Method for training an artificial neural network, artificial neural network and corresponding computer program

Abstract

A method for training an artificial neural network, particularly a Bayesian neural network, using a training data set includes a step of matching the parameters of the artificial neural network according to a loss function. This loss function includes a first term representing an estimate of the lower bound of the distance between the classification of the training data set by the artificial neural network and the desired classification of the training data set. Furthermore, the loss function includes a second term configured to adjust for differences in random uncertainty in the training data set by different samples passed through the artificial neural network.

Description

Technical Field

[0001] This invention relates to a method for training an artificial neural network, an artificial neural network, an application of an artificial neural network, a corresponding computer program, a machine-readable storage medium, and a corresponding device.

[0002] The preferred application area of ​​this invention is the field of autonomous systems, and in particular, at least partially automated driving.

[0003] At least partially automated driving means controlling a vehicle in which at least one vehicle system takes over at least part or all of the driving tasks. If all driving tasks are taken over, then it involves a fully or highly automated vehicle. The vehicle drives automatically by, for example, autonomously identifying road direction, other traffic participants, or obstacles through appropriate environmental sensors, and at least partially calculating corresponding control commands within the vehicle and transmitting these control commands to actuators within the vehicle, thereby affecting the vehicle's driving process accordingly. In fully or highly automated vehicles, the human driver no longer participates in the driving task.

[0004] As driver assistance systems (LES) that rely on full driver attention (so-called Level 1 and Level 2 LES) gradually transition to fully automated driving (so-called Level 3 to Level 5 LES), fundamental questions about system safety arise. In particular, the application of deep neural networks (DNNs) to safety-critical tasks (such as object recognition and classification) has generated entirely new questions regarding system safety.

[0005] Here, vehicles can be understood as land vehicles, aircraft, spacecraft, and water vehicles, and in particular, cars, trucks, buses, shuttle buses, two-wheelers, ships, airplanes, helicopters, and drones. Background Technology

[0006] As known from C. Guo, G. Pleis, Y. Sun, and KQ Weiterger's "Calibrating Modern Neural Networks" (ArXiv e-published, June 2017), the output probabilities of Deep Neutral Networks (DNNs) are not well calibrated. This means that a DNN used for object recognition only indicates what it has recognized, but not the certainty of that recognition. In reliable automated driving, understanding the degree of uncertainty in the recognition model is crucial. For example, an automated vehicle may identify an object ahead as a pedestrian, but its position may be uncertain. In such cases, the system can warn the driver in advance and request them to take over driving or brake to avoid a fatal accident.

[0007] As known from A. Kenndall and Y. Gal's "What Kind of Uncertainty Do We Need in Bayesian Deep Learning" (CoRR, vol. abs / 1703.04977, 2017, available online at http: / / arxiv.org / abs / 1703.04977), there are two types of uncertainty associated with artificial neural networks. Cognitive uncertainty, or model uncertainty, describes the uncertainty of the output of an artificial neural network with respect to its training data. On the other hand, accidental uncertainty reflects the uncertainty in the output based on defects in the processed data.

[0008] This could be due to sensor defects (e.g., noise, motion blur). Therefore, the observation of anomalous objects (not part of the training data set) could lead to high cognitive uncertainty, while the observation of distant objects could lead to high random uncertainty. For reliable automated driving, it is essential to consider both types of uncertainty in the artificial neural network used for object recognition, as cognitive uncertainty is a measure of the boundaries of the recognition model, while random uncertainty is a measure of sensor noise in object tracking situations. The authors suggest that artificial neural networks learn random uncertainty using unsupervised loss emphasis. Currently, this is practically the standard method for training artificial neural networks to predict random uncertainty.

[0009] As known from Y. Gal and Z. Ghahramani's "Dropout Bayesian Approximation: Insights and Applications" (Deep Learning Studio, ICML, 2016) and C. Blundell, J., Cornebise, K., Kavukcuoglou, and D. Wiestra's "Weight Uncertainty in Neural Networks" (ArXiv e-published, May 2015), Bayesian neural networks are suitable for modeling cognitive uncertainty. This is achieved by using probability distributions instead of point estimates as weights in artificial neural networks.

[0010] The drawback of known methods for training random uncertainty is that they cannot guarantee whether the output random uncertainty also contains a cognitive component. Summary of the Invention

[0011] In this context, the present invention proposes a method for training an artificial neural network using a training data set, the method comprising the step of matching the parameters of the artificial neural network according to a loss function, wherein the loss function includes a first term representing an estimate of the lower bound (ELBO) of the distance between the classification of the training data set by the artificial neural network and the expected classification of the training data set.

[0012] This invention is based on the following understanding: random uncertainty σ 2 It depends only on the input data present at runtime (e.g., camera images, radar signals, etc.) and not on the training data used as the basis. To determine the cognitive uncertainty in a Bayesian neural network, an implementation scheme is derived from the probability distribution of the weights (so-called Bayesian neural network samples), and multiple possible outputs of the artificial neural network are determined using this. The cognitive uncertainty is then estimated by the variance of the different outputs. Since the random uncertainty depends only on the input data, it should remain constant across different outputs.

[0013] Therefore, this invention proposes that the loss function includes a second term configured such that the difference in random uncertainty in the training data set is adjusted by different samples from the artificial neural network.

[0014] This means that during training, the differences in random uncertainty are “punished” by different outputs.

[0015] This is thus achieved advantageously: if σ during training... 2 The output not only represents random uncertainty, but also the "penalty" σ 2The output of this method separates random uncertainty from cognitive uncertainty. Therefore, cognitive uncertainty can be modeled reliably. This has the advantage that, during training, cognitive uncertainty can be used to estimate what situations still have insufficient training data. Furthermore, it can analyze the reasons for poor neural network performance. This can be used to answer questions such as: Is there insufficient training data, or does sensor information not allow for better conclusions?

[0016] Here, the loss function can be understood as follows: This function represents the distance between the output to be achieved by the trained artificial neural network and the output of the artificial network to be trained.

[0017] Typically, the log-likelihood function, especially the negative log-standard likelihood function (standard negative log-likelihood function), is used as the loss function.

[0018] Here, an artificial neural network should be understood as a network composed of artificial neurons used for information processing. An artificial neural network essentially goes through three stages. In the initial stage, a basic topology is typically pre-given based on the task. This is followed by a training stage, where the basic topology is taught to efficiently solve the task using training data. Topology matching can also be performed on the network during the training stage. The training data is characterized by the presence of desired output data for the input data. Finally, there is an application stage, where the taught network is applied to input data for which the desired output data does not exist. The output data of the taught network then represents the output data sought according to the task.

[0019] Bayesian neural networks can be trained as artificial neural networks. A key characteristic of Bayesian neural networks is that the weights are not represented as fixed values, but rather as a probability distribution of those weights.

[0020] If the probability distribution of the weight values ​​is configured such that the probability of considering the average value as 1, then there exists a “normal” artificial neural network with fixed weight values.

[0021] The implementation of Bayesian artificial neural networks forms a hybrid form that has weights as a probability distribution of weight values ​​and weights as fixed weight values.

[0022] To train a Bayesian artificial neural network, the network must be sampled during training. This means that the weights w must be determined based on the probability distribution. i The specific values ​​of t constitute the samples t of the Bayesian network.

[0023] The standard loss function used to train Bayesian neural networks is an estimate of the lower bound (ELBO):

[0024]

[0025] Here:

[0026] θ: Parameters of the probability distribution of the weights

[0027] w (t) Weights of sample t

[0028] D: Training data

[0029] T: Total number of all samples

[0030] -log P(x): Standard Negative Log Likelihood Function

[0031] q: Transformed posterior, i.e., the approximate posterior probability of the weights.

[0032] The training data set D can be understood as a set of data used to train an artificial neural network. Typically, the training data set involves annotated, i.e., labeled data. That is, on the corresponding date of the data set, the result y to be obtained by the artificial neural network is known, and this result is used in conjunction with the output generated by the network to be trained. A comparison is made between the expected result y and the produced output. The comparison is performed to match the parameters of the network to be trained based on the loss function.

[0033] In traditional deep neural networks (DNNs) used for object recognition, the network predicts so-called bounding boxes. (Typically represented by four parameters, such as the x and y coordinates of the top-left corner, width w, and height h). To train the artificial neural network in such a way that it predicts the desired bounding box y, the network should reflect... The loss function is minimized to determine the distance between the predicted value and the target value y (also known as the label). For example, if using the L1 loss function, the network is trained by minimizing the following loss function:

[0034]

[0035] To predict random uncertainty, the network's output is modeled as a normal distribution, and the network also additionally outputs a value σ. 2 , which represents the variance of the prediction. Therefore, the output variance σ 2 A high value of indicates high random uncertainty, and vice versa. To train an artificial neural network to predict this variance, the variance prediction is expanded using the standard loss function according to the following function:

[0036]

[0037] To incorporate not only random uncertainty but also cognitive uncertainty into a single model, the combined uncertainty U can be approximated by sampling the model with a predetermined number T, where random uncertainty is averaged, and the variance used for prediction is calculated using the following function:

[0038]

[0039] According to one embodiment of the method of the present invention, the first term represents the lower boundary (Expected Lower Bound, ELBO).

[0040] The first term may include the regularization part and the negative log-likelihood function.

[0041] According to one embodiment of the method of the present invention, the second term represents the squared distance between the variance determination of the training data set and the average variance determination of the training data set over all generated samples of the Bayesian neural network to be trained.

[0042] According to one configuration of this embodiment, the second term includes the hyperparameter α.

[0043] Hyperparameters are understood here as parameters that do not describe the artificial neural network being trained, but rather are used, for example, to control the training process of the network. A common hyperparameter is the so-called learning rate, which represents a measure of the network's fit for each learning process. Another traditional hyperparameter is the number of training epochs. An epoch represents the total number of traversals of the training data.

[0044] In this invention, the hyperparameter controls the effect of the second term on the loss function result, and thus illustrates the “penalty” or measure of random error.

[0045] According to one embodiment of the method of the present invention, the lower boundary is estimated using a loss function based on the following rules:

[0046]

[0047] Here:

[0048] α: Hyperparameter of artificial neural network

[0049] θ: Parameters of the probability distribution of the weights

[0050] σ 2 :variance

[0051] w (t) Weights of sample t

[0052] D: Training data

[0053] T: Total number of all samples

[0054] -log P(x): Negative log-likelihood function

[0055] function)

[0056] q: Transformed posterior, i.e., the approximate posterior probability of the weights.

[0057] Another aspect of the present invention is a computer program that sets up all the steps for implementing one embodiment of the method of the present invention.

[0058] Another aspect of the present invention is a machine-readable storage medium having a computer program according to the present invention stored thereon.

[0059] Another aspect of the present invention is an artificial neural network trained by means of an embodiment of the method of the present invention.

[0060] Another aspect of the present invention is an application of the artificial neural network according to the invention, which is used to control technical systems, particularly robots, vehicles, tools or machine tools.

[0061] Such trained artificial neural networks are preferably used in technical systems (especially robots, vehicles, tools, or machine tools) to determine output parameters based on input parameters. The input parameters for the artificial neural network can be sensor data or parameters derived from sensor data. The sensor data can originate from sensors within the technical system or be received by the technical system from outside the system. Based on the output parameters of the artificial neural network, at least one actuator of the technical system is manipulated by the system's computing unit using control signals. Therefore, for example, the movement of a robot or vehicle can be controlled, or the drive unit or driver assistance system of a vehicle can be controlled.

[0062] When analyzing and processing sensor data, the artificial neural network trained according to the method for training an artificial neural network according to the present invention provides not only the assignment to the category, but also a description of the determinism (Sicherheit) of that assignment.

[0063] Therefore, when applying such networks to control technical systems, the determinism of allocation can be considered in addition to category assignment. This can provide reliable control for the technical system.

[0064] Another aspect of the invention is another computer program configured to implement all steps of the application of the artificial neural network according to the invention for controlling the machine according to the invention.

[0065] Another aspect of the invention is another machine-readable storage medium on which another computer program according to the invention is stored.

[0066] Another aspect of the invention is a device for controlling a machine, the device being configured to use an artificial neural network according to the invention. Attached Figure Description

[0067] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0068] Figure 1 This illustrates a typical control system;

[0069] Figure 2 An embodiment of the control system is shown;

[0070] Figure 3 Another embodiment of the control system is shown;

[0071] Figure 4 Another embodiment of the control system is shown;

[0072] Figure 5 Another embodiment of the control system is shown;

[0073] Figure 6 Another embodiment of the control system is shown;

[0074] Figure 7 Another embodiment of the control system is shown;

[0075] Figure 8 Another embodiment of the control system is shown;

[0076] Figure 9 A flowchart illustrating an embodiment of a method for training an artificial neural network according to the present invention is shown;

[0077] Figure 10 A schematic diagram of the artificial neural network according to the present invention is shown. Detailed Implementation

[0078] Figure 1This illustrates the interaction between actuator 10 and control system 40 or technical system 40 within its surrounding environment 20. Actuator 10 and the surrounding environment 20 are collectively referred to as the actuator system. The state of the actuator system is detected by means of sensor 30 at preferred time intervals; this state can also be indicated by multiple sensors. Sensor signals S from sensor 30 (or individual sensor signals S in the case of multiple sensors) are transmitted to control system 40. Therefore, control system 40 receives the sequence of sensor signals S. Control system 40 thereby determines control signal A, which is transmitted to actuator 10.

[0079] Sensor 30 is any sensor that detects the state of the surrounding environment 20 and transmits it as a sensor signal. The sensor may be, for example, an imaging sensor (especially an optical sensor, such as an image sensor or video sensor), a radar sensor, an ultrasonic sensor, or a lidar sensor. The sensor may also be an acoustic sensor, which, for example, receives structured sound. Or voice signals. The sensors may also involve position sensors (e.g., GPS) or kinematic sensors (e.g., single-axis or multi-axis accelerometers). Sensors characterizing the orientation of actuator 10 in the surrounding environment 20 (e.g., a compass) are also possible. Sensors detecting the chemical composition of the environment 20 (e.g., an oxygen sensor) are also possible. Alternatively or additionally, sensor 30 may also include an information system that retrieves information about the state of the actuator system (e.g., a weather information system that retrieves the current or future state of the weather in the surrounding environment 20).

[0080] The control system 40 receives a sequence of sensor signals S from the sensor 30 in an optional receiving unit 50. This receiving unit converts the sequence of sensor signals S into an input signal sequence x (alternatively, the sensor signals S can be directly used as input signals x). The input signal x can be, for example, a segment of the sensor signals S or a further processed signal. The input signal x can, for example, include image data or a single frame of an image or video capture. In other words, the input signal x is obtained based on the sensor signals S. The input signal x is then provided to the artificial neural network 60.

[0081] Preferably, the artificial neural network 60 is parameterized by a parameter θ, which includes, for example, the weights w. 11 to w nm These are stored in the parameter memory P and provided by the parameter memory.

[0082] The artificial neural network 60 obtains an output signal y from the input signal x. Typically, the output signal y encodes the classification information of the input signal x. The output signal y is provided to an optional transformation unit 80, which obtains a control signal A, which is then provided to the actuator 10 to control the actuator 10 accordingly.

[0083] Actuator 10 receives control signal A, is controlled accordingly, and performs a corresponding action. Actuator 10 may include (not necessarily structurally integrated) control logic circuitry that obtains a second control signal from control signal A, and then controls actuator 10 by means of the second control signal.

[0084] In another embodiment, the control system 40 includes a sensor 30. In yet another embodiment, the control system 40 alternatively or additionally includes an actuator 10.

[0085] In another preferred embodiment, the control system 40 includes one or more processors 45 and at least one machine-readable storage medium 46 on which instructions are stored. When executed on the processor 45, the instructions cause the control system 40 to implement methods for controlling the control system 40.

[0086] In an alternative embodiment, a display unit 10a is provided as a replacement for or addition to the actuator 10.

[0087] Figure 2 One embodiment is shown in which the control system 40 is used to control at least partially autonomous robots (here, at least partially automated motor vehicles 100).

[0088] Sensor 30 may involve the combination of attachments Figure 1 One of the sensors mentioned herein preferably relates to one or more video sensors preferably arranged in the vehicle 100, or one or more radar sensors, or one or more ultrasonic sensors, or one or more lidar sensors, or one or more position sensors (e.g., GPS).

[0089] The artificial neural network 60 can, for example, detect objects in the environment surrounding a partially autonomous robot from input data x. The output signal y can involve information that characterizes the position of the object in the environment surrounding the partially autonomous robot. The output signal A can then be obtained based on or corresponding to this information.

[0090] The actuator 10 preferably arranged in the vehicle 100 may, for example, relate to the braking device, drive device, or steering device of the vehicle 100. Then, a control signal A can be obtained such that one or more actuators 10 are manipulated to prevent, for example, collision with an object identified by the artificial neural network 60 (especially when dealing with objects of a defined category, such as pedestrians). In other words, the control signal A can be obtained based on the determined category or corresponding to the determined category.

[0091] Alternatively, the at least partially autonomous robot may also involve another mobile robot (not shown), such as a mobile robot that moves by flying, floating, diving, or walking. The mobile robot may also involve, for example, a lawnmower or a cleaning robot that is at least partially autonomous. In these cases, the control signal A may be obtained such that the drive mechanism or steering mechanism of the mobile robot is manipulated to prevent, for example, collisions with objects identified by the artificial neural network 60.

[0092] In another alternative, the at least partially autonomous robot could also involve a gardening robot (not shown) that uses imaging sensors 30 and an artificial neural network 60 to determine the type or state of plants in the surrounding environment 20. The actuator 10 could then, for example, involve a chemical application device. A control signal A can be determined based on the determined plant type or state, causing the application of a chemical in an amount corresponding to the determined type or state.

[0093] In another alternative, at least partially autonomous robots can also involve household appliances (not shown), particularly washing machines, stoves, ovens, microwave ovens, or dishwashers. The state of an object being handled by the household appliance can be detected using sensor 30 (e.g., an optical sensor)—for example, the state of laundry inside the washing machine. The type or state of the object can then be determined using an artificial neural network 60, and the type or state is characterized by an output signal y. A control signal A can then be determined such that the household appliance is controlled according to the determined type or state of the object. For example, in the case of a washing machine, the washing machine can be controlled according to the material of the laundry inside. The control signal A can then be selected based on the determined material of the laundry.

[0094] Figure 3 One embodiment is shown in which the control system 40 operates the machine tool 11 of the manufacturing system 200 by manipulating the actuator 10 that controls the machine tool 11. The machine tool 11 may, for example, be a machine for stamping, sawing, drilling, or cutting.

[0095] Sensor 30 may involve combination Figure 1 One type of sensor, preferably, involves an optical sensor that detects, for example, the characteristics of the manufactured product 12. It is possible that the actuator 10 of the machine tool 11 is manipulated based on the desired characteristics of the manufactured product 12, so that the machine tool 11 accordingly performs subsequent processing steps on the manufactured product 12. Alternatively, the sensor 30 may determine the characteristics of the manufactured product 12 processed by the machine tool 11 and accordingly match the control of the machine tool 11 for subsequent product manufacturing.

[0096] Figure 4 One embodiment is shown in which the control system 40 is used to control the personal assistant 250. The sensor 30 may involve... Figure 1 One type of sensor described herein. Sensor 30 is preferably an acoustic sensor that receives voice signals from user 249. Alternatively or additionally, sensor 30 may also be configured to receive optical signals—such as video images of gestures from user 249.

[0097] The control system 40 determines the control signal A for the personal assistant 250 based on the signal from the sensor 30, for example, by using an artificial neural network to perform gesture recognition. The determined control signal A is then transmitted to the personal assistant 250, thereby controlling the personal assistant accordingly. The determined control signal A can be specifically selected to correspond to the desired control inferred by the user 249. This inferred desired control can be determined based on gestures recognized by the artificial neural network 60. The control system 40 can then select the control signal A to be transmitted to the personal assistant 250 based on the inferred desired control, or select the control signal A to be transmitted to the personal assistant based on the inferred desired control 250.

[0098] Such corresponding operations may include, for example, a personal assistant 250 retrieving information from a database and presenting the information to the user 249 in an acceptable manner.

[0099] As an alternative to the Personal Assistant 250, household appliances (not shown) – especially washing machines, stoves, ovens, microwave ovens, or dishwashers – can also be set up for operation.

[0100] Figure 5 One embodiment is shown in which a control system 40 is used to control an access system 300. The access system 300 may include physical access controls (e.g., door 401). Sensor 30 may be involved in... Figure 1One type of sensor, preferably an optical sensor (e.g., for detecting image or video data), is configured to detect faces. The detected image can be interpreted using an artificial neural network 60. For example, the identity of a person can be determined. The actuator 10 can be a lock that allows or disallows entry based on a control signal A (e.g., opening or closing door 401). For this purpose, the control signal A can be selected based on the interpretation of the artificial neural network 60 (e.g., based on the determined identity of the person). Logical entry control can also be configured to replace physical entry control.

[0101] Figure 6 One embodiment is shown in which the control system 40 is used to control the monitoring system 400. This embodiment is related to... Figure 5 The difference in the illustrated embodiment is that a display unit 10a is used instead of the actuator 10, and this display unit is controlled by the control system 40. For example, the artificial neural network 60 can determine whether an object captured by an optical sensor is suspicious. Then, the control signal A can be selected such that the display unit 10a displays the object in color with prominence.

[0102] Figure 7 One embodiment is shown in which the control system 40 controls a medical imaging system 500—such as an MRT, X-ray, or ultrasound device. The sensor 30, for example, can be provided by an imaging sensor, and the control system 40 manipulates the display unit 10a. For example, an artificial neural network 60 can determine whether the area captured by the imaging sensor is prominent, and then select a manipulation signal A such that the display unit 10a displays the area prominently in color.

[0103] Figure 8 An embodiment of a training system 140 is schematically illustrated for training an artificial neural network 60 using a training method. A training data unit 150 determines a suitable input signal x, which is provided to the artificial neural network 60. For example, the training data unit 150 accesses a computer-implemented database containing sets of training data D and randomly selects the input signal x from the sets of training data D. Optionally, the training data unit 150 also determines a desired or "actual" output signal y assigned to the input signal x, which is provided to an evaluation unit 180.

[0104] The artificial neural network x is configured to obtain its corresponding output signal from the input signal x provided to it. These output signals It is provided to evaluation unit 180.

[0105] The evaluation unit 180 can, for example, use the output signal The performance of the artificial neural network 60 is characterized by a loss function I, which is associated with the desired output signal y. The parameters θ can be optimized based on the loss function I.

[0106] In another preferred embodiment, the training system 140 includes one or more processors 145 and at least one machine-readable storage medium 146 on which instructions are stored, which, when executed on the processor 145, cause the control system 14 to perform a training method.

[0107] Figure 9 A flowchart illustrating an embodiment of a method 900 for training an artificial neural network 60 according to the present invention is shown.

[0108] In step 901, the parameters θ of the artificial neural network 60 to be trained are matched according to the loss function I, wherein the loss function I includes a first term, which represents the classification of the training data group D by the artificial neural network 60. The lower bound of the distance between the expected classification y of the training data set D and the training data set D.

[0109] Furthermore, the loss function I includes a second term configured such that the random uncertainty σ in the training data set D is adjusted through different samples from the artificial neural network 60. 2 The differences.

[0110] Figure 10 A schematic diagram of an artificial neural network 60 according to the present invention is shown. The artificial neural network 60 shown relates to a Bayesian neural network 60.

[0111] Weights w in a Bayesian Neural Network 60 11 -w nm As an illustration of the probability distribution. For graphical purposes, in Figure 2 The weights w of the model 11 -w nm It is presented as a Gaussian distribution.

[0112] This schematic diagram illustrates a Bayesian neural network 60, which not only outputs the random uncertainty σ 2 Moreover, the output is the variance of the network output. Cognitive uncertainty.

[0113] The artificial neural network 60 is trained using training data D.

[0114] By adjusting the model's weights w 11 -w nm Sampling is performed, and the values ​​of cognitive uncertainty are compared with each output dimension. Variance separation.

[0115] It should be noted that the random uncertainty σ 2 Should be independent of weight w 11 -w nm The corresponding sample t, because this accidental uncertainty only describes the uncertainty inherent in the training data D.

[0116] By “penalizing” or taking into account the random uncertainty σ in the output of the corresponding sample t of the artificial neural network 60 to be trained. 2 The change can reduce this random uncertainty σ 2 This is separated from cognitive uncertainty. This leads to artificial neural networks 60 with higher system reliability. This is because, on the one hand, the boundaries of the model represented by the network 60 are known, and on the other hand, the network can react to the known boundaries through appropriate training or through appropriate training data.

Claims

1. A method (900) for training an artificial neural network (60), said artificial neural network being a Bayesian neural network, the method being used to train the artificial neural network with the aid of a training data set D for controlling at least partially autonomous vehicles, said training data set D comprising sensor data of sensors arranged in the vehicle, said sensor data including imaging sensor data or acoustic sensor data, the method comprising a step (901) of matching the parameters of the artificial neural network according to a loss function, wherein, The loss function includes a first term, which represents an estimate of the lower bound of the distance between the classification of the training data set D by the artificial neural network (60) and the expected classification of the training data set D. The loss function is characterized by including a second term configured such that the difference in random uncertainty in the training data set D is adjusted for different samples t of the artificial neural network (60), wherein the artificial neural network is sampled during training, wherein specific values ​​of the weights of the artificial neural network are determined from a probability distribution, the specific values ​​constituting the sample t, and wherein the random uncertainty remains constant with different outputs. The artificial neural network (60) detects objects in the environment surrounding the vehicle by means of an input signal, wherein the input signal is obtained based on sensor data from sensors arranged in the vehicle, wherein the artificial neural network (60) obtains an output signal from the input signal, wherein the output signal obtains a control signal, and the movement of the vehicle is controlled by means of the control signal, wherein the output signal of the trained artificial neural network (60) provides, in addition to providing an assignment to the category of the object, a description of the random uncertainty of the assignment, the description of the random uncertainty being used to measure sensor defects.

2. The method (900) according to claim 1, wherein, The first item represents the lower boundary.

3. The method (900) according to claim 1 or 2, wherein, The second term represents the squared distance between the variance determination of the training data set D and the average variance determination of the training data set D over all samples of the Bayesian neural network.

4. The method (900) according to claim 3, wherein, The second term includes the hyperparameter α.

5. The method (900) according to any one of claims 1, 2, and 4, wherein, The lower boundary is estimated using the loss function according to the following rules: in, Weight The parameters of the probability distribution, Here, D represents the weights of sample t, and D represents the training data. It is the total number of samples. It is the a posteriori of the change. It is random uncertainty, and α is a hyperparameter.

6. The method (900) according to claim 2, wherein, The first term includes the regularization part and the negative log-standard likelihood function.

7. The method (900) according to claim 5, wherein, q is the weight The approximate posterior probability.

8. A computer program product configured to implement all steps of the method (900) according to any one of claims 1 to 7.

9. A machine-readable storage medium on which a computer program product according to claim 8 is stored.

10. A control system for a control technology system, the control system comprising an artificial neural network (60), the artificial neural network being a Bayesian neural network, the artificial neural network being trained by means of the method (900) according to any one of claims 1 to 7.

11. An application of the control system according to claim 10, wherein the control system is used to control a technical system, the technical system including a robot, vehicle, tool or machine tool (11).

12. A computer program product configured to implement all steps of the application of a control system according to claim 11, the control system being used to control a technical system.

13. A machine-readable storage medium on which a computer program product according to claim 12 is stored.

14. An apparatus for controlling a technology system, the apparatus being configured to use a control system to control the technology system according to claim 11.

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