENTATION DETAILS",
+        "text_level": 1,
+        "bbox": [
+            614,
+            609,
+            810,
+            622
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Experiments on domain adaptation. SGD with momentum is used as the optimizer, and the cosine annealing rule [73] is adopted for learning rate decay. For Digit-5, the CNN backbone is constructed with three convolution layers and two fully connected layers [18]. For each mini-batch, we sample from each domain 64 images. The model is trained with an initial learning rate of 0.05 for 30 epochs. For DomainNet, we use ResNet101 [58] as the CNN backbone and sample from each domain 6 images to form a mini-batch. The model is trained with an initial learning rate of 0.002 for 40 epochs. For miniDomainNet, we use ResNet18 [58] as the CNN backbone. Similarly, we sample 64 images from each domain to form a mini-batch and train the model for 60 epochs with an initial learning rate of 0.005. For all UDA experiments, we set  $\\lambda_u = 0.5$  in all datasets. The sensitivity of  $\\lambda_u = 0.5$  to performance is investigated in Fig. 5.",
+        "bbox": [
+            501,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Experiments on domain generalization. ResNet18 is used as the CNN backbone as in previous works [54, 67]. SGD with momentum is used to train the model for 40 epochs with an initial learning rate of 0.002. The learning rate is further decayed by the cosine annealing rule. Each mini-batch",
+        "bbox": [
+            501,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            76,
+            29,
+            418,
+            42
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "contains 30 images (10 per source domain). Note that the  $\\mathcal{L}_u$  term in Eq.(4) is discarded here as no target data is available for training.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "APPENDIX B PSEUDO-CODE",
+        "text_level": 1,
+        "bbox": [
+            230,
+            135,
+            336,
+            164
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "The full algorithm of domain adaptive ensemble learning is presented in Alg. 1.",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Pseudo-code for loss computation in DAEL.",
+        "text_level": 1,
+        "bbox": [
+            76,
+            215,
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+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "1: Require: labeled source mini-batches  $\\{(X^i,Y^i)\\}_{i = 1}^K$ , unlabeled target mini-batch  $X^t$ , source experts  $\\{E_i\\}_{i = 1}^K$ , weak/strong augmentation  $a(\\cdot) / A(\\cdot)$ , hyper-parameter  $\\lambda_{u}$ .",
+            "2: Return: loss  $\\mathcal{L}$ .",
+            "3:  $\\mathcal{L}_{ce} = 0$  // Initialize  $\\mathcal{L}_{ce}$",
+            "4:  $\\mathcal{L}_{cr} = 0$  // Initialize  $\\mathcal{L}_{cr}$",
+            "5: for  $i = 1$  to  $K$  do",
+            "6: // Domain-specific expert learning",
+            "7:  $\\tilde{X}^i = a(X^i)$  // Apply weak augmentation to  $X^i$",
+            "8:  $\\tilde{Y}^i = E_i(\\tilde{X}^i)$  // Compute prediction for expert-i",
+            "9:  $\\mathcal{L}_{ce} = \\mathcal{L}_{ce} + \\mathrm{CrossEntropy}(\\tilde{Y}^i, Y^i)$  // Compute cross-entropy loss for expert-i",
+            "10: // Collaborative ensemble learning for source data",
+            "11:  $\\hat{X}^i = A(X^i)$  // Apply strong augmentation to  $X^i$",
+            "12:  $\\hat{Y}^i = \\frac{1}{K - 1}\\sum_{j\\neq i}E_j(\\hat{X}^i)$  // Compute ensemble prediction of non-experts",
+            "13:  $\\mathcal{L}_{cr} = \\mathcal{L}_{cr} + \\mathrm{MSE}(\\hat{Y}^i, \\tilde{Y}^i)$  // Compute consistency loss for non-experts",
+            "14: end for",
+            "15:  $\\mathcal{L}_{ce} = \\mathcal{L}_{ce} / K$",
+            "16:  $\\mathcal{L}_{cr} = \\mathcal{L}_{cr} / K$",
+            "17:  $\\mathcal{L} = \\mathcal{L}_{ce} + \\mathcal{L}_{cr}$",
+            "18: if  $X^t$  is available then",
+            "19: // Collaborative ensemble learning for unlabeled target data",
+            "20:  $\\tilde{X}^t = a(X^t)$  // Apply weak augmentation to  $X^t$",
+            "21:  $\\tilde{Y}^t, M = \\text{PseudoLabel}(\\{E_i(\\tilde{X}^t)\\}_i) // \\text{Get pseudo labels and instance masks}$",
+            "22:  $\\hat{X}^t = A(X^t)$  // Apply strong augmentation to  $X^t$",
+            "23:  $\\hat{Y}^t = \\frac{1}{K}\\sum_iE_i(\\hat{X}^t)$  // Compute ensemble prediction of all experts",
+            "24:  $\\mathcal{L}_u =$  CrossEntropy  $(\\hat{Y}^t,\\tilde{Y}^t,M)$  // Compute cross-entropy loss for all experts",
+            "25:  $\\mathcal{L} = \\mathcal{L} + \\lambda_u\\mathcal{L}_u$",
+            "26: end if"
+        ],
+        "bbox": [
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+            236,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES",
+        "text_level": 1,
+        "bbox": [
+            235,
+            667,
+            330,
+            679
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+    {
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+        ],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "header",
+        "text": "JOURNAL OF LATEX CLASS FILES, VOL. 14, NO. 8, AUGUST 2015",
+        "bbox": [
+            75,
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+            41
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
+        "bbox": [
+            911,
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+# Domain Adaptive Ensemble Learning
+
+Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang.
+
+Abstract—The problem of generalizing deep neural networks from multiple source domains to a target one is studied under two settings: When unlabeled target data is available, it is a multi-source unsupervised domain adaptation (UDA) problem, otherwise a domain generalization (DG) problem. We propose a unified framework termed domain adaptive ensemble learning (DAEL) to address both problems. A DAEL model is composed of a CNN feature extractor shared across domains and multiple classifier heads each trained to specialize in a particular source domain. Each such classifier is an expert to its own domain but a non-expert to others. DAEL aims to learn these experts collaboratively so that when forming an ensemble, they can leverage complementary information from each other to be more effective for an unseen target domain. To this end, each source domain is used in turn as a pseudo-target-domain with its own expert providing supervisory signal to the ensemble of non-experts learned from the other sources. To deal with unlabeled target data under the UDA setting where real expert does not exist, DAEL uses pseudo labels to supervise the ensemble learning. Extensive experiments on three multi-source UDA datasets and two DG datasets show that DAEL improves the state of the art on both problems, often by significant margins.
+
+Index Terms—Domain adaptation, domain generalization, collaborative ensemble learning
+
+# I. INTRODUCTION
+
+Deep neural networks trained with sufficient labeled data typically perform well when the test data follows a similar distribution as the training data. However, when the test data distribution is different, neural networks often suffer from significant performance degradation. Such a problem is common to machine learning models and is often referred to as domain shift [1] (or distribution shift). To overcome the domain shift problem, two related areas have been studied extensively, namely unsupervised domain adaptation (UDA) [2, 3, 4, 5, 6, 7, 8, 9] and domain generalization (DG) [10, 11, 12, 13, 14, 15]. UDA aims to adapt a model from a labeled source domain to an unlabeled target domain. In contrast, DG aims to learn a model only from source data typically gathered from multiple distinct but related domains, and the model is directly deployed in a target domain without any fine-tuning or adaptation steps.
+
+Early UDA work focuses on single-source scenarios. Recently, multi-source UDA [16, 17, 18] has started to attract more attention, thanks to the introduction of large-scale multidomain datasets such as DomainNet [18]. In contrast, having multiple source domains has been the default setting for most DG methods from much early on [11]. This is understandable: without the guidance from target domain data, DG models rely on the diversity of source domain to learn generalizable
+
+knowledge. This paper focuses on the multi-source setting for both problems.
+
+How can multiple source domains be exploited to help generalization? Many DG methods [19, 20, 21] aim to learn a domain-invariant feature representation or classifier across the source domains, in the hope that it would also be invariant to domain shift brought by the target domain. However, there is an intrinsic flaw in this approach, that is, when the source domains become more diverse, learning a domain-invariant model becomes more difficult. This is because each domain now contains much domain-specific information. Simply removing the information may be detrimental to model generalization because such information could potentially be useful for a target domain, especially when combined across different source domains. An example can be found in Fig. 1(a) where the only thing in common of the five source domains for the airplane class seems to be shape. However, texture information is also useful for object recognition in the target sketch domain, which we want to maintain in the learned classifier. Existing multi-source UDA methods, on the other hand, attempt to align the data distribution of the target domain with each source domain individually [17, 18, 22] or by means of a hard [23] or soft [16] domain selector. Again, Fig. 1(a) suggests that aligning the target domain to each individual source domain is not only difficult but could also be counterproductive due to drastic variations among source domains.
+
+In this paper, we propose a novel unified framework for both multi-source DG and UDA based on the idea of collaborative ensemble learning. Our framework, termed domain adaptive ensemble learning (DAEL), takes a very different approach from previous work. Specifically, each domain is used to learn a model that is specialized in that domain (see Fig. 1(a)). We call it a domain expert—a relative term as an expert to a specific source domain would be a non-expert to all other source domains as well as the target domain. The key idea of DAEL is to learn these experts collaboratively so that when forming an ensemble, they can leverage complementary information to better tackle the target domain.
+
+To realize the DAEL framework for a UDA or DG model, a number of issues need to be addressed. (1) Scalability: Training an ensemble of models instead of a single model means higher computational cost. To solve this problem, we design a DAEL model as a deep multi-expert network consisting of a shared convolutional neural network (CNN) feature extractor and multiple classifier heads. Each head is trained to classify images from a particular source domain. Therefore, different heads learn different patterns from the shared features for classification. (2) Training: Since the target domain data is either non-existent (for DG) or has no label (for UDA), there is no target domain expert to provide supervisory
+
+![](images/9b927fbb2faa846ad4a795b968fd567693edefa270da9e89ff3bae6cd6e1cee0.jpg)  
+Fig. 1: Overview of domain adaptive ensemble learning (DAEL).
+
+signal for the source domain expert ensemble. To overcome this, each source domain is used in turn as a pseudo-target-domain with its own expert providing supervisory signal to the ensemble of non-experts learned from the other sources (see Fig. 1(b)). For unlabeled target data under the UDA setting where real expert does not exist, DAEL uses as pseudo-label the most confident estimation among all experts and train the ensemble to fit the pseudo-label (see Fig. 1(c)). (3) How to measure the effectiveness of a non-expert ensemble w.r.t. an expert: Inspired by consistency regularization (CR) [24, 25] used in semi-supervised learning, the ensemble's effectiveness is measured by how close its prediction is to that of an expert when both are fed with a data point from the expert's domain. To amplify the regularization effect brought by CR, we use weak and strong augmentation for input to an expert and a non-expert ensemble respectively. Such a strategy has been shown useful in recent semi-supervised learning methods [26, 27, 28]. Once these three issues are addressed, we have a simple but effective solution to both UDA and DG. By sending supervisory signal to an ensemble rather than each individual, different domain-specific experts are allowed to exploit complementary domain-specific information from each other, resulting in a more domain-generalizable ensemble.
+
+We summarize our contributions as follows. (1) We present a novel framework called domain adaptive ensemble learning (DAEL), which improves the generalization of a multi-expert network by explicitly training the ensemble to solve the target task. (2) A realization of DAEL is formulated which provides a simple yet effective solution for both multi-source UDA and DG, unlike previous methods that only tackle one of them. (3) We define miniDomainNet, a reduced version of DomainNet [18] to allow fast prototyping and experimentation. For benchmarking, a unified implementation and evaluation platform of all compared methods is created, called Dassl.pytorch, which has been made publicly available.
+
+(4) We demonstrate the effectiveness of DAEL on three multisource UDA datasets and two DG datasets where DAEL outperforms the current state of the art by a large margin (see Table 1 & 2).
+
+# II. RELATED WORK
+
+Unsupervised domain adaptation. Motivated by the seminal theory work by Ben-David et al. [29], numerous UDA methods seek to reduce distribution discrepancy between source and target features using some distance metrics, such as maximum mean discrepancy [3, 30, 31], optimal transport [32, 33], and graph matching [34, 35, 36]. Inspired by generative adversarial network (GAN) [37], several methods [2, 38, 39, 40, 41] additionally train a domain discriminator for feature alignment. GAN has also been exploited for pixel-level domain adaptation where target images are synthesized via image translation/generation [42, 43]. Instead of aligning the coarse marginal distribution, recent alignment methods have shown that fine-grained alignment such as aligning class centroids [44, 45, 46, 47] or using task-specific classifiers [6, 48, 49] can give a better adaptation performance.
+
+The multi-source UDA methods are more related to our work because of the same problem setting. Several works [17, 18, 22] extend the domain alignment idea to multi-source UDA by considering all possible source-target pairs. Kang et al. [47] propose contrastive adaptation network where a contrastive domain discrepancy loss is minimized for samples from the same class but of different domains while maximized for samples from different classes. Relationships between each source and the target are learned by Li et al. [23] and only the target-related sources are kept for model learning. Hoffman et al. [16] compute distribution-based weights for combining source classifiers. Our model architecture—a shared feature extractor and multiple domain-specific classifiers—is similar to  $\mathbf{M}^3\mathbf{SDA}$  [18]. However, DAEL is very different in that different domain-specific classifiers are learned collaboratively
+
+where each source domain is used in turn as a pseudo-target-domain to train the ensemble.
+
+Domain generalization. Many DG methods follow the idea of distribution alignment originated from the UDA community to learn domain-invariant features through minimizing in-between-source distances [19, 20, 21]. Data augmentation is another popular research direction where the motivation is to avoid overfitting to source data. This can be achieved by, for example, adding adversarial gradients to the input [13, 50], learning data generation networks [10, 14], or mixing instance-level feature statistics [15]. Meta-learning has also been investigated for learning domain-generalizable neural networks [51, 52, 53, 54]. Different from existing DG methods that mostly train a single classifier, our work for the first time introduces collaborative ensemble learning to mine domain-specific information using domain-specific classifiers. Although our pseudo-target-domain idea is related in spirit to meta-learning, no episodic training is required in DAEL, which makes the training procedure much simpler. We refer readers to Zhou et al. [1] for a comprehensive survey in DG.
+
+Ensemble methods have been extensively researched in the machine learning community [55]. The principle is to train multiple learners for the same problem and combine them for inference. Such technique has also been widely used in competitions like ILSVRC [56] where multiple CNNs are trained and combined to improve the test performance [57, 58]. In this work, to prompt the emergence of generalizable features, we learn an ensemble of classifiers (experts) in a collaborative way—using each individual expert to supervise the learning of the non-expert ensemble.
+
+# III. METHODOLOGY
+
+Problem definition. Given a labeled training dataset collected from  $K$  source domains,  $\mathcal{D}_S = \{\mathcal{D}_1,\dots ,\mathcal{D}_K\}$ , we aim to learn a model that can generalize well to a target domain  $\mathcal{D}_T$ . If the unlabeled target data is available during training, it is a multi-source unsupervised domain adaptation (UDA) problem [18], otherwise a domain generalization (DG) problem [11]. Our method addresses these two problems in a unified framework.
+
+Model. We aim to learn a multi-expert model, denoted by  $\{E_i\}_{i=1}^K$ , with each expert  $E_i$  specializing in a particular source domain  $\mathcal{D}_i$ . For clarity,  $E_i$  is called an expert to  $\mathcal{D}_i$  but a non-expert to  $\{\mathcal{D}_j\}_{j \neq i}$ . The ensemble prediction for an image  $x$  is used at test time, i.e.  $p(y|x) = \frac{1}{K} \sum_{i=1}^{K} E_i(x)$ . In implementation, the multi-expert model shares a CNN backbone for feature extraction, followed by domain-specific classification heads. To allow the ensemble to better exploit complementary information between experts, we propose domain adaptive ensemble learning (DAEL). The main idea of DAEL is to strengthen the ensemble's generalizability by simulating how it is tested—using an expert's output to supervise the learning of ensemble of non-experts. This is realized by consistency regularization (CR) training, as shown in Fig. 2. To amplify the regularization effect, we follow Sohn et al. [28] to use weak and strong augmentations, denoted by  $a(\cdot)$  and  $A(\cdot)$  respectively. Specifically, weak augmentation,
+
+which corresponds to simple flip-and-shift transformations, is used for pseudo-label generation; strong augmentation, which induces stronger noises like rotation and shearing, is used for ensemble prediction.
+
+Domain-specific expert learning. Next, we detail the DAEL training procedure, starting with how each expert is trained to be domain-specific. Let  $H(\cdot, \cdot)$  denote cross-entropy between two probability distributions, the loss function for domain-specific expert learning is
+
+$$
+\mathcal {L} _ {c e} = \frac {1}{K} \sum_ {i = 1} ^ {K} \mathbb {E} _ {x ^ {i}, y \left(x ^ {i}\right) \sim \mathcal {D} _ {i}} [ H (y \left(x ^ {i}\right), E _ {i} (a \left(x ^ {i}\right))) ], \tag {1}
+$$
+
+where  $y(x^{i})$  is the one-hot label of  $x^{i}$ ; the expectation is implemented by mini-batch sampling (same for the following equations).
+
+Collaborative ensemble learning using source domain data. Given an image  $x^{i}$  from the  $i$ -th source domain (treated as a pseudo-target-domain), the idea is to use as target the corresponding expert's prediction for the weakly augmented image,  $E_{i}(a(x^{i}))$ , and encourage the ensemble prediction of non-experts from other source domains for the strongly augmented image,  $\frac{1}{K - 1}\sum_{j\neq i}E_{j}(A(x^{i}))$ , to be close to the target. Such a design explicitly teaches the ensemble how to handle data from unseen domains (mimicked by strong augmentation and guided by a pseudo-target-domain expert), thus improving the robustness to domain shift. Formally, the loss is defined as the mean-squared error (MSE) between the two outputs:2
+
+$$
+\mathcal {L} _ {c r} = \frac {1}{K} \sum_ {i = 1} ^ {K} \mathbb {E} _ {x ^ {i} \sim \mathcal {D} _ {i}} \left[ \| E _ {i} \left(a \left(x ^ {i}\right)\right) - \frac {1}{K - 1} \sum_ {j \neq i} E _ {j} \left(A \left(x ^ {i}\right)\right) \| ^ {2} \right]. \tag {2}
+$$
+
+Collaborative ensemble learning using unlabeled target data. Given a weakly augmented target domain image  $a(x^t)$ , we first ask each source-expert to produce a class probability distribution,  $p_i(y|a(x^t)) = E_i(a(x^t))$ , and select as pseudolabel the most confident expert's prediction based on their maximum probability,  $\arg \max(p_{i*})$ , where  $i^*$  is the index of the most confident expert. This is inspired by the observation that correct predictions are usually confident with peaked value on the predicted class [28]. Then, we force the ensemble prediction of all source-experts for the strongly augmented image,  $\bar{E}(A(x^t)) = \frac{1}{K}\sum_{i=1}^{K}E_i(A(x^t))$ , to fit the one-hot pseudo-label  $\hat{y}(x^t) = \arg \max(p_{i*})$ . The loss is defined as
+
+$$
+\mathcal {L} _ {u} = \mathbb {E} _ {x ^ {t} \sim \mathcal {D} _ {T}} [ \mathbb {1} (\max  (p _ {i ^ {*}}) \geq \epsilon) H (\hat {y} (x ^ {t}), \bar {E} (A (x ^ {t}))) ], \tag {3}
+$$
+
+where  $\epsilon$  is a confidence threshold (fixed to 0.95 in this paper).
+
+Eq. (3) can be viewed as a combination of CR and entropy minimization [59] because the conversion from soft probability to one-hot encoding essentially reduces the entropy of the class distribution. The confidence threshold provides a curriculum for filtering out less confident (unreliable) pseudo labels in the early training stages [28, 60].
+
+2We chose MSE over KL divergence because the former led to a slightly higher performance.  
+3For simplicity we assume arg max converts soft probability to one-hot encoding.
+
+$x^{i}$  : data from  $i$  -th source domain  
+$x^t$ : data from target domain  
+$a(\cdot)$  : weak augmentation  
+$A(\cdot)$  : strong augmentation
+
+![](images/8d7573b2902ea306974e35afe91cd5422fd7b4b7b19a06ad713a7af504af7f2d.jpg)  
+Fig. 2: Illustration of domain adaptive ensemble learning. Left: collaborative learning using source domains. Right: collaborative learning using unlabeled target domain via pseudo-labeling. The ensemble of all experts is used for testing. Gradients are only back-propagated through the ensemble prediction path.
+
+![](images/d41be18c7c1b4a3f934d284cf58a51593b2a3834a6f135f4342b6a7e3b2f3b31.jpg)
+
+The full learning objective is a weighted sum of Eq. (1), (2) and (3),
+
+$$
+\mathcal {L} = \mathcal {L} _ {c e} + \mathcal {L} _ {c r} + \lambda_ {u} \mathcal {L} _ {u}, \tag {4}
+$$
+
+where  $\lambda_{u}$  is a hyper-parameter for balancing the weighting between  $\mathcal{L}_u$  and the losses for the labeled source domains. For multi-source UDA, DAEL uses Eq. (4). For DG,  $\mathcal{L}_u$  is removed due to the absence of target domain data. DAEL not only provides a unified solution to the two problems, but is also very easy to implement (see Appendix B for pseudo-code).
+
+Gradient analysis. To understand the benefit of collaborative learning (i.e.,  $\| \frac{1}{K}\sum_{i}p_{i} - p^{*}\|^{2}$ ) against individual learning (i.e.,  $\frac{1}{K}\sum_{i}\| p_i - p^*\|^2$ ) where  $p^*$  denotes the target, we analyze their gradients with respect to a single expert's output  $p_i$ . For collaborative learning, we have  $\Delta p_i = \frac{2}{K} (\frac{1}{K} (p_i + \sum_{j\neq i}p_j) - p^*)$ . For individual learning, we have  $\Delta p_i = \frac{2}{K} (p_i - p^*)$ . It is clear that collaborative learning updates an expert by combining information from other experts, which facilitates the exploitation of complementary information. Table 3a further confirms the advantage of collaborative learning.
+
+Relation to knowledge distillation. DAEL is similar to knowledge distillation (KD) [61] in the sense that the teacher-student training is used. However, in DAEL the boundary between teacher and student is blurred because each student can become a teacher when the input data come from its domain of expertise. Moreover, the collaborative ensemble learning strategy is specifically designed for dealing with multi-domain data—it encourages different experts to learn complementary information such that the ensemble is more generalizable to unseen domains.
+
+# IV. EXPERIMENTS
+
+# A. Experiments on Domain Adaptation
+
+Datasets. (1) Digit-5 consists of five different digit recognition datasets, which are MNIST [62], MNIST-M [2], USPS, SVHN [63] and SYN [2]. We follow the same setting as
+
+4The same conclusion can be drawn when using KL divergence as the objective.
+
+in  $\mathbf{M}^3\mathbf{SDA}$  [18] for experimentation. See Fig. 3 left for example images. (2) DomainNet [18] is a recently introduced benchmark for large-scale multi-source domain adaptation. It has six domains (Clipart, Infograph, Painting, Quickdraw, Real and Sketch) and 0.6M images of 345 classes. See Fig. 3 right for example images. (3) The full DomainNet requires considerable computing resources for training, preventing wide deployment and extensive ablative studies. Inspired by the miniImageNet dataset [64] that has been widely used in the few-shot learning community, we propose miniDomainNet, which takes a subset of DomainNet and uses a smaller image size ( $96 \times 96$ ). As noted by Saito et al. [49] that the labels of some domains and classes are very noisy in the original DomainNet, we follow them to select four domains and 126 classes. As a result, miniDomainNet contains 18,703 images of Clipart, 31,202 images of Painting, 65,609 images of Real and 24,492 images of Sketch. In general, miniDomainNet maintains the complexity of the original DomainNet, reduces the requirements for computing resources and allows fast prototyping and experimentation.
+
+The implementation details (of all experiments in this paper) are provided in Appendix A. To ensure the results are convincing, we run each experiment three times and report the mean accuracy and standard deviation. The results of baseline models are from either their papers (if reported) or our reimplementation (only when their source code is available).
+
+Results. Following the standard test protocol [18], one domain is used as target and the rest as sources, and classification accuracy on the target domain test set is reported. Table 1 shows the results on the multi-source UDA datasets. We summarize our findings as follows. (1) In terms of the overall performance (the rightmost Avg column), DAEL achieves the best results on all three datasets, outperforming the second-best methods by large margins:  $3.51\%$  on Digit-5,  $2.2\%$  on
+
+<sup>5</sup>We have noticed that the 't-shirt' class (index 327) is excluded from Painting's training set (see the official painting_train.txt file), but is included in the test set, which could affect the performance.  
+It usually takes several GPU days for training a deep model on the full DomainNet.
+
+![](images/b19fe76cfc2e7b7622b1381c204f98c287c9d5a27bbefb0ff363288aada4f117.jpg)  
+Fig. 3: Example images from Digit-5 and DomainNet.
+
+![](images/31aa26f65a43a6baceac5cfefc311890a53861a2afbd44d1af207a2ebe9e9829.jpg)  
+Fig. 4: Ablation study for evaluating each component in Eq. (4).
+
+DomainNet and  $6.21\%$  on miniDomainNet.
+
+(2) On the small Digit-5 dataset, DAEL achieves near-oracle performance (our  $96.47\%$  vs. oracle's  $97.00\%$ ). In particular, MNIST-M and SVHN are the two most difficult domains as can be seen in Fig. 3—MNIST-M has complex backgrounds while SVHN contains blurred and cluttered digits. Those distinctive features make MNIST-M and SVHN drastically different from other domains and thus make the adaptation task harder. Nonetheless, DAEL obtains the highest accuracy which beats  $\mathrm{M}^3\mathrm{SDA}$ —the 2nd best method—by  $11.62\%$  on MNIST-M and  $4.06\%$  on SVHN.  
+(3) On the large-scale DomainNet/miniDomainNet, DAEL achieves the best performance among all methods. Notably, compared with the latest state of the art on DomainNet, i.e. CMSS, DAEL obtains a clear margin of  $2.2\%$  on average, which demonstrates the advantage of exploiting complementarity between source domains for ensemble prediction.  
+(4) Compared with  $\mathbf{M}^3\mathbf{SDA}$ , the most related method to ours that also has domain-specific classifiers, DAEL is superior on all three datasets. This is because aligning distributions between the target and each individual source, as in  $\mathbf{M}^3\mathbf{SDA}$ , is difficult due to large domain variations between sources.
+
+# B. Experiments on Domain Generalization
+
+Datasets. (1) PACS [12] is a commonly used DG dataset with four domains: Photo (1,670 images), Art Painting (2,048 images), Cartoon (2,344 images) and Sketch (3,929 images). There are seven object categories: dog, elephant, giraffe, guitar, horse, house and person. (2) Office-Home [69] contains around 15,500 images of 65 categories, which are related to office and home objects. Similar to PACS, there are four
+
+domains: Artistic, Clipart, Product and Real World. For evaluation, we follow the prior works [12, 54, 67] to use the leave-one-domain-out protocol, i.e. choosing one domain as the (unseen) test domain and using the remaining three as source domains for model training.
+
+Results. The comparison with the state-of-the-art DG methods is shown in Table 2. Overall, DAEL achieves the best results on both datasets with clear margins against all competitors. We provide a more detailed discussion as follows. (1) DAEL is clearly better than the distribution alignment methods, i.e. CCSA and MMD-AAE, with  $\geq 4\%$  improvement on PACS and  $\geq 1.2\%$  improvement on Office-Home. This is not surprising because the distribution alignment theory [29] developed for DA does not necessarily work for DG (which does not have access to target data). (2) Compared with the recent self-supervised method JiGen, DAEL obtains a clear improvement of  $2.9\%$  on PACS. The gap is further increased to  $4.9\%$  on Office-Home. When it comes to CrossGrad, a state-of-the-art data augmentation method, DAEL achieves clear improvements as well. (3) The recently proposed Epi-FCR shares a similar design choice with DAEL—to simulate domain shift during training. Again, DAEL is clearly superior thanks to the design of collaborative ensemble learning. Further, Epi-FCR requires domain-specific feature extractors, as well as additional domain-agnostic feature extractors and classifiers, incurring much higher computational cost.
+
+# C. Analysis
+
+Ablation study. We start from the baseline ensemble model trained by  $\mathcal{L}_{ce}$  only and progressively add  $\mathcal{L}_{cr}$  and  $\mathcal{L}_u$  (see Eq. (4)). The results are shown in Fig. 4. Each of  $\mathcal{L}_{cr}$  and  $\mathcal{L}_u$  contributes positively to the performance. Combining  $\mathcal{L}_{cr}$
+
+TABLE 1: Comparing DAEL with state of the art on multi-source UDA datasets.  
+(a) Digit-5.  
+
+<table><tr><td>Method</td><td>MNIST-M</td><td>MNIST</td><td>USPS</td><td>SVHN</td><td>SYN</td><td>Avg</td></tr><tr><td>Oracle</td><td>95.36±0.15</td><td>99.50±0.08</td><td>99.18±0.09</td><td>92.28±0.14</td><td>98.69±0.04</td><td>97.00</td></tr><tr><td>Source-only</td><td>68.08±0.39</td><td>99.06±0.05</td><td>97.20±0.48</td><td>84.56±0.36</td><td>89.87±0.32</td><td>87.75</td></tr><tr><td>DCTN [17]</td><td>76.20±0.51</td><td>99.38±0.06</td><td>94.39±0.58</td><td>86.37±0.54</td><td>86.78±0.31</td><td>88.63</td></tr><tr><td>DANN [65]</td><td>83.44±0.12</td><td>98.46±0.07</td><td>94.19±0.31</td><td>84.08±0.60</td><td>92.91±0.23</td><td>90.61</td></tr><tr><td>CMSS [66]</td><td>75.30±0.57</td><td>99.00±0.08</td><td>97.70±0.13</td><td>88.40±0.54</td><td>93.70±0.21</td><td>90.80</td></tr><tr><td>MCD [6]</td><td>80.65±0.51</td><td>99.22±0.08</td><td>98.32±0.07</td><td>81.87±0.72</td><td>95.42±0.04</td><td>91.09</td></tr><tr><td>SE [60]</td><td>80.16±0.48</td><td>99.41±0.06</td><td>98.87±0.08</td><td>86.15±0.76</td><td>96.44±0.34</td><td>92.20</td></tr><tr><td>MME [49]</td><td>83.07±0.57</td><td>99.35±0.03</td><td>98.64±0.17</td><td>86.40±0.41</td><td>95.78±0.15</td><td>92.65</td></tr><tr><td>M3SDA [18]</td><td>82.15±0.49</td><td>99.38±0.07</td><td>98.71±0.12</td><td>88.44±0.72</td><td>96.10±0.10</td><td>92.96</td></tr><tr><td>DAEL (ours)</td><td>93.77±0.12</td><td>99.45±0.02</td><td>98.69±0.79</td><td>92.50±0.15</td><td>97.91±0.03</td><td>96.47</td></tr></table>
+
+(b) DomainNet.  
+
+<table><tr><td>Method</td><td>Clp</td><td>Inf</td><td>Pnt</td><td>Qdr</td><td>Rel</td><td>Skt</td><td>Avg</td></tr><tr><td>Oracle [18]</td><td>69.3±0.37</td><td>34.5±0.42</td><td>66.3±0.67</td><td>66.8±0.51</td><td>80.1±0.59</td><td>60.7±0.48</td><td>63.0</td></tr><tr><td>Source-only [18]</td><td>47.6±0.52</td><td>13.0±0.41</td><td>38.1±0.45</td><td>13.3±0.39</td><td>51.9±0.85</td><td>33.7±0.54</td><td>32.9</td></tr><tr><td>DANN [65]</td><td>45.5±0.59</td><td>13.1±0.72</td><td>37.0±0.69</td><td>13.2±0.77</td><td>48.9±0.65</td><td>31.8±0.62</td><td>32.6</td></tr><tr><td>DCTN [17]</td><td>48.6±0.73</td><td>23.5±0.59</td><td>48.8±0.63</td><td>7.2±0.46</td><td>53.5±0.56</td><td>47.3±0.47</td><td>38.2</td></tr><tr><td>MCD [6]</td><td>54.3±0.64</td><td>22.1±0.70</td><td>45.7±0.63</td><td>7.6±0.49</td><td>58.4±0.65</td><td>43.5±0.57</td><td>38.5</td></tr><tr><td>\( M^3 \)SDA [18]</td><td>58.6±0.53</td><td>26.0±0.89</td><td>52.3±0.55</td><td>6.3±0.58</td><td>62.7±0.51</td><td>49.5±0.76</td><td>42.6</td></tr><tr><td>CMSS [66]</td><td>64.2±0.18</td><td>28.0±0.20</td><td>53.6±0.39</td><td>16.0±0.12</td><td>63.4±0.21</td><td>53.8±0.35</td><td>46.5</td></tr><tr><td>DAEL (ours)</td><td>70.8±0.14</td><td>26.5±0.13</td><td>57.4±0.28</td><td>12.2±0.70</td><td>65.0±0.23</td><td>60.6±0.25</td><td>48.7</td></tr></table>
+
+(c) miniDomainNet.  
+
+<table><tr><td>Method</td><td>Clipart</td><td>Painting</td><td>Real</td><td>Sketch</td><td>Avg</td></tr><tr><td>Oracle</td><td>72.59±0.30</td><td>60.53±0.74</td><td>80.47±0.34</td><td>63.44±0.15</td><td>69.26</td></tr><tr><td>Source-only</td><td>63.44±0.76</td><td>49.92±0.71</td><td>61.54±0.08</td><td>44.12±0.31</td><td>54.76</td></tr><tr><td>MCD [6]</td><td>62.91±0.67</td><td>45.77±0.45</td><td>57.57±0.33</td><td>45.88±0.67</td><td>53.03</td></tr><tr><td>DCTN [17]</td><td>62.06±0.60</td><td>48.79±0.52</td><td>58.85±0.55</td><td>48.25±0.32</td><td>54.49</td></tr><tr><td>DANN [65]</td><td>65.55±0.34</td><td>46.27±0.71</td><td>58.68±0.64</td><td>47.88±0.54</td><td>54.60</td></tr><tr><td>\( M^3SDA \) [18]</td><td>64.18±0.27</td><td>49.05±0.16</td><td>57.70±0.24</td><td>49.21±0.34</td><td>55.03</td></tr><tr><td>MME [49]</td><td>68.09±0.16</td><td>47.14±0.32</td><td>63.33±0.16</td><td>43.50±0.47</td><td>55.52</td></tr><tr><td>DAEL (ours)</td><td>69.95±0.52</td><td>55.13±0.78</td><td>66.11±0.14</td><td>55.72±0.79</td><td>61.73</td></tr></table>
+
+![](images/200d2747e53f025f265c760f39cf8058eead6c75f86a90d826d881c8fa1d61f0.jpg)  
+Fig. 5: Sensitivity of  $\lambda_{u}$
+
+![](images/93840d511adba32c453dd56f06f06b3ae1cfe5ce15cf6dec8d65a0bb5f8a59f9.jpg)
+
+and  $\mathcal{L}_u$  gives the best performance, which confirms their complementarity.
+
+Sensitivity of  $\lambda_{u}$ . Fig. 5 shows that the performance soars from  $\lambda_{u} = 0$  to  $\lambda_{u} = 0.5$  and remains relatively stable between  $\lambda_{u} = 0.5$  and  $\lambda_{u} = 1.0$ . The overall results suggest that the model's performance is in general insensitive to  $\lambda_{u}$  around 0.5.
+
+Collaborative ensemble or individual expert training? As discussed in the gradient analysis part in Methodology, collaborative learning aggregates gradients from different ex
+
+perts, which can better exploit the complementarity between different sources. We justify this design in Table 3a where collaborative learning shows clear improvements over individual learning.
+
+Learning an ensemble of classifiers or a single classifier? The motivation for the former is to enable the model to better handle complicated source data distributions—as discussed before, learning a single classifier forces the model to erase domain-specific knowledge that could otherwise be useful for recognition in the target domain. To justify this design, we switch from the ensemble classifiers to a single classifier while keeping other designs unchanged. Table 3b confirms that learning an ensemble of classifiers is essential.
+
+Using expert's prediction or real label in  $\mathcal{L}_{cr}$ ? Table 3c shows that using real label  $(Y)$  is slightly worse than using expert's prediction  $(E_i)$ . This is because expert's prediction automatically encodes the relations between classes (reflected in the soft probability distribution [70]), thus providing better supervisory signal.
+
+Most confident expert's prediction vs. ensemble predic
+
+TABLE 2: Comparing DAEL with state of the art on DG datasets PACS (left) and Office-Home (right).  
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">PACS</td><td colspan="5">Office-Home</td></tr><tr><td>Art</td><td>Cat</td><td>Pho</td><td>Skt</td><td>Avg</td><td>Art</td><td>Clp</td><td>Prd</td><td>Rel</td><td>Avg</td></tr><tr><td>Vanilla</td><td>77.0</td><td>75.9</td><td>96.0</td><td>69.2</td><td>79.5</td><td>58.9</td><td>49.4</td><td>74.3</td><td>76.2</td><td>64.7</td></tr><tr><td>MMD-AAE [21]</td><td>75.2</td><td>72.7</td><td>96.0</td><td>64.2</td><td>77.0</td><td>56.5</td><td>47.3</td><td>72.1</td><td>74.8</td><td>62.7</td></tr><tr><td>CCSA [19]</td><td>80.5</td><td>76.9</td><td>93.6</td><td>66.8</td><td>79.4</td><td>59.9</td><td>49.9</td><td>74.1</td><td>75.7</td><td>64.9</td></tr><tr><td>JiGen [67]</td><td>79.4</td><td>75.3</td><td>96.0</td><td>71.6</td><td>80.5</td><td>53.0</td><td>47.5</td><td>71.5</td><td>72.8</td><td>61.2</td></tr><tr><td>CrossGrad [13]</td><td>79.8</td><td>76.8</td><td>96.0</td><td>70.2</td><td>80.7</td><td>58.4</td><td>49.4</td><td>73.9</td><td>75.8</td><td>64.4</td></tr><tr><td>Epi-FCR [54]</td><td>82.1</td><td>77.0</td><td>93.9</td><td>73.0</td><td>81.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DMG [68]</td><td>76.9</td><td>80.4</td><td>93.4</td><td>75.2</td><td>81.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>DAEL (ours)</td><td>84.6</td><td>74.4</td><td>95.6</td><td>78.9</td><td>83.4</td><td>59.4</td><td>55.1</td><td>74.0</td><td>75.7</td><td>66.1</td></tr></table>
+
+TABLE 3: Evaluation of design choices in DAEL. D-5: Digit-5. miniDN: miniDomainNet.  
+(a) Collaborative ensemble vs. individual expert learning.  
+
+<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Col.</td><td>96.47</td><td>61.73</td></tr><tr><td>Ind.</td><td>93.07</td><td>60.20</td></tr></table>
+
+(b) Learning an ensemble of classifiers vs. a single classifier.  
+
+<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ensemble</td><td>96.47</td><td>61.73</td></tr><tr><td>Single</td><td>95.02</td><td>60.09</td></tr></table>
+
+(c) Expert's prediction vs. real label (see  $\mathcal{L}_{cr}$ ).  
+
+<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ei</td><td>91.04</td><td>56.35</td></tr><tr><td>Y</td><td>90.84</td><td>56.11</td></tr></table>
+
+(d) Expert's prediction vs. ensemble prediction (see  $\mathcal{L}_u$ ).  
+
+<table><tr><td></td><td>D-5</td><td>miniDN</td></tr><tr><td>Ei</td><td>96.47</td><td>61.73</td></tr><tr><td>E</td><td>95.86</td><td>60.16</td></tr></table>
+
+tion for  $\mathcal{L}_u$ ? Table 3d suggests that using the most confident expert's output  $(E_{i^*})$  is better. A plausible explanation is that assembling smooths out the overall probability distribution when experts have disagreements, which may lead to potentially correct instances discarded due to weak confidence (i.e. probability less than the confidence threshold  $\epsilon$ ).
+
+Diagnosis into individual experts. Fig. 6 shows the performance of each individual source expert versus the ensemble on miniDomainNet trained with different losses. For  $\mathcal{L}_{ce}$  (blue bars), the variance between  $E_{1-3}$  is large and each individual's performance is low, indicating that the experts are themselves biased (overfitting). Comparing  $\mathcal{L}_{ce} + \mathcal{L}_{cr}$  (orange bars) with  $\mathcal{L}_{ce}$ , we observe that the variance between  $E_{1-3}$  is reduced and each individual's performance is significantly improved, leading to a much stronger ensemble. By adding  $\mathcal{L}_u$  (green bars), each individual's performance is further boosted, and hence the ensemble. To better understand how the ensemble helps prediction, we visualize the top-3 classes predicted by each expert and the ensemble in Fig. 7. In Fig. 7(a) top, expert-3 mis-recognizes the bear as dog but the ensemble prediction is dominated by the correct predictions made by expert-1 and -2. A similar pattern can be observed in Fig. 7(a) bottom. Fig. 7(b) provides examples of incorrect predictions where we observe that the model struggles to differentiate between classes of similar features. For example, the kangaroo in Fig. 7(b) top looks indeed similar to a dog due to the similarity in the face and skin texture—without looking at the body structure and the pouch. Such mistakes might be avoided by using neural networks that can extract features at multiple scales [71].
+
+Augmentation strategy. Recall that we use weak and strong augmentations for pseudo-label generation and prediction respectively. The rationales behind this design are: 1) We need the expert to provide accurate supervision (pseudo labels) to the non-expert ensemble so we feed the expert with weakly augmented data; 2) We apply strong augmentation to the non-expert ensemble in order to reduce overfitting to noisy pseudo
+
+TABLE 4: Comparison with baseline models trained using strong augmentation on miniDomainNet.  
+
+<table><tr><td>Model</td><td>Clipart</td><td>Painting</td><td>Real</td><td>Sketch</td><td>Avg</td></tr><tr><td>Source-only</td><td>63.44</td><td>49.92</td><td>61.54</td><td>44.12</td><td>54.76</td></tr><tr><td>Source-only+A(·)</td><td>64.34</td><td>49.31</td><td>58.81</td><td>48.02</td><td>55.12</td></tr><tr><td>MSDA</td><td>64.18</td><td>49.05</td><td>57.70</td><td>49.21</td><td>55.03</td></tr><tr><td>MSDA+A(·)</td><td>65.08</td><td>49.68</td><td>57.04</td><td>54.29</td><td>56.52</td></tr><tr><td>MME</td><td>68.09</td><td>47.14</td><td>63.33</td><td>43.50</td><td>55.52</td></tr><tr><td>MME+A(·)</td><td>68.25</td><td>49.21</td><td>60.26</td><td>44.23</td><td>55.49</td></tr><tr><td>DAEL</td><td>69.95</td><td>55.13</td><td>66.11</td><td>55.72</td><td>61.73</td></tr></table>
+
+labels. If we swap these two augmentations, i.e. using weak augmentation for prediction while strong augmentation for pseudo-label generation, the accuracy decreases from  $61.73\%$  to  $54.32\%$  on miniDomainNet. In addition, if strong augmentation is applied to both branches, the accuracy declines to  $58.05\%$ , which suggests the weak-strong augmentation strategy is essential. These observations have also been reported by Sohn et al. [28].
+
+To justify that using strong augmentation is not the sole contributor to our approach, we compare with top-performing baselines that also use strong augmentation in Table 4. We can see that the improvements brought by strong augmentation for the baselines are rather limited, and the gap with our method remains large. This result confirms that collaborative ensemble learning is the key to our superior performance.
+
+Visualization of features. We use t-SNE [72] to visualize the features learned by Source-only and our DAEL. Figure 8 shows that the target features learned by Source-only are poorly aligned—the model cannot clearly differentiate between “1”, “0”, “5”, “3”, and “8” (zoom-in to see the class labels). In contrast, the target features learned by DAEL have a much smaller domain discrepancy with the source features and exhibit clearer class-based clustering patterns.
+
+![](images/38063cb19f86bd478ac3c877f8a647c9c8bb0765ed3e543e5528abea29bba10a.jpg)  
+Fig. 6: Individual experts  $(E_{1-3})$  vs. ensemble  $(\bar{E})$  on miniDomainNet.
+
+![](images/05243daabaa0a56ecd59e96ccbfc597629f3d6e7f5a7c8df91d560431272dbff.jpg)
+
+![](images/41f8575dde3b48180cfc432fb3d3362e3dad8ed2b03fe6047df0575b6d42df26.jpg)
+
+![](images/5eb72f5fc937f5cb40df2da570c25f381420213c60ed7205b04bc7e716ee677d.jpg)
+
+![](images/a5bc9357ccda348daa5eea6002b991b64190fe9a3b21463a17f883e46a789970.jpg)  
+(a) Correct predictions
+
+![](images/bb925c10c758620fd020fea53628f0e01f9138a8fa323f49e363feb56f56b4bc.jpg)  
+(b) Incorrect predictions
+
+![](images/b7633cb56449e5192588742fb66716bb9d9f60b9cdbd4c25cfdbf0adb8af81de.jpg)  
+Fig. 7: Visualization of predicted classes (top-3) and the corresponding confidence by each expert and the ensemble.  
+(a) Source-only  
+Fig. 8: Visualization of features from Digit-5 using t-SNE [72].
+
+![](images/96ac3a79757f41cfdd0ac9a6951ca04b753facd6340a93e34289c57434efee10.jpg)  
+(b) DAEL
+
+# V. CONCLUSION
+
+Our approach, domain adaptive ensemble learning (DAEL), takes the first step toward a general framework for generalizing neural networks from multiple source domains to a target domain. When target data are not provided (the DG problem), DAEL shows promising out-of-distribution generalization performance on PACS and Office-Home. When unlabeled target data are accessible (the UDA problem), DAEL leverages pseudo labels and follows the same collaborative ensemble learning strategy as used in the DG setting to prompt the emergence of domain-generalizable features. Currently, to avoid overfitting to noisy pseudo labels, advanced data augmentation methods are used. However, the design of data augmentation is often task-specific, e.g., for digit recognition we cannot use random flip; for fine-grained recognition, color
+
+distortion might be discarded. Future work can focus on new algorithmic designs to mitigate the overfitting problem in a more flexible way.
+
+# APPENDIX A
+
+# IMPLEMENTATION DETAILS
+
+Experiments on domain adaptation. SGD with momentum is used as the optimizer, and the cosine annealing rule [73] is adopted for learning rate decay. For Digit-5, the CNN backbone is constructed with three convolution layers and two fully connected layers [18]. For each mini-batch, we sample from each domain 64 images. The model is trained with an initial learning rate of 0.05 for 30 epochs. For DomainNet, we use ResNet101 [58] as the CNN backbone and sample from each domain 6 images to form a mini-batch. The model is trained with an initial learning rate of 0.002 for 40 epochs. For miniDomainNet, we use ResNet18 [58] as the CNN backbone. Similarly, we sample 64 images from each domain to form a mini-batch and train the model for 60 epochs with an initial learning rate of 0.005. For all UDA experiments, we set  $\lambda_u = 0.5$  in all datasets. The sensitivity of  $\lambda_u = 0.5$  to performance is investigated in Fig. 5.
+
+Experiments on domain generalization. ResNet18 is used as the CNN backbone as in previous works [54, 67]. SGD with momentum is used to train the model for 40 epochs with an initial learning rate of 0.002. The learning rate is further decayed by the cosine annealing rule. Each mini-batch
+
+contains 30 images (10 per source domain). Note that the  $\mathcal{L}_u$  term in Eq.(4) is discarded here as no target data is available for training.
+
+# APPENDIX B PSEUDO-CODE
+
+The full algorithm of domain adaptive ensemble learning is presented in Alg. 1.
+
+# Algorithm 1 Pseudo-code for loss computation in DAEL.
+
+1: Require: labeled source mini-batches  $\{(X^i,Y^i)\}_{i = 1}^K$ , unlabeled target mini-batch  $X^t$ , source experts  $\{E_i\}_{i = 1}^K$ , weak/strong augmentation  $a(\cdot) / A(\cdot)$ , hyper-parameter  $\lambda_{u}$ .  
+2: Return: loss  $\mathcal{L}$ .  
+3:  $\mathcal{L}_{ce} = 0$  // Initialize  $\mathcal{L}_{ce}$  
+4:  $\mathcal{L}_{cr} = 0$  // Initialize  $\mathcal{L}_{cr}$  
+5: for  $i = 1$  to  $K$  do  
+6: // Domain-specific expert learning  
+7:  $\tilde{X}^i = a(X^i)$  // Apply weak augmentation to  $X^i$  
+8:  $\tilde{Y}^i = E_i(\tilde{X}^i)$  // Compute prediction for expert-i  
+9:  $\mathcal{L}_{ce} = \mathcal{L}_{ce} + \mathrm{CrossEntropy}(\tilde{Y}^i, Y^i)$  // Compute cross-entropy loss for expert-i  
+10: // Collaborative ensemble learning for source data  
+11:  $\hat{X}^i = A(X^i)$  // Apply strong augmentation to  $X^i$  
+12:  $\hat{Y}^i = \frac{1}{K - 1}\sum_{j\neq i}E_j(\hat{X}^i)$  // Compute ensemble prediction of non-experts  
+13:  $\mathcal{L}_{cr} = \mathcal{L}_{cr} + \mathrm{MSE}(\hat{Y}^i, \tilde{Y}^i)$  // Compute consistency loss for non-experts  
+14: end for  
+15:  $\mathcal{L}_{ce} = \mathcal{L}_{ce} / K$  
+16:  $\mathcal{L}_{cr} = \mathcal{L}_{cr} / K$  
+17:  $\mathcal{L} = \mathcal{L}_{ce} + \mathcal{L}_{cr}$  
+18: if  $X^t$  is available then  
+19: // Collaborative ensemble learning for unlabeled target data  
+20:  $\tilde{X}^t = a(X^t)$  // Apply weak augmentation to  $X^t$  
+21:  $\tilde{Y}^t, M = \text{PseudoLabel}(\{E_i(\tilde{X}^t)\}_i) // \text{Get pseudo labels and instance masks}$  
+22:  $\hat{X}^t = A(X^t)$  // Apply strong augmentation to  $X^t$  
+23:  $\hat{Y}^t = \frac{1}{K}\sum_iE_i(\hat{X}^t)$  // Compute ensemble prediction of all experts  
+24:  $\mathcal{L}_u =$  CrossEntropy  $(\hat{Y}^t,\tilde{Y}^t,M)$  // Compute cross-entropy loss for all experts  
+25:  $\mathcal{L} = \mathcal{L} + \lambda_u\mathcal{L}_u$  
+26: end if
+
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+    {
+        "type": "text",
+        "text": "Resolution Adaptive Networks for Efficient Inference",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Le Yang $^{1*}$  Yizeng Han $^{1*}$  Xi Chen $^{2*†}$  Shiji Song $^{1}$  Jifeng Dai $^{3}$  Gao Huang $^{1‡}$",
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+        "text": "Tsinghua University,",
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+        "text": "Beijing National Research Center for Information Science and Technology (BNRist)",
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+    {
+        "type": "text",
+        "text": "$^{2}$ Harbin Institute of Technology  $^{3}$ SenseTime",
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "{yangle15, hanyz18}@mails.tsinghua.edu.cn, {shijis, gaohuang}@tsinghua.edu.cn,",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "xi.chen@stu.hit.edu.cn, daijifeng@sensetime.com",
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+        "type": "text",
+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "Adaptive inference is an effective mechanism to achieve a dynamic tradeoff between accuracy and computational cost in deep networks. Existing works mainly exploit architecture redundancy in network depth or width. In this paper, we focus on spatial redundancy of input samples and propose a novel Resolution Adaptive Network (RANet), which is inspired by the intuition that low-resolution representations are sufficient for classifying \"easy\" inputs containing large objects with prototypical features, while only some \"hard\" samples need spatially detailed information. In RANet, the input images are first routed to a lightweight sub-network that efficiently extracts low-resolution representations, and those samples with high prediction confidence will exit early from the network without being further processed. Meanwhile, high-resolution paths in the network maintain the capability to recognize the \"hard\" samples. Therefore, RANet can effectively reduce the spatial redundancy involved in inferring high-resolution inputs. Empirically, we demonstrate the effectiveness of the proposed RANet on the CIFAR-10, CIFAR-100 and ImageNet datasets in both the anytime prediction setting and the budgeted batch classification setting.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Although advances in computer hardware have enabled the training of very deep convolutional neural networks (CNNs), such as ResNet [8] and DenseNet [14], the high computational cost of deep CNNs is still unaffordable in many applications. Many efforts have been made to speed up the inference of deep models, e.g., lightweight network architecture design [10, 31, 42, 13], network pruning",
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+        "type": "image",
+        "img_path": "images/b5928b30188545ce8634233f0503e93addd7478bd93cbea56dcd9f74f93618b1.jpg",
+        "image_caption": [
+            "Figure 1. Classifying images of owls. In (a), the canonical sample can be recognized by the Sub-network 1 with the lowest resolution, and thus the following sub-networks will be unused. For the \"hard\" image in (b), the Sub-network 1 fails to provide a reliable prediction. Therefore, classifying this sample requires computationally more expensive sub-networks with finer features."
+        ],
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+        "text": "[20, 22, 26] and weight quantization [15, 29, 17]. Among them, the adaptive inference scheme [24, 37, 12, 36], which aims to reduce the computational redundancy on \"easy\" samples by dynamically adjusting the network structure or parameters conditioned on each input, has been shown to yield promising performance.",
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+    {
+        "type": "text",
+        "text": "Most existing works on adaptive inference focus on reducing the network depth or width for images with easily",
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+    {
+        "type": "aside_text",
+        "text": "arXiv:2003.07326v5 [cs.CV] 18 May 2020",
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+    {
+        "type": "page_footnote",
+        "text": "*Equal Contribution.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "This work is done when Xi Chen was an intern at Tsinghua University.",
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+    {
+        "type": "page_footnote",
+        "text": "‡Corresponding author",
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+    {
+        "type": "page_number",
+        "text": "1",
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+    {
+        "type": "text",
+        "text": "recognizable features. It has been shown that the intrinsic classification difficulty for different samples varies drastically: some of them can be correctly classified by smaller models with fewer layers or channels, while some may need larger networks [24, 37, 12, 36]. By exploiting this fact, many works have been proposed recently. For example, the model in [24] executes runtime pruning of convolutional kernels with a policy learned by reinforcement learning strategies. The network in [37] inserts a linear layer before each convolutional layer to generate a binary decision on whether executing the following convolutional operation dynamically. Multi-Scale Dense Network (MSDNet) [12] allows some samples to exit at some auxiliary classifiers conditioned on their prediction confidence.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we consider adaptive inference from a novel perspective. In contrast to existing works focusing on the computational redundancy in the network structure, we aim to exploit the information redundancy in the data samples. Our motivation is that low-resolution feature representations are sufficient to classify \"easy\" samples (as shown in the top row in Figure 1), while applying high-resolution feature maps to probe the details is necessary for accurately recognizing some \"hard\" samples (as shown in the bottom row in Figure 1). This further agrees with the \"coarse to fine processing\" efficient algorithm design in [18]. From a signal frequency viewpoint [4], \"easy\" samples could be correctly classified with low-frequency information contained in low-resolution features. High-frequency information is only utilized as complementary for recognizing \"hard\" samples when we fail to precisely predict the samples with low-resolution features.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Based on the above intuition, we propose a Resolution Adaptive Network (RANet) that implements the idea of performing resolution adaptive learning in deep CNNs. Figure 1 illustrates the basic idea of RANet. It is composed of sub-networks with different input resolutions. The \"easy\" samples are classified by the sub-network with the feature maps in the lowest spatial resolution. The sub-networks with higher resolution will be applied when the previous sub-network fails to achieve a given criterion<sup>1</sup>. Meanwhile, the coarse features from the previous sub-network will be reused and fused into the current sub-network. The adaptation mechanism of RANet reduces computational budget by avoiding performing unnecessary convolutions on high-resolution features when samples can be accurately predicted with low-resolution representations, leading to improved computational efficiency.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We evaluate the RANet on three image classification datasets (CIFAR-10, CIFAR-100, and ImageNet) under the anytime classification setting and the budgeted batch classification setting, which are introduced in [12]. The exper",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "iments show the effectiveness of the proposed method in adaptive inference tasks.",
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+    {
+        "type": "text",
+        "text": "2. Related work",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Efficient inference for deep networks. Many previous works explore variants of deep networks to speed up the network inference. One direct solution is designing lightweight models, e.g., MobileNet [10, 31], ShuffleNet [42, 27] and CondenseNet [13]. Other lines of research focus on pruning redundant network connections [20, 22, 26], or quantizing network weights [15, 29, 17]. Moreover, knowledge distilling [9] is proposed to train a small (student) network which mimics outputs of a deeper and/or wider (teacher) network.",
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+    {
+        "type": "text",
+        "text": "The aforementioned approaches can be seen as static model acceleration techniques, which infer all input samples with a whole network consistently. In contrast, adaptive networks can strategically allocate appropriate computational resources for classifying input images based on input complexity. This research direction is gaining increasing attention in recent years due to its advantages. The most intuitive implementation is assembling multiple models and selectively executing a subset of the models in a cascading [2] or mixing way [32, 30]. Recent works also propose to adaptively skip layers or blocks [7, 37, 39, 40], or dynamically select channels [24, 3, 1] during inference time. Auxiliary predictors can also be attached at different locations of a deep network to allow early exiting \"easy\" examples [35, 12, 11, 23]. Furthermore, dynamically activating parts of network branches with multi-branch structure [36] also provide an alternate way for adaptive inference.",
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+    {
+        "type": "text",
+        "text": "However, most of these prior works focus on designing adaptive networks by exploiting architecture redundancy of networks. As spatial redundancy of input images has been certified in recent work [4], this paper proposes a novel adaptive learning model which exploits both structural redundancy of a neural network and spatial redundancy of input samples.",
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+    {
+        "type": "text",
+        "text": "Multi-scale feature maps and spatial redundancy. As the downsampling operation in networks with a single scale [8, 14] may restrict the networks' ability to recognize an object in an arbitrary scale, recent studies propose to adopt multi-scale feature maps in a network to simultaneously utilize both coarse and fine features, which significantly improves the network performance in many vision tasks, including image classification [18], object detection [25], semantic segmentation [43] and pose estimation [33]. Moreover, the multi-scale structure shows a promising ability in adaptive inference [12] and memory-efficient network [38].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "While keeping high-resolution feature maps through a deep neural network is found to be necessary for recognizing some atypical \"hard\" samples or some specific tasks such as pose estimation [33], frequently operating convolu",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>In this paper, we use the prediction confidence from the softmax probability.",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2",
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+    {
+        "type": "text",
+        "text": "tions on high-resolution features usually results in resource-hungry models. It has been observed that lightweight networks can yield a decent error rate for all samples with low-resolution inputs [10]. The spatial redundancy in these convolutional neural networks has also been studied in [4], where the octave convolution in the network processing feature maps with small scales improves the computational efficiency and the classification performance simultaneously. Moreover, ADASCALE proposed in [5] also adaptively selects the input image scale that improves both accuracy and speed for video object detection.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "However, none of these existing works considers designing an adaptive model by exploiting spatial redundancy in images. In this paper, we propose our RANet for resource-efficient image classification, motivated by the intuition that a smaller scale can be capable of handling most of input samples. Compared to ADASCALE [5], which also adaptively selects the input image scale for vision task, the proposed RANet can be implemented for the budgeted classification setting during adaptive inference. Our work achieves resolution adaptation by classifying some of inputs on small scales and allowing larger scales to be processed only when inputs can not be recognized with coarse representations. The resolution adaptation in RANet significantly improves its computational efficiency without sacrificing accuracy.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce the idea of adaptive inference, then we demonstrate the overall architecture and the network details of our proposed RANet.",
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+    {
+        "type": "text",
+        "text": "3.1. Adaptive Inference Setting",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We set up an adaptive inference model as a network with  $K$  classifiers, where these intermediate classifiers are attached at varying depths of the model. Given an input image  $\\mathbf{x}$ , the output of the  $k$ -th classifier  $(k = 1,\\dots ,K)$  can be represented by",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {p} ^ {k} = f _ {k} (\\mathbf {x}; \\theta_ {k}) = \\left[ p _ {1} ^ {k}, \\dots , p _ {C} ^ {k} \\right] ^ {\\mathrm {T}} \\in \\mathbb {R} ^ {C}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\theta_{k}$  denotes the parameters of the partial network corresponding to the  $k$ -th classifier, and each element  $p_c^k \\in [0,1]$  is the prediction confidence for the  $c$ -th class. Note that  $\\theta_{k}$ 's have shared parameters here.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The adaptive model infers a sample by dynamically allocating appropriate computational resources depending on the complexity of this sample. A sample will exit the network at the first classifier whose output satisfies a certain criterion. In this paper, we use the highest confidence of the softmax output as our decision basis, which means that the final output will be the prediction of the first classifier whose largest softmax output is greater than a given thresh-",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "old  $\\epsilon$ . This can be represented by",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nk ^ {*} = \\min  \\left\\{k \\mid \\max  _ {c} p _ {c} ^ {k} \\geq \\epsilon \\right\\}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {y} \\in \\arg \\max  _ {c} p _ {c} ^ {k ^ {*}}. \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "The threshold  $\\epsilon$  controls the trade-off between classification accuracy and computational cost at test time.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Overall Architecture",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Figure 2 illustrates the overall architecture of the proposed RANet. It contains an Initial Layer and  $H$  subnetworks corresponding to different resolutions. Each subnetwork has multiple classifiers at the last few blocks. Similar to MSDNet [12], we adopt a multi-scale architecture and dense connection in our approach. Although RANet and MSDNet have a similar multi-scale structure, their detailed architecture designs and computation graphs differ significantly. The most prominent difference is that RANet needs to extract low-resolution features first, which does not follow the traditional design routine in classical deep CNNs (including MSDNet, ResNet, DenseNet, etc.) that all extract high-resolution features first. More details of the differences between MSDNet and our RANet will be discussed in Section 3.4.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The basic idea of RANet is that the network will first predict a sample with the first sub-network, using feature maps of the lowest spatial resolution to avoid the high computational cost induced by performing convolutions on large scale features. If the first sub-network makes an unreliable prediction of the sample, the small scale intermediate features will be fused into the next sub-network with a higher resolution. The classification task is then conducted by the next sub-network with larger scale features. This procedure is repeated until one sub-network yields a confident prediction, or the last sub-network is utilized.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The adaptive inference procedure of RANet is further illustrated in Figure 2: with  $H$  sub-networks ( $H = 3$  in the illustration) and an input sample  $\\mathbf{x}$ , the network will first generate  $H$  base feature maps in  $S$  scales (For instance, there are 3 scales in the illustration, and  $s = 1$  represents the lowest resolution). The base features in scale  $s$  corresponding to Sub-network  $h$  can be denoted as  $\\mathbf{x}_0^{s,h}$ ,  $s = 1,2,\\ldots,S, h = 1,2,\\ldots,H$ . Then the classification task is first conducted by Sub-network 1 using features  $\\mathbf{x}_0^{1,1}$  at the bottom. If Sub-network 1 fails to achieve the classification result with a high confidence, Sub-network 2, which processes larger scale features ( $\\mathbf{x}_0^{2,2}$ ), will be utilized for further classifying the sample. The intermediate features in Sub-network 1 are successively fused into Sub-network 2. We repeat this procedure for Sub-network 3 if Sub-network 2 fails to make a confident prediction.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It is worth noting that even RANet processes inputs from coarse to fine in general, each sub-network in RANet",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/4920a6f6ccea20eb44ad20bd858f48141cb9344783aedee1a6fb9e1d4c28c18b.jpg",
+        "image_caption": [
+            "Figure 2. The illustration of an RANet with three scales. Classifiers only operate on feature maps at the lowest resolution."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "still downsamples features during forward propagation until reaching the lowest resolution  $(s = 1)$ , and all the classifiers are only attached at the last few blocks with  $s = 1$  in each sub-network.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The aforementioned inference procedure meets our intuition for image recognition. An \"easy\" sample with representative characteristics can be correctly classified sometimes with high confidence even only low-resolution representations are provided. A \"hard\" sample with atypical features can only be correctly recognized based on global information accompanied with fine details, which are extracted from high-resolution feature maps.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Network Details",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This subsection provides more detailed introductions about each component in RANet.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3.1 Initial Layer",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "An Initial layer is implemented to generate  $H$  base features in  $S$  scales and it only includes vertical connections in Figure 2. One could view its vertical layout as a miniature \"H-layers\" convolutional network ( $H$  is the number of base features in the network). Figure 2 shows an RANet with 3 base features in 3 scales. The first base features with the largest scale is derived from a Regular-Conv layer $^2$ , and the coarse features are obtained via a Strided-Conv layer $^3$  from the former higher-resolution features. It is worth noting that the scales of these base features can be the same. For instance, one could have an RANet with 4 base features in 3 scales, where the scales of the last two base features are of the same resolution.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/76200f16aa6df6eb417894eca44c8fcd39ec857bdbac71f399bd396e89182111.jpg",
+        "image_caption": [
+            "Figure 3. Two kinds of Conv Blocks in RANet: Dense Block, (a), and Fusion Block, (b,c). Moreover, the block in (b) maintains the input resolution of the feature maps, while the block in (c) down-samples the features by a factor of 2 at the end of the block."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3.2 Sub-networks with Different Scales",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "As the Initial layer generates  $H$  base features, the proposed network can then be separated into  $H$  sub-networks, which are further composed by different Conv Blocks. Each subnetwork, except the first one, conducts the classification task with its corresponding base feature maps and features from the previous sub-network.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Sub-network 1. Sub-network 1 with input  $\\mathbf{x}_0^{1,1}$  processes the lowest-resolution features. We adopt regular Dense Blocks [14] with  $l$  layers in Sub-network 1, which is shown in Figure 3 (a). Moreover, the  $i$ -th layer's output  $\\mathbf{x}_i^{1,1}, i = 1,2,\\ldots l$  in each Dense Block is also propagated to Sub-network 2 to reuse the early features. In general, one can view Sub-network 1 as a DenseNet with multiple classifiers, processing the lowest-resolution feature maps.",
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+    {
+        "type": "text",
+        "text": "Sub-networks on larger-scale features. Sub-network  $h$  ( $h > 1$ ) with scale  $s$  processes the base features  $\\mathbf{x}^{s,h}$  and",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "2A Regular-Conv layer in this paper is consisted of a bottleneck layer and a regular convolution layer. Each layer is composed of a Batch normalization (BN) layer [16], a ReLU layer [28] and a convolution layer. 3A Strided-Conv layer is realized by setting the stride of the second convolution in Regular-Conv layer as 2.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "fuses the features from Sub-network  $(h - 1)$ . We call Conv Blocks with feature fusion as Fusion Blocks (shown in Figure 3 (b, c)). Suppose that Sub-network  $(h - 1)$  has  $b_{h - 1}$  blocks, then the first  $b_{h - 1}$  blocks in Sub-network  $h$  will all be Fusion Blocks.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We design two different ways of feature fusion. One maintains the input resolution, which is illustrated in Figure 3 (b), while the other reduces the feature scale by a Strided-Conv layer, as shown in Figure 3 (c). To generate new feature maps with higher resolution as inputs, the Fusion Block in Figure 3 (b) first produces  $\\mathbf{x}_{\\mathrm{in}}^{s,h}$  with a Regular-Conv layer. Features in scale  $(s - 1)$  from the previous subnetwork is processed by an Up-Conv layer, which is composed of a Regular-Conv layer and an up-sampling bilinear interpolation. This ensures the produced features are of the same spatial resolution. The resulting features are then fused through concatenation with dense connection.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As shown in Figure 3 (c), a Fusion Block with downsampling utilizes a Strided-Conv layer to reduce the spatial resolution at the end of the block. Concatenation with dense connection is also conducted after a pooling operation as shown by a blue dashed arrow. Since the feature scale is reduced in the current sub-network, features from the previous sub-network are processed by a Regular-Conv layer to maintain the low resolution, and then fused by concatenation at the end of the block in Figure 3 (c).",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Sub-network  $h$  with scale  $s$  can be established as follow: for a sub-network with  $b_h$  blocks, block 1 to block  $b_{h-1}$  ( $b_{h-1} < b_n$ ) are all Fusion Blocks, while the rest of them are regular Dense Blocks. Moreover, we downsample the feature maps  $s$  times at the  $b_{h-s}, \\ldots, b_{h-1}$ -th blocks during forward propagation. This ensures that at the end of each sub-network where we attach classifiers, the features must be of the lowest resolution.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Transition layer. Similar to the architecture design in [14] and [12], we implement Transition layers to further compress the feature maps in each sub-network. The design of a Transition layer is exactly the same as the one in [14] and [12], which is composed of a  $1 \\times 1$  convolution operator following by a BN layer and a ReLU layer. Transition layers further guarantee the computational efficiency of the proposed network. For simplicity, we omit these Transition Layers in Figure 2.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Classifiers and loss function. The classifiers are implemented at the last few blocks of different sub-networks. At the training stage, we let input samples pass through Subnetwork 1 to Sub-network  $H$  sequentially and cross-entropy loss function is used for each classifier. We set the overall loss function for RANet as a weighted cumulative loss of these classifiers. We empirically follow the settings in [12] and use the same weight for all loss functions in this paper.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/03a74cd60a41820c9a9c586d9647cba683f05d9ec9f4238376d3723841fea9d4.jpg",
+        "image_caption": [
+            "(a) MSDNet"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            531,
+            99,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/f55daff2b0199288c97c246caca331c517508fb1976a7a382750d7add671274a.jpg",
+        "image_caption": [
+            "(b) RANet",
+            "Figure 4. Depth adaptation in MSDNet (a) and resolution-depth adaptation in our RANet (b). Different shaded areas represent the network blocks with varied computational costs, and the colored arrows represent the feature propagation path. The lighter the color is, the earlier the propagation is executed. The dashed arrows in (b) indicate that RANet adopts a zigzag-shape computation graph from the bottom to the top."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            671,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.4. Resolution and Depth Adaptation",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our proposed RANet can simultaneously implement the idea of depth adaptation, which is adopted in MSDNet [12], and resolution adaptation. Figure 4 illustrates the main differences between MSDNet (left) and our RANet (right). In MSDNet, the classifiers are located at the lowest resolution scale, and once an intermediate predictor does not yield a confident prediction, the following layers of all scales will be executed. However, in our RANet, the Dense Blocks with the smallest scale input are first activated sequentially and the depth adaptation is conducted within a single scale. If the previous sub-network cannot make a confident prediction, the input sample will be propagated to the next subnetwork and repeat the depth adaptation process until the prediction confidence meets the criterion, or the last classifier of the whole network is reached. Such an inference scheme naturally combines resolution and depth adaptation, achieving significant improvement over MSDNet.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the effectiveness of our approach, we conducted experiments on the CIFAR [19] and ImageNet [6] datasets. The code is available at https://github.com/yangle15/RANet-pytorch. The implementation details of RANets and MSDNets in our experiments are described in Appendix A.",
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+    {
+        "type": "text",
+        "text": "Datasets. The CIFAR-10 and CIFAR-100 datasets contain  $32 \\times 32$  RGB natural images, corresponding to 10 and 100 classes, respectively. The two datasets both contain 50,000 training and 10,000 testing images. Following [12], we hold out 5,000 images in the training set as a validation set to search the optimal confidence threshold for adaptive inference. The ImageNet dataset contains 1.2 million images of 1,000 classes for training, and 50,000 images for validation. For adaptive inference tasks, we use the original validation set for testing, and hold out 50,000 images from",
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+        "text": "5",
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+        "type": "text",
+        "text": "the training set as a validation set.",
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+    {
+        "type": "text",
+        "text": "Training policy. We train the proposed models using stochastic gradient descent (SGD) with a multi-step learning rate policy. The batch size is set to 64 and 256 for the CIFAR and ImageNet datasets, respectively. We use a momentum of 0.9 and a weight decay of  $1 \\times 10^{-4}$ . Moreover, for the CIFAR datasets, the models are trained from scratch for 300 epochs with an initial learning rate of 0.1, which is divided by a factor of 10 after 150 and 225 epochs. The same training scheme is applied to the ImageNet dataset. And we train the models for 90 epochs from scratch and the initial learning rate decreases after 30 and 60 epochs.",
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+    {
+        "type": "text",
+        "text": "Data augmentation. We follow [8] and apply standard data augmentation schemes on the CIFAR and ImageNet datasets. On the two CIFAR datasets, images are randomly cropped to samples with  $32 \\times 32$  pixels after zero-padding (4 pixels on each side). Furthermore, images are horizontally flipped with probability 0.5 and RGB channels are normalized by subtracting the corresponding channel mean and divided by their standard deviation. On ImageNet, we follow the data augmentation scheme in [8] for training, and apply a  $224 \\times 224$  center crop to images at test time.",
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+    {
+        "type": "text",
+        "text": "4.1. Anytime Prediction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In the anytime prediction setting [12], we evaluate all classifiers in an adaptive networks and report their classification accuracies with corresponding FLOPs (floating point operations).",
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+        "type": "text",
+        "text": "Baseline models. Following the setting in [12], in addition to MSDNet, we also evaluate several competitive models as our baselines, including ResNet $^{\\text{MC}}$ , DenseNet $^{\\text{MC}}$  [21], and ensembles of ResNets and DenseNets of varying sizes. Details on architectural configurations of MSDNets and RANets in the experiments are described in Appendix A. As recent research in [23] investigates improved techniques for training adaptive networks, we further evaluate these techniques on both RANet and MSDNet. The experiments show that the computational efficiency of the RANet can be further improved and outperforms the improved MSDNet. The results are provided in Appendix B.",
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+    {
+        "type": "text",
+        "text": "Results. We report classification accuracies of all individual classifiers in our model and other baselines. The results are summarized in Figure 5. The evaluated MSD-Nets and RANets are depicted by black and yellow lines, respectively. In general, MSDNet substantially outperforms other baseline models, and RANet are superior to MSDNet, especially when the computational budget is low.",
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+        "type": "text",
+        "text": "In particular, on CIFAR-10 (CIFAR-100), the accuracies of different classifiers for RANet are over  $1\\%$ $(2\\% -5\\%)$  higher than those of MSDNet when the computational budget ranges from  $0.1\\times 10^{8}$  to  $0.5\\times 10^{8}$  FLOPs. Moreover, compared to MSDNet, RANet achieves its highest accuracy with less computational demands (around  $0.25\\times 10^{8}$",
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+    {
+        "type": "text",
+        "text": "FLOPS). On ImageNet, the proposed network outperforms MSDNet by around  $1\\% - 7\\%$  when the budget ranges of  $0.5 \\times 10^{9}$  to  $1.5 \\times 10^{9}$  FLOPs. Although both MSDNet and RANet achieve similar classification accuracy ( $74\\%$ ) at the last classifier, our model only uses around  $27\\%$  fewer FLOPs compared to MSDNet.",
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+    {
+        "type": "text",
+        "text": "At the first classifier, the accuracies of RANets are  $2\\%$  and  $5\\%$  higher than those of MSDNets on CIFAR-10 and CIFAR-100, respectively. On the ImageNet dataset, RANet still slightly outperforms MSDNet at the first classifier. With  $1.0 \\times 10^{9}$  FLOPs, RANet can achieve a classification accuracy of around  $68\\%$ , which is around  $5\\%$  higher than that achieved by MSDNet. We also observe that ensembles of ResNets outperform MSDNets in low-budget regimes, because the predictions of ensembles are performed by the first lightweight networks, which are optimized exclusively for the low budget. However, RANets are consistently superior to ensembles of ResNets on all datasets. This meets our expectation that Sub-network 1 with the first classifier in RANet is specially optimized for recognizing \"easy\" samples. Since Sub-network 1 directly operates on the feature maps with the lowest resolution, it avoids performing the convolutions on high-resolution feature maps, which results in the high computational efficiency of the first classifier. Furthermore, as Sub-network 1 in RANets can be viewed as exclusively optimized lightweight models, the early classifiers of RANets show their advantages in the classification tasks. Different from ResNet ensembles, which repeat the computation of similar low-level representations, RANets fuse the feature maps from previous lightweight networks into a large network to make full use of the obtained features. This mechanism effectively improves classification accuracies when we have more computational resources.",
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+    {
+        "type": "text",
+        "text": "4.2. Budgeted Batch Classification",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The budgeted batch classification setting is described in [12]. We set a series of thresholds that depend on different computational budgets. For a given input image, we let it pass through each classifier in an adaptive network, sequentially. The forward propagation stops at the classifier whose output confidence reaches the given threshold, and then we report its prediction as the final result for this image.",
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+        "type": "text",
+        "text": "Baseline models. For CIFAR-10 and CIFAR-100, we use ResNet, DenseNet and DenseNet* [12] as baseline models. For ImageNet, we additionally evaluate ResNet and DenseNet with multi-classifier [21]. Performance of some classical deep models are also reported in the experimental results, such as WideResNet [41] (for CIFAR) and GoogLeNet [34] (for ImageNet). See Appendix A for details about the architecture configurations of MSDNets and RANets in the experiments. Moreover, we implement the techniques in [23] to further evaluate the improved RANets and MSDNets. The results are provided in Appendix B.",
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+        "image_caption": [
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+        "image_caption": [
+            "Figure 5. Accuracy (top-1) of anytime prediction models as a function of computational budget on CIFAR-10 (left), CIFAR-100 (middle) and ImageNet (right). Higher is better.",
+            "(a)",
+            "Figure 6. Accuracy (top-1) of budgeted batch classification models as a function of average computational budget per image on CIFAR-10 (left), CIFAR-100 (middle) and ImageNet (right). Higher is better."
+        ],
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+    {
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+        "text": "Results. The results are summarized in Figure 6. We plot the classification accuracy of each MSDNet and RANet in a gray and a light-yellow curve, respectively. We select the best model for each budget based on its accuracy on the test set, and plot the corresponding accuracy as a black curve (for MSDNet) or a golden curve (for RANet).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The results on the two CIFAR datasets show that RANets consistently outperform MSDNets and other baseline models across all budgets. In general, the networks with multiscale dense connection architecture are always substantially more accurate than other baseline models with the same amount of computation cost under the budgeted batch classification setting. For low computational budget (less than  $0.2 \\times 10^{8}$  FLOPs), on CIFAR-10, the proposed model uses  $20\\%$  fewer FLOPs to achieve the classification accuracy of  $92\\%$  compared to MSDNet. On CIFAR-100, RANet can achieve the classification accuracy of  $68\\%$  with only about  $60\\%$  FLOPs compared to MSDNet. Even though our model and MSDNet show close performance on CIFAR-10 when the computational budget ranges from  $0.2 \\times 10^{8}$  to  $0.3 \\times 10^{8}$ , the classification accuracies of RANets are consistently higher than ( $1\\%$ ) these of MSDNets on CIFAR-",
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+    {
+        "type": "text",
+        "text": "100 in median and high budget intervals (over  $0.2 \\times 10^{8}$  FLOPs). Moreover, our model can achieve an accuracy of  $94.2\\%$  when the budget is higher than  $0.2 \\times 10^{8}$  FLOPs. This accuracy is  $0.5\\%$  higher than that of MSDNet under the same computational budget condition. The experiments also show that RANets are up to 4 times more efficient than WideResNets on CIFAR-10 and CIFAR-100.",
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+    {
+        "type": "text",
+        "text": "The experiments on ImageNet yield similar results to those on CIFAR. We observe that RANets consistently surpass MSDNets. Our networks win about  $0.5\\%$ ,  $1\\%$  and  $1.2\\%$  in terms of top-1 accuracy with  $0.75 \\times 10^{9}$ ,  $1 \\times 10^{9}$  and  $1.75 \\times 10^{9}$  FLOPs respectively. The results indicate that our RANet outperforms MSDNet by a larger margin as more computational resources are provided. With the same FLOPs, our models achieve more accurate classification results than these popular deep neural networks. With the same classification accuracy, our model reduces the computational budget by around  $65\\%$ ,  $56\\%$  and  $44\\%$  compared to GoogLeNet, ResNets and DenseNets, respectively. All these results demonstrate that the resolution adaptation along with the depth adaptation can significantly improve the performance of adaptive networks under the budgeted",
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+        "type": "page_number",
+        "text": "7",
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+    {
+        "type": "image",
+        "img_path": "images/d5a96413de90a31db4499c9082879b08edfcd8ebe56a32db6837e259755797fe.jpg",
+        "image_caption": [
+            "Figure 7. Visualization of ImageNet samples: Owl, Hummingbird and German Shepherd. The column on the left of each sub-figure: the images that exit from the earlier classifiers (\"easy\" samples); The column on the right of each sub-figure: the images that fail to be correctly classified at the earlier classifiers but are successfully recognized at the last few classifiers (\"hard\" samples)."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "batch classification setting.",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.3. Visualization and Discussion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Figure 7 illustrates the ability of RANet to recognize samples with different difficulties. In each sub-figure, the left column shows \"easy\" samples that are correctly classified by the earlier classifiers with high classification confidence. The right column shows \"hard\" samples that fail to reach sufficient confidence at the early exits and are passed on to the deeper sub-networks handling high-resolution features. The figure suggests that the earlier classifiers can recognize prototypical samples of a category, whereas the later classifiers are able to recognize non-typical samples, which is similar to the experimental results in [12].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "It is also observed that the high-resolution feature maps and their corresponding sub-networks are necessary for accurately classifying the object in three different cases.",
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+    {
+        "type": "text",
+        "text": "- Multiple objects. We find that an image containing multiple objects can be viewed as a \"hard\" sample for RANet. The co-occurrence of different objects may corrupt the feature maps and therefore confuse the early classifiers. In this case, the relationship between each object is a key factor that can seriously affect the categorical prediction of the whole image. For example, in Figure 7 (a), the ImageNet dataset refers the image with an owl on a man's hand as the class \"owl\", even though there are two people in this image. Apparently, rapid downsampling could submerge the own in the image and the network can recognize it as the class \"person\". Furthermore, categorizing this image as the class \"owl\" may result from human perception that we consider objects on a person's hand at the center of an image as more important information. This complex relationship can only be exploited with stronger representations learned by a powerful network.",
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+    {
+        "type": "text",
+        "text": "- Tiny objects. It is observed that the images with tiny",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "objects always pass through the whole network and thus are also considered as \"hard\" samples for RANet. A possible explanation for this phenomenon is that the information of these tiny target objects in the images can be completely lost after rapidly downsampling the images. The clues for classifying those tiny objects can only be obtained by processing the high-resolution feature maps. For instance, in the right image on the second row of Figure 7 (b), the hummingbird drinking water is too small. Therefore, the representations of the hummingbird can easily be lost due to the rapid downsample operations and might be completely vanished in the coarse feature maps. This makes the image unable to be recognized until the high-resolution feature maps are used for inference, which results in its late exiting in our adaptive inference network.",
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+    {
+        "type": "text",
+        "text": "- Objects without representative characteristics. Another kind of \"hard\" samples for RANet contain objects without representative characteristics. Such samples are not uncommon due to various factors (such as lighting conditions and shooting angles). In this scenario, we conjecture that the network learns to utilize alternative characteristics instead of representative ones for image recognition. For instance, by comparing the \"easy\" and \"hard\" samples in Figure 7 (c), the network can easily recognize the German Shepherd as long as its facial features are presented completely in the images. However, without complete facial features, a German Shepherd can only be correctly classified at the last classifier. For those \"hard\" samples, the network may take the fur texture of the German Shepherd as the alternative discriminative features during inference. Therefore, without complete facial information, the network learns to correctly classify German Shepherd by searching useful alternative characteristics in high-resolution feature maps.",
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+    {
+        "type": "text",
+        "text": "The rationality and effectiveness of the resolution adaptation can be further understood from the signal frequency perspective, which has been demonstrated and verified in [4]. The low-frequency information encoded in low-resolution features, which usually contains global information, can be sufficient for successful classification of most input samples. Nevertheless, higher frequencies encoded with fine details are obligatory for classifying those untypical samples.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we proposed a novel resolution adaptive neural network based on a multi-scale dense connection architecture, which we refer to as RANet. RANet is designed in a way that lightweight sub-networks processing coarse features are first utilized for image classification. Samples with high prediction confidence will exit early from the network and larger scale features with finer details will only be further utilized for those non-typical images which achieve",
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+    {
+        "type": "page_number",
+        "text": "8",
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+    {
+        "type": "text",
+        "text": "unreliable predictions in previous sub-networks. This resolution adaptation mechanism and the depth adaptation in each sub-network of RANet guarantee its high computational efficiency. On three image classification benchmarks, the experiments demonstrate the effectiveness of the proposed RANet in both the anytime prediction setting and the budgeted batch classification setting.",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "This work is supported by grants from the Institute for Guo Qiang of Tsinghua University, National Natural Science Foundation of China (No. 61906106) and Beijing Academy of Artificial Intelligence (BAAI).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            296,
+            174,
+            311
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
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+        ],
+        "bbox": [
+            78,
+            90,
+            467,
+            659
+        ],
+        "page_idx": 9
+    },
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+        "text": "10",
+        "bbox": [
+            477,
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+            936
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Supplementary Materials for: Resolution Adaptive Networks for Efficient Inference",
+        "text_level": 1,
+        "bbox": [
+            112,
+            128,
+            854,
+            172
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "1. Appendix A: Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            78,
+            250,
+            410,
+            268
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce the architecture configurations for our RANets and MSDNets in the experiments of the main paper.",
+        "bbox": [
+            75,
+            277,
+            468,
+            324
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "1.1. CIFAR-10 and CIFAR-100",
+        "text_level": 1,
+        "bbox": [
+            76,
+            335,
+            318,
+            349
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "MSDNet: For CIFAR-10 and CIFAR-100, features with 3 different scales  $(32 \\times 32, 16 \\times 16, 8 \\times 8)$  are used for MSDNets in our experiments. The trained MSDNets have  $\\{6, 8, 10\\}$  classifiers, where their depths are  $\\{16, 20, 24\\}$ , respectively.",
+        "bbox": [
+            75,
+            359,
+            468,
+            435
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "RANet: The same 3 scales features are utilized for our RANets in the experiments. However, as mentioned in section 3.3.1, different from MSDNet, the scales of the generated base features can be different, and we could have a RANet with three or four base features in three scales. We test 3 architecture configurations as follows:",
+        "bbox": [
+            75,
+            460,
+            468,
+            549
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model-C-1: The size of three base features are  $32 \\times 32, 16 \\times 16, 8 \\times 8$ . Three sub-networks corresponding to these base features have 6, 4, 2 Conv Blocks, respectively. We set two step mode for RANet to control the number of layers in each Conv Block: 1) even: the number of layers in each Conv Block is set to 4; 2) linear growth (lg): the number of layers in a Conv Block is added 2 to the previous one, and the base number of layers is 2. The channel numbers in these base features are 16, 32, 64, which are input channels numbers for different sub-networks. The growth rates of the 3 sub-networks are 6, 12, 24. Moreover, for each Fusion Block, a compress factor of 0.25 is applied, which means that  $75\\%$  of the new added channels are generated from the current sub-network and the other  $25\\%$  are calculated from the previous sub-network with lower feature resolution. Furthermore, we add  $s$  transition layers for Sub-network  $s$ . E.g., we add one 3 transition layers for Sub-network 3. The Model-C-1 has six classifiers in total, and its overall architecture is illustrated in Figure 1(a).",
+        "bbox": [
+            75,
+            551,
+            468,
+            838
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model-C-2: The size of four base features are  $32 \\times 32$ ,  $16 \\times 16$ ,  $16 \\times 16$ ,  $8 \\times 8$ . These four sub-networks corresponding to the base features have 8, 6, 4, 2 Conv Blocks, respectively. Moreover, the numbers of input channels and",
+        "bbox": [
+            75,
+            840,
+            468,
+            900
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "the growth rates are 16, 32, 32, 64 and 6, 12, 12, 24, respectively. All Up-Conv Layers are substituted to Regular Conv Layers if the feature fusion happens between two same scales. The Model-C-2 has eight classifiers in total, and its overall architecture is illustrated in Figure 1(b).",
+        "bbox": [
+            496,
+            252,
+            890,
+            327
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model-C-3: The size of four base features are  $32 \\times 32, 16 \\times 16, 8 \\times 8, 8 \\times 8$ . The numbers of input channels and the growth rates are 16, 16, 32, 64 and 6, 6, 12, 24, respectively. All Up-Conv Layers are substituted to Regular Conv Layers if the feature fusion happens between two same scales. The Model-C-3 has eight classifiers in total, and its overall architecture is illustrated in Figure 1(c).",
+        "bbox": [
+            496,
+            328,
+            890,
+            433
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "In the experiments, the Model-C-3 (even) are evaluated under the anytime classification setting (Figure 5 of the main paper), and all three models (lg) are evaluated under the budgeted batch classification setting (Figure 6 of the main paper).",
+        "bbox": [
+            496,
+            434,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "1.2. ImageNet",
+        "text_level": 1,
+        "bbox": [
+            500,
+            521,
+            611,
+            537
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "MSDNet: On the ImageNet, features with 4 different scales  $(56 \\times 56, 28 \\times 28, 14 \\times 14, 7 \\times 7)$  are used for MSDNets in our experiments. Three different MSDNets with five classifiers and different depth are evaluated. Specifically, the  $i^{th}$  classifier is attached at the  $(t \\times i + 3)^{th}$  layer where  $i \\in \\{1, \\dots, 5\\}$ , and  $t \\in \\{4, 6, 7\\}$  is the step (number of layers) for each network block.",
+        "bbox": [
+            496,
+            545,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "RANet: The same 4 feature scales are utilized for our RANets in the experiments. The spatial resolutions of the base features are  $56 \\times 56$ ,  $28 \\times 28$ ,  $14 \\times 14$ ,  $7 \\times 7$ , respectively. We test 2 architecture configurations as follows:",
+        "bbox": [
+            496,
+            672,
+            890,
+            733
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model-I-1: Four sub-networks corresponding to the base features have 8, 6, 4, 2 Conv Blocks, respectively, and the number of layers in each Conv Block is set to 8. Moreover, the numbers of base feature channels and the growth rates are 32, 64, 64, 128 and 16, 32, 32, 64. For each Fusion Block, compress factor of 0.25 is applied. The Model-I-1 has eight classifiers in total, and its overall architecture is illustrated in Figure 2.",
+        "bbox": [
+            496,
+            734,
+            890,
+            853
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Model-I-2: The architecture of the Model-I-2 is exactly the same as the Model-I-1. However, the numbers of base feature channels are 64, 128, 128, 256.",
+        "bbox": [
+            496,
+            854,
+            890,
+            898
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "aside_text",
+        "text": "arXiv:2003.07326v5 [cs.CV] 18 May 2020",
+        "bbox": [
+            22,
+            253,
+            57,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "1",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "image",
+        "img_path": "images/cabce86770193eb4acd75d4bae64bf1b2e5377dcf2735091883cdadaaa2292af.jpg",
+        "image_caption": [
+            "(a) Model-C-1 Architecture for CIFAR"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            95,
+            733,
+            231
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/87b5c5ad0b7c5d47e7e90fec958d2865bbad43fa4595b3fd14511cd27de092ef.jpg",
+        "image_caption": [
+            "(b) Model-C-2 Architecture for CIFAR"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            250,
+            883,
+            417
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/ebf5cbab3e4bebcde720dfdcfac423f29386169e30ef33e5cdc8cb557d2a4147.jpg",
+        "image_caption": [
+            "(c) Model-C-3 Architecture for CIFAR"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            436,
+            885,
+            604
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/530c7653e5c536a53ddb6f5ca0801a195e6304113208acf1b9f53aafd1da85d3.jpg",
+        "image_caption": [
+            "Figure 1. Architecture of RANets for CIFAR-10 and CIFAR-100.",
+            "Figure 2. Architecture of RANets for ImageNet."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            84,
+            662,
+            885,
+            832
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "In the experiments, the Model-I-2 is evaluated under the anytime classification setting (Figure 5 of the main paper), and both models are evaluated under the budgeted batch classification setting (Figure 6 of the main paper).",
+        "bbox": [
+            75,
+            90,
+            470,
+            151
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "2. Appendix B: Improved Techniques",
+        "text_level": 1,
+        "bbox": [
+            76,
+            167,
+            393,
+            185
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "As some training techniques for adaptive inference models with multiple exits have been proposed in [2], we further evaluated the proposed RANet and MSDNet [1] with the implementation of these improved techniques on CIFAR-100. Inline Sub-network Collaboration (ISC) and One-ForAll (OFA) knowledge distillation approaches are utilized in the experiments under anytime prediction and budgeted batch classification settings. Specifically, we implement these techniques (ISC and OFA) on our Model-C-3 and MSDNet with 8 and 10 classifiers. The results are shown in Figure 3 (anytime) and 4 (budgeted batch).",
+        "bbox": [
+            75,
+            194,
+            470,
+            359
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/3e956153acda38fa7570516bc1c4ebd42cf37ed3e81510b717e6f64b94f7ab46.jpg",
+        "image_caption": [
+            "Figure 3. Accuracy (top-1) of anytime classification models as a function of average computational budget per image the on CIFAR-100, higher is better. MSDNet and RANet are trained with and without ISC and OFA techniques."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            94,
+            378,
+            450,
+            574
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For anytime prediction, Model-C-3 (even) and MSDNet with 10 classifiers are tested. From the results, we observe that the improved RANet can outperform the improved MSDNet, especially when the budget ranges from  $0.3 \\times 10^{8}$  to  $0.6 \\times 10^{8}$  FLOPs. Moreover, the improved RANet can achieve the highest accuracy ( $75\\%$ ) with around  $0.2 \\times 10^{8}$  less FLOPs. We further observe that the techniques (ISC and OFA) do not work well on the first classifier of the RANet.",
+        "bbox": [
+            75,
+            657,
+            468,
+            792
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "For budgeted batch classification, the results of RANet, Model-C-3 and MSDNet with 8 classifiers are tested. From the results, we observe that the improved RANet is still superior to the improved MSDNet, especially when the budget greater than  $0.3 \\times 10^{8}$ . The original RANet can outperform the improved RANet can be due to the performance dropping of the first classifiers. However, compared with",
+        "bbox": [
+            75,
+            795,
+            468,
+            902
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "image",
+        "img_path": "images/7ff36face91dc71d542053c20ec687f5960655e75e58c74bed4b3d19bb6754a4.jpg",
+        "image_caption": [
+            "Figure 4. Accuracy (top-1) of budgeted batch classification models as a function of average computational budget per image the on CIFAR-100, higher is better. MSDNet and RANet are trained with and without ISC and OFA techniques."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            517,
+            90,
+            875,
+            324
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "MSDNet and improved MSDNet, the accuracy of improved RANet can be  $1\\%$  and  $0.5\\%$  higher respectively, which demonstrated the effectiveness of our RANet when implemented with the improved techniques.",
+        "bbox": [
+            500,
+            415,
+            892,
+            476
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            501,
+            489,
+            596,
+            503
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. In ICLR, 2018. 3",
+            "[2] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In ICCV, 2019. 3"
+        ],
+        "bbox": [
+            500,
+            513,
+            890,
+            611
+        ],
+        "page_idx": 12
+    }
+]

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2003.07xxx/2003.07326/full.md

@@ -0,0 +1,349 @@
+# Resolution Adaptive Networks for Efficient Inference
+
+Le Yang $^{1*}$  Yizeng Han $^{1*}$  Xi Chen $^{2*†}$  Shiji Song $^{1}$  Jifeng Dai $^{3}$  Gao Huang $^{1‡}$
+
+Tsinghua University,
+
+Beijing National Research Center for Information Science and Technology (BNRist)
+
+$^{2}$ Harbin Institute of Technology  $^{3}$ SenseTime
+
+{yangle15, hanyz18}@mails.tsinghua.edu.cn, {shijis, gaohuang}@tsinghua.edu.cn,
+
+xi.chen@stu.hit.edu.cn, daijifeng@sensetime.com
+
+# Abstract
+
+Adaptive inference is an effective mechanism to achieve a dynamic tradeoff between accuracy and computational cost in deep networks. Existing works mainly exploit architecture redundancy in network depth or width. In this paper, we focus on spatial redundancy of input samples and propose a novel Resolution Adaptive Network (RANet), which is inspired by the intuition that low-resolution representations are sufficient for classifying "easy" inputs containing large objects with prototypical features, while only some "hard" samples need spatially detailed information. In RANet, the input images are first routed to a lightweight sub-network that efficiently extracts low-resolution representations, and those samples with high prediction confidence will exit early from the network without being further processed. Meanwhile, high-resolution paths in the network maintain the capability to recognize the "hard" samples. Therefore, RANet can effectively reduce the spatial redundancy involved in inferring high-resolution inputs. Empirically, we demonstrate the effectiveness of the proposed RANet on the CIFAR-10, CIFAR-100 and ImageNet datasets in both the anytime prediction setting and the budgeted batch classification setting.
+
+# 1. Introduction
+
+Although advances in computer hardware have enabled the training of very deep convolutional neural networks (CNNs), such as ResNet [8] and DenseNet [14], the high computational cost of deep CNNs is still unaffordable in many applications. Many efforts have been made to speed up the inference of deep models, e.g., lightweight network architecture design [10, 31, 42, 13], network pruning
+
+![](images/b5928b30188545ce8634233f0503e93addd7478bd93cbea56dcd9f74f93618b1.jpg)  
+Figure 1. Classifying images of owls. In (a), the canonical sample can be recognized by the Sub-network 1 with the lowest resolution, and thus the following sub-networks will be unused. For the "hard" image in (b), the Sub-network 1 fails to provide a reliable prediction. Therefore, classifying this sample requires computationally more expensive sub-networks with finer features.
+
+[20, 22, 26] and weight quantization [15, 29, 17]. Among them, the adaptive inference scheme [24, 37, 12, 36], which aims to reduce the computational redundancy on "easy" samples by dynamically adjusting the network structure or parameters conditioned on each input, has been shown to yield promising performance.
+
+Most existing works on adaptive inference focus on reducing the network depth or width for images with easily
+
+recognizable features. It has been shown that the intrinsic classification difficulty for different samples varies drastically: some of them can be correctly classified by smaller models with fewer layers or channels, while some may need larger networks [24, 37, 12, 36]. By exploiting this fact, many works have been proposed recently. For example, the model in [24] executes runtime pruning of convolutional kernels with a policy learned by reinforcement learning strategies. The network in [37] inserts a linear layer before each convolutional layer to generate a binary decision on whether executing the following convolutional operation dynamically. Multi-Scale Dense Network (MSDNet) [12] allows some samples to exit at some auxiliary classifiers conditioned on their prediction confidence.
+
+In this paper, we consider adaptive inference from a novel perspective. In contrast to existing works focusing on the computational redundancy in the network structure, we aim to exploit the information redundancy in the data samples. Our motivation is that low-resolution feature representations are sufficient to classify "easy" samples (as shown in the top row in Figure 1), while applying high-resolution feature maps to probe the details is necessary for accurately recognizing some "hard" samples (as shown in the bottom row in Figure 1). This further agrees with the "coarse to fine processing" efficient algorithm design in [18]. From a signal frequency viewpoint [4], "easy" samples could be correctly classified with low-frequency information contained in low-resolution features. High-frequency information is only utilized as complementary for recognizing "hard" samples when we fail to precisely predict the samples with low-resolution features.
+
+Based on the above intuition, we propose a Resolution Adaptive Network (RANet) that implements the idea of performing resolution adaptive learning in deep CNNs. Figure 1 illustrates the basic idea of RANet. It is composed of sub-networks with different input resolutions. The "easy" samples are classified by the sub-network with the feature maps in the lowest spatial resolution. The sub-networks with higher resolution will be applied when the previous sub-network fails to achieve a given criterion<sup>1</sup>. Meanwhile, the coarse features from the previous sub-network will be reused and fused into the current sub-network. The adaptation mechanism of RANet reduces computational budget by avoiding performing unnecessary convolutions on high-resolution features when samples can be accurately predicted with low-resolution representations, leading to improved computational efficiency.
+
+We evaluate the RANet on three image classification datasets (CIFAR-10, CIFAR-100, and ImageNet) under the anytime classification setting and the budgeted batch classification setting, which are introduced in [12]. The exper
+
+iments show the effectiveness of the proposed method in adaptive inference tasks.
+
+# 2. Related work
+
+Efficient inference for deep networks. Many previous works explore variants of deep networks to speed up the network inference. One direct solution is designing lightweight models, e.g., MobileNet [10, 31], ShuffleNet [42, 27] and CondenseNet [13]. Other lines of research focus on pruning redundant network connections [20, 22, 26], or quantizing network weights [15, 29, 17]. Moreover, knowledge distilling [9] is proposed to train a small (student) network which mimics outputs of a deeper and/or wider (teacher) network.
+
+The aforementioned approaches can be seen as static model acceleration techniques, which infer all input samples with a whole network consistently. In contrast, adaptive networks can strategically allocate appropriate computational resources for classifying input images based on input complexity. This research direction is gaining increasing attention in recent years due to its advantages. The most intuitive implementation is assembling multiple models and selectively executing a subset of the models in a cascading [2] or mixing way [32, 30]. Recent works also propose to adaptively skip layers or blocks [7, 37, 39, 40], or dynamically select channels [24, 3, 1] during inference time. Auxiliary predictors can also be attached at different locations of a deep network to allow early exiting "easy" examples [35, 12, 11, 23]. Furthermore, dynamically activating parts of network branches with multi-branch structure [36] also provide an alternate way for adaptive inference.
+
+However, most of these prior works focus on designing adaptive networks by exploiting architecture redundancy of networks. As spatial redundancy of input images has been certified in recent work [4], this paper proposes a novel adaptive learning model which exploits both structural redundancy of a neural network and spatial redundancy of input samples.
+
+Multi-scale feature maps and spatial redundancy. As the downsampling operation in networks with a single scale [8, 14] may restrict the networks' ability to recognize an object in an arbitrary scale, recent studies propose to adopt multi-scale feature maps in a network to simultaneously utilize both coarse and fine features, which significantly improves the network performance in many vision tasks, including image classification [18], object detection [25], semantic segmentation [43] and pose estimation [33]. Moreover, the multi-scale structure shows a promising ability in adaptive inference [12] and memory-efficient network [38].
+
+While keeping high-resolution feature maps through a deep neural network is found to be necessary for recognizing some atypical "hard" samples or some specific tasks such as pose estimation [33], frequently operating convolu
+
+tions on high-resolution features usually results in resource-hungry models. It has been observed that lightweight networks can yield a decent error rate for all samples with low-resolution inputs [10]. The spatial redundancy in these convolutional neural networks has also been studied in [4], where the octave convolution in the network processing feature maps with small scales improves the computational efficiency and the classification performance simultaneously. Moreover, ADASCALE proposed in [5] also adaptively selects the input image scale that improves both accuracy and speed for video object detection.
+
+However, none of these existing works considers designing an adaptive model by exploiting spatial redundancy in images. In this paper, we propose our RANet for resource-efficient image classification, motivated by the intuition that a smaller scale can be capable of handling most of input samples. Compared to ADASCALE [5], which also adaptively selects the input image scale for vision task, the proposed RANet can be implemented for the budgeted classification setting during adaptive inference. Our work achieves resolution adaptation by classifying some of inputs on small scales and allowing larger scales to be processed only when inputs can not be recognized with coarse representations. The resolution adaptation in RANet significantly improves its computational efficiency without sacrificing accuracy.
+
+# 3. Method
+
+In this section, we first introduce the idea of adaptive inference, then we demonstrate the overall architecture and the network details of our proposed RANet.
+
+# 3.1. Adaptive Inference Setting
+
+We set up an adaptive inference model as a network with  $K$  classifiers, where these intermediate classifiers are attached at varying depths of the model. Given an input image  $\mathbf{x}$ , the output of the  $k$ -th classifier  $(k = 1,\dots ,K)$  can be represented by
+
+$$
+\mathbf {p} ^ {k} = f _ {k} (\mathbf {x}; \theta_ {k}) = \left[ p _ {1} ^ {k}, \dots , p _ {C} ^ {k} \right] ^ {\mathrm {T}} \in \mathbb {R} ^ {C}, \tag {1}
+$$
+
+where  $\theta_{k}$  denotes the parameters of the partial network corresponding to the  $k$ -th classifier, and each element  $p_c^k \in [0,1]$  is the prediction confidence for the  $c$ -th class. Note that  $\theta_{k}$ 's have shared parameters here.
+
+The adaptive model infers a sample by dynamically allocating appropriate computational resources depending on the complexity of this sample. A sample will exit the network at the first classifier whose output satisfies a certain criterion. In this paper, we use the highest confidence of the softmax output as our decision basis, which means that the final output will be the prediction of the first classifier whose largest softmax output is greater than a given thresh-
+
+old  $\epsilon$ . This can be represented by
+
+$$
+k ^ {*} = \min  \left\{k \mid \max  _ {c} p _ {c} ^ {k} \geq \epsilon \right\}, \tag {2}
+$$
+
+$$
+\hat {y} \in \arg \max  _ {c} p _ {c} ^ {k ^ {*}}. \tag {3}
+$$
+
+The threshold  $\epsilon$  controls the trade-off between classification accuracy and computational cost at test time.
+
+# 3.2. Overall Architecture
+
+Figure 2 illustrates the overall architecture of the proposed RANet. It contains an Initial Layer and  $H$  subnetworks corresponding to different resolutions. Each subnetwork has multiple classifiers at the last few blocks. Similar to MSDNet [12], we adopt a multi-scale architecture and dense connection in our approach. Although RANet and MSDNet have a similar multi-scale structure, their detailed architecture designs and computation graphs differ significantly. The most prominent difference is that RANet needs to extract low-resolution features first, which does not follow the traditional design routine in classical deep CNNs (including MSDNet, ResNet, DenseNet, etc.) that all extract high-resolution features first. More details of the differences between MSDNet and our RANet will be discussed in Section 3.4.
+
+The basic idea of RANet is that the network will first predict a sample with the first sub-network, using feature maps of the lowest spatial resolution to avoid the high computational cost induced by performing convolutions on large scale features. If the first sub-network makes an unreliable prediction of the sample, the small scale intermediate features will be fused into the next sub-network with a higher resolution. The classification task is then conducted by the next sub-network with larger scale features. This procedure is repeated until one sub-network yields a confident prediction, or the last sub-network is utilized.
+
+The adaptive inference procedure of RANet is further illustrated in Figure 2: with  $H$  sub-networks ( $H = 3$  in the illustration) and an input sample  $\mathbf{x}$ , the network will first generate  $H$  base feature maps in  $S$  scales (For instance, there are 3 scales in the illustration, and  $s = 1$  represents the lowest resolution). The base features in scale  $s$  corresponding to Sub-network  $h$  can be denoted as  $\mathbf{x}_0^{s,h}$ ,  $s = 1,2,\ldots,S, h = 1,2,\ldots,H$ . Then the classification task is first conducted by Sub-network 1 using features  $\mathbf{x}_0^{1,1}$  at the bottom. If Sub-network 1 fails to achieve the classification result with a high confidence, Sub-network 2, which processes larger scale features ( $\mathbf{x}_0^{2,2}$ ), will be utilized for further classifying the sample. The intermediate features in Sub-network 1 are successively fused into Sub-network 2. We repeat this procedure for Sub-network 3 if Sub-network 2 fails to make a confident prediction.
+
+It is worth noting that even RANet processes inputs from coarse to fine in general, each sub-network in RANet
+
+![](images/4920a6f6ccea20eb44ad20bd858f48141cb9344783aedee1a6fb9e1d4c28c18b.jpg)  
+Figure 2. The illustration of an RANet with three scales. Classifiers only operate on feature maps at the lowest resolution.
+
+still downsamples features during forward propagation until reaching the lowest resolution  $(s = 1)$ , and all the classifiers are only attached at the last few blocks with  $s = 1$  in each sub-network.
+
+The aforementioned inference procedure meets our intuition for image recognition. An "easy" sample with representative characteristics can be correctly classified sometimes with high confidence even only low-resolution representations are provided. A "hard" sample with atypical features can only be correctly recognized based on global information accompanied with fine details, which are extracted from high-resolution feature maps.
+
+# 3.3. Network Details
+
+This subsection provides more detailed introductions about each component in RANet.
+
+# 3.3.1 Initial Layer
+
+An Initial layer is implemented to generate  $H$  base features in  $S$  scales and it only includes vertical connections in Figure 2. One could view its vertical layout as a miniature "H-layers" convolutional network ( $H$  is the number of base features in the network). Figure 2 shows an RANet with 3 base features in 3 scales. The first base features with the largest scale is derived from a Regular-Conv layer $^2$ , and the coarse features are obtained via a Strided-Conv layer $^3$  from the former higher-resolution features. It is worth noting that the scales of these base features can be the same. For instance, one could have an RANet with 4 base features in 3 scales, where the scales of the last two base features are of the same resolution.
+
+![](images/76200f16aa6df6eb417894eca44c8fcd39ec857bdbac71f399bd396e89182111.jpg)  
+Figure 3. Two kinds of Conv Blocks in RANet: Dense Block, (a), and Fusion Block, (b,c). Moreover, the block in (b) maintains the input resolution of the feature maps, while the block in (c) down-samples the features by a factor of 2 at the end of the block.
+
+# 3.3.2 Sub-networks with Different Scales
+
+As the Initial layer generates  $H$  base features, the proposed network can then be separated into  $H$  sub-networks, which are further composed by different Conv Blocks. Each subnetwork, except the first one, conducts the classification task with its corresponding base feature maps and features from the previous sub-network.
+
+Sub-network 1. Sub-network 1 with input  $\mathbf{x}_0^{1,1}$  processes the lowest-resolution features. We adopt regular Dense Blocks [14] with  $l$  layers in Sub-network 1, which is shown in Figure 3 (a). Moreover, the  $i$ -th layer's output  $\mathbf{x}_i^{1,1}, i = 1,2,\ldots l$  in each Dense Block is also propagated to Sub-network 2 to reuse the early features. In general, one can view Sub-network 1 as a DenseNet with multiple classifiers, processing the lowest-resolution feature maps.
+
+Sub-networks on larger-scale features. Sub-network  $h$  ( $h > 1$ ) with scale  $s$  processes the base features  $\mathbf{x}^{s,h}$  and
+
+fuses the features from Sub-network  $(h - 1)$ . We call Conv Blocks with feature fusion as Fusion Blocks (shown in Figure 3 (b, c)). Suppose that Sub-network  $(h - 1)$  has  $b_{h - 1}$  blocks, then the first  $b_{h - 1}$  blocks in Sub-network  $h$  will all be Fusion Blocks.
+
+We design two different ways of feature fusion. One maintains the input resolution, which is illustrated in Figure 3 (b), while the other reduces the feature scale by a Strided-Conv layer, as shown in Figure 3 (c). To generate new feature maps with higher resolution as inputs, the Fusion Block in Figure 3 (b) first produces  $\mathbf{x}_{\mathrm{in}}^{s,h}$  with a Regular-Conv layer. Features in scale  $(s - 1)$  from the previous subnetwork is processed by an Up-Conv layer, which is composed of a Regular-Conv layer and an up-sampling bilinear interpolation. This ensures the produced features are of the same spatial resolution. The resulting features are then fused through concatenation with dense connection.
+
+As shown in Figure 3 (c), a Fusion Block with downsampling utilizes a Strided-Conv layer to reduce the spatial resolution at the end of the block. Concatenation with dense connection is also conducted after a pooling operation as shown by a blue dashed arrow. Since the feature scale is reduced in the current sub-network, features from the previous sub-network are processed by a Regular-Conv layer to maintain the low resolution, and then fused by concatenation at the end of the block in Figure 3 (c).
+
+Sub-network  $h$  with scale  $s$  can be established as follow: for a sub-network with  $b_h$  blocks, block 1 to block  $b_{h-1}$  ( $b_{h-1} < b_n$ ) are all Fusion Blocks, while the rest of them are regular Dense Blocks. Moreover, we downsample the feature maps  $s$  times at the  $b_{h-s}, \ldots, b_{h-1}$ -th blocks during forward propagation. This ensures that at the end of each sub-network where we attach classifiers, the features must be of the lowest resolution.
+
+Transition layer. Similar to the architecture design in [14] and [12], we implement Transition layers to further compress the feature maps in each sub-network. The design of a Transition layer is exactly the same as the one in [14] and [12], which is composed of a  $1 \times 1$  convolution operator following by a BN layer and a ReLU layer. Transition layers further guarantee the computational efficiency of the proposed network. For simplicity, we omit these Transition Layers in Figure 2.
+
+Classifiers and loss function. The classifiers are implemented at the last few blocks of different sub-networks. At the training stage, we let input samples pass through Subnetwork 1 to Sub-network  $H$  sequentially and cross-entropy loss function is used for each classifier. We set the overall loss function for RANet as a weighted cumulative loss of these classifiers. We empirically follow the settings in [12] and use the same weight for all loss functions in this paper.
+
+![](images/03a74cd60a41820c9a9c586d9647cba683f05d9ec9f4238376d3723841fea9d4.jpg)  
+(a) MSDNet
+
+![](images/f55daff2b0199288c97c246caca331c517508fb1976a7a382750d7add671274a.jpg)  
+(b) RANet  
+Figure 4. Depth adaptation in MSDNet (a) and resolution-depth adaptation in our RANet (b). Different shaded areas represent the network blocks with varied computational costs, and the colored arrows represent the feature propagation path. The lighter the color is, the earlier the propagation is executed. The dashed arrows in (b) indicate that RANet adopts a zigzag-shape computation graph from the bottom to the top.
+
+# 3.4. Resolution and Depth Adaptation
+
+Our proposed RANet can simultaneously implement the idea of depth adaptation, which is adopted in MSDNet [12], and resolution adaptation. Figure 4 illustrates the main differences between MSDNet (left) and our RANet (right). In MSDNet, the classifiers are located at the lowest resolution scale, and once an intermediate predictor does not yield a confident prediction, the following layers of all scales will be executed. However, in our RANet, the Dense Blocks with the smallest scale input are first activated sequentially and the depth adaptation is conducted within a single scale. If the previous sub-network cannot make a confident prediction, the input sample will be propagated to the next subnetwork and repeat the depth adaptation process until the prediction confidence meets the criterion, or the last classifier of the whole network is reached. Such an inference scheme naturally combines resolution and depth adaptation, achieving significant improvement over MSDNet.
+
+# 4. Experiments
+
+To demonstrate the effectiveness of our approach, we conducted experiments on the CIFAR [19] and ImageNet [6] datasets. The code is available at https://github.com/yangle15/RANet-pytorch. The implementation details of RANets and MSDNets in our experiments are described in Appendix A.
+
+Datasets. The CIFAR-10 and CIFAR-100 datasets contain  $32 \times 32$  RGB natural images, corresponding to 10 and 100 classes, respectively. The two datasets both contain 50,000 training and 10,000 testing images. Following [12], we hold out 5,000 images in the training set as a validation set to search the optimal confidence threshold for adaptive inference. The ImageNet dataset contains 1.2 million images of 1,000 classes for training, and 50,000 images for validation. For adaptive inference tasks, we use the original validation set for testing, and hold out 50,000 images from
+
+the training set as a validation set.
+
+Training policy. We train the proposed models using stochastic gradient descent (SGD) with a multi-step learning rate policy. The batch size is set to 64 and 256 for the CIFAR and ImageNet datasets, respectively. We use a momentum of 0.9 and a weight decay of  $1 \times 10^{-4}$ . Moreover, for the CIFAR datasets, the models are trained from scratch for 300 epochs with an initial learning rate of 0.1, which is divided by a factor of 10 after 150 and 225 epochs. The same training scheme is applied to the ImageNet dataset. And we train the models for 90 epochs from scratch and the initial learning rate decreases after 30 and 60 epochs.
+
+Data augmentation. We follow [8] and apply standard data augmentation schemes on the CIFAR and ImageNet datasets. On the two CIFAR datasets, images are randomly cropped to samples with  $32 \times 32$  pixels after zero-padding (4 pixels on each side). Furthermore, images are horizontally flipped with probability 0.5 and RGB channels are normalized by subtracting the corresponding channel mean and divided by their standard deviation. On ImageNet, we follow the data augmentation scheme in [8] for training, and apply a  $224 \times 224$  center crop to images at test time.
+
+# 4.1. Anytime Prediction
+
+In the anytime prediction setting [12], we evaluate all classifiers in an adaptive networks and report their classification accuracies with corresponding FLOPs (floating point operations).
+
+Baseline models. Following the setting in [12], in addition to MSDNet, we also evaluate several competitive models as our baselines, including ResNet $^{\text{MC}}$ , DenseNet $^{\text{MC}}$  [21], and ensembles of ResNets and DenseNets of varying sizes. Details on architectural configurations of MSDNets and RANets in the experiments are described in Appendix A. As recent research in [23] investigates improved techniques for training adaptive networks, we further evaluate these techniques on both RANet and MSDNet. The experiments show that the computational efficiency of the RANet can be further improved and outperforms the improved MSDNet. The results are provided in Appendix B.
+
+Results. We report classification accuracies of all individual classifiers in our model and other baselines. The results are summarized in Figure 5. The evaluated MSD-Nets and RANets are depicted by black and yellow lines, respectively. In general, MSDNet substantially outperforms other baseline models, and RANet are superior to MSDNet, especially when the computational budget is low.
+
+In particular, on CIFAR-10 (CIFAR-100), the accuracies of different classifiers for RANet are over  $1\%$ $(2\% -5\%)$  higher than those of MSDNet when the computational budget ranges from  $0.1\times 10^{8}$  to  $0.5\times 10^{8}$  FLOPs. Moreover, compared to MSDNet, RANet achieves its highest accuracy with less computational demands (around  $0.25\times 10^{8}$
+
+FLOPS). On ImageNet, the proposed network outperforms MSDNet by around  $1\% - 7\%$  when the budget ranges of  $0.5 \times 10^{9}$  to  $1.5 \times 10^{9}$  FLOPs. Although both MSDNet and RANet achieve similar classification accuracy ( $74\%$ ) at the last classifier, our model only uses around  $27\%$  fewer FLOPs compared to MSDNet.
+
+At the first classifier, the accuracies of RANets are  $2\%$  and  $5\%$  higher than those of MSDNets on CIFAR-10 and CIFAR-100, respectively. On the ImageNet dataset, RANet still slightly outperforms MSDNet at the first classifier. With  $1.0 \times 10^{9}$  FLOPs, RANet can achieve a classification accuracy of around  $68\%$ , which is around  $5\%$  higher than that achieved by MSDNet. We also observe that ensembles of ResNets outperform MSDNets in low-budget regimes, because the predictions of ensembles are performed by the first lightweight networks, which are optimized exclusively for the low budget. However, RANets are consistently superior to ensembles of ResNets on all datasets. This meets our expectation that Sub-network 1 with the first classifier in RANet is specially optimized for recognizing "easy" samples. Since Sub-network 1 directly operates on the feature maps with the lowest resolution, it avoids performing the convolutions on high-resolution feature maps, which results in the high computational efficiency of the first classifier. Furthermore, as Sub-network 1 in RANets can be viewed as exclusively optimized lightweight models, the early classifiers of RANets show their advantages in the classification tasks. Different from ResNet ensembles, which repeat the computation of similar low-level representations, RANets fuse the feature maps from previous lightweight networks into a large network to make full use of the obtained features. This mechanism effectively improves classification accuracies when we have more computational resources.
+
+# 4.2. Budgeted Batch Classification
+
+The budgeted batch classification setting is described in [12]. We set a series of thresholds that depend on different computational budgets. For a given input image, we let it pass through each classifier in an adaptive network, sequentially. The forward propagation stops at the classifier whose output confidence reaches the given threshold, and then we report its prediction as the final result for this image.
+
+Baseline models. For CIFAR-10 and CIFAR-100, we use ResNet, DenseNet and DenseNet* [12] as baseline models. For ImageNet, we additionally evaluate ResNet and DenseNet with multi-classifier [21]. Performance of some classical deep models are also reported in the experimental results, such as WideResNet [41] (for CIFAR) and GoogLeNet [34] (for ImageNet). See Appendix A for details about the architecture configurations of MSDNets and RANets in the experiments. Moreover, we implement the techniques in [23] to further evaluate the improved RANets and MSDNets. The results are provided in Appendix B.
+
+![](images/02a9b3cb46608f2ff981b4236de6afddc931c35bb36be54133aef9e98a5dacdb.jpg)  
+(a)
+
+![](images/89eaefcbc6968f1204529cd9adae411f4cdff1a38652d9cfbed178b882a8abc5.jpg)  
+(b)
+
+![](images/b61e746083691b9c04656569e5e8778b5b894ebaea6123beb85d52a85bd9d28d.jpg)  
+(c)
+
+![](images/896951cd87e4dc56e4b11ef49cd1ea5ae721cb08e057b4fd24e622b2ea237d93.jpg)  
+Figure 5. Accuracy (top-1) of anytime prediction models as a function of computational budget on CIFAR-10 (left), CIFAR-100 (middle) and ImageNet (right). Higher is better.  
+(a)  
+Figure 6. Accuracy (top-1) of budgeted batch classification models as a function of average computational budget per image on CIFAR-10 (left), CIFAR-100 (middle) and ImageNet (right). Higher is better.
+
+![](images/be19b2d20e0bc56718695991ce0cb0550f984e273bf1bf4395fc77882f4600e0.jpg)  
+(b)
+
+![](images/200a09634e30a94ffe8d236e20ff11e34c331250139e63286c3cf68b9fa517ad.jpg)  
+(c)
+
+Results. The results are summarized in Figure 6. We plot the classification accuracy of each MSDNet and RANet in a gray and a light-yellow curve, respectively. We select the best model for each budget based on its accuracy on the test set, and plot the corresponding accuracy as a black curve (for MSDNet) or a golden curve (for RANet).
+
+The results on the two CIFAR datasets show that RANets consistently outperform MSDNets and other baseline models across all budgets. In general, the networks with multiscale dense connection architecture are always substantially more accurate than other baseline models with the same amount of computation cost under the budgeted batch classification setting. For low computational budget (less than  $0.2 \times 10^{8}$  FLOPs), on CIFAR-10, the proposed model uses  $20\%$  fewer FLOPs to achieve the classification accuracy of  $92\%$  compared to MSDNet. On CIFAR-100, RANet can achieve the classification accuracy of  $68\%$  with only about  $60\%$  FLOPs compared to MSDNet. Even though our model and MSDNet show close performance on CIFAR-10 when the computational budget ranges from  $0.2 \times 10^{8}$  to  $0.3 \times 10^{8}$ , the classification accuracies of RANets are consistently higher than ( $1\%$ ) these of MSDNets on CIFAR-
+
+100 in median and high budget intervals (over  $0.2 \times 10^{8}$  FLOPs). Moreover, our model can achieve an accuracy of  $94.2\%$  when the budget is higher than  $0.2 \times 10^{8}$  FLOPs. This accuracy is  $0.5\%$  higher than that of MSDNet under the same computational budget condition. The experiments also show that RANets are up to 4 times more efficient than WideResNets on CIFAR-10 and CIFAR-100.
+
+The experiments on ImageNet yield similar results to those on CIFAR. We observe that RANets consistently surpass MSDNets. Our networks win about  $0.5\%$ ,  $1\%$  and  $1.2\%$  in terms of top-1 accuracy with  $0.75 \times 10^{9}$ ,  $1 \times 10^{9}$  and  $1.75 \times 10^{9}$  FLOPs respectively. The results indicate that our RANet outperforms MSDNet by a larger margin as more computational resources are provided. With the same FLOPs, our models achieve more accurate classification results than these popular deep neural networks. With the same classification accuracy, our model reduces the computational budget by around  $65\%$ ,  $56\%$  and  $44\%$  compared to GoogLeNet, ResNets and DenseNets, respectively. All these results demonstrate that the resolution adaptation along with the depth adaptation can significantly improve the performance of adaptive networks under the budgeted
+
+![](images/d5a96413de90a31db4499c9082879b08edfcd8ebe56a32db6837e259755797fe.jpg)  
+Figure 7. Visualization of ImageNet samples: Owl, Hummingbird and German Shepherd. The column on the left of each sub-figure: the images that exit from the earlier classifiers ("easy" samples); The column on the right of each sub-figure: the images that fail to be correctly classified at the earlier classifiers but are successfully recognized at the last few classifiers ("hard" samples).
+
+batch classification setting.
+
+# 4.3. Visualization and Discussion
+
+Figure 7 illustrates the ability of RANet to recognize samples with different difficulties. In each sub-figure, the left column shows "easy" samples that are correctly classified by the earlier classifiers with high classification confidence. The right column shows "hard" samples that fail to reach sufficient confidence at the early exits and are passed on to the deeper sub-networks handling high-resolution features. The figure suggests that the earlier classifiers can recognize prototypical samples of a category, whereas the later classifiers are able to recognize non-typical samples, which is similar to the experimental results in [12].
+
+It is also observed that the high-resolution feature maps and their corresponding sub-networks are necessary for accurately classifying the object in three different cases.
+
+- Multiple objects. We find that an image containing multiple objects can be viewed as a "hard" sample for RANet. The co-occurrence of different objects may corrupt the feature maps and therefore confuse the early classifiers. In this case, the relationship between each object is a key factor that can seriously affect the categorical prediction of the whole image. For example, in Figure 7 (a), the ImageNet dataset refers the image with an owl on a man's hand as the class "owl", even though there are two people in this image. Apparently, rapid downsampling could submerge the own in the image and the network can recognize it as the class "person". Furthermore, categorizing this image as the class "owl" may result from human perception that we consider objects on a person's hand at the center of an image as more important information. This complex relationship can only be exploited with stronger representations learned by a powerful network.
+
+- Tiny objects. It is observed that the images with tiny
+
+objects always pass through the whole network and thus are also considered as "hard" samples for RANet. A possible explanation for this phenomenon is that the information of these tiny target objects in the images can be completely lost after rapidly downsampling the images. The clues for classifying those tiny objects can only be obtained by processing the high-resolution feature maps. For instance, in the right image on the second row of Figure 7 (b), the hummingbird drinking water is too small. Therefore, the representations of the hummingbird can easily be lost due to the rapid downsample operations and might be completely vanished in the coarse feature maps. This makes the image unable to be recognized until the high-resolution feature maps are used for inference, which results in its late exiting in our adaptive inference network.
+
+- Objects without representative characteristics. Another kind of "hard" samples for RANet contain objects without representative characteristics. Such samples are not uncommon due to various factors (such as lighting conditions and shooting angles). In this scenario, we conjecture that the network learns to utilize alternative characteristics instead of representative ones for image recognition. For instance, by comparing the "easy" and "hard" samples in Figure 7 (c), the network can easily recognize the German Shepherd as long as its facial features are presented completely in the images. However, without complete facial features, a German Shepherd can only be correctly classified at the last classifier. For those "hard" samples, the network may take the fur texture of the German Shepherd as the alternative discriminative features during inference. Therefore, without complete facial information, the network learns to correctly classify German Shepherd by searching useful alternative characteristics in high-resolution feature maps.
+
+The rationality and effectiveness of the resolution adaptation can be further understood from the signal frequency perspective, which has been demonstrated and verified in [4]. The low-frequency information encoded in low-resolution features, which usually contains global information, can be sufficient for successful classification of most input samples. Nevertheless, higher frequencies encoded with fine details are obligatory for classifying those untypical samples.
+
+# 5. Conclusion
+
+In this paper, we proposed a novel resolution adaptive neural network based on a multi-scale dense connection architecture, which we refer to as RANet. RANet is designed in a way that lightweight sub-networks processing coarse features are first utilized for image classification. Samples with high prediction confidence will exit early from the network and larger scale features with finer details will only be further utilized for those non-typical images which achieve
+
+unreliable predictions in previous sub-networks. This resolution adaptation mechanism and the depth adaptation in each sub-network of RANet guarantee its high computational efficiency. On three image classification benchmarks, the experiments demonstrate the effectiveness of the proposed RANet in both the anytime prediction setting and the budgeted batch classification setting.
+
+# Acknowledgment
+
+This work is supported by grants from the Institute for Guo Qiang of Tsinghua University, National Natural Science Foundation of China (No. 61906106) and Beijing Academy of Artificial Intelligence (BAAI).
+
+# References
+
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+networks for resource efficient image classification. In ICLR, 2018. 1, 2, 3, 5, 6, 8  
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+
+# Supplementary Materials for: Resolution Adaptive Networks for Efficient Inference
+
+# 1. Appendix A: Implementation Details
+
+In this section, we introduce the architecture configurations for our RANets and MSDNets in the experiments of the main paper.
+
+# 1.1. CIFAR-10 and CIFAR-100
+
+MSDNet: For CIFAR-10 and CIFAR-100, features with 3 different scales  $(32 \times 32, 16 \times 16, 8 \times 8)$  are used for MSDNets in our experiments. The trained MSDNets have  $\{6, 8, 10\}$  classifiers, where their depths are  $\{16, 20, 24\}$ , respectively.
+
+RANet: The same 3 scales features are utilized for our RANets in the experiments. However, as mentioned in section 3.3.1, different from MSDNet, the scales of the generated base features can be different, and we could have a RANet with three or four base features in three scales. We test 3 architecture configurations as follows:
+
+Model-C-1: The size of three base features are  $32 \times 32, 16 \times 16, 8 \times 8$ . Three sub-networks corresponding to these base features have 6, 4, 2 Conv Blocks, respectively. We set two step mode for RANet to control the number of layers in each Conv Block: 1) even: the number of layers in each Conv Block is set to 4; 2) linear growth (lg): the number of layers in a Conv Block is added 2 to the previous one, and the base number of layers is 2. The channel numbers in these base features are 16, 32, 64, which are input channels numbers for different sub-networks. The growth rates of the 3 sub-networks are 6, 12, 24. Moreover, for each Fusion Block, a compress factor of 0.25 is applied, which means that  $75\%$  of the new added channels are generated from the current sub-network and the other  $25\%$  are calculated from the previous sub-network with lower feature resolution. Furthermore, we add  $s$  transition layers for Sub-network  $s$ . E.g., we add one 3 transition layers for Sub-network 3. The Model-C-1 has six classifiers in total, and its overall architecture is illustrated in Figure 1(a).
+
+Model-C-2: The size of four base features are  $32 \times 32$ ,  $16 \times 16$ ,  $16 \times 16$ ,  $8 \times 8$ . These four sub-networks corresponding to the base features have 8, 6, 4, 2 Conv Blocks, respectively. Moreover, the numbers of input channels and
+
+the growth rates are 16, 32, 32, 64 and 6, 12, 12, 24, respectively. All Up-Conv Layers are substituted to Regular Conv Layers if the feature fusion happens between two same scales. The Model-C-2 has eight classifiers in total, and its overall architecture is illustrated in Figure 1(b).
+
+Model-C-3: The size of four base features are  $32 \times 32, 16 \times 16, 8 \times 8, 8 \times 8$ . The numbers of input channels and the growth rates are 16, 16, 32, 64 and 6, 6, 12, 24, respectively. All Up-Conv Layers are substituted to Regular Conv Layers if the feature fusion happens between two same scales. The Model-C-3 has eight classifiers in total, and its overall architecture is illustrated in Figure 1(c).
+
+In the experiments, the Model-C-3 (even) are evaluated under the anytime classification setting (Figure 5 of the main paper), and all three models (lg) are evaluated under the budgeted batch classification setting (Figure 6 of the main paper).
+
+# 1.2. ImageNet
+
+MSDNet: On the ImageNet, features with 4 different scales  $(56 \times 56, 28 \times 28, 14 \times 14, 7 \times 7)$  are used for MSDNets in our experiments. Three different MSDNets with five classifiers and different depth are evaluated. Specifically, the  $i^{th}$  classifier is attached at the  $(t \times i + 3)^{th}$  layer where  $i \in \{1, \dots, 5\}$ , and  $t \in \{4, 6, 7\}$  is the step (number of layers) for each network block.
+
+RANet: The same 4 feature scales are utilized for our RANets in the experiments. The spatial resolutions of the base features are  $56 \times 56$ ,  $28 \times 28$ ,  $14 \times 14$ ,  $7 \times 7$ , respectively. We test 2 architecture configurations as follows:
+
+Model-I-1: Four sub-networks corresponding to the base features have 8, 6, 4, 2 Conv Blocks, respectively, and the number of layers in each Conv Block is set to 8. Moreover, the numbers of base feature channels and the growth rates are 32, 64, 64, 128 and 16, 32, 32, 64. For each Fusion Block, compress factor of 0.25 is applied. The Model-I-1 has eight classifiers in total, and its overall architecture is illustrated in Figure 2.
+
+Model-I-2: The architecture of the Model-I-2 is exactly the same as the Model-I-1. However, the numbers of base feature channels are 64, 128, 128, 256.
+
+![](images/cabce86770193eb4acd75d4bae64bf1b2e5377dcf2735091883cdadaaa2292af.jpg)  
+(a) Model-C-1 Architecture for CIFAR
+
+![](images/87b5c5ad0b7c5d47e7e90fec958d2865bbad43fa4595b3fd14511cd27de092ef.jpg)  
+(b) Model-C-2 Architecture for CIFAR
+
+![](images/ebf5cbab3e4bebcde720dfdcfac423f29386169e30ef33e5cdc8cb557d2a4147.jpg)  
+(c) Model-C-3 Architecture for CIFAR
+
+![](images/530c7653e5c536a53ddb6f5ca0801a195e6304113208acf1b9f53aafd1da85d3.jpg)  
+Figure 1. Architecture of RANets for CIFAR-10 and CIFAR-100.  
+Figure 2. Architecture of RANets for ImageNet.
+
+In the experiments, the Model-I-2 is evaluated under the anytime classification setting (Figure 5 of the main paper), and both models are evaluated under the budgeted batch classification setting (Figure 6 of the main paper).
+
+# 2. Appendix B: Improved Techniques
+
+As some training techniques for adaptive inference models with multiple exits have been proposed in [2], we further evaluated the proposed RANet and MSDNet [1] with the implementation of these improved techniques on CIFAR-100. Inline Sub-network Collaboration (ISC) and One-ForAll (OFA) knowledge distillation approaches are utilized in the experiments under anytime prediction and budgeted batch classification settings. Specifically, we implement these techniques (ISC and OFA) on our Model-C-3 and MSDNet with 8 and 10 classifiers. The results are shown in Figure 3 (anytime) and 4 (budgeted batch).
+
+![](images/3e956153acda38fa7570516bc1c4ebd42cf37ed3e81510b717e6f64b94f7ab46.jpg)  
+Figure 3. Accuracy (top-1) of anytime classification models as a function of average computational budget per image the on CIFAR-100, higher is better. MSDNet and RANet are trained with and without ISC and OFA techniques.
+
+For anytime prediction, Model-C-3 (even) and MSDNet with 10 classifiers are tested. From the results, we observe that the improved RANet can outperform the improved MSDNet, especially when the budget ranges from  $0.3 \times 10^{8}$  to  $0.6 \times 10^{8}$  FLOPs. Moreover, the improved RANet can achieve the highest accuracy ( $75\%$ ) with around  $0.2 \times 10^{8}$  less FLOPs. We further observe that the techniques (ISC and OFA) do not work well on the first classifier of the RANet.
+
+For budgeted batch classification, the results of RANet, Model-C-3 and MSDNet with 8 classifiers are tested. From the results, we observe that the improved RANet is still superior to the improved MSDNet, especially when the budget greater than  $0.3 \times 10^{8}$ . The original RANet can outperform the improved RANet can be due to the performance dropping of the first classifiers. However, compared with
+
+![](images/7ff36face91dc71d542053c20ec687f5960655e75e58c74bed4b3d19bb6754a4.jpg)  
+Figure 4. Accuracy (top-1) of budgeted batch classification models as a function of average computational budget per image the on CIFAR-100, higher is better. MSDNet and RANet are trained with and without ISC and OFA techniques.
+
+MSDNet and improved MSDNet, the accuracy of improved RANet can be  $1\%$  and  $0.5\%$  higher respectively, which demonstrated the effectiveness of our RANet when implemented with the improved techniques.
+
+# References
+
+[1] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens van der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. In ICLR, 2018. 3  
+[2] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In ICCV, 2019. 3

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+# Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning
+
+Jize Zhang<sup>1</sup> Bhavya Kailkhura<sup>1</sup> T. Yong-Jin Han<sup>1</sup>
+
+# Abstract
+
+This paper studies the problem of post-hoc calibration of machine learning classifiers. We introduce the following desiderata for uncertainty calibration: (a) accuracy-preserving, (b) data-efficient, and (c) high expressive power. We show that none of the existing methods satisfy all three requirements, and demonstrate how Mix-n-Match calibration strategies (i.e., ensemble and composition) can help achieve remarkably better data-efficiency and expressive power while provably maintaining the classification accuracy of the original classifier. Mix-n-Match strategies are generic in the sense that they can be used to improve the performance of any off-the-shelf calibrator. We also reveal potential issues in standard evaluation practices. Popular approaches (e.g., histogram-based expected calibration error (ECE)) may provide misleading results especially in small-data regime. Therefore, we propose an alternative data-efficient kernel density-based estimator for a reliable evaluation of the calibration performance and prove its asymptotically unbiasedness and consistency. Our approaches outperform state-of-the-art solutions on both the calibration as well as the evaluation tasks in most of the experimental settings. Our codes are available at https://github.com/zhang64-llnl/Mix-n-Match-Calibration.
+
+# 1. Introduction
+
+Machine learning (ML) models, e.g., deep neural networks, are increasingly used for making potentially important decisions in applications ranging from object detection (Girshick, 2015), autonomous driving (Chen et al., 2015) to medical diagnosis (Litjens et al., 2017). Several of these applications are high-regret in nature and incorrect deci
+
+$^{1}$ Lawrence Livermore National Laboratories Livermore, CA 94550. Correspondence to: Jize Zhang <zhang64@llnl.gov>.
+
+Proceedings of the  $37^{th}$  International Conference on Machine Learning, Vienna, Austria, PMLR 119, 2020. Copyright 2020 by the author(s).
+
+![](images/87ca8ff4999136b05a82dab8b08ebe6674dbde2efbcf20add2a6895c83c0a9fc.jpg)
+
+![](images/78c2ab1ee6ad69f449378683803c0791c043b1936bf3872de08b9d69d3e67df2.jpg)
+
+![](images/6d8b00aae96c03c59720a165dcb698520d8db5252a252c6728c97855ad06a648.jpg)  
+Figure 1. (Top): (left) Temperature Scaling (TS) (Guo et al., 2017) is data-efficient (initial rapid ECE drop) but not expressive (fails to make progress later); in contrast, Isotonic Regression (IR) (Zadrozny & Elkan, 2002) is more expressive but data-inefficient; (right) IR does not preserve accuracy and introduces significant accuracy drop. (Bottom) Mix-n-Match: (left) Data Ensemble and Composition improve the data efficiency of IR, and (right) Model Ensemble enhances the expressive power of TS. All results are for calibrating a 50-layer Wide ResNet on ImageNet, apart from (a) left (28-layer Wide ResNet on CIFAR-10).
+
+![](images/ab78f8c910165a712db5d3e7e735fcd21c50696c3f2f4334050eaa0a5b6d4f6e.jpg)
+
+sions have significant costs. Therefore, besides achieving high accuracy, it is also crucial to obtain reliable uncertainty estimates, which can help deciding whether the model predictions can be trusted (Jiang et al., 2018; Kendall & Gal, 2017). Specifically, a classifier should provide a calibrated uncertainty measure in addition to its prediction. A classifier is well-calibrated, if the probability associated with the predicted class label matches the probability of such prediction being correct (Brocker, 2009; Dawid, 1982). Unfortunately, many off-the-shelf ML models are not well calibrated (Niculescu-Mizil & Caruana, 2005; Zadrozny & Elkan, 2001; 2002). Poor-calibration is particularly promi
+
+nent in highly complex models such as deep neural network classifiers (Guo et al., 2017; Hein et al., 2019; Lakshminarayanan et al., 2017; Nguyen et al., 2015).
+
+A popular calibration approach is to learn a transformation (referred to as a calibration map) of the trained classifier's predictions on a calibration dataset in a post-hoc manner. Pioneering work along this direction include Platt scaling (Platt, 2000), histogram binning (Zadrozny & Elkan, 2001), isotonic regression (Zadrozny & Elkan, 2002), Bayesian binning into quantiles (Naeini et al., 2015). Recently, calibration methods for multi-class deep neural network classifiers have been developed, which include: temperature, vector & matrix scaling (Guo et al., 2017), Dirichlet scaling (Kull et al., 2019), intra order-preserving method (Rahimi et al., 2020) and Gaussian processes based calibration methods (Milios et al., 2018; Wenger et al., 2020). Besides post-hoc calibrations, there also exist approaches for training ab-initio well calibrated models (Kumar et al., 2018; Lakshminarayanan et al., 2017; Pereyra et al., 2017; Seo et al., 2019; Tran et al., 2019), or representing the prediction uncertainty in a Bayesian framework (Blundell et al., 2015; Gal & Ghahramani, 2016; Maddox et al., 2019).
+
+Ideally, an uncertainty calibration method should satisfy the following properties: (a) accuracy-preserving - calibration process should not degrade the classification accuracy of the original classifier, (b) data-efficiency - the ability to achieve well-calibration without requiring a large amount of calibration data, and (c) high expressive power - sufficient representation power to approximate the canonical calibration function given enough calibration data. Despite the popularity of post-hoc calibration, we found that none of the existing methods satisfy all requirements simultaneously (Figure 1). Yet given practical constraints, such as high data collection costs, high complexity of calibration tasks, and need for accurate classifiers, the development of calibration methods which satisfy all three requirements simultaneously is crucial for the success of real-world ML systems.
+
+After calibrating a classifier, the next equally important step is to reliably evaluate the calibration performance. Most of the existing works judge the calibration performance by the expected calibration error $^{1}$  (ECE) (Naeini et al., 2015). ECE is usually estimated from a reliability diagram and its associated confidence histogram (Guo et al., 2017; Naeini et al., 2015). However, histogram-based ECE estimators can be unreliable (e.g., asymptotically biased or noisy) due to their sensitivity to binning schemes (Ashukha et al., 2020; Ding et al., 2020; Nixon et al., 2019; Vaicenavicius et al., 2019). Additionally, as a density estimator, histogram is known to be less data-efficient than alternative choices, such
+
+as kernel density estimators (Scott, 1992). Therefore, it is of utmost importance to develop reliable and data-efficient methods to evaluate the calibration performance.
+
+To achieve the aforementioned objectives, this paper makes the following contributions:
+
+1. We introduce the following desiderata for uncertainty calibration – (a) accuracy-preserving, (b) data-efficient, and (c) expressive.  
+2. We propose ensemble and compositional calibration strategies to achieve high data-efficiency and expressive power while provably preserving accuracy.  
+3. We propose a data-efficient kernel density estimator for a reliable evaluation of the calibration performance.  
+4. Using extensive experiments, we show that the proposed Mix-n-Match calibration schemes achieve remarkably better data-efficiency and expressivity upon existing methods while provably preserve accuracy.
+
+# 2. Definitions and Desiderata
+
+Consider a multi-class classification problem. The random variable  $X \in \mathcal{X}$  represents the input feature, and  $Y = (Y_{1},\ldots ,Y_{L}) \in \mathcal{V}$  represents the  $L$ -class one-hot encoded label. Let  $f: \mathcal{X} \to \mathcal{Z} \subseteq \Delta^{L}$  be a probabilistic classifier that outputs a prediction probability (or confidence) vector  $z = f(x) = (f_{1}(x),\dots,f_{L}(x))$ , where  $\Delta^L$  is the probability simplex  $\{(z_1,\dots,z_L)\in [0,1]^L|\sum_{l = 1}^L z_l = 1\}$ . Let  $\mathbb{P}(Z,Y)$  denote the joint distribution of the prediction  $Z$  and label  $Y$ . Expectations  $(\mathbb{E})$  are taken over this distribution unless otherwise specified. Let the canonical calibration function  $\pi (z)$  represents the actual class probability conditioned on the prediction  $z$  (Vaicenavicius et al., 2019):
+
+$$
+\begin{array}{l} \pi (z) = \left(\pi_ {1} (z), \dots , \pi_ {L} (z)\right) \\ \text {w i t h} \pi_ {l} (z) = \mathbb {P} [ Y _ {l} = 1 | f (X) = z ]. \tag {1} \\ \end{array}
+$$
+
+We would like the predictions to be calibrated, which intuitively means that it represents a true probability. The formal definition of calibration is as follows:
+
+Definition 2.1. The classifier  $f$  is perfectly calibrated, if for any input instances  $x \in \mathcal{X}$ , the prediction and the canonical calibration probabilities match:  $z = \pi(z)$  (Dawid, 1982).
+
+We focus on a post-hoc approach for calibrating a pretrained classifier, which consists of two steps: (1) finding a calibration map  $T:\Delta^L\to \Delta^L$  that adjusts the output of an existing classifier to be better calibrated, based on a set of  $n_c$  calibration data samples; and (2) evaluate the calibration performance based on a set of  $n_e$  evaluation data samples. Next, we discuss both steps in detail and highlight shortcomings of current methods.
+
+# 2.1. Calibration Step
+
+The first task in the calibration pipeline is to learn a calibration map  $T$  based on  $n_c$  calibration data samples  $\{(z^{(i)},y^{(i)})\}_{i = 1}^{n_c}$ . Existing calibration methods can be categorized into two groups:
+
+Parametric methods assume that the calibration map belongs to a finite-dimensional parametric family  $\mathcal{T} = \{T(z;\theta)|\theta \in \Theta \subseteq \mathbb{R}^M\}$ . As an example, for binary classification problems, Platt scaling (Platt, 2000) uses the logistic transformation to modify the prediction probability of a class (assuming  $z_{1}$ ):  $T(z_{1};a,b) = (1 + \exp (-az_{1} - b))^{-1}$ , where the scalar parameters  $a$ ,  $b$  are learned by minimizing the negative log likelihood on the calibration data set. Parametric methods are easily extendable to multi-class problems, such as temperature, matrix scaling (Guo et al., 2017) and Dirichlet scaling (Kull et al., 2019).
+
+Non-parametric methods assume that the calibration map is described with infinite-dimensional parameters. For binary classification problems, popular methods include: histogram binning (Zadrozny & Elkan, 2001) which leverages histograms to estimate the calibration probabilities  $\pi(z)$  as the calibrated prediction  $T(z)$ , Bayesian Binning (Naeini et al., 2015) performs Bayesian averaging to ensemble multiple histogram binning calibration maps, and isotonic regression (Zadrozny & Elkan, 2002) learns a piecewise constant isotonic function that minimizes the residual between the calibrated prediction and the labels. A common way to extend these methods to a multi-class setting is to decompose the problem as  $L$  one-versus-all problems (Zadrozny & Elkan, 2002), separately identify the calibration map  $T_l$  for each class probability  $(z_l)$  in the binary manner, and finally normalize the calibrated predictions into  $\Delta^L$ .
+
+While there are existing approaches tailored for calibrating multi-class deep neural network models, none of them simultaneously satisfy all three proposed desiderata (accuracy-preserving, data-efficient, expressive). Figure 1 (top right) highlights that good calibration capability might come at the cost of classification accuracy for approaches such as isotonic regression. This motivates us to design provably accuracy-preserving calibration methods. Furthermore, the effectiveness of calibration method changes with the amount of calibration data. Parametric approaches are usually data-efficient but have very limited expressive power. On the other hand, non-parametric approaches are expressive but highly data-inefficient. Therefore, in Figure 1 (top left), we see that temperature scaling is the best calibration method in data-limited regime, while isotonic regression is superior in data-rich regime. It is thus naturally desirable to design a calibrator that is effective in both data-limited and data-rich regime. However, earlier studies examined calibration methods with fixed dataset size (Guo et al., 2017; Kull et al., 2019; Wenger et al., 2020), and shed no light on this issue.
+
+# 2.2. Calibration Error Evaluation Step
+
+The next task in the calibration pipeline is to evaluate the calibration performance based on  $n_e$  evaluation data points  $\{(z^{(i)},y^{(i)})\}_{i = 1}^{n_e}$ . A commonly used statistics is the expected deviation from  $z$  to  $\pi (z)$ , also called expected calibration error (Naeini et al., 2015):
+
+$$
+\operatorname {E C E} ^ {d} (f) = \mathbb {E} \| Z - \pi (Z) \| _ {d} ^ {d} = \int \| z - \pi (z) \| _ {d} ^ {d} p (z) d z \tag {2}
+$$
+
+where  $\| \cdot \|_d^d$  denotes the  $d$ -th power of the  $\ell_d$  norm, and  $p(z)$  represents the marginal density function of  $Z = f(X)$ . The original ECE definition adopts  $d = 1$  (Guo et al., 2017; Naeini et al., 2015), while  $d = 2$  is also commonly used (Brocker, 2009; Hendrycks et al., 2019; Kumar et al., 2019).
+
+Note that probabilities in Eq. (1) and Eq. (2) cannot be computed directly using finite samples, since  $\pi(z)$  is a continuous random variable. This motivates the need of designing reliable ECE estimators. A popular estimation approach is based on histograms (Naeini et al., 2015). It partitions the evaluation data points into  $b$  bins  $\{B_1, \ldots, B_b\}$  according to the predictions  $z$ , calculate the average prediction  $\bar{f}(B_i)$  and label  $\bar{\pi}(B_i)$  inside the bins  $B_i$ , and estimate ECE by:
+
+$$
+\overline {{\mathrm {E C E}}} ^ {d} (f) = \sum_ {i = 1} ^ {b} \frac {\# B _ {i}}{n _ {e}} \| \bar {f} (B _ {i}) - \bar {\pi} (B _ {i}) \| _ {d} ^ {d}. \tag {3}
+$$
+
+where  $\# B_{i}$  denotes the number of instances in  $B_{i}$ .
+
+Despite its simplicity, histogram-based estimator suffers from several issues. First, it has bias-variance dilemma with respect to the selection of bin amount and edge locations. For example, too few bins lead to under-estimation of ECE (Kumar et al., 2019), while too many bins leads to noisy estimates as each bin becomes sparsely populated (Ashukha et al., 2020; Ding et al., 2020; Nixon et al., 2019; Vaicenavicius et al., 2019). Therefore, histogram-based ECE estimators are unreliable (e.g., asymptotically biased or noisy) due to their sensitivity to the binning scheme. Unfortunately, a consistently reliable binning selection scheme does not exist (Scott, 1992; Simonoff & Udina, 1997). Finally, histogram-based estimator is known to converge slower than other advanced non-parametric density estimators (Scott, 1992), leading to a data-inefficient estimation of ECE.
+
+Next (in Sec. 3), we discuss the proposed Mix-n-Match calibration strategies which satisfy the above discussed desiderata. Later (in Sec. 4), we will address the issue of designing a reliable and data-efficient ECE estimator.
+
+# 3. Designing Calibration Methods
+
+We first present (in Sec. 3.1) a general strategy to design provably accuracy-preserving calibration methods. Next,
+
+we discuss strategies for parametric (in Sec. 3.2) and nonparametric calibration methods (in Sec. 3.3) to fulfill remaining desiderata.
+
+# 3.1. Accuracy-preserving Calibration
+
+We present a general form of accuracy-preserving calibration maps and validate its accuracy-preserving property.
+
+Definition 3.1 (Accuracy-Preserving Calibration Map). Let  $g:[0,1]\to \mathbb{R}_{\geq 0}$  be a non-negative strictly isotonic function. Then, an accuracy-preserving calibration map is given by:
+
+$$
+T (z) = \left(g \left(z _ {1}\right), g \left(z _ {2}\right), \dots , g \left(z _ {L}\right)\right) / \sum_ {l = 1} ^ {L} g \left(z _ {l}\right). \tag {4}
+$$
+
+In Eq. (4), we apply the same function  $g$  to transform all entries in the prediction probability vector  $z$  to an unnormalized vector  $g(z) = (g(z_1),\dots ,g(z_L))$ ; and normalize  $g(z)$  to a probability simplex  $\Delta^L$ . The single strictly isotonic function  $g$  maintains the ordering of class prediction probabilities, and preserves the classification accuracy.
+
+Proposition 3.1. The calibration map in Eq. (4) preserves the classification accuracy of the uncalibrated classifier.
+
+Proof. Please see supplementary material Sec. A.
+
+# 3.2. Parametric Calibrations
+
+Parametric methods are already data-efficient, thus, one simply needs to enforce the accuracy-preserving requirement and improve their insufficient expressive power.
+
+# 3.2.1. PRESERVING ACCURACY
+
+As discussed in Proposition 3.1, the use of a strictly isotonic function preserves the accuracy. Fortunately, several existing parametric methods, such as, Platt (Platt, 2000) or temperature scaling (Guo et al., 2017), and beta scaling (Kull et al., 2017), employ strictly isotonic functions – logistic function and beta function, respectively. Therefore, these methods are already accuracy-preserving. Otherwise, the general form as provided in Eq. (4) can be used for designing accuracy-preserving calibration maps.
+
+# 3.2.2. IMPROVING EXPRESSIVITY BY MODEL ENSEMBLE
+
+We outline a strategy compatible with any parametric calibration method to improve its expressivity. The idea is to use an ensemble of calibration maps from the same accuracy-preserving parametric family, but with different parameters (see Figure 2):
+
+$$
+T (z) = w _ {1} T (z; \theta_ {1}) + w _ {2} T (z; \theta_ {2}) + \ldots + w _ {M} T (z; \theta_ {M}),
+$$
+
+where  $w$  are non-negative coefficients summing up to one. The weighted sum preserves isotonicity, thus the ensemble
+
+![](images/4c36c20b3b41e539894c8c0ed4e87d71063a486097bac0c357f121d48630b72e.jpg)  
+Figure 2. Model Ensemble calibration for improving expressivity. The idea is to use the weighted averaged outputs of an ensemble of  $M$  calibration maps to get the final calibrated prediction. Trainable parameters are highlighted in red.
+
+inhibits the accuracy-preserving property from its individual components. The increased expressivity stems from the fact that more parameters become adjustable, including  $\theta_{j}$  and the weights  $w_{j}$  for each component  $j$  in the ensemble. We find the weights  $w$  and parameters  $\theta$  by minimizing the loss  $R(.)$  between calibrated predictions  $T(z)$  and labels  $y$ :
+
+$$
+\underset {w, \theta} {\text {m i n i m i z e}} \quad \sum_ {i = 1} ^ {n _ {c}} R \left(\sum_ {j = 1} ^ {M} w _ {j} T \left(z ^ {(i)}; \theta_ {j}\right), y ^ {(i)}\right)
+$$
+
+$$
+s. t. \quad \mathbf {1} _ {1 \times M} w = 1; w \geq \mathbf {0} _ {M \times 1}.
+$$
+
+Using the above formulation, we show a specific generalization of temperature scaling (TS) (Guo et al., 2017) to satisfy the proposed desiderata.
+
+Ensemble Temperature Scaling (ETS). Note that TS is already accuracy-preserving and data-efficient. Next, we propose an ensemble formulation to improve the expressivity of TS while maintaining its accuracy-preserving and data-efficiency properties. Specifically, we propose a three-component ensemble as follows:
+
+$$
+T (z; w, t) = w _ {1} T (z; t) + w _ {2} z + w _ {3} \frac {1}{L}, \tag {5}
+$$
+
+where the calibration map for original TS is expressed by  $T(z; t) = (z_1^{1/t}, z_2^{1/t}, \ldots, z_L^{1/t}) / \sum_{l=1}^{L} z_l^{1/t}$ . Interestingly, the remaining two components in the ensemble are also TS calibration maps but with fixed temperature  $t$ :
+
+- TS calibration map with  $t = 1$  (outputs uncalibrated prediction  $z$ ). It increases the stability when the original classifier is well calibrated (Kull et al., 2017).  
+- TS calibration map with  $t = \infty$  (outputs uniform prediction  $z_{l} = 1 / L$  for each class). It 'smoths' the predictions, similar to how label-smoothing training technique smoothes the one-hot labels (Szegedy et al., 2016), which has shown to be successful in training better calibrated neural networks (Müller et al., 2019).
+
+The weight  $w$  and temperature  $t$  of ensemble is identified
+
+![](images/23a7d32059869c778829c94c49c729f4f5cd128b25df5c1b874555ef58b4f73b.jpg)  
+Figure 3. Data Ensemble calibration for improving data-efficiency. The idea is to ensemble the prediction-label pairs from all  $L$  classes and learn a single calibration map (e.g., strictly isotonic function for IRM) that is highlighted in red.
+
+by solving the following convex optimization problem:
+
+$$
+\underset {t, w} {\text {m i n i m i z e}} \quad \sum_ {i = 1} ^ {n _ {c}} R \left(w _ {1} T \left(z ^ {(i)}; t\right) + w _ {2} z ^ {(i)} + w _ {3} \frac {1}{L}, y ^ {(i)}\right)
+$$
+
+s.t.  $t > 0;\mathbf{1}_{1\times 3}w = 1;w\geq \mathbf{0}_{3\times 1}.$
+
+ETS preserves the accuracy, as it uses a convex combination of (strictly) isotonic function  $g = z_l^{1/t}$  across all classes/components. Further, as ETS only has three additional parameters (the weights) compared to TS, we expect it to be data-efficient. We will see later in Sec. 5.1, ETS is significantly more expressive than TS while maintaining its accuracy-preserving and data-efficiency properties.
+
+# 3.3. Non-parametric Calibrations
+
+Since non-parametric methods are generally expressive, we focus on providing solutions to enforce the accuracy-preserving requirement, and to improve their data-efficiency.
+
+# 3.3.1.PRESERVING ACCURACY
+
+Following Proposition 3.1, in order to preserve accuracy, a strictly isotonic calibration function is needed to be constructed non-parametrically. For binary classification, this requirement is satisfied by the isotonic regression (IR) calibration (Zadrozny & Elkan, 2002): for class 1 (class 2 is the complement), it sorts data points according to their predictions  $(z_{1}^{(1)} \leq z_{1}^{(2)} \dots \leq z_{1}^{(n_{c})})$ , then fits an isotonic function  $g$  to minimize the residual between  $g(z_{1})$  and  $y_{1}$ . The common way to extend this method to a multi-class setting is to decompose the problem as  $L$  one-versus-all problem, which we further denote as IROvA. Unfortunately, this formulation is neither accuracy-preserving nor data-efficient. To extend IR to multi-class problems while preserving accuracy, we use the accuracy-preserving calibration map as defined in Def. 3.1. This calibration map work identically on all the classes and does not distinguish among them. Next, we explain how this procedure is also more data-efficient than the conventional IROvA approach.
+
+# 3.3.2. IMPROVING EFFICIENCY BY DATA ENSEMBLE
+
+We first explain the proposed multi-class isotonic regression (IRM) procedure, and then comment on its data-efficiency.
+
+![](images/e2ac02a5de1a21de600a4dbc4e67ee312b8572b27af9650b88108fd73b9df39f.jpg)  
+Figure 4. Composition-based calibration for achieving both high data-efficiency as well as high expressivity. The uncalibrated prediction is transformed by the parametric (or efficient) calibrator, followed by the non-parametric (or expressive) calibrator. Trainable parameters are highlighted in red.
+
+IRM first ensembles the predictions and labels from all the classes, then learn a strictly isotonic function  $g$  that best fits the transformed predictions versus labels (see Figure 3):
+
+Step 1 (Data ensemble): extract all entries of prediction vector  $\{z^{(i)}\}_{i = 1}^{n_c}$  and label vector  $\{y^{(i)}\}_{i = 1}^{n_c}$ . Let  $\{a^{(j)}\}_{j = 1}^{n_cL}$  and  $\{b^{(j)}\}_{j = 1}^{n_cL}$  denote the set of  $n_cL$  prediction and label entries. Sort both vectors such that  $a^{(1)} \leq a^{(2)} \leq \ldots \leq a^{(n_cL)}$ .
+
+Step 2 (Isotonic regression): learn an isotonic function  $g^{*}$  by minimizing the squared error loss between  $g(a)$  and  $b$ :
+
+$$
+\underset {g \in \mathcal {G}} {\text {m i n i m i z e}} \quad \sum_ {j = 1} ^ {n _ {c} L} [ g (a ^ {(j)}) - b ^ {(j)} ] ^ {2},
+$$
+
+where  $\mathcal{G}$  is a family of piecewise constant isotonic functions (Zadrozny & Elkan, 2002). The pair-adjacent violator algorithm (Ayer et al., 1955) is used to find the best function.
+
+Step 3 (Imposing strict isotonicity): the learned function  $g^{*}$  is only isotonic. To make it strictly isotonic, we modify it to  $\hat{g}(a) = g^{*}(a) + \epsilon a$ , where  $\epsilon$  is a very small positive number, such that  $g(a) < g(a')$  whenever  $a < a'$ . Plugging the strictly isotonic function  $\hat{g}$  back to Eq. (4), we can obtain the non-parametric calibration map.
+
+Remark. Comparing to IROvA, the proposed IRM preserves the accuracy. In addition, it is more data-efficient, since it uses  $n_c L$  data points to identify one isotonic function in contrast to  $n_c$  data points in IROvA. We should also highlight that these benefits do not come free: by enforcing the same calibration map on all the classes, the proposed approach is less expressive than IROvA. In fact, we expect an efficiency-expressivity trade-off for the proposed solution – with the number of classes  $L$  increasing, it will become more data-efficient but less expressive comparing to one-vs-all. This phenomenon is later verified in Sec. 5.2.
+
+# 3.4. The Best of Both Worlds by Composition
+
+Parametric and non-parametric approaches each have their own advantages. To get the best of both worlds, i.e., high data-efficiency of parametric methods and high expressivity of non-parametric methods, we propose a compositional method as well. Specifically, we propose to apply a data-efficient parametric calibration method first, and then conduct non-parametric calibration on the parametric calibrated entries (see Figure 4). Intuitively, first fitting a parametric
+
+function acts like a baseline for variance reduction (Kumar et al., 2019) and then conducting a non-parametric calibration enjoys higher data-efficiency than the non-parametric calibration alone. Expressivity is unaffected by the composition since no additional restriction is imposed on the non-parametric layer. Accuracy-preserving property is satisfied if the adopted parametric and non-parametric calibration maps satisfy Def. 3.1, since the composition of strictly isotonic functions remains strictly isotonic.
+
+# 4. Evaluating Calibration Errors
+
+Next step in the calibration pipeline is to evaluate the calibration performance by estimating the expected calibration error as given in Eq. (2). The primary challenge is the involvement of two unknown densities  $p(z)$  and  $\pi(z)$ . Histogram-based estimator (Naeini et al., 2015) replaces the unknown densities by their bin-discretized version as given in Eq. (3). It is easy to implement, but also inevitably inherits drawbacks from histograms, such as the sensitivity to the binning schemes, and the data-inefficiency.
+
+We alleviate these challenges by replacing histograms with non-parametric density estimators that are continuous (thus, avoid the binning step) and, are more data-efficient. Specifically, we use kernel density estimation (KDE) (Parzen, 1962; Rosenblatt, 1956) to estimate the ECE for its implementation easiness and tractable theoretical properties.
+
+# 4.1. KDE-based ECE Estimator
+
+Let  $K:\mathbb{R}\to \mathbb{R}_{\geq 0}$  denote a smoothing kernel function (Tsybakov, 2008). Given a fixed bandwidth  $h > 0$  we have  $K_{h}(a) = h^{-1}K(a / h)$ . Based on the evaluation dataset, the unknown probabilities are estimated using KDE as follows:
+
+$$
+\tilde {p} (z) = \frac {h ^ {- L}}{n _ {e}} \sum_ {i = 1} ^ {n _ {e}} \prod_ {l = 1} ^ {L} K _ {h} (z _ {l} - z _ {l} ^ {(i)}),
+$$
+
+$$
+\tilde {\pi} (z) = \frac {\sum_ {i = 1} ^ {n _ {e}} y ^ {(i)} \prod_ {l = 1} ^ {L} K _ {h} (z _ {l} - z _ {l} ^ {(i)})}{\sum_ {i = 1} ^ {n _ {e}} \prod_ {l = 1} ^ {L} K _ {h} (z _ {l} - z _ {l} ^ {(i)})}.
+$$
+
+- Plugging them back in Eq. (2), we obtain the KDE-based ECE estimator:
+
+$$
+\widetilde {\mathrm {E C E}} ^ {d} (f) = \int \| z - \tilde {\pi} (z) \| _ {d} ^ {d} \tilde {p} (z) d z. \tag {6}
+$$
+
+The integration in Eq. (6) can be performed numerically (e.g., using Trapzoidal rule).
+
+We next provide a theoretical analysis of statistical properties of the proposed KDE ECE estimator when  $d = 1$ . The results for  $d = 2$  can be obtained similarly.
+
+Theorem 4.1 (Statistical properties). Assuming the unknown densities  $p(z)$  and  $\pi(z)$  are smooth ( $\beta$ -Hölder) and
+
+bounded, with the bandwidth  $h \asymp n_e^{-1 / (\beta + L)}$ , the KDE ECE is asymptotically unbiased and consistent, with a convergence rate  $|\mathbb{E}[\widetilde{ECE}^1(f)] - ECE^1(f)| \in O(n_e^{-\beta / (\beta + L)})$ .
+
+Proof. Please see supplementary material Sec. B.
+
+As verifying these smoothness assumptions in practice is highly non-trivial (Kumar et al., 2019), we corroborate our theoretical results using empirical comparisons in Sec. 5.1. The implementation details for KDE is provided in the supplementary material Sec. C.
+
+Dimensional reduction for multi-class problems. Convergence rates of non-parametric density estimators depend undesirably on the class dimension  $L$ , making the estimation challenging for multi-class problems. A way around this curse of dimensionality problem is to use the top-label ECE $^d$  (Guo et al., 2017) or the class-wise ECE $^d$  (Kull et al., 2019; Kumar et al., 2019). Both reduce the effective dimension to one, but weaken the calibration notion in Def. 2.1, meaning that they can be zero even if the model is not perfectly calibrated (Vaicenavicius et al., 2019).
+
+# 4.2. A Dimensionality-Independent Ranking Method
+
+In many practical situations, the main goal for evaluating calibration errors is to compare (or rank) calibration maps. However, rankings based on the approximations, e.g., top-label and class-wise  $\mathrm{ECE}^d$ , have been observed to be contradictory (Kull et al., 2019; Nixon et al., 2019). This raises the question rankings based on these approximations are indicative of the ranking based on actual  $\mathrm{ECE}^d$  in Eq. (2).
+
+Next, we present a dimensionality-independent solution to compare calibration maps according to their actual calibration capabilities, rather than resorting to weaker variants. The solution relies on the well-known calibration refinement decomposition (Murphy, 1973) for the strictly proper scoring loss (Gneiting & Raftery, 2007). Thus, it is applicable only when  $d = 2$ , since the absolute loss ( $d = 1$ ) is improper (Buja et al., 2005). Since  $\mathrm{ECE}^1$  and  $\mathrm{ECE}^2$  are closely related ( $\sqrt{\mathrm{ECE}^2} < \mathrm{ECE}^1 < \sqrt{L \cdot \mathrm{ECE}^2}$ ), we anticipate comparisons based on  $\mathrm{ECE}^2$  and  $\mathrm{ECE}^1$  should be similar. Specifically, we propose to use calibration gain (defined next) for the comparison.
+
+Definition 4.1. The calibration gain is defined as the reduction in  $\mathrm{ECE}^d$  after applying a calibration map  $(T\circ f)$ :
+
+$$
+\Delta \mathrm {E C E} ^ {2} (T) = \mathrm {E C E} ^ {2} (f) - \mathrm {E C E} ^ {2} (T \circ f).
+$$
+
+Higher gain indicates a better calibration map.
+
+Proposition 4.2. For accuracy-preserving maps in Def. 3.1, the calibration gain equals the reduction of squared loss between predictions and labels after calibration:
+
+$$
+\Delta E C E ^ {2} (T) = \mathbb {E} \| Z - Y \| _ {2} ^ {2} - \mathbb {E} \| T (Z) - Y \| _ {2} ^ {2}. \tag {7}
+$$
+
+Proof. Please see supplementary material Sec. D.
+
+For non accuracy-preserving methods (Table 1), the squared loss reduction in Eq. (7) bounds its actual calibration gain from below, and may not facilitate a fair comparison.
+
+Finally, given an evaluation dataset, Eq. (7) is estimated by:
+
+$$
+\widehat {\Delta \mathrm {E C E}} ^ {2} (T) = \frac {1}{n _ {e}} \sum_ {i = 1} ^ {n _ {e}} \left(\| z ^ {(i)} - y ^ {(i)} \| _ {2} ^ {2} - \| T \left(z ^ {(i)}\right) - y ^ {(i)} \| _ {2} ^ {2}\right) \tag {8}
+$$
+
+which converges at the rate of  $O(n_{e}^{-1 / 2})$  independent of the class dimension  $L$  and avoids the curse of dimensionality.
+
+# 5. Experiments
+
+# 5.1. Calibration Error Evaluations
+
+We compare the finite sample performance of proposed KDE-based  $\mathrm{ECE}^d$  estimator with histogram-based ones on a synthetic binary classification problem (Vaicenavicius et al., 2019). The classifier is parameterized by two parameters  $\beta_0, \beta_1$  (described in detail in supplementary material Sec. E). We consider a less-calibrated case  $\beta_0 = 0.5, \beta_1 = -1.5$ , and a better-calibrated case with  $\beta_0 = 0.2, \beta_1 = -1.9$ . The canonical calibration probability  $\pi^{(f)}(z)$  has a closed-form expression (Eq. (14)), allowing us to obtain the ground truth ECE (Eq. (2)) using Monte Carlo integration with  $10^6$  samples. We compare the ground truth to the estimation of  $\mathrm{ECE}^1$  using KDE and histogram-based estimators – one with 15 equal-width bins and other with data-dependent binning scheme (Sturges, 1926). In Figure 5, we vary the size of evaluation samples  $n_e$  from 64 to 1024 and plot the mean absolute error (averaged over 1000 independent experiments) between KDE/Histograms estimates and the ground truth. KDE consistently outperforms histogram-based estimators regardless of the binning schemes. The discrepancy is particularly noticeable with small  $n_e$ , highlighting KDE's superior efficiency in data-limited regime. In rest of the paper, we adopt KDE for estimating ECE, unless otherwise specified. Additional results can be found in the supplementary material, e.g., the distribution of the estimation errors in Figure 7 and comparison of the proposed KDE estimators with recently proposed debiased histogram ECE estimators (Kumar et al., 2019) in Figure 9.
+
+# 5.2. Calibrating Neural Network Classifiers
+
+We calibrate various deep neural network classifiers on popular computer vision datasets: CIFAR-10/100 (Krizhevsky, 2009) with 10/100 classes and ImageNet (Deng et al., 2009) with 1000 classes. For CIFAR-10/100, we trained DenseNet (Huang et al., 2017), LeNet (LeCun et al., 1998), ResNet (He et al., 2016) and WideResNet (WRN) (Zagoruyko & Komodakis, 2016). The training detail is described in Sec. F.
+
+![](images/561331123a33ecb8f84acfd637d5c5722423f26405f0f2500ed099d92305b7be.jpg)  
+Figure 5. Average absolute error for different ECE estimators as a function of the number of samples used in the ECE estimation. KDE-based ECE estimator achieves lower estimation error, especially when the evaluation dataset is small.
+
+![](images/d72cee399a885688932a5c488f0836f3e215e22784fe4baa1f470d883c7bcf0d.jpg)
+
+We use 45000 images for training and hold out 15000 images for calibration and evaluation. For ImageNet, we acquired 4 pretrained models from (Paszke et al., 2019) which were trained with 1.3 million images, and 50000 images are hold out for calibration and evaluation.
+
+We compare seven calibration methods: for parametric approaches, we use TS, our proposed three-component model ensemble approach ETS, and the Dirichlet calibration with off-diagonal regularization (DirODIR) (Kull et al., 2019). Following (Kumar et al., 2019), we use the squared error as the loss function to fit TS and ETS. For non-parametric approaches, we compare IROvA, our proposed multi-class accuracy-preserving scheme IRM, and the composition method that combines IROvA with TS as described in Sec. 3.3 (referred to as IROvA-TS). In addition, we include the Gaussian Process calibration (GPC) (Wenger et al., 2020). Among all examined methods, only TS, ETS and IRM are accuracy-preserving.
+
+For our first experiment, we adopt a standard calibration setup (Guo et al., 2017) with fixed-size calibration  $n_c$  and evaluation  $n_e$  datasets. We randomly split the hold-out dataset into  $n_c = 5000$ ,  $n_e = 10000$  for CIFAR-10/100 and  $n_c = n_e = 25000$  for ImageNet. We randomly split the hold-out dataset into  $n_c$  calibration points to learn the calibration map, and  $n_e$  evaluation points to evaluate ECE and classification accuracy. All results are averaged over 100 independent runs. On ImageNet, GPC fails to converge due to its high computational cost, thus we exclude its results.
+
+Table 1 displays top-label  $\mathrm{ECE}^1$  and Table 2 displays the calibration gain  $\Delta \mathrm{ECE}^2$ . Overall the rankings of calibration methods by top-label  $\mathrm{ECE}^1$  or by  $\Delta \mathrm{ECE}^2$  are very similar. Our proposed strategies consistently lead to better performance than the baseline implementations (ETS over TS; IRM and IROvA-TS over IROvA). Depending on the model/data complexity, either parametric or non-parametric variants may be more suitable.
+
+Note that calibration methods may perform differently with
+
+Table 1. Top-label  ${\mathrm{{ECE}}}^{1}\left( \% \right)$  (lower is better). The number following a models name denotes the network depth (and width if applicable).  
+
+<table><tr><td>Dataset</td><td>Model</td><td>Uncalibrated</td><td>TS</td><td>ETS (ours)</td><td>IRM (ours)</td><td>IROvA</td><td>IROvA-TS (ours)</td><td>DirODIR</td><td>GPC</td></tr><tr><td>CIFAR-10</td><td>DenseNet 40</td><td>3.30</td><td>1.04</td><td>1.04</td><td>1.18</td><td>1.16</td><td>1.11</td><td>1.23</td><td>1.68</td></tr><tr><td>CIFAR-10</td><td>LeNet 5</td><td>1.42</td><td>1.16</td><td>1.13</td><td>1.19</td><td>1.26</td><td>1.26</td><td>1.29</td><td>1.14</td></tr><tr><td>CIFAR-10</td><td>ResNet 110</td><td>4.25</td><td>2.05</td><td>2.05</td><td>1.53</td><td>1.45</td><td>1.39</td><td>1.82</td><td>1.40</td></tr><tr><td>CIFAR-10</td><td>WRN 28-10</td><td>2.53</td><td>1.61</td><td>1.61</td><td>1.02</td><td>0.994</td><td>0.967</td><td>1.49</td><td>1.05</td></tr><tr><td>CIFAR-100</td><td>DenseNet 40</td><td>12.22</td><td>1.55</td><td>1.54</td><td>3.32</td><td>4.48</td><td>2.22</td><td>1.56</td><td>1.51</td></tr><tr><td>CIFAR-100</td><td>LeNet 5</td><td>2.76</td><td>1.11</td><td>1.05</td><td>1.33</td><td>3.67</td><td>3.18</td><td>1.17</td><td>1.36</td></tr><tr><td>CIFAR-100</td><td>ResNet 110</td><td>13.61</td><td>2.75</td><td>1.93</td><td>4.78</td><td>5.27</td><td>3.00</td><td>2.46</td><td>1.98</td></tr><tr><td>CIFAR-100</td><td>WRN 28-10</td><td>4.41</td><td>3.24</td><td>2.80</td><td>3.16</td><td>3.45</td><td>2.92</td><td>3.11</td><td>1.58</td></tr><tr><td>ImageNet</td><td>DenseNet 161</td><td>5.09</td><td>1.72</td><td>1.33</td><td>2.13</td><td>3.97</td><td>3.01</td><td>4.61</td><td>-</td></tr><tr><td>ImageNet</td><td>ResNeXt 101</td><td>7.44</td><td>3.03</td><td>2.02</td><td>3.51</td><td>4.64</td><td>3.09</td><td>5.02</td><td>-</td></tr><tr><td>ImageNet</td><td>VGG 19</td><td>3.31</td><td>1.64</td><td>1.36</td><td>1.85</td><td>3.77</td><td>3.03</td><td>4.04</td><td>-</td></tr><tr><td>ImageNet</td><td>WRN 50-2</td><td>4.83</td><td>2.52</td><td>1.81</td><td>2.54</td><td>3.91</td><td>3.03</td><td>4.80</td><td>-</td></tr></table>
+
+Table 2. Calibration Gain  $\Delta\mathrm{ECE}^2$  (\%) (higher is better). Reported  $\Delta\mathrm{ECE}^2$  underestimate the actual calibration gains for IROvA, IROvA-TS, DirODIR, GPC. The number following a models name denotes the network depth (and width if applicable).  
+
+<table><tr><td>Dataset</td><td>Model</td><td>TS</td><td>ETS (ours)</td><td>IRM (ours)</td><td>IROvA</td><td>IROvA-TS (ours)</td><td>DirODIR</td><td>GPC</td></tr><tr><td>CIFAR-10</td><td>DenseNet 40</td><td>0.611</td><td>0.611</td><td>0.562</td><td>0.560</td><td>0.593</td><td>0.606</td><td>0.457</td></tr><tr><td>CIFAR-10</td><td>LeNet 5</td><td>0.027</td><td>0.028</td><td>-0.028</td><td>-0.004</td><td>-0.007</td><td>-0.119</td><td>0.022</td></tr><tr><td>CIFAR-10</td><td>ResNet 110</td><td>0.821</td><td>0.821</td><td>0.976</td><td>1.11</td><td>1.15</td><td>1.13</td><td>1.02</td></tr><tr><td>CIFAR-10</td><td>WRN 28-10</td><td>0.403</td><td>0.403</td><td>0.596</td><td>0.614</td><td>0.617</td><td>0.297</td><td>0.624</td></tr><tr><td>CIFAR-100</td><td>DenseNet 40</td><td>2.74</td><td>2.75</td><td>2.50</td><td>1.99</td><td>2.17</td><td>2.36</td><td>2.57</td></tr><tr><td>CIFAR-100</td><td>LeNet 5</td><td>0.077</td><td>0.085</td><td>0.028</td><td>-0.576</td><td>-0.558</td><td>-0.445</td><td>0.055</td></tr><tr><td>CIFAR-100</td><td>ResNet 110</td><td>3.14</td><td>3.17</td><td>2.90</td><td>2.63</td><td>3.09</td><td>3.50</td><td>3.14</td></tr><tr><td>CIFAR-100</td><td>WRN 28-10</td><td>0.204</td><td>0.263</td><td>0.534</td><td>0.134</td><td>0.218</td><td>0.0289</td><td>0.841</td></tr><tr><td>ImageNet</td><td>DenseNet 161</td><td>0.397</td><td>0.423</td><td>0.368</td><td>-0.518</td><td>-0.438</td><td>-1.63</td><td>-</td></tr><tr><td>ImageNet</td><td>ResNeXt 101</td><td>0.915</td><td>0.995</td><td>0.90</td><td>0.028</td><td>0.233</td><td>-1.35</td><td>-</td></tr><tr><td>ImageNet</td><td>VGG 19</td><td>0.147</td><td>0.168</td><td>0.115</td><td>-0.989</td><td>-0.969</td><td>-1.68</td><td>-</td></tr><tr><td>ImageNet</td><td>WRN 50-2</td><td>0.266</td><td>0.317</td><td>0.321</td><td>-0.604</td><td>-0.543</td><td>-1.51</td><td>-</td></tr></table>
+
+varying amounts of calibration data. A critically missing aspect of the standard practice of fixed-size comparison is that it does not reveal the data-amount-dependent behavior, and it may provide an incomplete picture of the calibration method's performance. To explore this holistically, we next conduct a learning curve analysis by varying the calibration dataset size and evaluating three desiderata-related properties (accuracy, data-efficiency and expressivity) of calibration approaches. While such learning curve analysis has been extensively used in the standard machine learning literature, its use in the calibration of deep neural network classifiers is scarce. Specifically, we reserve the same set of 5000 data points for evaluation, and vary the number of calibration data from 128 to 10000 (CIFAR-10/100) or 45000 (ImageNet). This process is repeated 100 times on the baseline (TS, IROvA) and their variants (ETS, IRM, IROvA-TS) to validate the effectiveness of Mix-n-Match.
+
+For Wide ResNets, Figure 6 shows how the average ECE
+
+and the accuracy over the repetitions change as a function of calibration dataset size  $n_c$ . Results for other cases are provided in the supplementary material Sec. F. We provide a thorough analysis on the learning curves below.
+
+Accuracy. From Figure 6 bottom, we observe that IROvA and IROvA-TS lead to serious accuracy reduction in the data-limited regime, and require a large calibration datasets to recover the original accuracy, while the accuracy-preserving approaches maintain the accuracy.
+
+Data-efficiency. Parametric methods (TS, ETS) enjoy the fastest converge of ECE (see Figure 6 top), which is anticipated. Our proposed data ensemble (IRM) and compositional (IROvA-TS) solutions also converge faster than IROvA. To quantify their data-efficiency gain, we record the required amount of data for non-parametric approaches to reach a reference calibration level (see Figure 10 right) in Table 4. The proposed data ensemble and compositional approaches achieve remarkable data-efficiency gains.
+
+![](images/aa7fd91641284a50091eebe8614dd764f5eea8227a1fb6e67550f1991edc0ebe.jpg)
+
+![](images/87cac74b2d8560b599eeb2ab576b10fa9b94d285373f5930a37fb44fa6b1e4c7.jpg)
+
+![](images/fc05952729fbdf452664321abd2c8607b892904f9dc5032dcfb9d32090c8f914.jpg)
+
+![](images/0fb41571932250c88ce16055c81c44087199c30f639b0cd03a03b61a3c82f559.jpg)  
+Figure 6. Learning curve comparisons of various calibration methods on top-label  $\mathrm{ECE}^1$  (top) and the classification accuracy (bottom).
+
+![](images/5d1d4a9b8e65584820babea6bda58cbad69441ebfc6b08f06f78f7db537bfbc3.jpg)
+
+![](images/21b09dd21fa6aeebdfd4e123bad49b57b09c920e9886e913b66d7451af1fb810.jpg)
+
+**Expressivity.** Note that a more expressive method should attain lower ECE with a sufficiently large calibration dataset. From Figure 6 top, we see that the proposed ensemble approach ETS is significantly more expressive than TS. This gain is particularly visible in many-class datasets, e.g., CIFAR-100 and ImageNet, where the canonical calibration function is expected to be complex. Also, the reduced expressivity of IRM over IROvA can be observed, verifying our hypothesis of its efficiency-expressivity trade-off. In Table 3, we provide a quantitative comparison on the expressivity of TS and ETS by measuring their final ECE (at the highest values of  $n_c$ , see Figure 10 left). We see that ETS is consistently more expressive and achieves lower final ECE value than TS across different models/datasets.
+
+Finally, we provide general guidelines on choosing an appropriate calibration method. We recommend ETS for general use and IRM as a strong alternative when the parametric form of ETS is misspecified (see Figure 6 left). Both approaches are accuracy-preserving and can be compared based on the proposed calibration gain metric. For complex calibration tasks, we recommend IROvA-TS if a large calibration dataset is available and the user does not have hard constraints on preserving the accuracy (see Figure 6 middle-right). We expand the analysis and the recommendation in the supplementary material Sec. G.
+
+To summarize, our proposed Mix-n-Match strategies provide substantial benefits for calibration, and can be easily incorporated into many existing calibration methods. We
+
+also provide guidelines on determining the most appropriate calibration method for a given problem in Sec. G. We expect the observed trends to generalize to other potential extensions. For example, the ensemble beta scaling method should be more expressive than the original beta scaling method (Kull et al., 2017), and the composition of TS with other non-parametric methods, e.g., IRM, should also be more data-efficient. We also anticipate additional efficiency gain if one substitutes TS with ETS in the composition, since ETS has been shown to be more expressive.
+
+# 6. Conclusion
+
+We demonstrated the practical importance of designing calibration methods with provable accuracy-preserving characteristics, high data-efficiency, and high expressivity. We proposed general Mix-n-Match calibration strategies (i.e., ensemble and composition) to extend existing calibration methods to fulfill such desiderata simultaneously. Furthermore, we proposed a data-efficient kernel density-based estimator for a reliable evaluation of the calibration performance. Comparisons with existing calibration methods across various datasets and neural network models showed that our proposed strategies consistently outperform their conventional counterparts. We hope that our developments will advance research on this essential topic further.
+
+# Acknowledgements
+
+This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and LLNL-LDRD Program Project No. 19-SI-001.
+
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+# A. Proofs of Proposition 3.1: Accuracy-Preserving Calibration Maps
+
+For an arbitrary pair of classes  $(\forall i,j\in [L]$ , where  $[L]$  denotes the set of positive integers up to  $L$ ) of the prediction probability vector  $z$ , let us assume that  $z_{i} < z_{j}$  without loss of generality. By definition, the strictly isotonic function  $g$  will output  $g(z_{i}) < g(z_{j})$  after the transformation. After dividing by the same normalization constant  $G(z)$ , the following relationship holds:  $[T(z)]_i < [T(z)]_j$ , where  $[\cdot ]_i$  represents the  $i$ -th entry of the vector. Since the order of entries in the prediction vector is unchanged after the calibration, the classification accuracy is preserved.
+
+# B. Proofs of Theorem 4.1: Statistical Properties of KDE-based ECE
+
+Mirror image KDE for boundary correction. Considering that we work with the probability simplex  $\Delta^L$  in the context of calibration, KDE can suffer from excessively large bias near the boundary of the simplex. To suitably correct for boundary bias without compromising the estimation quality, we adopt the mirror image KDE strategy (Singh & Poczos, 2014b). The convergence/consistency properties will be proved for such a choice.
+
+Smoothness assumption on the underlying densities. Let  $\beta$  and  $N$  be positive numbers. Given a vector  $s = (s_1, \ldots, s_L)$  with non-negative integer entries, let us use  $D^s \coloneqq \frac{\partial^{\|s\|_1}}{\partial^{s_1}z_1\cdots\partial^{s_L}z_L}$  to denote the differential operator. The  $\beta$ -Hölder class of densities  $\Sigma(\beta, N)$  contains those densities  $p: [0, 1]^L \to \mathbb{R}$  satisfying the following relationship:
+
+$$
+\left| D ^ {s} p (z) - D ^ {s} p (z ^ {\prime}) \right| \leq N \| z - z ^ {\prime} \| ^ {\beta - \| s \| _ {1}},
+$$
+
+for all  $z, z' \in \mathcal{Z}$  and all  $s$  with  $\| s \|_1 = \beta - 1$ . We assume that the distribution for predictions  $p(z)$  as well as the calibration probabilities  $\pi_l$  for each class  $l \in [L]$  belongs to the  $\beta$ -Hölder class.
+
+Assumption on the kernel function. We assume that the kernel function  $K: \mathbb{R} \to \mathbb{R}_{\geq 0}$  has bounded support  $[-1, 1]$  and satisfies:
+
+$$
+\int_ {- 1} ^ {1} K (u) d u = 1; \| K \| _ {1} = \int_ {- 1} ^ {1} | K (u) | d u <   \infty ; \forall j \in [ \beta - 1 ], \int_ {- 1} ^ {1} u ^ {j} K (u) d u = 1.
+$$
+
+Boundedness assumption. We denote  $C_{\pi} \coloneqq \sup_{z} \| z - \pi(z) \|_1$  and  $C_z \coloneqq \sup_{z} \tilde{p}(z)$  and assume they are both finite.
+
+We can bound the KDE estimation error of  $|\mathrm{ECE}(f) - \widetilde{\mathrm{ECE}}(f)|$  after applying the triangle inequality:
+
+$$
+\begin{array}{l} | \mathrm {E C E} (f) - \widetilde {\mathrm {E C E}} (f) | = \left| \int \| z - \pi (z) \| _ {1} p (z) d z - \int \| z - \tilde {\pi} (z)) \| _ {1} \tilde {p} (z) d z \right| \\ \leq \int \left| p (z) \| z - \pi (z) \| _ {1} - \tilde {p} (z) \| z - \pi (z) \| _ {1} \right| d z + \int \left| \tilde {p} (z) \left(\| z - \pi (z) \| _ {1} - \| z - \tilde {\pi} (z) \| _ {1}\right) \right| d z \tag {9} \\ \leq \sup  _ {z} \| z - \pi (z) \| _ {1} \int | p (z) - \tilde {p} (z) | d z + \sup  _ {z} \tilde {p} (z) \int \| \pi (z) - \tilde {\pi} (z) \| _ {1} d z \\ \leq C _ {\pi} \int | p (z) - \tilde {p} (z) | d z + C _ {z} \int \| \pi (z) - \tilde {\pi} (z) \| _ {1} d z \\ \end{array}
+$$
+
+which connects the absolute estimation error of ECE to the integrated estimation errors on the unknown densities  $p(z)$  and  $\pi (z)$ . We then borrow the established convergence rate and consistency proofs for (conditional) density functional of mirror KDE (Singh & Poczos, 2014a) to derive the statistical properties for the proposed KDE-based ECE estimator.
+
+Bias convergence rate. Taking the expectation and applying the Fubini's theorem on both sides in Eq. (9), we can derive:
+
+$$
+\begin{array}{l} \mathbb {E} | \mathrm {E C E} (f) - \widetilde {\mathrm {E C E}} (f) | \leq C _ {\pi} \int \mathbb {E} | p (z) - \tilde {p} (z) | d z + C _ {z} \int \mathbb {E} \| \pi (z) - \tilde {\pi} (z)) \| _ {1} d z \\ \leq C _ {\pi} C _ {B 1} (h ^ {\beta} + h ^ {2 \beta} + \frac {1}{n _ {e} h ^ {L}}) + C _ {z} C _ {B _ {2}} (h ^ {\beta} + h ^ {2 \beta} + \frac {1}{n _ {e} h ^ {L}}) \leq C (h ^ {\beta} + h ^ {2 \beta} + \frac {1}{n _ {e} h ^ {L}}), \\ \end{array}
+$$
+
+where  $C_{B1}$  and  $C_{B2}$  are constants given the sample size  $n_e$  and bandwidth  $h$  and  $C = C_{\pi}C_{B1} + C_zC_{B2}$ . The quantity  $h^{2\beta}$  is introduced by the Bias Lemma (Singh & Póczos, 2014b) from the mirror image KDE. For  $\int \mathbb{E}|p(z) - \tilde{p}(z)|dz$ ,
+
+we follow the standard KDE results (see Prop 1.1,1.2 and 1.2.3 (Tsybakov, 2008)) while the bound on the other term  $\int \mathbb{E}\| \pi (z) - \tilde{\pi} (z))\| _1dz$  follows 6.2 in (Singh & Poczos, 2014a) or (Döring et al., 2016; Györfi et al., 2006).
+
+The optimal bandwidth is  $h \asymp n_e^{-1 / (\beta + L)}$ , leading to a convergence rate of  $O\big(n_e^{-\beta / (\beta + L)}\big)$ .
+
+Consistency. Let  $\tilde{p}^{\prime}$  denote the KDE marginal density of  $z$  when an existing sample point is replaced by a new sample from the same distribution  $p(z)$ , and similarly  $\tilde{\pi}^{\prime}$  denote the KDE canonical calibration function after replacing a sample. Following (Singh & Poczos, 2014a), we can bound the density discrepancy before/after replacing a single sample by:
+
+$$
+\int \left| \tilde {p} (z) - \tilde {p} ^ {\prime} (z) \right| d z \leq \frac {C _ {V 1}}{n _ {e}}; \int \| \tilde {\pi} (z) - \tilde {\pi} ^ {\prime} (z) \| _ {1} d z \leq \frac {C _ {V 2}}{n _ {e}}, \tag {10}
+$$
+
+where  $C_{V1}$  and  $C_{V2}$  are constants in the class-dimension  $L$  and the kernel norm  $\| K\| _1$  for exact values. Suppose that we use two sets of  $n_e$  independent samples to estimate  $p$  and  $\pi$ , respectively. Since  $\widetilde{\mathrm{ECE}} (f)$  depends on  $2n_e$  independent variables, combining Eq. (10) with Eq. (9), we can use McDiarmids Inequality (McDiarmid, 1989) to derive that:
+
+$$
+\mathbb {P} (| \widetilde {\mathrm {E C E}} (f) - \widetilde {\mathrm {E E C E}} (f) | > \varepsilon) \leq 2 \exp \left(- \frac {2 \varepsilon^ {2}}{2 n _ {e} (2 C _ {V} / n _ {e}) ^ {2}}\right) = 2 \exp \left(- \frac {\varepsilon^ {2} n _ {e}}{4 C _ {V} ^ {2}}\right).
+$$
+
+for  $C_V = \max (C_{V1},C_{V2})$ . As  $\mathbb{P}(|\widetilde{\mathrm{ECE}} (f) - \widetilde{\mathrm{EECE}} (f)| > \varepsilon)$  approaches 0 when  $n_e\to \infty$ , the KDE-based ECE estimator is consistent.
+
+# C. KDE Implementation Detail
+
+Kernel function choice. Different types of kernel functions  $K(u)$  can be used, such as the Gaussian and Epanechnikov functions. Our choice is the Triweight Kernel  $K_{h}(u) = (1 / h)\frac{35}{32} (1 - (u / h)^{2})^{3}$  on  $[-1, 1]$ , since it has been recommended for problems with limited support interval (de Haan, 1999).
+
+Bandwidth selection. We use the popular rule-of-thumb  $h = 1.06\hat{\sigma} n_{e}^{-1 / 5}$  (Scott, 1992), where  $\hat{\sigma}$  is the standard deviation of the samples.
+
+# D. Proof for Proposition 4.2: Calibration Gain for Accuracy-Preserving Methods
+
+According to the calibration refinement decomposition (Murphy, 1973), the expected calibration error  $\mathrm{ECE}^2$  is equal to:
+
+$$
+\operatorname {E C E} ^ {2} (f) = \mathbb {E} \| z - \pi (z) \| _ {2} ^ {2} = \mathbb {E} \| z - y \| _ {2} ^ {2} - \mathbb {E} \| \pi (z) - y \| _ {2} ^ {2}, \tag {11}
+$$
+
+where  $\mathbb{E}\| z - y\| _2^2$  is the standard square loss and  $\mathbb{E}\| \pi (z) - y\| _2^2$  is the refinement error (Murphy, 1973) that penalizes the existence of inputs sharing the same prediction but different class labels. Before proceeding further, we first introduce the definition of injective calibration maps:
+
+Definition D.1 (Injective Calibration Map). The calibration map is injective if different prediction vectors remain different after calibration:  $\forall z, z' \in \mathcal{Z}, T(z) \neq T(z)$  if  $z \neq z'$ .
+
+Proposition D.1. The accuracy-preserving calibration map  $T$  in Def. 3.1 is injective.
+
+Proof. Given  $z \neq z'$ , without loss of generality assume  $G(z) \geq G(z')$  for their normalization constants. Since  $z \neq z'$ , there must exist at least one class  $l$  where  $z_l < z_l'$ . After the transformation by a strictly isotonic function  $g$ , we know that  $g(z_l) < g(z_l')$ . Then we can derive that:
+
+$$
+[ T (z) ] _ {l} - [ T (z ^ {\prime}) ] _ {l} = \frac {g (z _ {l})}{G (z)} - \frac {g (z _ {l} ^ {\prime})}{G (z ^ {\prime})} = \frac {g (z _ {l}) G (z ^ {\prime}) - g (z _ {l} ^ {\prime}) G (z)}{G (z) G (z ^ {\prime})} <   0.
+$$
+
+Therefore,  $T(z) \neq T(z')$  because their  $l$ -th entry is not equal. The calibration map is then injective.
+
+Note that the canonical calibration function in Eq. (1) is essentially the conditional expectation of binary random variables  $Y$ , as  $\pi_l(z) = \mathbb{P}[Y_l = 1 | f(X) = z] = \mathbb{E}[Y_l | f(X) = z]$ . By elementary properties of the conditional expectation, one can
+
+easily show that injective calibration maps will not change the canonical calibration probabilities, thus  $\pi (z) = \pi (T(z))$  for injective  $T$ . Combining this with the decomposition relationship in Eq. (11), we can show that:
+
+$$
+\begin{array}{l} \Delta \mathrm {E C E} ^ {2} (T) = \mathrm {E C E} ^ {2} (f) - \mathrm {E C E} ^ {2} (T \circ f) \\ = \mathbb {E} \| z - y \| _ {2} ^ {2} - \mathbb {E} \| \pi (z) - y \| _ {2} ^ {2} - \left(\mathbb {E} \| T (z) - y \| _ {2} ^ {2} - \mathbb {E} \| \pi (T (z)) - y \| _ {2} ^ {2}\right) \tag {12} \\ = \mathbb {E} \| z - y \| _ {2} ^ {2} - \mathbb {E} \| T (z) - y \| _ {2} ^ {2}. \\ \end{array}
+$$
+
+Therefore, after applying an injective calibration map, which include the proposed accuracy-preserving ones, any changes in the squared loss will be due to the change in  $\mathrm{ECE}^2$ .
+
+Remark. Most existing calibration methods are not injective. For example, in histogram binning (Zadrozny & Elkan, 2001) or the original isotonic regression method (Zadrozny & Elkan, 2002), all predictions inside certain intervals will be mapped to be identical, and violate the injective requirement. For parametric methods, such as vector, matrix (Guo et al., 2017), or Dirichlet scaling (Kull et al., 2019), different logits can be transformed to produce the same prediction probability vectors, and violate the injective requirement.
+
+# E. Experimental Details and Additional Results in Section 5.1
+
+# E.1. Experimental details
+
+For the synthetic example, the labels  $(Y)$  and input features  $(X)$  are distributed as:
+
+$$
+\mathbb {P} \left(Y _ {1} = 1\right) = \mathbb {P} \left(Y _ {2} = 1\right) = 1 / 2; \mathbb {P} \left(X = x \mid Y _ {1} = 1\right) = \mathcal {N} (x; - 1, 1); \mathbb {P} \left(X = x \mid Y _ {2} = 1\right) = \mathcal {N} (x; 1, 1). \tag {13}
+$$
+
+The probability of observing the label  $Y_{1} = 1$  conditioned on the input  $x$  can be written as:
+
+$$
+\mathbb {P} \left(Y _ {1} = 1 | X = x\right) = 1 / \left[ 1 + \exp (2 x) \right].
+$$
+
+We assume the prediction models to be in the following form, parameterized by  $\beta_0$  and  $\beta_{1}$
+
+$$
+z = f (x) = \left(z _ {1}, z _ {2}\right) = \left(\frac {1}{1 + \exp \left(- \beta_ {0} - \beta_ {1} x\right)}, \frac {\exp \left(- \beta_ {0} - \beta_ {1} x\right)}{1 + \exp \left(- \beta_ {0} - \beta_ {1} x\right)}\right).
+$$
+
+This leads to close-form expressions for the canonical calibration functions  $\pi (z) = (\pi_1(z),\pi_2(z))$
+
+$$
+\pi_ {1} (z) = \left[ 1 + \exp \left(- 2 \frac {\beta_ {0} + \log \left(1 / z _ {1} - 1\right)}{\beta_ {1}}\right) \right] ^ {- 1}, \pi_ {2} (z)) = 1 - \pi_ {1} (z). \tag {14}
+$$
+
+Finally, we estimate the ground-truth  $\mathrm{ECE}^d$  based on Monte Carlo integration: (i) generate  $10^{6}$  random input-output sample pairs according to Eq. (13), and (ii) record the sample average value of the quantity  $|z_1 - \pi_1(z)|^d$  as the ground-truth.
+
+# E.2. Additional results
+
+We plot the distribution of the errors between the ECE estimates and the ground-truth ECE in two representative scenarios: a data-limited scenario with  $n_e = 64$  in Figure 7 and a data-rich scenario with  $n_e = 1024$  in Figure 8. The KDE estimation errors are generally less biased (more concentrated around zero) as compared to histograms, corroborating the findings in Sec. 5.1. Judging from the variance of the estimation errors, the KDE estimation errors are generally less dispersed than the two histogram estimators, indicating that the KDE estimators are more reliable. In contrast, histogram ECE estimators tend to severely over-estimates ECE in data-limited regime, with the majority of their estimation errors being positive. Their sensitivity to the binning schemes can be also observed from the distribution discrepancies between using equal-width and data-dependent bins: the histogram estimator with data-dependent bins generally performs better than the one with equal-width bins, although it cannot reach the accuracy level of KDE estimators. However, it performs the worst in the data-rich scenario of Case 2 (Figure 8 bottom).
+
+![](images/73ae67b866dae4c9075e8aabc4eddaa6f4d0f7f3daee66b02b866b62121ceaaf.jpg)
+
+![](images/088d658650e4b2224b2ed541ed274db20954d0d45f5cac883b5f781fab517ecb.jpg)
+
+![](images/784e18910cdbe1c4105274dea40c419544ddf36a06dadc35926ca281eb07c591.jpg)
+
+![](images/273104f053916c843e15aa9b2b5f134fa1baefb1ecb76099077d330159add08d.jpg)  
+(b)  $n_e = 1024$
+
+![](images/0b74015f73ee152345a2c42b130aab38e33a8a1e236d85876dbd3a33d2334872.jpg)  
+(a)  $n_e = 64$
+
+![](images/c526906e769689da73e24ae3e22163e0365e6441c2f4f581bb3daaeddf382bea.jpg)
+
+![](images/66c70424d74193af58ca2a27f1ea4bdee18ede2fd3f5569430b055db7505598c.jpg)  
+Figure 7. Distribution of ECE estimation errors in Case 1:  $\beta_0 = 0.5$ ,  $\beta_{1} = -1.5$  with (a)  $n_e = 64$  and, (b)  $n_e = 1024$ .
+
+![](images/ddc781c8f95907fee0c790368a4060c93744d0bd0c5e273054be0e0e0126fe6b.jpg)
+
+![](images/16180712f085374fbe9b7d2c6d7af51470b61d07d1ce0db4048a9bbbfb32b55a.jpg)
+
+![](images/dc8d70ea19cbde7cf2bcb174f28f1165e0785c554ceb7d43e429fd2423c4d09c.jpg)
+
+![](images/8a9db29b029c4b0265cca83cad3d0503fc0cb3230df3724d8916a9ffd84dd460.jpg)  
+(a)  $n_e = 64$  
+(b)  $n_e = 1024$
+
+![](images/a37251221a875598fbc8ccc9dcc51de9a5a22dcd70964db832f1e0de054c87a7.jpg)  
+Figure 8. Distribution of ECE estimation errors in Case 2:  $\beta_0 = 0.2$ ,  $\beta_{1} = -1.9$  with (a)  $n_e = 64$ , and (b)  $n_e = 1024$ .
+
+Recently (Kumar et al., 2019) proposed a debiased histogram-based estimator for  $\mathrm{ECE}^{d = 2}$ , by leveraging error cancellations across different bins. We compare the proposed KDE ECE estimator with the debiased versions of histogram-based ECE estimators with both equal-width and data-dependent binning schemes. We vary the size of evaluation samples  $n_e$  from 64 to 1024 and plot the mean absolute error (averaged over 1000 independent experiments) between KDE/Debiased-Histograms estimates for  $\mathrm{ECE}^2$  and the ground truth in Figure 9. We observe that KDE-based estimator consistently performs better than the best-performing debiased histogram-based ECE estimators. This agrees with the findings in Sec. 5.1 and confirms the advantage of using KDE-based estimator over histograms-based estimators.
+
+![](images/e6db07687d364da1b4e50e133f3fd0ce9ab736f87dfe485c102fc59840bdb8b2.jpg)  
+Figure 9. Average absolute error for KDE ECE and debiased histogram ECE estimators as a function of the number of samples used in the ECE estimation. KDE-based ECE estimator achieves lower estimation error, especially when the evaluation dataset is small.
+
+![](images/3adb52ea3a8ba5c2b087cc9a197b00e208e8942169e578d7e63d63ce42f22f2c.jpg)
+
+# F. Experimental Detail and Additional Results in Section 5.2
+
+# F.1. Training details
+
+For training neural networks on CIFAR-10/100, we use SGD with Nesterov momentum and the cross-entropy loss. The weight decay is set to 0.0005, dampening to 0, momentum to 0.9, and minibatch size to 128. The initial learning rate is set to 0.1, and is dropped by a factor of 0.2 at 60, 120 and 160 epochs. For Wide ResNets, we use a dropout rate of 0.3. We train the models for a total of 500 epochs. We use standard mean/std normalization with flipping and data cropping augmentation as described in (Zagoruyko & Komodakis, 2016) on CIFAR-10/100 images.
+
+# F.2. Expanded results
+
+The quantitative measure of expressive power and data-efficiency is illustrated graphically in Figure 10 and discussed in Table 3 and Table 4. To summarize, ETS is comparably expressive to TS on CIFAR-10 and noticeably more expressive on CIFAR-100 and ImageNet. Both IRM and IROvA-TS are more efficient than IROvA. The relative efficiency gain of IRM increases as the problems become more complex. On the other hand, the relative efficiency gain of IROvA-TS appears to be quite stable on a wide range of problems.
+
+We also provide expanded results on the learning curve analysis for additional neural network classifiers (see Figure 11 to Figure 13). From the visual comparison of the ECE learning curves of ETS and TS, or IRM/irovA-TS and IROvA, we can confirm the importance to preserve the classification accuracy and the consistent benefit of employing the proposed Mix-n-Match strategies. Overall, in data-limited regime, parametric variants (TS, ETS) perform better than traditional
+
+non-parametric variants (IROvA, IROvA-TS) due to their high data-efficiency. ETS significantly outperforms TS and performs the best as the added expressive power from ensembles allows ETS to make further descent on ECE. The proposed accuracy-preserving non-parametric variant IRM also performs good: it is sometimes more effective than TS, although it cannot outperform ETS in most examined cases. The relatively good performance of IRM can be accredited to its high data-efficiency on complex calibration tasks. Going to the data-rich regime, the ECE reduction progress stalls for parametric methods. On complex problems, such as CIFAR-100 and ImageNet, this also applies to the accuracy-preserving non-parametric variants (IRM) due to its expressivity-efficiency trade-off. In contrast, the high expressive power of non-parametric variants (IROvA, IROvA-TS) allow them to keep minimizing the ECE and eventually outperform less expressive methods (ETS, TS or IRM) with sufficient amount of data – although, this cannot be verified in all the examined cases due to our limited data budget. In such regime, the composition method IROvA-TS significantly outperforms IROvA and performs the best due to its enhanced data-efficiency. Based on such observations, our further discussion on the guidelines of calibration methods will be restricted to ETS, IRM and IROvA-TS.
+
+![](images/786c654cf923c5579079e60942b069f41413f2416a8b2991a001b0c2bdd9dc41.jpg)  
+Expressive power by their final ECE value  
+Figure 10. Graphical illustration for the proposed measure of expressive power and data-efficiency.
+
+![](images/a520a6aaaf781d0d6ef633eac378b056020a51616210ba46dacaccd7dc604892.jpg)  
+Data Efficiency by their required data amount
+
+Table 3. ECE  ${}^{1}$  (%) with  ${n}_{c} = {10000}$  for CIFAR and  ${n}_{c} = {45000}$  for ImageNet; lower values imply more expressive power.  
+
+<table><tr><td>Dataset</td><td>Model</td><td>TS</td><td>ETS</td></tr><tr><td>CIFAR-10</td><td>DenseNet 40</td><td>1.32</td><td>1.32</td></tr><tr><td>CIFAR-10</td><td>LeNet 5</td><td>1.49</td><td>1.48</td></tr><tr><td>CIFAR-10</td><td>ResNet 110</td><td>2.12</td><td>2.12</td></tr><tr><td>CIFAR-10</td><td>WRN 28-10</td><td>1.67</td><td>1.67</td></tr><tr><td>CIFAR-100</td><td>DenseNet 40</td><td>1.73</td><td>1.72</td></tr><tr><td>CIFAR-100</td><td>LeNet 5</td><td>1.39</td><td>1.31</td></tr><tr><td>CIFAR-100</td><td>ResNet 110</td><td>2.81</td><td>2.15</td></tr><tr><td>CIFAR-100</td><td>WRN 28-10</td><td>3.23</td><td>2.85</td></tr><tr><td>ImageNet</td><td>DenseNet 161</td><td>1.95</td><td>1.75</td></tr><tr><td>ImageNet</td><td>ResNeXt 101</td><td>2.97</td><td>2.22</td></tr><tr><td>ImageNet</td><td>VGG 19</td><td>1.89</td><td>1.83</td></tr><tr><td>ImageNet</td><td>WRN 50-2</td><td>2.52</td><td>2.10</td></tr></table>
+
+Table 4. Required calibration data amount  ${n}_{c}$  to reach IRM’s performance with  ${n}_{c} = {128}$  samples; lower value means more data-efficient. All values are normalized (divided by 128) to show how many samples are equivalent to one sample in IRM for each method.  
+
+<table><tr><td>Dataset</td><td>Model</td><td>IRM</td><td>IROvA</td><td>IROvA-TS</td></tr><tr><td>CIFAR-10</td><td>DenseNet 40</td><td>1.0</td><td>2.45</td><td>2.10</td></tr><tr><td>CIFAR-10</td><td>LeNet 5</td><td>1.0</td><td>3.15</td><td>2.92</td></tr><tr><td>CIFAR-10</td><td>ResNet 110</td><td>1.0</td><td>1.84</td><td>1.70</td></tr><tr><td>CIFAR-10</td><td>WRN 28-10</td><td>1.0</td><td>1.98</td><td>1.90</td></tr><tr><td>CIFAR-100</td><td>DenseNet 40</td><td>1.0</td><td>37.6</td><td>17.9</td></tr><tr><td>CIFAR-100</td><td>LeNet 5</td><td>1.0</td><td>58.7</td><td>43.0</td></tr><tr><td>CIFAR-100</td><td>ResNet 110</td><td>1.0</td><td>28.1</td><td>10.7</td></tr><tr><td>CIFAR-100</td><td>WRN 28-10</td><td>1.0</td><td>24.2</td><td>15.6</td></tr><tr><td>ImageNet</td><td>DenseNet 161</td><td>1.0</td><td>282</td><td>174</td></tr><tr><td>ImageNet</td><td>ResNeXt 101</td><td>1.0</td><td>226</td><td>98.6</td></tr><tr><td>ImageNet</td><td>VGG 19</td><td>1.0</td><td>251</td><td>180</td></tr><tr><td>ImageNet</td><td>WRN 50-2</td><td>1.0</td><td>258</td><td>161</td></tr></table>
+
+![](images/95149e02b3967b9e5d5f4fb524f2fc0eef51afe74423b01dcf5014a621b2d611.jpg)  
+(a) CIFAR-10+DenseNet 40
+
+![](images/9187bc8f6e69d8812f1313fd96fa9fae50a103ceb76dc4b82f1b396c97b6304b.jpg)
+
+![](images/006265480ee60b9628e433cce1fa1aa1cc66a672f71c1bbf14e058d661ca6b9c.jpg)  
+(b) CIFAR-10+LeNet 5
+
+![](images/e2a82e2929b517203b3ba3bedb32256d21d17b6bcb32cddc48f6989db1501606.jpg)
+
+![](images/dd7f236bcf8bf0856b155f093dc04ecb67d15b509a0c41ee73a2ff909df59602.jpg)  
+(c) CIFAR-10+ResNet 110
+
+![](images/4548dfc1ff2832296f731d40b8fcbd83e0dfc40093358009a5de0424f6783ae2.jpg)  
+Figure 11. Learning curve comparisons of various calibration methods on top-label ECE $^1$  (left) and the classification accuracy (right) on CIFAR-10 dataset with (a) DenseNet 40 model; (b) LeNet 5 model; and (c) ResNet 110 model.
+
+![](images/336cdcf84897adb848c05f75b7520301347e0d98ca5608c208f68b97d8f89509.jpg)  
+(a) CIFAR-100+DenseNet 40
+
+![](images/d582977e141dab9e32d758c0044a18da368279be4100e2201a14b0336eb4c7a9.jpg)
+
+![](images/f4c3851d51a73f0eb308ebb66bc3e89024a72d643539e06541b89ac67ecb265d.jpg)  
+(b) CIFAR-100+LeNet 5
+
+![](images/024faef2818de0e61c4bed8fcd368e71c8098aeb5fe758ed3017532543747f47.jpg)
+
+![](images/8382771e9e4650750034b655231721c0632b7609b0d05de1363dbbb1ddeb6517.jpg)  
+(c) CIFAR-100+ResNet 110
+
+![](images/3ecf45a58951f79e9807a351d027775b14391489771e0f25a186f09a03f51b08.jpg)  
+Figure 12. Learning curve comparisons of various calibration methods on top-label ECE $^{1}$  (left) and the classification accuracy (right) on CIFAR-100 dataset with (a) DenseNet 40 model; (b) LeNet 5 model; and (c) ResNet 110 model.
+
+![](images/e34bebd280c498abe7ec07038a7bb21a8b19a77638a01098106bfdaa06a9d1c8.jpg)  
+(a) ImageNet+DenseNet 161
+
+![](images/a8bcdfc08721e26cf0f0863090d2cec6a6d684fa0c1f5f2139dfe5b8a41fdaf6.jpg)
+
+![](images/13c6e3516f5da4e27a5ac6751efeb2a88c737ce82422b5f1d1941fc6e0ed1461.jpg)  
+(b) ImageNet+ResNext 101
+
+![](images/513bd2a870cf5426a43a5876e5d726fc6334fce3bb5b47e39a8c0e25aab31e16.jpg)
+
+![](images/cb92be614ff66b1dbe1c5ffc6817a19afc3318259c001f7d496a0fd29cf47111.jpg)  
+(c) ImageNet+VGG19
+
+![](images/165519c5f7ad52c2c516aaff7f42fc058788b2ac4edbf04d2fbd2cb0e8e15ff5.jpg)  
+Figure 13. Learning curve comparisons of various calibration methods on top-label  $\mathrm{ECE}^1$  (left) and the classification accuracy (right) on ImageNet dataset with (a) DenseNet 161 model; (b) ResNext 101 model; and (c) VGG 19 model.
+
+# G. Guidelines
+
+First, we provide guidelines on choosing an appropriate calibration evaluation metric. If knowing the exact value of ECE is important, we recommend KDE-based top-label ECE estimator for its superior data-efficiency as compared to histograms. If the goal is to infer just the rankings not actual calibration errors, one should use the calibration gain metric. It provides a reliable and faithful comparison of different methods based on their actual calibration capabilities. We also note that calibration gain metric might be a lower bound for certain calibration methods, e.g., non accuracy-preserving methods.
+
+We next provide general guidelines on selecting the best calibration method (ETS vs. IRM vs. IROvA-TS), based on: (a) the complexity of the calibration task which is a function of the model complexity (number of free parameters) and the data complexity (number of classes), and (b) resources at hand (the amount of the calibration data).
+
+The complexity of the calibration task is directly related to the complexity of the canonical calibration function in Eq. (1). Although, we do not have the knowledge of the canonical calibration function, we expect a learning task with low model complexity and low data complexity to result in a low complexity calibration task (see Figure 11 (b)). Next, a learning task with low model complexity but high data complexity (Figure 12 (b)), or high model complexity but low data complexity (Figure 11 (a) and (c)) is expected to result in a moderately complex calibration task. Finally, we expect a learning task with high model & data complexity to result in a highly complex calibration task (Figure 12 (a) and (c), Figure 13).
+
+For low complexity calibration tasks, we see that the performance of uncalibrated models are already satisfactory. This observation agrees with results in (Guo et al., 2017). Further, all the calibration methods perform similarly, however, proposed variants performing slightly better than the baseline approaches. The use case of the most practical interest is where the calibration task is expected to be complex. In such scenarios, an ideal calibration map should have enough expressive power to accurately approximate the canonical calibration function in Eq. (1). However, to fit an expressive calibration map, sufficiently large amount of calibration data is required which may or may not be available. In data limited regime, ETS is recommended as the first choice, while IRM is a potential alternative when the parametric assumptions of ETS are improper (see Figure 6 top left and Figure 11 (c)). In data rich regime, we recommend using IROvA-TS for its high expressive power. For moderate complexity calibration tasks, the patterns are similar to high complexity calibration tasks. The only difference is that the gain of the proposed Mix-n-Match strategies are not as drastic as of the case where calibration task is of high complexity. Of course, if the user has hard-constraints on accuracy-preservation, the choice would be limited to the accuracy-preserving calibrators regardless of the data size or the task complexity. In such scenarios, we recommend ETS and IRM. We also want to emphasize that both ETS and IRM are fairly efficient and perform well on all ranges of the calibration data size.
+
+In summary, our take-home messages on the most appropriate calibration method are the following:
+
+- For complex calibration task (poorly calibrated model, large number of classes), when a large calibration dataset is available and the user does not have hard constraints on preserving accuracy, the proposed compositional method IROvA-TS is recommended to achieve the best degree of calibration.  
+- For all other cases, the proposed ensemble method ETS is recommended when the parametric assumption is proper. IRM is a strong alternative to be considered in order to avoid the risk of parametric form mis-specification of ETS in certain cases. Both approaches preserve the classification accuracy, and one can conveniently compare them based on the proposed calibration gain metric.

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+# RSVQA: Visual Question Answering for Remote Sensing Data
+
+Sylvain Lobry, Member, IEEE, Diego Marcos, Jesse Murray, Devis Tuia, Senior Member, IEEE
+
+This is the pre-acceptance version, to read the final version published in the journal IEEE Transactions on Geoscience and Remote Sensing, please go to: https://doi.org/10.1109/TGRS.2020.2988782.
+
+Abstract—This paper introduces the task of visual question answering for remote sensing data (RSVQA). Remote sensing images contain a wealth of information which can be useful for a wide range of tasks including land cover classification, object counting or detection. However, most of the available methodologies are task-specific, thus inhibiting generic and easy access to the information contained in remote sensing data. As a consequence, accurate remote sensing product generation still requires expert knowledge. With RSVQA, we propose a system to extract information from remote sensing data that is accessible to every user: we use questions formulated in natural language and use them to interact with the images. With the system, images can be queried to obtain high level information specific to the image content or relational dependencies between objects visible in the images. Using an automatic method introduced in this article, we built two datasets (using low and high resolution data) of image/question/answer triplets. The information required to build the questions and answers is queried from OpenStreetMap (OSM). The datasets can be used to train (when using supervised methods) and evaluate models to solve the RSVQA task. We report the results obtained by applying a model based on Convolutional Neural Networks (CNNs) for the visual part and on a Recurrent Neural Network (RNN) for the natural language part to this task. The model is trained on the two datasets, yielding promising results in both cases.
+
+Index Terms—Visual Question Answering, Deep learning, Dataset, Natural Language, Convolution Neural Networks, Recurrent Neural Networks, Very High Resolution, OpenStreetMap
+
+# I. INTRODUCTION
+
+REMOTE sensing data is widely used as an indirect source of information. From land cover/land use to crowd estimation, environmental or urban area monitoring, remote sensing images are used in a wide range of tasks of high societal relevance. For instance, remote sensing data can be used as a source of information for 6 of the 17 sustainable development goals as defined by the United Nations [1]. Due to the critical nature of the problems that can be addressed using remote sensing data, significant effort has been made to increase its availability in the last decade. For instance, Sentinel-2 satellites provide multispectral data with a relatively short revisiting time, in open-access. However, while substantial effort has been dedicated to improving the means of direct information extraction from Sentinel-2 data
+
+Sylvain Lobry, Diego Marcos, Jesse Murray and Devis Tuia are with Laboratory of Geo-Information Science and Remote Sensing, Wageningen University, The Netherlands email: work@sylvainlobry.com
+
+![](images/fce53a7f2e31ba56670489fc5da7b5fb1d5480b32c69f2b2b114467f44f4459b.jpg)
+
+![](images/5045a582181511a191b88a988d1efe273a8e3edfcc009589435b46971803e05a.jpg)
+
+![](images/7708202057985780002fa09c822480672aa94c06ad76a3c284fb84a08437a816.jpg)
+
+![](images/d95d7cd031e25bb3aaf1990b7db5df65222e76cc62039e7987a819697dc68f0a.jpg)  
+Fig. 1. Example of tasks achievable by a visual question answering model for remote sensing data.
+
+in the framework of a given task (e.g. classification [2], [3]), the ability to use remote sensing data as a direct source of information is currently limited to experts within the remote sensing and computer vision communities. This constraint, imposed by the technical nature of the task, reduces both the scale and variety of the problems that could be addressed with such information as well as the number of potential end-users. This is particularly true when targeting specific applications (detecting particular objects, e.g. thatched roofs or buildings in a developing country [4]) which would today call for important research efforts. The targeted tasks are often multiple and changing in the scope of a project calls for strong expert knowledge, limiting the information which can be extracted from remote sensing data. To address these constraints, we introduce the problem of visual question answering (VQA) for remote sensing data.
+
+VQA is a new task in computer vision, introduced in its current form by [5]. The objective of VQA is to answer a free-form and open-ended question about a given image. As the questions can be unconstrained, a VQA model applied to remote sensing data could serve as a generic solution to classical problems involving remote sensing data (e.g. "Is there a thatched roof in this image?" for thatched roof detection), but also very specific tasks involving relations between objects of different nature (e.g. "Is there a thatched roof on the right of the river?"). Examples of potential questions are shown in Figure 1.
+
+To the best of our knowledge, this is the first time (after the first exploration in [6]) that VQA has been applied to extract information from remote sensing data. It builds on the task of generating descriptions of images through combining image and natural language processing to provide the user with easily accessible, high-level semantic information. These descriptions are then used for image retrieval and intelligence generation [7]. As seen in this introduction, VQA systems rely on the recent advances in deep learning. Deep learning based methods, thanks to their ability to extract high-level features, have been successfully developed for remote sensing data as reviewed in [8]. Nowadays, this family of methods is used to tackle a variety of tasks; for scene classification, an early work by [9] evaluated the possibility to adapt networks pre-trained on large natural image databases (such as ImageNet [10]) to classify hyperspectral remote sensing images. More recently, [11] used an intermediate high level representation using recurrent attention maps to classify images. Object detection is also often approached using deep learning methods. To this effect, [12] introduced an object detection dataset and evaluated classical deep learning approaches. Methods taking into account the specificity of remote sensing data have been developed, such as [13] which proposed to modify the classical approach by generating rotatable region proposal which are particularly relevant for top-view imagery. Deep learning methods have also been developed for semantic segmentation. In [14], the authors evaluated different strategies for segmenting remote sensing data. More recently, a contest organized on the dataset of building segmentation created by [15] has motivated the development of a number of new methods to improve results on this task [16]. Similarly, [17] introduced a contest including three tasks: road extraction, building detection and land cover classification. Best results for each challenge were obtained using deep neural networks: [18], [19], [20].
+
+Natural language processing has also been used in remote sensing. For instance, [21] used a convolutional neural network (CNN) to generate classification probabilities for a given image, and used a recurrent neural network (RNN) to generate its description. In a similar fashion, [7] used a CNN to obtain a multi semantic level representation of an image (object, land class, landscape) and generate a description using a simple static model. More recently, [22] uses an encoder/decoder type of architecture where a CNN encodes the image and a RNN decodes it to a textual representation, while [23] projects the textual representation and the image to a common space. While these works are use cases of natural
+
+language processing, they do not enable interactions with the user as we propose with VQA.
+
+A VQA model is generally made of 4 distinct components: 1) a visual feature extractor, 2) a language feature extractor, 3) a fusion step between the two modalities and 4) a prediction component. Since VQA is a relatively new task, an important number of methodological developments have been published in both the computer vision and natural language processing communities during the past 5 years, reviewed in [24]. VQA models are able to benefit from advances in the computer vision and automatic language processing communities for the features extraction components. However, the multi-modal fusion has been less explored and therefore, an important amount of work has been dedicated to this step. First VQA models relied on a non-spatial fusion method, i.e. a point-wise multiplication between the visual and language feature vectors [5]. Being straightforward, this method does not allow every component from both feature vectors to interact with each other. This interaction would ideally be achieved by multiplying the first feature vector by the transpose of the other, but this operation would be computationally intractable in practice. Instead, [25] proposed a fusion method which first selects relevant visual features based on the textual feature (attention step) and then, combines them with the textual feature. In [26], the authors used Tucker decomposition to achieve a similar purpose in one step. While these attention mechanisms are interesting for finding visual elements aligned with the words within the question, they require the image to be divided in a regular grid for the computation of the attention, and this is not suitable to objects of varying size. A solution is presented in [27], which learns an object detector to select relevant parts of the image. In this research, we use a non-spatial fusion step to keep the model part relatively simple. Most traditional VQA works are designed for a specific dataset, either composed of natural images (with questions covering an unconstrained range of topics) or synthetic images. While interesting for the methodological developments that they have facilitated, these datasets limit the potential applications of such systems to other problems. Indeed, it has been shown in [28] that VQA models trained on a specific dataset do not generalize well to other datasets. This generalization gap raises questions concerning the applicability of such models to specific tasks.
+
+A notable use-case of VQA is helping visually impaired people through natural language interactions [29]. Images acquired by visually impaired people represent an important domain shift, and as such a challenge for the applicability of VQA models. In [30], the authors confirm that networks trained on generic datasets do not generalize to their specific one. However, they manage to obtain much better results by fine-tuning or training models from scratch on their task-specific dataset.
+
+In this study, we propose a new application for VQA, specifically for the interaction with remote sensing images. To this effect, we propose the first remote sensing-oriented VQA datasets, and evaluate the applicability of this task on remote sensing images. We propose a method to automatically
+
+![](images/28591302f1bedc0a0168af656cf7b33fa0dc62e1428400523f4f8db704b22da2.jpg)  
+(a) Question construction procedure. Dash lines represent optional paths
+
+![](images/1b902dd01731dd741be10917cea5b989d8c6bc1549a4565770e93709b3d256d4.jpg)
+
+![](images/324eb500c2fb80096d34697a7cd6aeeb6846c534c66f9ea2f2f9c9d29e118ec2.jpg)
+
+"How many roads are present in the image?"
+
+![](images/230aa42bd420e81afca19f31ed354164c922e35dd19fd4ac875f1ba2da452a66.jpg)
+
+"Is there a small retail place?"
+
+![](images/2e32f5f278d620a2515143ed34a2e534f2481024e8703a5b9cc818aab758de47.jpg)  
+"Is there more buildings at the top of a circular religious place than roads in the image?"
+
+![](images/e10e579e1ddcd617cf7355827b4020c3e9c50686e763da08e0274e2deae3fb6d.jpg)  
+(b) Construction path for sample questions.  
+Fig. 2. Illustration of the question construction procedure.
+
+generate remote sensing-oriented VQA datasets from already available human annotations in section II and generate two datasets. We then use this newly-generated data to train our proposed RSVQA model with a non-spatial fusion step described in section III. Finally, the results are evaluated and discussed in section IV.
+
+Our contribution are the following:
+
+- a method to generate remote sensing-oriented VQA datasets;  
+2 datasets;  
+- the proposed RSVQA model.
+
+This work extends the preliminary study of [6] by considering and disclosing a second larger dataset consisting of very high resolution images. This second dataset helps testing the spatial generalization capability of VQA and provides an extensive discussion highlighting remaining challenges. The method to generate the dataset, the RSVQA model and the two datasets are available on https://rsvqa.sylvainlobry.com/.
+
+# II. DATASETS
+
+# A. Method
+
+As seen in the introduction, a main limiting factor for VQA is the availability of task-specific datasets. As such, we aim at providing a collection of remote sensing images with questions and answers associated to them. To do so, we took inspiration from [31], in which the authors build a dataset of question/answer pairs about synthetic images following an automated procedure. However, in this study we are interested in real data (discussed in subsection II-B). Therefore, we use the openly accessible OpenStreetMap data containing geo-localized information provided by volunteers. By leveraging this data, we can automatically extract the
+
+information required to obtain question/answer pairs relevant to real remotely sensed data and create a dataset made of (image, question, answer) triplets.
+
+The first step of the database construction is to create the questions. The second step is to compute the answers to the questions, using the OSM features belonging to the image footprint. Note that multiple question/answer pairs are extracted for each image.
+
+1) Question construction: Our method to construct the questions is illustrated in Figure 2. It consists of four main components:
+
+1) choice of an element category (highlighted in red in Figure 2(a));  
+2) application of attributes to the element (highlighted in green in Figure 2(a));  
+3) selection based on the relative location to another element (highlighted in green in Figure 2(a))  
+4) construction of the question (highlighted in blue in Figure 2(a)).
+
+Examples of question constructions are shown in Figure 2(b). These four components are detailed in the following.
+
+Element category selection: First, an element category is randomly selected from the element catalog. This catalog is built by extracting the elements from one of the following OSM layers: road, water area, building and land use. While roads and water areas are directly treated as elements, buildings and land use related objects are defined based on their "type" field, as defined in the OSM data specification. Examples of land use objects include residential area, construction area, religious places, ... Buildings are divided in two categories: commercial (e.g. retail, supermarket, ...) and residential (e.g. house, apartments, ...).
+
+Attributes application: The second (optional) step is to refine the previously selected element category. To do so, we randomly select from one of the two possible attribute categories:
+
+- Shape: each element can be either square, rectangular or circular. Whether an element belongs to one of these shape types is decided based on basic geometrical properties (i.e. hard thresholds on area-to-perimeter ratio and area-to-circumscribed circle area ratio).  
+- Size: using hard thresholds on the surface area, elements can be considered "small", "medium" or "large". As we are interested in information at different scales in the two datasets, we use different threshold values, which are described in Table I.
+
+Relative position: Another possibility to refine the element is to look at its relative position compared to another element. We define 5 relations: "left of", "top of", "right of", "bottom of", "next to". Note that these relative positions are understood in the image space (i.e. geographically). The special case of
+
+<table><tr><td>Scale</td><td>Small</td><td>Medium</td><td>Large</td></tr><tr><td>Low resolution</td><td>&lt; 3000m2</td><td>&lt; 10000m2</td><td>≥ 10000m2</td></tr><tr><td>High resolution</td><td>&lt; 100m2</td><td>&lt; 500m2</td><td>≥ 500m2</td></tr></table>
+
+TABLEI
+
+THRESHOLDS FOR SIZE ATTRIBUTES ACCORDING TO THE DATASET SCALE. WHEN DEALING WITH LOW RESOLUTION DATA, VISIBLE OBJECTS OF INTEREST ARE LARGER. TO DEAL WITH THIS DISPARITY, WE ADAPT THE SIZE THRESHOLDS TO THE RESOLUTION OF THE IMAGES.
+
+"next to" is handled as a hard threshold on the relative distance between the two objects (less than  $1000\mathrm{m}$ ). When looking at relative positions, we select the second element following the procedure previously defined.
+
+Question construction: At this point of the procedure, we have an element (e.g. road), with an optional attribute (e.g. small road) and an optional relative position (e.g. small road on the left of a water area). The final step is to generate a "base question" about this element. We define 5 types of questions of interest ("Question catalog" in Figure 2(a)), from which a specific type is randomly selected to obtain a base question. For instance, in the case of comparison questions, we randomly choose among "less than", "equals to" and "more than" and construct a second element.
+
+This base question is then turned into a natural language question using pre-defined templates for each question type and object. For some question types (e.g. count), more than one template is defined (e.g. 'How many _ are there?', 'What is the number of _?' or 'What is the amount of _?'). In this case, the template to be used is randomly selected. The stochastic process ensures the diversity, both in the question types and the question templates used.
+
+2) Answer construction: : To obtain the answer to the constructed question, we extract the objects from the OSM database corresponding to the image footprint. The objects  $b$  corresponding to the element category and its attributes are then selected and used depending on the question type:
+
+- Count: In the case of counting, the answer is simply the number of objects  $b$ .  
+- Presence: A presence question is answered by comparing the number of objects  $b$  to 0.  
+- Area: The answer to a question about the area is the sum of the areas of the objects  $b$ .  
+- Comparison: Comparison is a specific case for which a second element and the relative position statement is needed. This question is then answered by comparing the number of objects  $b$  to the ones of the second element.  
+- Rural/Urban: The case of rural/urban questions is handled in a specific way. In this case, we do not create a specific element, but rather count the number of buildings (both commercial or residential). This number of buildings is then thresholded to a predefined number depending on the resolution of the input data (to obtain a density) to answer the question. Note that we are using a generic definition of rural and urban areas but this can be easily adapted using the precise definition of each
+
+![](images/60e9ee459ab437266d74a1064caeb4d64fd6e7888f938f0dd9484fcb71401eb8.jpg)  
+Fig. 3. Images selected for the LR dataset over the Netherlands. Each point represent one Sentinel-2 image which was later split into tiles. Red points represent training samples, green pentagon represents the validation image, and blue triangle is for the test image. Note that one training image is not visible (as it overlaps with the left-most image).
+
+country.
+
+# B. Data
+
+Following the method presented in subsection II-A, we construct two datasets with different characteristics.
+
+Low resolution (LR): this dataset is based on Sentinel-2 images acquired over the Netherlands. Sentinel-2 satellites provide 10m resolution (for the visible bands used in this dataset) images with frequent updates (around 5 days) at a global scale. These images are openly available through ESA's Copernicus Open Access Hub<sup>1</sup>.
+
+To generate the dataset, we selected 9 Sentinel-2 tiles covering the Netherlands with a low cloud cover (selected tiles are shown in Figure 3). These tiles were divided in 772 images of size  $256 \times 256$  (covering  $6.55km^2$ ) retaining the RGB bands. From these, we constructed  $77'232$  questions and answers following the methodology presented in subsection II-A. We split the data in a training set ( $77.8\%$  of the original tiles), a validation set ( $11.1\%$ ) and a test set ( $11.1\%$ ) at the tile level (the spatial split is shown in Figure 3). This allows to limit spatial correlation between the different splits.
+
+High resolution (HR): this dataset uses 15cm resolution aerial RGB images extracted from the High Resolution Orthoimagery (HRO) data collection of the USGS. This collection
+
+![](images/63353412946460fea7179199a88f61906206f66ac6f1376107700311362ed9d6.jpg)  
+Fig. 4. Extent of the HR dataset with a zoom on the Portland, Manhattan (New York City) and Philadelphia areas. Each point represent one image (generally of size  $5000 \times 5000$ ) which was later split into tiles. The images cover the New York City/Long Island region, Philadelphia and Portland. Red points represent training samples, green pentagons represent validation samples, and blue indicators are for the test sets (blue triangles for test set 1, blue stars for test set 2).
+
+covers most urban areas of the USA, along with a few areas of interest (e.g. national parks). For most areas covered by the dataset, only one tile is available with acquisition dates ranging from year 2000 to 2016, with various sensors. The tiles are openly accessible through USGS' EarthExplorer tool<sup>2</sup>.
+
+From this collection, we extracted 161 tiles belonging to the North-East coast of the USA (see Figure 4) that were split into  $10^{\prime}659$  images of size  $512 \times 512$  (each covering  $5898m^{2}$ ). We constructed  $1^{\prime}066^{\prime}316$  questions and answers following the methodology presented in subsection II-A. We split the data in a training set ( $61.5\%$  of the tiles), a validation set ( $11.2\%$ ), and test sets ( $20.5\%$  for test set 1,  $6.8\%$  for test set 2). As it can be seen in Figure 4, test set 1 covers similar regions as the training and validation sets, while test set 2 covers the city of Philadelphia, which is not seen during the training. Note that this second test set also uses another sensor (marked as unknown on the USGS data catalog), not seen during training.
+
+# Differences between the two datasets:
+
+Due to their characteristics, the two datasets represent two different possible use cases of VQA:
+
+- The LR dataset allows for large spatial and temporal coverage thanks to the frequent acquisitions made by Sentinel-2. This characteristic could be of interest for future applications of VQA such as large scale queries (e.g. rural/urban questions) or temporal (which is out of the scope of this study). However, due to the relatively low resolution  $(10\mathrm{m})$ , some objects can not be seen on such images (such as small houses, roads, trees, ...). This fact severely limits the questions to which the model
+
+could give an accurate answer.
+
+- Thanks to the much finer resolution of the HR dataset, a quantity of information of interest to answer typical questions is present. Therefore, in contrast to the LR dataset, questions concerning objects' coverage or counting relatively small objects can possibly be answered from such data. However, data of such resolution is generally less frequently updated and more expensive to acquire.
+
+Based on these differences, we constructed different types of questions for the two datasets. Questions concerning the area of objects are only asked in the HR dataset. On the other hand, questions about urban/rural area classification are only asked in the LR dataset, as the level of zoom of images from the HR dataset would prevent a meaningful answer from being provided.
+
+To account for the data distributions and error margins we also quantize different answers in both datasets:
+
+- Counting in LR: as the coverage is relatively large  $(6.55\mathrm{km}^2)$ , the number of small objects contained in one tile can be high, giving a heavy tailed distribution for the numerical answers, as shown in Figure 6. More precisely, while  $26.7\%$  of the numerical answers are '0' and  $50\%$  of the answers are less than '7', the highest numerical answer goes up to '17139'. In addition to making the problem complex, we can argue that allowing such a range of numerical answers does not make sense on data of this resolution. Indeed, it would be in most cases impossible to distinguish 17139 objects on an image of 65536 pixels. Therefore, numerical answers are quantized into the following categories:
+
+- '0';  
+- 'between 1 and  $10^{\prime}$  
+- 'between 11 and 100';  
+- 'between 101 and 1000';  
+- 'more than 1000'.
+
+- In a similar manner, we quantize questions regarding the area in the HR dataset. A great majority (60.9%) of the answer of this type are '0m²', while the distribution also presents a heavy tail. Therefore, we use the same quantization as the one proposed for counts for the LR dataset. Note that we do not quantize purely numerical answers (i.e. answers to questions of type 'count') as the maximum number of objects is 89 in our dataset. Counting answers therefore correspond to 89 classes in the model in this case (see section III).
+
+# C. Discussion
+
+# Questions/Answers distributions:
+
+We show the final distribution of answers per question type for both datasets in Figure 5. We can see that most question types (with the exception of 'rural/urban' questions in the LR dataset, asked only once per image) are close to evenly distributed by construction. The answer 'no' is dominating the answers' distribution for the HR dataset with a frequency of  $37.7\%$ . In the LR dataset, the answer 'yes' occurs  $34.9\%$  of the time while the 'no' frequency is  $34.3\%$ . The strongest
+
+![](images/b13aba5c075c99aa8e96ade555ec2d640b6c5b5c7f44e8f5654fb25594fb420d.jpg)  
+(a) Distribution of answers for the LR dataset
+
+![](images/e994b2bd5fc58ce00b01609eff923c962cc396564c7cf8ddd60cba4494e97f6b.jpg)  
+(b) Distribution of answers for the HR dataset (numerical answers are ordered, and 0 is the most frequent)
+
+![](images/a654066161a3e8d9dd482ebe7a9af3094d0a0544e2cf390c01359bbbc9e8c358.jpg)  
+Fig. 5. Distributions of answers in the Low resolution (LR) and High resolution (HR) datasets.  
+Fig. 6. Frequencies of exact counting answers in the LR dataset. Only the left part of the histogram is shown (until 200 objects), the largest (single) count being 17139.  $50\%$  of the answers are less than 7 objects in the tile.
+
+imbalance occurs for the answer '0' in the HR dataset (with a frequency of  $60.9\%$  for the numerical answer). This imbalance is greatly reduced by the quantization process described in the previous paragraph.
+
+# Limitations of the proposed method:
+
+While the proposed method for image/question/answer triplets generation has the advantage of being automatic and easily scalable while using data annotated by humans, a few limitations have been observed. First, it can happen that some annotations are missing or badly registered [4]. Furthermore, it was not possible to match the acquisition date of the imagery to the one of OSM. The main reason being that it is impossible to know if a newly added element appeared at the same time in reality or if it was just entered for the first time in OSM. As OSM is the main source of data for our process, errors in OSM will negatively impact the accuracy of our databases.
+
+Furthermore, due to the templates used to automatically construct questions and provide answers, the set of questions and answers is more limited than what it is in traditional VQA datasets (9 possible answers for the LR dataset, 98 for the HR
+
+dataset).
+
+# III. VQA MODEL
+
+We investigate the difficulty of the VQA task for remote sensing using a basic VQA model based on deep learning. An illustration of the proposed network is shown in Figure 7. In their simple form, VQA models are composed of three parts [24]:
+
+A. feature extraction;
+
+B. fusion of these features to obtain a single feature vector representing both the visual information and the question;  
+C. prediction based on this vector.
+
+As the model shown in Figure 7 is learned end-to-end, the vector obtained after the fusion (in green in Figure 7) can be seen as a joint embedding of both the image and the question which is used as an input for the prediction step. We detail each of these 3 parts in the following.
+
+# A. Feature extraction
+
+The first component of our VQA model is the feature extraction. Its purpose is to obtain a low-dimensional representation of the information contained in the image and the question.
+
+1) Visual part: To extract information from a 2D image, a common choice is to use a Convolutional Neural Network (CNN). Specifically, we use a Resnet-152 model [32] pretrained on ImageNet [10]. The principal motivation for this choice is that this architecture manages to avoid the undesirable degradation problem (decreasing performance with deeper networks) by using residual mappings of the layers' inputs which are easier to learn than the common choice of direct mappings. This architecture has been successfully used in a wide range of work in the remote sensing community (e.g. [8], [17], [33]). The last average pooling layer and fully connected layer are replaced by a  $1 \times 1$  2D convolution which outputs a total of 2048 features which are vectorized. A final
+
+![](images/d98fa00ed91ac0588b803e78593cdb02b737d018399eb2d52c46e1471f7677ae.jpg)  
+Fig. 7. Framework of the proposed Visual Question Answering model.
+
+fully connected layer is learned to obtain a 1200 dimension vector.
+
+2) Language part: The feature vector is obtained using the skip-thoughts model [34] trained on the BookCorpus dataset [35]. This model is a recurrent neural network, which aims at producing a vector representing a sequence of words (in our case, a question). To make this vector informative, the model is trained in the following way: it encodes a sentence from a book in a latent space, and tries to decode it to obtain the two adjacent sentences in the book. By doing so, it ensures that the latent space embeds semantic information. Note that this semantic information is not remote sensing specific due to the BookCorpus dataset it has been trained on. However, several works, including [36], have successfully applied non-domain specific NLP models to remote sensing. In our model, we use the encoder which is then followed by a fully-connected layer (from size 2400 elements to 1200).
+
+# B. Fusion
+
+At this step, we have two feature vectors (one representing the image, one representing the question) of the same size. To merge them into a single vector, we use a simple strategy: a point-wise multiplication after applying the hyperbolic tangent function to the vectors' elements. While being a fixed (i.e. not learnt) operation, the end-to-end training of our model encourages both feature vectors to be comparable with respect to this operation.
+
+# C. Prediction
+
+Finally, we project this 1200 dimensional vector to the answer space by using a MLP with one hidden layer of 256 elements. We formulate the problem as a classification task, in which each possible answer is a class. Therefore, the size of the output vector depends on the number of possible answers.
+
+![](images/cac460e63ef2106ff5989d8cf6f6bc9abff50a26bc109925f92a3895d428e28e.jpg)
+
+# D. Training procedure
+
+We train the model using the Adam optimizer [37] with a learning rate of  $10^{-5}$  until convergence (150 epochs in the case of the LR dataset, and 35 epochs in the case of the HR dataset). We use a dropout of 0.5 for every fully connected layer. Due to the difference of input size between the two datasets (HR images are 4 times larger), we use batches of 70 instances for the HR dataset and 280 for the LR dataset. Furthermore, when the questions do not contain a positional component relative to the image space (i.e. "left of", "top of", "right of" or "bottom of", see subsection II-A), we augment the image space by randomly applying vertical and/or horizontal flipping
+
+# IV. RESULTS AND DISCUSSION
+
+We report the results obtained by our model on the test sets of the LR and HR datasets. In both cases, 3 model runs have been trained and we report both the average and the standard deviation of our results to limit the variability coming from the stochastic nature of the optimization.
+
+The numerical evaluation is achieved using the accuracy, defined in our case as the ratio of correct answers. We report the accuracy per question type (see subsection II-A), the average of these accuracies (AA) and the overall accuracy (OA).
+
+We show some predictions of the model on the different test sets in Figure 8 and Figure 9 to qualitatively assess the results. Numerical performance of the proposed model on the LR dataset is reported in Table II and the confusion matrix is shown in Figure 10. The performance on both tests sets of the HR dataset are reported in Table III and the confusion matrices are shown in Figure 11.
+
+# General accuracy assessment:
+
+The proposed model achieves an overall accuracy of  $79\%$
+
+![](images/9dc6f69f0c5773a1e73b705b03c027ee295871c2b1c2e7542bf8f5aa3ad2be0c.jpg)
+
+<table><tr><td colspan="2">What is the area covered by residential buildings?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>0 m2</td><td>0 m2</td></tr></table>
+
+(a) HR, test set 1
+
+![](images/bb6668a9cd2d3e670268e0ba5fbc8b26dd35524db891ffc99b4eb825b2a1271d.jpg)
+
+What is the area covered by rectangular buildings?  
+
+<table><tr><td>Ground truth
+Between 100 and
+1000 m²</td><td>Prediction
+Between 100 and
+1000 m²</td></tr></table>
+
+![](images/e6603c8a5a14011079f030c76cd07bc750039dd1ccb0022375b4d9f45a89d59f.jpg)
+
+(b) HR, test set 1  
+
+<table><tr><td colspan="2">Is there a residential building at the bottom of the place of worship?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>yes</td><td>yes</td></tr></table>
+
+![](images/7b834b4dc5b4610069e4b9f2ea2883e1c8206324ceccd5c027949728b9ace465.jpg)
+
+(c) HR, test set 1  
+
+<table><tr><td colspan="2">How many residential buildings at the bottom of a road are there?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>4</td><td>3</td></tr></table>
+
+![](images/f39fee0e950ad4e8b62363685249183ba76e7ac3e6e9f71964a8fd0a466b3774.jpg)
+
+(d) HR, test set 1  
+
+<table><tr><td colspan="2">How many buildings on the left of a road are there in the image?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>38</td><td>0</td></tr></table>
+
+![](images/e9f139cf49e2ed2e4e82f853513f8c24ef2f74a5683b2f0e1811c287f2cf823a.jpg)
+
+(e) HR, test set 1  
+
+<table><tr><td colspan="2">What is the amount of large buildings?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>3</td><td>1</td></tr></table>
+
+![](images/faf2dfd66437707e38a8128f1572eb0143d56b7376ac5bd881e4c71b9a1e0591.jpg)  
+Fig. 8. Samples from the high resolution test sets: (a)-(f) are from the first set of the HR dataset, (g)-(i) are from the second set of the HR dataset.
+
+(f) HR, test set 1  
+
+<table><tr><td colspan="2">What is the area covered by rectangular parkings?</td></tr><tr><td>Ground truth between 100m2 and 1000m2</td><td>Prediction between 100m2 and 1000m2</td></tr></table>
+
+![](images/e89c2d217b0b1665c5d5812146b5d97ed8dc5aaa593e8a4facf670fd697ea877.jpg)
+
+(g) HR, test set 2  
+
+<table><tr><td colspan="2">What is the amount of small buildings?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>9</td><td>0</td></tr></table>
+
+![](images/14a6fb67d4cd85fdb0814524d7eeec6b2ecffe0402568aea176e3ede4920d946.jpg)
+
+(h) HR, test set 2  
+
+<table><tr><td colspan="2">What is the amount of large residential buildings?</td></tr><tr><td>Ground truth</td><td>Prediction</td></tr><tr><td>2</td><td>1</td></tr></table>
+
+(i) HR, test set 2
+
+TABLE II RESULTS ON THE TEST SET OF THE LOW RESOLUTION DATASET. THE STANDARD DEVIATION IS REPORTED IN BRACKETS.  
+
+<table><tr><td>Type</td><td>Accuracy</td></tr><tr><td>Count</td><td>67.01% (0.59%)</td></tr><tr><td>Presence</td><td>87.46% (0.06%)</td></tr><tr><td>Comparison</td><td>81.50% (0.03%)</td></tr><tr><td>Rural/Urban</td><td>90.00% (1.41%)</td></tr><tr><td>AA</td><td>81.49% (0.49%)</td></tr><tr><td>OA</td><td>79.08% (0.20%)</td></tr></table>
+
+TABLE III RESULTS ON BOTH TEST SETS OF THE HIGH RESOLUTION DATASET. THE STANDARD DEVIATION IS REPORTED IN BRACKETS.  
+
+<table><tr><td>Type</td><td>Accuracy Test set 1</td><td>Accuracy Test set 2</td></tr><tr><td>Count</td><td>68.63% (0.11%)</td><td>61.47% (0.08%)</td></tr><tr><td>Presence</td><td>90.43% (0.04%)</td><td>86.26% (0.47%)</td></tr><tr><td>Comparison</td><td>88.19% (0.08%)</td><td>85.94% (0.12%)</td></tr><tr><td>Area</td><td>85.24% (0.05%)</td><td>76.33% (0.50%)</td></tr><tr><td>AA</td><td>83.12% (0.03%)</td><td>77.50% (0.29%)</td></tr><tr><td>OA</td><td>83.23% (0.02%)</td><td>78.23% (0.25%)</td></tr></table>
+
+on the low resolution dataset (see Table II) and of  $83\%$  on the first test set of the high resolution dataset (Table III), indicating that the task of automatically answering question based on remote sensing images is possible. When looking at the accuracies per question type (in Tables II and III), it can be noted that the model performs inconsistently with respect to the task the question is tackling: while a question about the presence of an object is generally well answered (87.46% in the LR dataset, 90.43% in the first test set of the HR dataset), counting questions gives poorer performances (67.01% and 68.63% respectively). This can be explained by the fact that presence questions can be seen as simplified counting questions to which the answers are restricted to two options: "0" or "1 or more". Classical VQA models are known to struggle with the counting task [38]. An issue which partly explains these performances in the counting task is the separation of connected instances. This problem has been raised for the case of buildings in [33] and is illustrated in Figure 8(f), where the ground truth is indicating three buildings, which could also be only one. We found another illustration of this phenomenon in the second test set in Figure 8(i). This issue mostly arises when counting roads or buildings.
+
+Thanks to the answers' quantization, questions regarding the areas of objects are generally well answered with an accuracy of  $85.24\%$  in the first test set of the HR dataset. This is illustrated in Figures 8(a,b), where presence of buildings (by the mean of the covered area) is well detected.
+
+However, we found that our model performs poorly with questions regarding the relative positions of objects, such as those illustrated in Figures 8(c-e). While Figure 8(c) is correct, despite the question being difficult, Figure 8(d) shows a small mistake from the model and Figure 8(e) is completely incorrect. These problems can be explained by the fact that the questions are on high semantic level and therefore difficult for a model considering a simple fusion scheme, as the one presented in section III.
+
+![](images/9c85c98d250b980a9a3f916a1b9ead7f9f88802d67652d2aff5688af52e6340f.jpg)
+
+![](images/0a26e102b4824ee50f96b7ac0d3e8c93eb12fb5ff407d4b736dd792297c3b7ef.jpg)  
+(a) LR, test set
+
+![](images/7bbbb5eb5091aadc935d1c6eb15418ea941bc7418975a4c542fa9b03f68f4324.jpg)
+
+![](images/df6702642613b25ce3947d0fe56a6666d6a6c2dba40f0f3ea5f853bfd11c5649.jpg)  
+(b) LR, test set
+
+![](images/3567f833239d958d68cd17677fbe120a131ba21d8fb5f525b4bd8928f88a4859.jpg)
+
+![](images/ea0bc36a7de198a866e012d91a3836e1997305462aad279911e95ec9d54a4555.jpg)  
+(c) LR, test set
+
+![](images/f86bbba4b9bf13aef41763128646b7b839a866d9541b58e9ec021c46594f9dcb.jpg)
+
+![](images/5f362839321fb217b7439bba9d7cbd3be63bdfd6eeb1ed30d9ad94708a1001f8.jpg)  
+(d) LR, test set  
+Fig. 9. Samples from the low resolution test set.
+
+Regarding the low resolution dataset, rural/urban questions are generally well answered (90% of accuracy), as shown in Figure 9(a,b). Note that the ground truth for this type of questions is defined as a hard threshold on the number of buildings, which causes an area as the one shown in Figure 9(b) to be labeled as urban.
+
+However, the low resolution of Sentinel-2 images can be problematic when answering questions about relatively small objects. For instance, in Figures 9(c,d), we can not see any water area nor determine the type of buildings, which causes the model's answer to be unreliable.
+
+# Generalization to unseen areas:
+
+The performances on the second test set of the HR dataset show that the generalization to new geographic areas is problematic for the model, with an accuracy drop of approximately  $5\%$ . This new domain has a stronger impact on the most difficult tasks (counting and area computation). This can be explained when looking at Figures 8(g-i). We can see that the domain shift is important on the image space, as a different sensor was used for the acquisition. Furthermore, the urban organization of Philadelphia is different from that of the city of New York. This causes the buildings to go
+
+![](images/4539a1eef4bb30c00bbc3bbafb19a93f33721c6ad264b6d11abbff3f5a1e8859.jpg)  
+Fig. 10. Confusion matrix for the low resolution dataset (logarithm scale) on the test set. Red lines group answers by type ("Yes/No", "Rural/Urban", numbers).
+
+undetected by the model in Figure 8(h), while the parkings can still be detected in Figure 8(g) possibly thanks to the cars. This decrease in performance could be reduced by using domain adaptation techniques. Such a method could be developed for the image space only (a review of domain adaptation for remote sensing is done in [39]) or at the question/image level (see [40], which presents a method for domain adaptation in the context of VQA).
+
+# Answer's categories:
+
+The confusion matrices indicate that the models generally provide logical answers, even when making mistakes (e.g. it might answer "yes" instead of "no" to a question about the presence of an object, but not a number). Rare exceptions to this are observed for the first test set of the HR dataset (see Figure 11(a)), on which the model gives 23 illogical answers (out of the 316941 questions of this test set).
+
+# Language biases:
+
+A common issue in VQA models, raised in [41], is the fact that strong language biases are captured by the model. When this is the case, the answer provided by the model mostly depends on the question, rather than on the image. To assess this, we evaluated the proposed models by randomly selecting an image from the test set for each question. We obtained an overall accuracy of  $73.78\%$  on the LR test set,  $73.78\%$  on the first test set of the HR dataset and  $72.51\%$  on the second test set. This small drop of accuracy indicates that indeed, the models rely more on the questions than on the image to provide an answer. Furthermore, the strongest drop of accuracy is seen on the HR dataset, indicating that the proposed model extracts more information from the high resolution data.
+
+# Importance of the number of training samples:
+
+We show in Figure 12 the evolution of the accuracies when the model is trained with a fraction of the HR training samples. When using only  $1\%$  of the available training samples, the model already gets  $65\%$  in average accuracy (vs  $83\%$  for the
+
+model trained on the whole training set). However, it can be seen that, for numerical tasks (counts and area estimation), larger amounts of samples are needed to achieve the performances reported in Table III. This experiment also shows that the performances start to plateau after  $10\%$  of the training data is used: this indicates that the proposed model would not profit substantially from a larger dataset.
+
+# Restricted set of questions:
+
+While not appearing in the numerical evaluation, an important issue with our results is the relative lack of diversity in the dataset. Indeed, due to the source of our data (OSM), the questions are only on a specific set of static objects (e.g. buildings, roads, ...). Other objects of interest for applications of a VQA system to remote sensing would also include different static objects (e.g. thatched roofs mentioned in section I), moving objects (e.g. cars), or seasonal aspects (e.g. for crop monitoring). Including these objects would require another source of data, or manual construction of question/answer pairs.
+
+Another limitation comes from the dataset construction method described in subsection II-A. We defined five types of questions (count, comparison, presence, area, rural/urban classification). However, they only start to cover the range of questions which would be of interest. For instance, questions about the distance between two points (defined by textual descriptions), segmentation questions (e.g. "where are the buildings in this image?") or higher semantic level question (e.g. "does this area feel safe?") could be added.
+
+While the first limitation (due to the data source) could be tackled using other databases (e.g. from national institutes) and the second limitation (due to the proposed method) could be solved by adding other question construction functions to the model, it would be beneficial to use human annotators using a procedure similar to [5] to diversify the samples.
+
+# V. CONCLUSION
+
+We introduce the task of Visual Question Answering from remote sensing images as a generic and accessible way of extracting information from remotely sensed data. We present a method for building datasets for VQA, which can be extended and adapted to different data sources, and we proposed two datasets targeting different applications. The first dataset uses Sentinel-2 images, while the second dataset uses very high resolution (30cm) aerial orthophotos from USGS.
+
+We analyze these datasets using a model based on deep learning, using both convolutional and recurrent neural networks to analyze the images and associated questions. The most probable answer from a predefined set is then selected.
+
+This first analysis shows promising results, suggesting the potential for future applications of such systems. These results outline future research directions which are needed to overcome language biases and difficult tasks such as counting. The former can be tackled using an attention mechanism [24], while the latter could be tackled by using dedicated components for counting questions [33] in a modular approach.
+
+![](images/2fb45caa97ebd873dc16400817a6f6b172d78aeb3ca3cd009adaa8545d524607.jpg)  
+(a) Test set 1
+
+![](images/3874f4f01c12f50cc2b68cec8a7ca76f845d7567bb002a7a6fb9cc0cf4cc6c0f.jpg)  
+(b) Test set 2  
+Fig. 11. Subsets of the confusion matrices for the high resolution dataset (counts are at logarithm scale) on both test sets. Red lines group answers by type ("Yes/No", areas, numbers).
+
+![](images/a868a5fca9f52147f8e59ba1652865f0bd9d4131ee398b27b6116e0230dd5834.jpg)  
+Fig. 12. Evolution of the accuracies (evaluated on the first HR test set) after training with subsets of different size of the HR training set.
+
+Issues regarding the current database raised in section IV also need to be addressed to obtain a system capable of answering a more realistic range of questions. This can be done by making the proposed dataset construction method more complex or by using human annotators.
+
+# ACKNOWLEDGMENT
+
+The authors would like to thank CNES for the funding of this study (R&T project "Application des techniques de Visual Question Answering à des données d'imagerie satellitaire").
+
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+[32] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," IEEE Conference on Computer Vision and Pattern Recognition, 2016.  
+[33] S. Lobby and D. Tuia, "Deep Learning Models to Count Buildings in High-Resolution Overhead Images," in Joint Urban Remote Sensing Event, 2019.  
+[34] R. Kiros, Y. Zhu, R. Salakhutdinov, R. Zemel, A. Torralba, R. Urtasun, and S. Fidler, "Skip-thought vectors," Neural Information Processing Systems, 2015.  
+[35] Y. Zhu, R. Kiros, R. Zemel, R. Salakhutdinov, R. Urtasun, A. Torralba, and S. Fidler, "Aligning books and movies: Towards story-like visual explanations by watching movies and reading books," in IEEE international conference on computer vision, 2015, pp. 19-27.  
+[36] A. Li, Z. Lu, L. Wang, T. Xiang, and J.-R. Wen, "Zero-shot scene classification for high spatial resolution remote sensing images," IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 7, pp. 4157-4167, 2017.  
+[37] D. Kingma and J. Ba, “Adam: A method for stochastic optimization,” International Conference on Learning Representations, 2015.  
+[38] Y. Zhang, J. Hare, and A. Prgel-Bennett, “Learning to count objects in natural images for visual question answering,” in International Conference on Learning Representations, 2018.  
+[39] D. Tuia, C. Persello, and L. Bruzzone, "Domain adaptation for the classification of remote sensing data: An overview of recent advances,"
+
+IEEE Geoscience and Remote Sensing Magazine, vol. 4, no. 2, pp. 41-57, June 2016.  
+[40] W.-L. Chao, H. Hu, and F. Sha, “Cross-dataset adaptation for visual question answering,” in IEEE Conference on Computer Vision and Pattern Recognition, 2018, pp. 5716-5725.  
+[41] Y. Goyal, T. Khot, D. Summers-Stay, D. Batra, and D. Parikh, "Making the V in VQA matter: Elevating the role of image understanding in Visual Question Answering," in IEEE Conference on Computer Vision and Pattern Recognition, 2017.
+
+![](images/2c071ca7fe054870402ee9c1250ceccf05e30dae72e567acad3121132a40fb67.jpg)
+
+Sylvain Lobry (S16 - M17) received the Engineering degree from Ecole pour l'Informatique et les Techniques Avances (EPITA), Kremlin Bicetre, France in 2013, the Masters degree in science and technology from the University Pierre et Marie Currie (Paris 6), Paris in 2014, and the Ph.D. degree from Telecom Paris, Paris, France, in 2017. He is currently a Post-Doctoral Researcher with the GeoInformation Science and Remote Sensing Laboratory, Wageningen University, The Netherlands. His research interests include radar image processing
+
+and multimodal processing of heterogeneous satellite data.
+
+![](images/d301f67363b08696c07a4c5cafc8a2b709f1ae4eb6f131aceec7d5c0fc78330c.jpg)
+
+Diego Marcos Diego Marcos obtained an MSc degree on Computational Sciences and Engineering from the Ecole Polytechnique Fédérale de Lausanne, Switzerland, in 2014 and a Ph.D. degree in environmental sciences from Wageningen University, The Netherlands, in 2019. He is currently a Post-Doctoral Researcher with the Geo-Information Science and Remote Sensing Laboratory, at Wageningen University. His research interests include computer vision and deep learning interpretability applied to geospatial data.
+
+![](images/c20078e85cfb5bcaa183a1a9fed59802029efb3d37c6bf9aa354257c7525bc98.jpg)
+
+Jesse Murray received an MSc degree in GeoInformation Science from Wageningen University, Wageningen, The Netherlands, in 2019. He is currently a Ph.D. candidate with the Geodetic Engineering Laboratory, at the Ecole Polytechnique Fdrale de Lausanne, Switzerland. His research interests include image processing and 3D geometry reconstruction using computer vision and spatio-temporal data.
+
+![](images/6b17204e0a3b56bb9b62caeedbe70f67111b5071d9b66073bc8d9221b399b483.jpg)
+
+Devis Tuia Devis Tuia (S07 - M09 - SM15) received the Ph.D. degree from the University of Lausanne, Lausanne, Switzerland, in 2009. He was a Post-Doctoral Researcher in Valencia, Boulder, CO, USA, and Ecole polytechnique federale de Lausanne (EPFL), Lausanne. From 2014 to 2017, he was an Assistant Professor with the University of Zurich, Zurich, Switzerland. He is currently a Full Professor with the Geo-Information Science and Remote Sensing Laboratory, Wageningen University, Wageningen, The Netherlands. His research interests include
+
+algorithms for data fusion of geospatial data (including remote sensing) using machine learning and computer vision.

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+    {
+        "type": "text",
+        "text": "Building a COVID-19 Vulnerability Index",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "DAVE DECAPRIO*",
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+    {
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+        "text": "ClosedLoop.ai",
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+    {
+        "type": "text",
+        "text": "JOSEPH GARTNER†",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "CAROL J. McCALL, FSA, MPH†",
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+    {
+        "type": "text",
+        "text": "THADEUSBURGESS",
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+        ],
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+    },
+    {
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+    {
+        "type": "text",
+        "text": "KRISTIAN GARCIA",
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+    {
+        "type": "text",
+        "text": "Healthfirst",
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+    {
+        "type": "text",
+        "text": "SARTHAK KOTHARI",
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+        "text": "ClosedLoop.ai",
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+    },
+    {
+        "type": "text",
+        "text": "SHAAYAAN SAYED",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ClosedLoop.ai",
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+    {
+        "type": "text",
+        "text": "July 21, 2020",
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "COVID-19 is an acute respiratory disease that has been classified as a pandemic by the World Health Organization. Characterization of this disease is still in its early stages; however, it is known to have high mortality rates, particularly among individuals with preexisting medical conditions. Creating models to identify individuals who are at the greatest risk for severe complications due to COVID-19 will be useful for outreach campaigns to help mitigate the disease's worst effects. While information specific to COVID-19 is limited, a model using complications due to other upper respiratory infections can be used as a proxy to help identify those individuals who are at the greatest risk. We present the results for three models predicting such complications, with each model increasing predictive effectiveness at the expense of ease of implementation.",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1. INTRODUCTION",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1.1. COVID-19 Illness",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Coronaviruses (CoV) are a large family of viruses that cause illnesses ranging from the common cold to more severe diseases such as Middle East respiratory syndrome (MERS-CoV) and severe acute respiratory syndrome (SARS-CoV). CoV are zoonotic, meaning they are transmitted between animals and people. Coronavirus disease 2019 (COVID-19) is caused by a new strain discovered in 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), that has not been previously identified in humans[1].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "COVID-19 is a highly contagious respiratory infection with common signs that include respiratory symptoms, fever, cough, shortness of breath, and breathing difficulties. In more severe cases, infection can cause pneumonia, severe acute respiratory syndrome, kidney failure, cardiac arrest, and death[17][18]. Experts continue to learn more about COVID-19, including its etiology, symptoms, complications, and potential treatments.",
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+    {
+        "type": "aside_text",
+        "text": "arXiv:2003.07347v3 [stat.AP] 18 Jul 2020",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author: dave.decaprio@closedloop.ai",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "†Corresponding author: joseph.gartner@closedloop.ai",
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+        "page_idx": 0
+    },
+    {
+        "type": "page_footnote",
+        "text": "‡Corresponding author: carol.mccall@closedloop.ai",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "page_number",
+        "text": "1",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1.2. Flattening the Curve",
+        "text_level": 1,
+        "bbox": [
+            143,
+            112,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "On March 11, 2020, the World Health Organization (WHO) declared COVID-19 to be a pandemic[2]. Public health and healthcare experts agree that mitigation is required in order to slow the spread of COVID-19 and prevent the collapse of healthcare systems. Health systems in the United States run close to capacity[3], and so every transmission that can be avoided and every case that can be prevented has enormous impact.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "1.3. Identifying Vulnerable People",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The risk of severe complications from COVID-19 is higher for certain vulnerable populations, particularly people who are elderly, frail, or have multiple chronic conditions. The risk of death has been difficult to calculate[4], but a small study[5] of people who contracted COVID-19 in Wuhan along with patterns also seen in early reports from the United States suggest that the risk of death increases with age, and is also higher for those who have diabetes, heart disease, blood clotting problems, or have shown signs of sepsis. With an average death rate of  $1\\%$ , the death rate rose to  $6\\%$  for people with cancer, high blood pressure, or chronic respiratory disease,  $7\\%$  for people with diabetes, and  $10\\%$  for people with heart disease. There was also a steep age gradient; the death rate among people age 80 and over was  $15\\%$  [6].",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Identifying who is most vulnerable is not necessarily straightforward. More than  $55\\%$  of Medicare beneficiaries meet at least one of the risk criteria listed by the US Centers for Disease Control and Prevention (CDC)[7]. People with the same chronic condition don't have the same risk, and many people will have other comorbidities, which compounds their vulnerability. Simple rules can't reflect these differences or capture complex factors like frailty[9] which makes people more vulnerable to severe infections.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. METHODS",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Proxy Outcome",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Since real-world data on COVID-19 cases are not readily available, the C-19 Index was developed using close proxy events. A person's C-19 Index is measured in terms of their near-term risk of severe complications from respiratory infections (e.g. pneumonia, influenza). The most direct proxy event is Acute respiratory distress syndrome (ARDS), identified by ICD-10 diagnosis code J80. ARDS is extremely rare, with an annual occurrence of less than  $0.05\\%$  in Medicare members. To create a viable machine learning model, the outcome was broadened to include 4 closely related categories of respiratory diagnoses from the Clinical Classifications Software Refined (CCSR)[12] classification system. Patient's were considered to have the proxy event if they had any of the following diagnosis codes in any position on a medical claim associated with a hospital inpatient visit or observation stay:",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "ICD-10-CM J80 - Acute respiratory distress syndrome",
+            "RSP002 - Pneumonia (except that caused by tuberculosis)",
+            "RSP003 - Influenza",
+            "RSP005 - Acute bronchitis",
+            "RSP006 - Other specified upper respiratory infections"
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Machine learning models were created that predict the likelihood that a patient will have an inpatient hospital stay due to one of the above conditions in the next 3 months. While claims-based machine learning models typically focus on longer term predictions such as outcomes with the",
+        "bbox": [
+            143,
+            835,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
+            65,
+            702,
+            80
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "2",
+        "bbox": [
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+            917
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Population Size",
+        "text_level": 1,
+        "bbox": [
+            156,
+            113,
+            277,
+            126
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3,114,713",
+        "bbox": [
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+            128,
+            225,
+            143
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Fee-for-service members with 6 months of continuous coverage prior to 9/30/2016",
+        "bbox": [
+            156,
+            143,
+            900,
+            160
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "1,511,950 65 years old or older",
+        "bbox": [
+            156,
+            161,
+            449,
+            175
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "1,506,659 Exclude members who died before 9/30/2016",
+        "bbox": [
+            156,
+            176,
+            633,
+            191
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "1,500,700 Exclude members who lose coverage before 12/31/2016 not due to death.",
+        "bbox": [
+            156,
+            191,
+            833,
+            208
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Table 1: Cohort selection for the CMS population",
+        "bbox": [
+            344,
+            220,
+            650,
+            234
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "next 6 months or one year, this model is expected to be used for immediate targeting decisions around COVID-19, and so a shorter window was deemed appropriate.",
+        "bbox": [
+            143,
+            261,
+            849,
+            292
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Datasets",
+        "text_level": 1,
+        "bbox": [
+            143,
+            313,
+            272,
+            329
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "These models were trained and initially tested using historical medical claims data. Two different data sets were obtained, representing different segments of the population. The first was the Center for Medicare & Medicaid Services (CMS) Limited Data Set (LDS) [14] for 2015 & 2016. The LDS contains beneficiary level health information for  $5\\%$  of the Medicare population, and is available to the public subject to a Data Use Agreement. The second was medical claims data for 2.5 million beneficiaries obtained from Healthfirst, which provides health insurance for New Yorkers. These two data sets represented different demographics within the US population. The LDS data contains only Medicare beneficiaries, who are predominantly over the age of 65 or disabled. The Healthfirst data set is primarily a Medicaid population, which includes more healthy adults.",
+        "bbox": [
+            142,
+            338,
+            852,
+            494
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In order to build a predictive model appropriate for the overall US population, these two data sets were combined into a single population that has a demographic profile consistent with the overall US population. Cohorts were individually created for each data set and then the resulting cohorts were combined to create the final training and test sets for the models.",
+        "bbox": [
+            143,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2.1 CMS Data Preparation",
+        "text_level": 1,
+        "bbox": [
+            143,
+            579,
+            370,
+            594
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The CMS data cohort was created by identifying all living members above the age of 65 on 9/30/2016. This particular date was chosen because it was 3 months from the end of the data set and was therefore the latest prediction date possible in the data set. Using the latest date minimized the use of ICD-9 data in the prediction histories since this data spanned the transition from International Classification of Diseases version 9 to version 10 (ICD-10) on October 1, 2015. Members under 65 were excluded because the second population we had was a better representation of the under 65 population. Only fee-for-service members were included because medical claims histories for other members are not reliably complete. We then excluded all members who had less than 6 months of continuous eligibility prior to 9/30/2016. We also excluded members who lost coverage within 3 months after 9/30/2016, except for those members who lost coverage due to death. Because these members lost coverage, we cannot be confident that a negative label s Table 1 below summarizes the population selection.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2.2 Healthfirst Data Preparation",
+        "text_level": 1,
+        "bbox": [
+            143,
+            811,
+            410,
+            827
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The Healthfirst cohort contained a longer history, from 2017 to the present. For this data set members were evaluated at multiple points in time rather instead of having a single prediction date. Each person was evaluated using each month of eligibility as a prediction date. This",
+        "bbox": [
+            143,
+            835,
+            851,
+            883
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
+            66,
+            702,
+            82
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "3",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "PopulationSize Selection Criteria",
+        "text_level": 1,
+        "bbox": [
+            155,
+            112,
+            424,
+            127
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3,008,781 Total members in the Healthfirst dataset",
+        "bbox": [
+            155,
+            128,
+            584,
+            143
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "30,898,086 Total member-months of eligibility",
+        "bbox": [
+            156,
+            143,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "29,388,003 3 months of eligibility after the prediction date",
+        "bbox": [
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+            160,
+            633,
+            176
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "19,470,511 18 years or older on the prediction date",
+        "bbox": [
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+            176,
+            581,
+            191
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/cedd6cfa36944fc4ccd8b802446d8cb788519d064e73846ebc7f5a17b259ab8d.jpg",
+        "table_caption": [
+            "Table 2: Cohort selection for the Healthfirst population"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>Algorithm</td><td>Deployment</td><td>Features</td><td>SLA @ 5%</td></tr><tr><td>Survey</td><td>Logistic Regression</td><td>Online survey</td><td>14</td><td>49.8%</td></tr><tr><td>Open Source</td><td>XGBoost</td><td>Open Source</td><td>559</td><td>53.8%</td></tr><tr><td>Full</td><td>XGBoost</td><td>Hosted</td><td>892</td><td>54.1%</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Table 3: Different models created and their tradeoffs in terms of accuracy versus ease of implementation. The full model has the highest accuracy while the survey model has a very constrained feature set that is easy to implement. Accuracy is measured using Sensitivity and Low Alert Rates (SLA).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "approach was not used with the CMS data because that data didn't cover a long enough time period to allow for multiple months. Members had to have 3 months of eligibility after and had to be at least 18 years old on the prediction date. Table 2 below summarizes the population selection.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2.2.3 Combined Population",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Each data set was split by person  $80\\% / 20\\%$  into train and test sets. In the Healthfirst data set, doing the split by person ensures that all prediction dates for a given individual were in the same set, eliminating the possibility of data leakage. The data set for training was taken by taking all of the positive examples from each data set along with a sampling of the negative examples in the training set. The sampling was designed to meet two criteria. First, the percentage of the adult population 65 or older was set to match that of the US population (21% of adults). Second, the difference in prevalence between those under and over 65 from the Healthfirst data set was maintained in the overall data set. This difference was 3.9X.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The combined test population was created by unioning the full test set from the CMS data and a random  $20\\%$  sample of the Healthfirst test set. The full test population contained 1,621,149 training examples with a prevalence of  $3.86\\%$ . The test population had 761,898 examples with a prevalence of 0.36",
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+    },
+    {
+        "type": "text",
+        "text": "2.3. Models",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "In order to encourage wide adoption and rapid implementation of the predictive models, we created three separate models which represent different tradeoffs between accuracy and ease of implementation. All three models were trained and tested on the same data set. The models were built using the ClosedLoop platform on the AWS cloud. The models are summarized in Table 3 below.",
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+    },
+    {
+        "type": "text",
+        "text": "The \"Survey\" model is the simplest and uses only a small number of features that were designed to be able to be generated from a simple health risk assessment questionnaire. This model requires no technical implementation, and we have made it available through a web-based survey[15]. The \"Open source\" model uses approximately 600 features derived from medical claims diagnosis and utilization data. We have made this model available on GitHub[16]. Finally, the \"Full\" model was created that uses an extensive feature set derived generated from medical claims data along",
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+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
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+            702,
+            83
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with linked geographical and social determinants of health data. This model is being made freely available to healthcare organization. Information about accessing the platform can be found at https://cv19index.com.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2.3.1 Survey Model",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The first model is aimed at using a simple health history survey to enrich the high-level recommendations from the CDC website[8] for identifying those individuals who are at risk. The CDC identifies risk factors as:",
+        "bbox": [
+            142,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Older adults",
+            "- Individuals with heart disease",
+            "- Individuals with diabetes",
+            "- Individuals with lung disease"
+        ],
+        "bbox": [
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+            256,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The purpose of the survey to let an individual know their risk relative to the general population with more detail than is available through the CDC. The way this is achieved is by mapping questions related to an individuals medical history into diagnosis code categories from the CCSR. We also included age and gender as well as prior year hospital inpatient or emergency room (ER) visits. In addition to the conditions coming from the recommendations of the CDC, we included features that our other modeling efforts surfaced as important. The mapping between the survey questions and CCSR codes is described in Table 4. To turn this into a model, we extract ICD-10 diagnosis codes from the claims in the year before the prediction date and aggregate them using the CCSR categories. We create indicator features for the presence of any code in the CCSR category. A logistic regression model is then trained on the available claims data. A person's percentile risk score is based on risk relative to the other values in the training distribution. In addition to the CCSR codes, Table 4 includes the coefficients associated with these features in the logistic regression model.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2.3.2 Open Source Model",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The Open Source model uses gradient boosted trees. Gradient boosted trees are a machine learning method that use an ensemble of simple models to create highly accurate predictions[10]. The resulting models demonstrate higher accuracy. A drawback to these models is that they are significantly more complex; consequently, \"by hand\" implementations of such models are impractical. A nice feature of gradient boosted trees is that they are fairly robust against learning features that are eccentricities of the training data, but do not extend well to future data. As such, we allow full diagnosis histories to be leveraged within our simpler XGBoost model. In this approach, every category in the full CCSR is converted into an indicator feature, resulting in 559 features. A 3-month delay was imposed on the claims data, so that claims within the most recent 3 months before the prediction date were not used to make the predictions. This 3-month delay simulates the delay in claims processing that usually occurs in practical settings and enables the model to be used with current claims data. This delay was not imposed in the survey model since questionnaires would generally use current data. The Github repository for the open source model contains scripts that automatically prepare the features for this model from simple CSV files containing claims data.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "2.3.3 Full Model",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We additionally built a model within the ClosedLoop platform. The ClosedLoop platform is a software system designed to enable rapid creation of machine learning models utilizing healthcare",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
+            66,
+            702,
+            82
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "5",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/8a4ddb6d72c4d187e2658b312f8c899478e2f183e03296fdf521426549378d26.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Feature name</td><td>Coefficient</td><td>CCSR Code</td></tr><tr><td>Intercept</td><td>-6.74</td><td>n/a</td></tr><tr><td>Age</td><td>0.041</td><td>n/a</td></tr><tr><td>Gender Male</td><td>0.171</td><td>n/a</td></tr><tr><td>Prior Admissions</td><td>0.682</td><td>n/a</td></tr><tr><td>Prior ER Visits</td><td>0.413</td><td>n/a</td></tr><tr><td>Chronic obstructive pulmonary disease (COPD) or emphysema, cystic fibrosis, or chronic bronchitis</td><td>1.167</td><td>CCSR:RSP008,CCSR:END012</td></tr><tr><td>Asthma</td><td>1.393</td><td>CCSR:RSP009</td></tr><tr><td>Obesity</td><td>0.935</td><td>CCSR:END009</td></tr><tr><td>Diabetes (other than when you were pregnant)</td><td>0.096</td><td>CCSR:END002,CCSR:END003,CCSR:END004,CCSR:END005</td></tr><tr><td>Hypertension (also called high blood pressure)</td><td>0.832</td><td>CCSR:CIR007,CCSR:CIR008</td></tr><tr><td>Congestive Heart Failure</td><td>0.982</td><td>CCSR:CIR019</td></tr><tr><td>Heart attack (also called myocardial infarction)</td><td>0.159</td><td>CCSR:CIR009,CCSR:CIR010</td></tr><tr><td>Rheumatic heart disease</td><td>0.788</td><td>CCSR:CIR001,CCSR:CIR002,CCSR:CIR011,CCSR:CIR014,CCSR:CIR015</td></tr><tr><td>Stroke</td><td>0.285</td><td>CCSR:CIR020,CCSR:CIR021</td></tr><tr><td>Sickle cell anemia/HIV infection/Transplant</td><td>2.582</td><td>CCSR:BLD005,CCSR:INF006,CCSR:FAC023</td></tr><tr><td>Chronic kidney disease</td><td>0.966</td><td>CCSR:GEN003</td></tr><tr><td>Hemodialysis</td><td>1.369</td><td>CCSR:GEN002</td></tr><tr><td>Liver disease</td><td>0.055</td><td>CCSR:DIG019</td></tr><tr><td>Pneumonia, acute bronchitis, influenza or other</td><td>0.696</td><td>CCSR:RSP002,CCSR:RSP003,CCSR:RSP005,CCSR:RSP006</td></tr><tr><td>acute respiratory infection</td><td></td><td></td></tr><tr><td>Cancer</td><td>1.091</td><td>CCSR:NEO</td></tr><tr><td>Neurocognitive conditions</td><td>0.294</td><td>CCSR:NVS011,CCSR:CIR022,CCSR:CIR025</td></tr><tr><td>Pregnancy</td><td>0.789</td><td>CCSR:PRG</td></tr><tr><td>COPD x Age</td><td>-0.002</td><td>n/a</td></tr><tr><td>Asthma x Age</td><td>-0.015</td><td>n/a</td></tr><tr><td>Obesity x Age</td><td>-0.004</td><td>n/a</td></tr><tr><td>Diabetes x Age</td><td>0.000</td><td>n/a</td></tr><tr><td>Hypertension x Age</td><td>0.005</td><td>n/a</td></tr><tr><td>Congestive heart failure x Age</td><td>-0.007</td><td>n/a</td></tr><tr><td>Myocardial infarction x Age</td><td>0.003</td><td>n/a</td></tr><tr><td>Rheumatic heart disease x Age</td><td>-0.008</td><td>n/a</td></tr><tr><td>Stroke x Age</td><td>-0.003</td><td>n/a</td></tr><tr><td>Sickle cell/HIV/Transplate x Age</td><td>-0.028</td><td>n/a</td></tr><tr><td>Chronic kidney disease x Age</td><td>-0.008</td><td>n/a</td></tr><tr><td>Hemodialysis x Age</td><td>-0.018</td><td>n/a</td></tr><tr><td>Liver disease x Age</td><td>0.001</td><td>n/a</td></tr><tr><td>Pneumonia, acute bronchitis, influenza or other</td><td>-0.005</td><td>n/a</td></tr><tr><td>acute respiratory infection x Age</td><td></td><td></td></tr><tr><td>Cancer x Age</td><td>-0.009</td><td>n/a</td></tr><tr><td>Neurocognitive conditions x Age</td><td>0.004</td><td>n/a</td></tr><tr><td>Pregnancy, childbirth and the puerperium x Age</td><td>-0.003</td><td>n/a</td></tr></table>",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 4: Features used associated with risk factors identified by CDC and their corresponding CCSR codes",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "6",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d516b3558b3d534ec14aebdce269f272c107dccd73f3e535280c9bc080e9fce8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>ROC AUC</td><td>Sensitivity at 5% Alert Rate</td></tr><tr><td>Survey</td><td>.86</td><td>.498</td></tr><tr><td>Open Source</td><td>.87</td><td>.538</td></tr><tr><td>Full</td><td>.87</td><td>.541</td></tr><tr><td>Charlson Comorbidity</td><td>.79</td><td>.291</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 5: Measures of effectiveness for the three models",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "data. The full details of the platform are outside the bounds of this paper; however, using the platform allows us to leverage engineered features coming from peer-reviewed studies. Examples are social determinants of health and the Charlson Comorbidity Index[13]. The computation of these features from claims data is often complex or involves the linking of additional data. These are operations handled by the CLosedLoop platform that were not easy to extract into an open source format, but do provide improved model accuracy.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3. RESULTS AND MODEL INTERPRETATION",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We quantify the performance of the C-19 Index using metrics that are relevant for it's intended use. The standard receiver operating characteristic curves show that all 3 models have identical areas under the curve, at 0.87. However, if we consider the intended use of the model, which is to identify highly vulnerable populations for additional targeting, a more appropriate metric is sensitivity at low alerts rates. This metric measures the sensitivity of the model when looking only at some small percentage of the population. This sensitivity if plotted for alert rates up to  $20\\%$  of the population in Figure 1. Additionally, the metrics quantifying the effectiveness of our models are presented in Table 5. To provide a baseline for comparison, the models are compared to the Charleson Comorbidity Index (CCI)[13]. The CCI is a typical risk scoring algorithm based on claims data. In this case, we see that models explicitly built for the proxy outcome are more accurate than the CCI.",
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+    },
+    {
+        "type": "text",
+        "text": "3.1. Validation",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "The model has subsequently been validated by evaluating its results against approximately 14,000 hospital admissions for known COVID-19 cases in New York City from 2/1/2020 until mid-May 2020. These admissions were We validated the Vulnerability Index by comparing the mortality rate for these admissions with their Vulnerability Index. All cases were insured by Healthfirst, and each patient's prior claims data was used to compute their Vulnerability Index.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Members who were admitted and survived had an average score of  $2.4\\%$  and members who were admitted and passed away had an average score of  $3.3\\%$  (a  $38\\%$  relative difference). The ROC AUC was 0.68. This is lower than the test ROC, but that drop is expected since this test set consisted only of patients who had already been admitted for COVID-19, presumably removing many of the low vulnerability patients and increasing the difficulty of the prediction problem.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The 14,000 cases were divided into a adult Medicaid population and a Medicare population. Table 6 sorts each population by their vulnerability index and shows the detah rate of each decile along with the lift relative to the overall death rate.",
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/cdf38281847490abdeb7044b2bcd6f551db6c54117c09059edae347f7e801c6a.jpg",
+        "image_caption": [
+            "Sensitivity At Low Alert Rate for CV19 Index Models",
+            "Figure 1: Sensitivity of each model at alert rates up to  $20\\%$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            276,
+            191,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/84b296299027e46dbe7b00d7dc3d61dc54665f9a22a73411dac474c736b7b652.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Decile</td><td>Medicaid Mortality %</td><td>Medicaid Lift</td><td>Medicare Mortality %</td><td>Medicare Lift</td></tr><tr><td>Top 10%</td><td>6.48</td><td>1.30</td><td>5.56</td><td>2.99</td></tr><tr><td>Top 20%</td><td>6.43</td><td>1.29</td><td>3.70</td><td>2.00</td></tr><tr><td>Top 30%</td><td>6.39</td><td>1.29</td><td>3.09</td><td>1.66</td></tr><tr><td>Top 40%</td><td>6.39</td><td>1.28</td><td>2.78</td><td>1.50</td></tr><tr><td>Top 50%</td><td>6.21</td><td>1.25</td><td>2.59</td><td>1.40</td></tr><tr><td>Top 60%</td><td>5.80</td><td>1.17</td><td>3.10</td><td>1.67</td></tr><tr><td>Top 70%</td><td>5.51</td><td>1.11</td><td>2.65</td><td>1.43</td></tr><tr><td>Top 80%</td><td>5.25</td><td>1.06</td><td>2.32</td><td>1.25</td></tr><tr><td>Top 90%</td><td>5.11</td><td>1.03</td><td>2.06</td><td>1.11</td></tr><tr><td>Full</td><td>4.97</td><td>-</td><td>1.86</td><td>-</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6: Validation of the Vulnerability Index using COVID-19 admissions",
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index  $\\cdot$  April, 2020",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "8",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3.2. Accessing Models",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In an effort to make these models as broadly available as possible we have provided several different avenues for the models to be used, each optimized for a different user base. The logistic regression model powers a publicly available web-based survey at http://c19survey.closedloop.ai. The open source model is available through github at https://github.com/closedloop-ai/cv19index. This model is written in the Python programming language. We have included synthetic data for testing an wrapper code that converts tabular medical claims data to the input format specific for our models. We encourage the healthcare data science community to fork the repository and adapt it to their own purposes. We encourage collaboration from the open-source community, and pull requests will be considered for inclusion in the main branch of the package. Finally, for those wishing to take advantage of the full model, we are providing access to the COVID-19 model hosted on the ClosedLoop platform free of charge. Please visit https://closedloop.ai/cv19index for instructions on how to gain access.",
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+    {
+        "type": "text",
+        "text": "3.3. Limitations",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The approach taken in this paper has several limitations. Most notably, no actual COVID-19 cases were used in the training of the model. The usefulness of the model in predicting COVID-19 vulnerability is entirely dependent on the actual occurrence of COVID-19 matching the proxy outcome. While the logic behind these decisions is defensible, they are not currently backed up with actual data. As COVID-19 case data becomes available, we expect to validate the proxy outcome and determine if it is in fact appropriate. Eventually, enough data will be available to build models on COVID-19 Vulnerability itself without having to use a proxy.",
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+    },
+    {
+        "type": "text",
+        "text": "Anther major limitation of these models is their reliance on claims data, which does not contain enough clinical detail, such as lab values. For this reason, we do not recommend using the C-19 Vulnerability Index in inpatient settings, where more detailed data is likely available. The C-19 Index is most useful in a population health context where the only data available is claims data.",
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+    {
+        "type": "text",
+        "text": "Finally, based on medical guidance the authors have decided exclude pediatric populations from the training and test sets for the C-19 Index. At the time of development, there was so little information available on COVID-19 that we could not confidently assert that the proxy endpoint we were using was appropriate for those under 18 years of age.",
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+    {
+        "type": "text",
+        "text": "4. CONCLUSIONS",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This pandemic has already claimed tens of thousands of lives as of this writing, and sadly this number is sure to grow. As healthcare resources are constrained by the same scarcity constraints that affect us all, it is important to empower intervention policy with the best information possible. We have provided several implementations of the C-19 Index and means of access for those individuals with varying levels of technical expertise. It is our hope that by providing this tool quickly to the healthcare data science community, widespread adoption will lead to more effective intervention strategies and, ultimately, help to curtail the worst effects of this pandemic.",
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+    {
+        "type": "text",
+        "text": "5. ADDENDUM",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Due to the early release of the first versions of the C19 Index, several organizations were able to quickly apply the model to their populations. The authors have been in contact with several organizations that have used the vulnerability index to prioritize proactive outreach towards the",
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+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "page_number",
+        "text": "9",
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+    },
+    {
+        "type": "text",
+        "text": "most vulnerable members. In many cases, these organizations had existing care management teams that were able to rapidly shift to COVID-19 by applying a different prioritization and focus to their interventions. In other cases, new phone or text messaging campaigns were developed for COVID-19 that used the C-19 Index as a prioritization mechanism. As the response to the pandemic continues to develop, we will continue to update the C-19 Index and provide more information on its usage.",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "6. ETHICS",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "All relevant ethical guidelines have been followed in this study. For the CMS LDS data, we submitted a research proposal as part of our data use agreement that discussed our plans to build predictive models using this data. For the Healthfirst data, which did contain identifiable PHI, the data was covered under a Business Associate Agreement between ClosedLoop.ai and Healthfirst and the data was stored in ClosedLoop's HIPAA compliant cloud storage. The project was part of an ongoing Quality Improvement effort at Healthfirst and so did not require preapproval by an Institutional Review Board. The study protocol and this manuscript were reviewed and approved by Healthfirst's compliance team.",
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+    },
+    {
+        "type": "text",
+        "text": "7. ACKNOWLEDGEMENTS",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We would like to thank Healthfirst for their collaboration on this work and for allowing us to use insights from their dat ain generation of the model. We would also like to thank Amazon Web Services for sponsoring this work with AWS platform credits.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "REFERENCES",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[1] World Health Organization. aAIJCoronavirus. Who.Int, 2019, www.who.int/emergencies/diseases/novel-coronavirus-2019. Accessed 15 Mar. 2020.",
+            "[2] World Health Organization. àAIJWHO Director-General's Opening Remarks at the Media Briefing on COVID-19 - 11 March 2020.àAI Who.Int, 11 Mar. 2020, www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19—11-march-2020. Accessed 15 Mar. 2020. àAN",
+            "[3] Specht, Liz. aIJSimple Math Offers Alarming Answers about Covid-19, Health Care. aAI STAT, 10 Mar. 2020, www.statnews.com/2020/03/10/simple-math-alarming-answers-covid-19/. Accessed 15 Mar. 2020.",
+            "[4] Page, Michael Le. âIJWhy Is It so Hard to Calculate How Many People Will Die from Covid-19?âI New Scientist, 11 Mar. 2020, www.newscientist.com/article/mg24532733-700-why-is-it-so-hard-to-calculate-how-many-people-will-die-from-covid-19/. Accessed 15 Mar. 2020.",
+            "[5] Zhou F, Yu T, Du R, et al. Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study [published online ahead of print, 2020 Mar 11] [published correction appears in Lancet. 2020 Mar 12;]. Lancet. 2020;S0140-6736(20)30566-3. doi:10.1016/S0140-6736(20)30566-3."
+        ],
+        "bbox": [
+            145,
+            544,
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+            883
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
+            66,
+            702,
+            82
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "page_number",
+        "text": "10",
+        "bbox": [
+            145,
+            906,
+            166,
+            919
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
+        "list_items": [
+            "[6] Wu Z, McGoogan JM. Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China: Summary of a Report of 72314 Cases From the Chinese Center for Disease Control and Prevention [published online ahead of print, 2020 Feb 24]. JAMA. 2020;10.1001/jama.2020.2648. doi:10.1001/jama.2020.2648 àÑ",
+            "[7] Centers for Disease Control and Prevention. àAIJCoronavirus Disease 2019 (COVID-19).aAI Centers for Disease Control and Prevention, 11 Feb. 2020, www.cdc.gov/coronavirus/2019ncov/specific-groups/high-risk-complications.html.",
+            "[8] Centers for Disease Control and Prevention. àAIJCoronavirus Disease 2019 (COVID-19).aAI Centers for Disease Control and Prevention, 11 Feb. 2020, www.cdc.gov/coronavirus/2019ncov/specific-groups/high-risk-complications.html.",
+            "[9] Hubbard, Ruth E, et al. aIJFrailty Status at Admission to Hospital Predicts Multiple Adverse Outcomes. Age and Ageing, vol. 46, no. 5, 2017, pp. 801aA806, www.ncbi.nlm.nih.gov/pubmed/28531254, 10.1093/ageing/afx081. Accessed 11 Jan. 2020.",
+            "[10] James, Gareth, et al. An Introduction to Statistical Learning, with Applications in R. Springer, 2013.",
+            "[11] aAIJMeasures and Data Sources | County Health Rankings and Roadmaps. aAI Countyhealthrankings.org, University of Wisconsin Population Health Institute, 2019, wwwcountyhealthrankings.org/explore-health-rankings/measures-data-sources. Accessed 1 Feb. 2020.",
+            "[12] The Healthcare Cost and Utilization Project. aAJClinical Classifications Software Refined (CCSR) for ICD-10-CM Diagnoses.aAI www.Hcup-Us.Ahrq.Gov, www.hcupus.ahrq.gov/toolssoftware/ccsr/ccs refined.jsp. Accessed 15 Mar. 2020.",
+            "[13] Charlson, M E, et al. aAIJA New Method of Classifying Prognostic Comorbidity in Longitudinal Studies: Development and Validation. aAI Journal of Chronic Diseases, vol. 40, no. 5, 1987, pp. 373aA83, 10.1016/0021-9681(87)90171-8.",
+            "[14] Centers for Medicare & Medicaid Services. aAIJLimited Data Set (LDS) Files.aAI www.cms.gov, https://www.cms.gov/Research-Statistics-Data-and-Systems/Files-for-Order/LimitedDataSets. Accessed 14 Apr. 2020.",
+            "[15] ClosedLoop.ai. âAIJCOVID-19 Vulnerability IndexâAï closedloop.ai, https://closedloop.ai/cv19index/. Accessed 14 Apr. 2020.",
+            "[16] ClosedLoop.ai. ĀAIJCOVID-19 Vulnerability Index GitHub Āi github.com, https://github.com/closedloop.ai/cv19index. Accessed 14 Apr. 2020.",
+            "[17] Sanche, Steven, et al. aAIHigh Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2.aAI Emerging Infectious Diseases, vol. 26, no. 7, July 2020, wwwnc.cdc.gov/eid/article/26/7/20-0282_article, 10.3201/eid2607.200282. Accessed 21 Apr. 2020.",
+            "[18] Markian Hawryluk. âAIJMysterious Heart Damage, Not Just Lung Troubles, Befalling COVID-19 Patients. âAİ Kaiser Health News, 6 Apr. 2020, khn.org/news/mysterious-heart-damage-not-just-lung-troubles-befalling-covid-19-patients/. Accessed 21 Apr. 2020."
+        ],
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
+            295,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "page_number",
+        "text": "11",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Gender Age Admission Count ED Visit Count Office Visit Count Medical Eligibility Months # Distinct DME Catego",
+        "bbox": [
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+            112,
+            1000,
+            130
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/ea4b64b1c0ac11cf12cc787bf8d9ea17e7f9c3c4da2b359e6cb7c0e5b756e851.jpg",
+        "table_caption": [
+            "Table 7: Full feature list available within platform"
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Evidence of smokeless tobacco</td></tr><tr><td>Evidence of tobacco non-use</td></tr><tr><td>Falls risk assessment performed</td></tr><tr><td>Abnormal BMI</td></tr><tr><td>Normal BMI</td></tr><tr><td>LDL</td></tr><tr><td>LVEF</td></tr><tr><td>Systolic Blood Pressure</td></tr><tr><td>Diastolic Blood Pressure</td></tr><tr><td>Continuity of Care Index (12M)</td></tr><tr><td>PQI Any</td></tr><tr><td>PQI Diabetes</td></tr><tr><td>PQI 5</td></tr><tr><td>PQI 7</td></tr><tr><td>PQI 8</td></tr><tr><td>PQI 11</td></tr><tr><td>PQI 12</td></tr><tr><td># Distinct CCSR Body Systems</td></tr><tr><td># Distinct CCSR Diagnosis Categories (12M)</td></tr><tr><td>PCS Procedure History</td></tr><tr><td>Prior Respiratory Infections</td></tr><tr><td>Prior Hospital Acquired Infections</td></tr><tr><td>Diagnosis History High-Level</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Table 8: Full feature list available within platform (continued)",
+        "bbox": [
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+            689,
+            563
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "[19] Chow, Nancy, et al. aAJPreliminary Estimates of the Prevalence of Selected Underlying Health Conditions Among Patients with Coronavirus Disease 2019 aA'T United States, February 12aA\\$March 28, 2020.aAIMMWR. Morbidity and Mortality Weekly Report, vol. 69, no. 13, 3 Apr. 2020, pp. 382aA\\$386, www.cdc.gov/mmwr/volumes/69/wr/mm6913e2.htm?s_cid=mm6913e2_w, 10.15585/mmwr.mm6913e2. Accessed 21 Apr. 2020. aA'N",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "aAN",
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "8. APPENDIX: FULL FEATURE LIST",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We include the list of features used in the Full model. This was a feature set that could be implemented across the 2 data sets and utilizes just medical claims data. The ClosedLoop platform is capable of incorporating a wide variety of other health data, including pharmacy claims, electronic health records, patient reported data, and linked census data. That additional data was not used in this model due to the constraints around our usage of the CMS data. The majority of features are binary variables indicating if a patient has had one type of medical event 15 moths prior to the date of prediction, excluding the 3 most recent months.",
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+    },
+    {
+        "type": "header",
+        "text": "Building a COVID-19 Vulnerability Index • April, 2020",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "page_number",
+        "text": "12",
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+    }
+]