Inference device, learning device and program

Abstract

This invention provides an inference device that can estimate fault tolerance even for networks of a certain size expected to be commercial in scale, without having to deploy and verify actual equipment each time. [Solution] The inference device 20 receives a feature graph output from the conversion unit 21, in which network elements are represented as nodes and the presence or absence of connection relationships between network elements is represented as the presence or absence of edges between nodes. This feature graph is then given feature quantities that reflect network state information and information about the source node and destination node within the network. The inference unit 22 receives this feature graph as input and applies inference using a pre-trained model to the input to estimate the fault tolerance of the traffic flow from the source node to the destination node.

Description

[Technical Field]

[0001] The present invention relates to inference measures, learning devices, and programs related to estimating the fault tolerance of a network. [Background technology]

[0002] Networks are a vital social infrastructure, and maintaining network quality is essential to provide stable services. In particular, when introducing new networks or making design changes, thorough prior verification is necessary to understand fault tolerance. Patent document 1 describes a conventional technology that "makes it possible to comprehensively identify fault test locations and easily understand the impact of fault testing when conducting fault tests on a system consisting of multiple virtual servers and virtual networks." [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2021-47928 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] However, while Patent Document 1 examines the comprehensiveness of fault testing during network operation verification, it requires a test unit, i.e., actual equipment, and therefore commercial-scale verification may not be possible due to equipment shortages, etc. In other words, building a commercial-scale network with a test unit is difficult from a cost standpoint because it generally requires many expensive actual devices for commercial use.

[0005] On the other hand, while using a simulator can be considered as a way to reduce the cost of using actual equipment, simulator-based verification results in a decrease in verification quality because the operation differs from that of an actual router.

[0006] In other words, conventional technology had the challenge of making it difficult to understand fault tolerance even in networks of a certain size that are expected to be commercially viable, taking into account the operation of actual equipment.

[0007] In view of the problems of the prior art described above, the first objective of the present invention is to provide an inference device that can estimate fault tolerance without introducing and verifying actual equipment each time, even for networks of a certain size that are expected to be commercial in scale. The second objective is to provide a learning device that learns the model used by the inference device. The third objective is to provide a program corresponding to the inference device and the learning device. [Means for solving the problem]

[0008] To achieve the first objective described above, the present invention is an inference device that accepts a feature-equipped graph as input, in which network elements are represented as nodes and the presence or absence of connection relationships between network elements is represented as the presence or absence of edges between nodes, and features are added that reflect network state information and information about source and destination nodes within the network. The first feature of the device is that it estimates the fault tolerance of the traffic flow from the source node to the destination node by applying inference using a pre-trained model to the input.

[0009] Furthermore, in order to achieve the second objective described above, the present invention provides a learning device for the inference device that learns the pre-trained model, and its second feature is that it accepts the following as learning data: first data, which is a feature graph in which network elements are represented as nodes and the presence or absence of connection relationships between network elements is represented as the presence or absence of edges between nodes, and features that reflect network state information and information about source and destination nodes within the network; and second data, which is the result of a fault tolerance test when traffic flow from a source node to a destination node according to the first data is passed through a network constructed by providing the network elements with an actual device according to the first data, and the device learns a model that takes the first data as input and outputs the second data using the learning data.

[0010] Furthermore, the present invention is a program characterized by causing a computer to function as the inference device or as the learning device. [Effects of the Invention]

[0011] According to the first feature described above, by applying inference using a pre-trained model, the fault tolerance of a network of a certain size can be estimated without requiring actual device verification each time. According to the second feature described above, a model used to estimate the fault tolerance of the said network can be trained. [Brief explanation of the drawing]

[0012] [Figure 1] This is a functional block diagram of a pre-verification system according to one embodiment. [Figure 2] This figure illustrates an example of how to apply a graph neural network in this embodiment. [Figure 3] This figure illustrates an example of how to apply a graph neural network in this embodiment. [Figure 4] This figure illustrates an example of the graph neural network used in this embodiment. [Figure 5] It is a diagram showing an example of the hardware configuration in a general computer device.

Embodiments for Carrying out the Invention

[0013] FIG. 1 is a functional block diagram of a pre-verification system 100 according to an embodiment. As shown, the pre-verification system 100 includes a learning device 10, a test facility 13, and an inference device 20. The learning device 10 includes a graph generation unit 11, a test setting generation unit 12, a test result acquisition unit 14, a learning data storage unit 15, a learning execution unit 16, and a learning model storage unit 17. The inference device 20 includes a conversion unit 21 and an inference unit 22.

[0014] Note that both the learning device 10 and the inference device 20 can be realized by a general computer as described later with reference to FIG. 5, and the test facility 13 can be realized by network equipment constructed using actual machines and operated for testing, as described later with reference to FIG. 2 (Example EX1).

[0015] The overall operation flow of the pre-verification system 100 is to construct a learning model by performing learning in the learning device 10 and the test facility 13 as the first step, and to obtain an inference result of the fault tolerance in the network to be pre-verified by performing inference in the inference device 20 using this learned model as the second step.

[0016] First, a general and formal description of the processing of each functional unit in FIG. 1 that executes the learning process in the first step and the inference process in the second step will be given, and then the details of each process will be described. Note that since a graph neural network is used for the learning model in this embodiment as described later, each functional unit will handle information related to the graph.

[0017] In the graph generation unit 11, parameters such as a graph creation algorithm, the number of nodes, the number of graphs to be created, the type of feature quantity, and the generation conditions of the feature quantity are received from an engineer (a user who uses the pre-verification system 100) as input, and a plurality (hereinafter, assumed to be N for the sake of explanation) of graphs with feature quantities G(k) (k = 1, 2,..., N) are generated in a form according to the input parameters, and the generated graphs with feature quantities G(k) are output to the test setting generation unit 12 and the learning data storage unit 15. (Note that hereinafter, for the sake of clarity of explanation, data processed using so-called variable notations and function notations such as the graph G(k) will also be referred to. Note that function notations use conversions F and f described later.)

[0018] In the test setting generation unit 12, for each of the large number of graphs with feature quantities G(k) (k = 1, 2,..., N) obtained from the graph generation unit 11, an operation setting of the network configured by the corresponding actual machine is generated as a test setting Config(k) (k = 1, 2,..., N), and the large number of test settings are output to the test equipment 13 (output by notifying the engineer who operates the test equipment 13). (Note that, as will also be described later regarding the conversion unit 21, in the test setting generation unit 12, a test setting Config(k) can be generated from the graph G(k) as Config(k) = f(G(k)) using a predetermined conversion f.)

[0019] The test equipment 13 is constructed by an engineer as an actual machine network as described above and is operated for testing. That is, the test equipment 13 is configured as a network configuration NW(k) (k = 1, 2,..., N) provided according to each of the N types of test settings Config(k) (k = 1, 2,..., N). By constructing and operating the test equipment 13 by the engineer in all N types of network configurations, test results Result(k) (k = 1, 2,..., N) regarding the presence or absence of fault tolerance in the actual machine are obtained.

[0020] The test result acquisition unit 14 receives the test results Result(k) (k=1,2,…,N) from the test equipment 13 for the N network configurations Config(k) (k=1,2,…,N) as described above, and outputs the test results Result(k) to the training data storage unit 15 as correct labels for building the learning model.

[0021] Furthermore, the test result Result(k) in the test equipment 13 can be recorded by an engineer who has constructed the network configuration NW(k) of the test equipment 13, performed test operation, and confirmed the presence or absence of fault tolerance, and this record can be accepted as input by the test result acquisition unit 14.

[0022] In the training data storage unit 15, for each feature-enhanced graph G(k) (k=1,2,…,N) obtained from the graph generation unit 11, the corresponding test result Result(k) (k=1,2,…,N) obtained from the test result acquisition unit 14 is associated as the correct label and stored as training data D. D={(G(k),Result(k))|k=1,2,…,N}

[0023] As will be explained in more detail later, the graph G(k) in this training data D contains network topology information, features of each node, and features of each edge. Here, the topology information is composed of a set of directed edges. The node features include information about the source and destination of a given traffic flow. As mentioned above, the test result Result(k) in training data D has meaning as the correct label.

[0024] Furthermore, edge features can include information about the communication protocol and flags indicating the occurrence of failures. The ground truth labels may be given as binary values, for example, 1 if there is a communication impact and 0 if there is no communication impact, given the topology and each feature, or a continuous value between 0 and 1 that evaluates the magnitude of the communication impact may be used. In order to generalize the network model in the learning of this embodiment, it is necessary to create training data that covers a large number of patterns, where N is the number of patterns.

[0025] The learning execution unit 16 performs training using the training data D stored in the training data storage unit 15 and constructs a model. The constructed trained model is output to and stored in the training model storage unit 17.

[0026] Furthermore, the learning framework using the training data D in the learning execution unit 16 can use any existing method that conforms to a general-purpose framework that is not dependent on a specific task, similar to those used in deep learning and machine learning. That is, the training data is divided into training and test sets, the training data is used to train the model in the learning execution unit 16, and the final learning model is saved as a candidate or target for further improvement. In addition, the test data may be used to evaluate the model and improve the learning algorithm to obtain the final learning model. Here, any existing method may be used for detailed testing procedures and improvement of the learning algorithm; for example, cross-validation may be used to suppress overfitting and to obtain a learning model with generalization performance in the end.

[0027] As described above, the learning process is performed by the learning device 10 and the testing equipment 13, and the inference process can be performed in the inference device 20 using the constructed trained model.

[0028] The conversion unit 21 receives the network configuration information Config from the engineer, converts the network configuration information Config into a feature-enhanced graph G, and outputs it to the inference unit 22. The inference unit 22 performs inference processing on the input feature-enhanced graph G using the trained model stored in the training model storage unit 17, and obtains the fault tolerance inference result for the network NW configured with the network configuration information Config as a predicted label using the trained model.

[0029] The conversion F(Config)=G from network configuration information Config to feature-enhanced graph G in the conversion unit 21 is the inverse conversion F=f of the conversion process f(G(k))=Config(k)(k=1,2,…,N) in the test setting generation unit 12. -1 This can be used. Both transformation F and transformation f, which are inverse transformations of each other, can be used in accordance with the predetermined rules when the graph generation unit 11 generates the graph, and the predetermined transformation can be used.

[0030] Figures 2 and 3, described later, show examples of the network configuration information Config to be inferred, the corresponding feature graph G, and the training data D={(G(k),Result(k))|k=1,2,…,N} used during training. As shown in this example, in the network configuration information and the corresponding feature graph G, the case where traffic flow is routed from a specific source to a specific destination in the corresponding network is considered as the test target in the form of node weights, and the source and destination information in the traffic flow when considering fault tolerance is included in the graph G and G(k) themselves.

[0031] Having provided a general and formal explanation of each functional component in Figure 1, the following section will provide a more detailed explanation of the application of a graph neural network (GNN) as a learning model for estimating the fault tolerance of the network (a communication network using actual equipment) in this embodiment. Figures 2 and 3 are examples EX1 to EX5 for this explanation, illustrating examples of how the graph neural network is applied in this embodiment, and will be referred to as appropriate below.

[0032] In this embodiment, the (communication) network can be a network necessary to implement a closed network service, an internet service, a mobile network service, etc. As an example, the following will be an example of determining the impact on traffic flow in the event of a link failure in a network configured with OSPF single area.

[0033] In the graph generation unit 11, a directed graph is randomly created based on the Barabási-Albert model regarding the graph structure, ensuring that no isolated nodes are generated. This graph is then represented as a graph with N feature vectors G(k) (k=1,2,…,N). Here, actual routers present in the network are treated as nodes in the graph, and when there is a connection relationship between routers, edges are created between the corresponding nodes, thereby representing a network composed of multiple routers as a graph. The graph represents the case where there is a connection relationship between the i-th node and the j-th node, with corresponding matrix element A. ij Set = 1, and the corresponding matrix element A if there is no connection relationship. ij It can be represented by an adjacency matrix with =0. (Note that information about edge orientation as a directed graph can be considered when dealing with the flow from the i-th node to the j-th node, for example, and specifically, edge orientation can be considered in the OSPF cost value described later.) Example EX1 in Figure 2 is an OSPF area network example EX1, and Examples EX2 to EX5 in Figure 3 show examples of data settings when representing this network example EX1 as a feature-enhanced graph.

[0034] Network example EX1 consists of nine routers R0 to R8 as shown in the diagram, and these routers R0 to R8 are represented as nodes N0 to N8, with rows 1 to 9 of the matrix corresponding to them, and this is represented in the adjacency matrix as shown in example EX2. For example, since there is a connection relationship between nodes N0 and N1, which correspond to routers R0 and R1, we assume that there is a connection relationship between the first and second nodes, A 12 =A 21 = 1

[0035] Furthermore, in the feature-enhanced graph G(k) (k=1,2,…,N) generated by the graph generation unit 11, the node features can include, in this embodiment, a distinction between whether each node is the source, destination, or neither of the above for the source and destination information of the traffic flow flowing through the network NW(k) as the subject of the test.

[0036] Example EX3 shows an example where the distinguishing node features are assigned a 3-value: (1 0) if the node is the source of the traffic flow, (0 1) if it is the destination, and (0 0) if it is neither a source nor a destination. In other words, network example EX1 includes information such as estimating the fault tolerance when traffic flows from source node N0 (router R0) to destination node N8 (router R8) in a network where the topology etc. is given in the graph, and providing the results of actual hardware tests of that fault tolerance as the correct label for training.

[0037] Therefore, for example, even if a network is composed of the same topology as network example EX1, if the (source node, destination node) of the traffic flow considering fault tolerance is different from (N0, N8), then separate node weights will be assigned as features from those shown in example EX3, and the entire feature graph will consist of different information.

[0038] Although not illustrated in the figure, as other information constituting the feature amount of the nodes in the feature amount - attached graph G(k) (k = 1, 2, …, N) generated by the graph generation unit 11, information regarding the model type, specifications, etc. of the router corresponding to the node, and information on parameters set when flowing traffic flow may be included.

[0039] Also, as the feature amount of the edges in the feature amount - attached graph G(k) (k = 1, 2, …, N) generated by the graph generation unit 11, when using an OSPF network in this embodiment, the OSPF cost value can be included. Further, as the link state of the link corresponding to the edge, information on whether or not a failure has occurred in the link may be included.

[0040] In Example EX4, as an example using the above - mentioned edge feature amount, the feature amount e of the edge between nodes i and j ij is given in the form of a two - dimensional vector as e ij =(a b). The first element a represents whether or not there is a link failure, where a = 1 when there is a failure and a = 0 when there is no failure. The second element b is set as the value of the OSPF cost. In network example EX1, a failure has occurred only in the link between nodes N1 and N3, and no failure has occurred in other links. Therefore, for the edge feature amounts e 13 ,e 31 only, the first element a = 1. Also, for the second element b, as the value of the OSPF cost, the OSPF cost value between nodes i and j can be set, for example, with respect to the traffic flow from node i to node j. (Note that in Example EX4, the OSPF cost is the same value when going from node i to node j and vice versa as an illustrative example, but generally, values corresponding to the direction can be set.)

[0041] The correct label represents the fault tolerance test result Result(k). This can be done by performing a test in which traffic flow is actually sent from source to destination in network N(k) in the given state. If the result is affected, for example, if the evaluation value of communication quality, such as packet loss rate, is judged to be large by a threshold judgment, then 1 is given. If the result is not affected, for example, if the evaluation value is not judged to be large, then 0 is given. This can be done as a binary value. Example EX5 shows an example of giving a binary value, but the correct label can also be a continuous value representing the magnitude of the impact on communication, such as between 0 and 1, depending on the packet loss rate.

[0042] Next, we will describe a graph neural network used for learning and model construction in the learning execution unit 16, and for inference in the inference unit 22 using the constructed model. Figure 4 shows a general network configuration (architecture) example of the graph neural network used as Example EX6, and an example of the parameters used as Example EX7. In this embodiment, a unique feature design as described above is used to handle communication networks, referring to Figures 2 and 3. However, the graph neural network itself and the learning method used under this feature design can be general ones disclosed in Non-Patent Literature 1, etc. [Non-patent document 1] You, J., Ying, Z., & Leskovec, J. (2020). Design space for graph neural networks. Advances in Neural Information Processing Systems, 33, 17009-17021.

[0043] As shown in Example EX6, in the context of machine learning, an architecture is adopted that combines a graph neural network (Conv-16, a convolutional layer that processes the graph, shown as reference codes 101, 201, 301, and 401), an activation function (Leaky-ReLU, shown as reference codes 102, 202, 302, and 402), dropout (Dropout, shown as reference codes 103, 203, 303, and 403), and fully connected layers (linear layer 501 (Linear-16) and sigmoid function 502 in the output stage). The activation function is used to introduce nonlinearity in converting input information to output. Dropout has the effect of suppressing overfitting by deactivating a certain percentage of neurons during training. Fully connected layers are necessary to solve the final classification task. Since the task is binary classification, binary cross-entropy is used as the error function. In example EX6 in Figure 4, the graph neural network, activation function, and dropout are repeated four times (the last of which also involves the mean pooling layer 4021) before outputting through a fully connected layer. However, the number of repetitions is an example and can be changed as appropriate.

[0044] Similar to the framework of a typical GNN, the input to the graph neural network during both training and inference is a feature-enhanced graph, and the output is an estimated fault tolerance result, either binary (during inference) or continuous (during training). As with general machine learning and deep learning, during training, the continuous output of the sigmoid function is compared with the binary ground truth label (0 or 1) to evaluate the error, and the network parameters are sequentially updated using backpropagation. During inference, the continuous output of the sigmoid function is compared with a threshold value, such as 0.5, to output a binary result indicating whether or not there is communication interference (i.e., the fault tolerance determination result).

[0045] The graph neural network splits the created dataset (training data D stored in the training data storage unit 15) into training and validation sets, inputs the training set, and starts training. To prevent overfitting, it is desirable to incorporate early stopping, which checks the accuracy of the validation data each time a high-accuracy model is created on the training data, to ensure that no degradation in accuracy has occurred on the validation data. Training stops when early stopping is activated or after a predetermined number of epochs have elapsed, and the model with the best performance on the training data is adopted as the final network model.

[0046] As described above, according to the embodiments of the present invention, once a trained model is created by collecting test results from actual equipment, a verification device as actual equipment is no longer necessary. Considering the actual equipment characteristics, it becomes possible to quickly pre-verify whether or not there is an impact on traffic flow in the event of a failure (i.e., the result of fault tolerance determination) even in networks larger than the network scale during the test. Furthermore, even if the network scale pre-verified using the constructed model for inference processing is larger than the network scale during the test for training, if the overall network structures of both are similar to some extent, the learning process in graph neural networks takes the overall network structure into consideration during convolution, which can be expected to further ensure the accuracy of the inference processing. For example, while the network size used during testing (and during training using the results of said testing) is limited to a maximum of 100 network devices (number of nodes in the graph), and a network of 80 to 100 devices is used, the network size used for pre-verification with the trained model can be limited to a maximum of 150 network devices, and a network of 120 to 150 devices can be used, while still ensuring the required accuracy and evaluating fault tolerance. As a constraint to make the network structure somewhat similar, for example, a predetermined upper limit may be set on the number of neighboring nodes of a given node, and this constraint may be observed during both training and inference.

[0047] The following sections will explain various supplementary examples, alternative examples, and additional examples.

[0048] (1) According to embodiments of the present invention, it is possible to contribute to increased efficiency and reduced costs when constructing networks that function as various industrial bases and social infrastructures, thereby contributing to Goal 9 of the United Nations Sustainable Development Goals (SDGs), "Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation."

[0049] (2) In the above explanation, as an example of a network handled by the pre-verification system 100, an OSPF network was used, which utilizes the OSPF (Open Shortest Path First) protocol, a routing protocol for exchanging route information between routers on an IP network. In this case, the OSPF network elements are routers, and the edge cost was the OSPF cost, which is set considering the line speed, etc.

[0050] Networks using other protocols, such as the BGP (Border Gateway Protocol), can also be handled similarly by modifying the data definitions and other settings as appropriate in the pre-validation system 100. While OSPF deals with networks within a common AS (Autonomous System), BGP controls routing between different ASs. Therefore, instead of using routers within the same AS as in OSPF, BGP can use multiple separate ASs as network elements (nodes in the graph). Similarly, edges in BGP should be established between adjacent ASs.

[0051] As for node features, similar to OSPF, it is sufficient to use features that reflect whether the AS is the source, destination, or neither source nor destination for the traffic flow to be evaluated for fault tolerance. Other node features may include information about the corresponding AS type (a type given by the type of policy used by the AS, the size of the AS, etc.) and information about the parameters set when routing the traffic flow.

[0052] Similarly, for edge features, the BGP cost between ASs corresponding to the edge can be used, and the presence or absence of link failures between those ASs may also be included as edge features.

[0053] For the correct label, the results of fault tolerance tests conducted by actually flowing traffic between ASs can be used as the correct label.

[0054] Furthermore, in the above explanation, we have assumed that the network handled by the pre-verification system 100 is composed of actual equipment, but even if all or part of the network is composed of virtual servers or virtual networks, the fault tolerance can be evaluated in advance by handling the corresponding feature-rich graph, in exactly the same way. In other words, all or part of the network elements handled by the pre-verification system 100 are not limited to actual equipment, but may also be virtual servers or virtual routers.

[0055] (3) Figure 5 is a diagram showing an example of the hardware configuration of a typical computer device 70. The learning device 10 and inference device 20 in the pre-verification system 100 can be realized as one or more computer devices 70 having such a configuration. When the learning device 10 and inference device 20 are realized with two or more computer devices 70, information necessary for processing may be sent and received via a network. The computer device 70 includes a CPU (Central Processing Unit) 71 that executes predetermined instructions, a GPU (Graphics Processing Unit) 72 as a dedicated processor that executes some or all of the execution instructions of the CPU 71 on behalf of or in cooperation with the CPU 71, RAM 73 as main memory that provides a work area to the CPU 71 (and GPU 72), ROM 74 as auxiliary memory, a communication interface 75, a display 76 that outputs a display, an input interface 77 that accepts user input via a mouse, keyboard, touch panel, etc., a speaker 78 that outputs sound, and a bus BS for sending and receiving data between these.

[0056] Each functional unit in the learning device 10 and the inference device 20 can be implemented by a CPU 71 and / or GPU 72 that reads and executes a predetermined program corresponding to the function of each unit from ROM 74. The data storage functions in the learning data storage unit 15 and the learning model storage unit 17 can be provided as memory devices by RAM 73 and / or ROM 74. Both the CPU 71 and GPU 72 are types of arithmetic units (processors). When display-related processing is performed, the display 76 also operates in conjunction; when communication-related processing for data transmission and reception is performed, the communication interface 75 also operates in conjunction; and when audio output-related processing is performed, the speaker 78 also operates in conjunction. [Explanation of Symbols]

[0057] 100...Pre-verification system, 10...Learning device, 13...Test equipment, 20...Inference device 11...Graph generation unit, 12...Test setting generation unit, 14...Test result acquisition unit, 15...Training data storage unit, 16...Training execution unit, 17...Training model storage unit 21...Transformation unit, 22...Inference unit

Claims

1. The system accepts a feature-enhanced graph as input. This graph represents network elements as nodes, with the presence or absence of connections between network elements represented by the presence or absence of edges between nodes. The feature-enhanced graph is then given features that reflect information about the network state and the source and destination nodes within that network. An inference device characterized by estimating the fault tolerance of the traffic flow from the source node to the destination node by applying inference using a pre-trained model to the input.

2. The inference device according to claim 1, characterized in that the pre-trained model is a model that conforms to a graph neural network.

3. The inference apparatus according to claim 1, characterized in that the features to be assigned include, as features for each node, features that reflect the distinction between whether each node is a source, a destination, or neither a source nor a destination of the traffic flow.

4. The inference device according to claim 1, characterized in that the features to be assigned include, as features for each edge, features that reflect the link state between network elements corresponding to each edge.

5. The inference device according to claim 1, characterized in that the features to be assigned include, as features for each edge, features that reflect the costs between network elements corresponding to each edge, which are set in the protocol that controls the traffic flow.

6. A learning device for learning the pre-trained model used in the inference device described in claim 1, The first data set is a feature-enhanced graph in which network elements are represented as nodes, and the presence or absence of connections between network elements is represented as the presence or absence of edges between nodes, and features are added that reflect network state information and information about the source and destination nodes within that network. In a network configured by providing the network elements using actual equipment according to the first data, the system accepts the second data, which is the result of a fault tolerance test when a traffic flow from a source node to a destination node according to the first data is transmitted, as training data. A learning device characterized by training a model that takes a first data as input and outputs a second data using the training data.

7. The learning device according to claim 6, characterized in that the network size in the training data is smaller than the network size used by the inference device to estimate fault tolerance.

8. A program characterized by causing a computer to function as an inference device according to any one of claims 1 to 5, or as a learning device according to claim 6 or 7.

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