DE102020105785A1 - Method for generating a reduced neural network for a control device of a vehicle using eigenvectors - Google Patents

Abstract

The invention relates to a method for generating a reduced neural network (40) for a control device (2) of a vehicle (1) and / or a vehicle component (7, 8, 9), comprising the following steps: - Reading in a first data field from a first neural network (30), the first data field having entries which in their entirety at least partially represent an internal logic of the first neural network (30), in a first step (11), - generating the reduced neural network (40) at least with the aid of of the first data field in a second step (12), the reduced neural network having a reduced data field with entries which in their entirety at least partially represent internal logic of the reduced neural network (40) and the reduced data field is less than non-zero entries than has the first data field.

Description

The invention relates to a method for generating a reduced neural network for a control device of a vehicle and / or a vehicle component, a control device for a vehicle and / or a vehicle component, a vehicle, a reduced neural network and a computer program product.

The DE 10 2018 103 113 discloses a control device of a vehicle with a neural network.

The proposed method for creating a reduced neural network for a control device of a vehicle and / or a vehicle component comprises the following steps. In a first step, a first data field of a first neural network is read in, the first data field having entries which in their entirety at least partially represent an internal logic of the first neural network. In a second step, the reduced neural network is generated at least with the aid of the first data field, the reduced neural network having a reduced data field with entries which, at least in their entirety, represent an internal logic of the reduced neural network. The reduced data field has fewer non-zero entries than the first data field. The first data field can be read into the control unit and the following variants of the method can be carried out on the control unit. It is also possible for the first data field to be read in on an external computer outside the vehicle and for the method to be carried out on the external computer.

The term “network” is used below for the term “neural network”.

A data field means a field, also called an “array”, which has several entries. In most cases, the first data field and the reduced data field have real positive entries. A single entry of the first data field or reduced data field influences at least one calculation of an output value of a neuron of the first network or reduced network depending on a corresponding input value of the neuron of the corresponding network. Furthermore, the entries preferably indicate how strongly an output value of an individual neuron of the first network or reduced network influences a calculation of a further output value of a further neuron of the first network or reduced network. In this sense, the entries can also be weights of the first network or reduced network.

The first or reduced data field can have two or more dimensions and in this case can be viewed as a first matrix or reduced matrix with two or more dimensions. In this case, these two data fields can each be viewed as a data structure that contains entries from a two-dimensional or a plurality of two-dimensional matrices of the first or reduced network. The entries of the two-dimensional matrices of the first or reduced network can be values of connection weights between individual neurons of a layer of the corresponding network and individual neurons of a subsequent layer of the corresponding network.

The control device of the vehicle and / or the vehicle component is set up to control at least one operating parameter of the vehicle and / or the vehicle component. The operating parameter can be, for example, a speed, an acceleration, distances between the vehicle and another vehicle, an engine speed, a braking force or a steering angle. The vehicle and / or the vehicle component can advantageously be used for autonomous and / or partially autonomous driving.

The proposed method and the control device enable control of the autonomous and / or partially autonomous vehicle and / or the vehicle component in various driving situations. Driving situations can be, for example, driving on the motorway and / or driving within cities and / or driving in traffic-calmed areas.

The proposed computer program product causes a computer, when the computer program product is executed by the computer, to carry out the proposed method, preferably according to the variants mentioned below. The computer program product can be stored in the control device or, in a further variant, can be present as a program on an external data carrier outside the vehicle. The computer is advantageously located in the control unit and can be designed in the form of a microcontroller. Because the proposed method can be carried out on the computer with the aid of the computer product, it has the advantages mentioned below for the method.

The first and reduced network can be designed in the form of a respective special data structure which, when loaded from a memory of the computer into a main memory of the computer and called up from the main memory by the computer program product can take the following actions. A corresponding physical neural first or reduced network with neurons can preferably be simulated with the aid of the first or reduced data field, output signals from a plurality of neurons of the corresponding physical network being routed to inputs of further neurons of the corresponding physical network. The first or reduced data field thus represents an internal logic of the first or reduced network or the corresponding physical network. The neurons of the first and reduced networks thus correspond to the respective neurons of the corresponding physical networks and can be viewed as models with inputs and outputs, preferably only one output.

In addition, the first or reduced network can have respective activation functions and / or threshold values for each neuron of the corresponding network. The activation functions and / or threshold values can also be in the corresponding special data structure, i.e. in the first or reduced network.

Because the reduced data field has fewer non-zero entries than the first data field, the reduced network can be loaded into the working memory faster than the first network. Furthermore, a computing time can be reduced when the reduced network is used in the control device compared to the first network, since the reduced network is less complex than the first network.

Furthermore, because the reduced data field has fewer non-zero entries than the first data field, one dimension of a diversity of the reduced network can be smaller than one dimension of a diversity of the first network. This can mean that difference quotients that can be formed using the reduced network can be lower than difference quotients that can be formed using the first network. This advantage and the lower computing effort when using the reduced network improves the possible uses of the reduced network compared to the first network, in particular when the reduced network is used in a control loop of the control device.

In a further embodiment, the first data field is designed in the form of the first matrix and the reduced data field in the form of the reduced matrix, the reduced matrix being constructed using at least one eigenvector or singular vector of the first matrix. If the terms eigenvalue and eigenvector are used in the following, it is assumed that the first matrix is quadratic. If the terms singular value and singular vector are used in the following, it is assumed that the first matrix is not quadratic.

With the help of the eigenvector or singular vector, information which contains the first matrix can be represented compactly. In particular, a plurality of pieces of information which the first matrix contains can be represented or summarized in a compact manner with the aid of a plurality of eigenvectors or singular vectors of the first matrix. In other words, the eigenvectors or singular vectors can map information contained in the first matrix in a compact form. Because of this compact form, the reduced data field has fewer non-zero entries than the first data field.

Using the eigenvectors or singular vectors is a particularly simple variant for constructing the reduced network. A method for singular value decomposition is preferably used to determine the singular vectors. The eigenvectors or singular vectors are preferably linearly independent of one another.

The proposed reduced neural network can be generated according to one of the configurations mentioned above, preferably also according to one of the configurations mentioned below.

The proposed control device is suitable for the vehicle and / or the vehicle component and is set up by a method and / or for carrying out a method according to one of the embodiments already described, preferably also according to one of the embodiments mentioned below. The control device advantageously has the reduced neural network, as can be generated according to one of the above-mentioned, preferably also according to one of the following, configurations after the method has been carried out.

The proposed vehicle includes the control unit. Because the proposed control unit and the proposed vehicle have the reduced network or can generate this when the method is carried out, the same advantages can be achieved with the vehicle and the control unit as with the reduced network.

• 1 Ein Fahrzeug mit einem Steuergerät und Fahrzeugkomponenten,
• 2 Schritte eines Verfahrens zur Erzeugung eines reduzierten neuronalen Netzes für das Steuergerät nach 1,
• 3 eine erste Matrix eines erste neuronalen Netzes,
• 4 ein erstes neuronales Netz,
• 5 ein reduziertes neuronales Netz,
• 6 eine reduzierte Matrix des reduzierten neuronalen Netzes nach 5,
• 7 Teilschritte eines zweiten Schrittes des in 2 gezeigten Verfahrens.

The dependent claims describe further advantageous embodiments of the invention. Preferred exemplary embodiments are explained in more detail with reference to the following figures. The figures show schematically in:

• 1 A vehicle with a control unit and vehicle components,
• 2nd Steps of a method for generating a reduced neural network for the control device 1 ,
• 3rd a first matrix of a first neural network,
• 4th a first neural network,
• 5 a reduced neural network,
• 6 a reduced matrix of the reduced neural network 5 ,
• 7 Sub-steps of a second step of the in 2nd shown procedure.

1 shows a vehicle according to the invention 1 with a control device according to the invention 2nd . The vehicle 1 can a camera 3rd , a distance sensor 4th , a measuring device 5 for recording operating parameters of the vehicle 1 and a facility 6 for detecting a state of a driver of the vehicle 1 exhibit. The operating parameters can be the above parameters. In addition, the vehicle has at least a first vehicle component 7 , a second vehicle component 8th and a third vehicle component 9 , each of which can be, for example, a drive unit, a chassis component or a safety element, such as an airbag or a belt system.

2nd shows individual steps of the inventive method for generating a reduced network 40 for the control unit 2nd of the vehicle 1 .

A first step 11 comprises reading a first data field of a first network 30th . In the following example, the first data field is in the form of a first matrix 21 trained and has entries that in 3rd exemplary with 20 _ji are shown. The entries 20 _ji the first matrix 21 in their entirety at least partially represent an internal logic of the first network 30th . In a second step 12th the procedure becomes the reduced network 40 , which has a reduced data field, at least using the first data field, in this example using the first matrix 21 , generated. The reduced data field is in the following example in the form of a reduced matrix 51 trained and has entries that in 6 exemplary with 50 _ji are shown. The entries 50 _ji the reduced matrix 51 in their entirety at least partially represent an internal logic of the reduced network 40 .

1 still shows a computer program product 10th which, when it is executed by a computer, causes the computer to carry out a method according to the variants mentioned above or mentioned below. The computer program product 10th can in the control unit 2nd be saved or in a further variant as a program on an external data carrier outside the vehicle 1 available. The computer is advantageously located in the control unit and can be designed in the form of a microcontroller. By using the computer product 10th the proposed method can be carried out on the computer, it has the advantages already mentioned for the method.

In 4th is the first network as an example 30th with a first layer 31 , a second layer 32 , a jth layer 33 and an nth layer 34 shown. Each of the layers 31 , 32 , 33 , 34 has a respective number of neurons or cells or elements. In the in 4th The example shown is the respective number of neurons for the corresponding layer 31 , 32 , 33 , 34 equal to m. In general, however, it is possible that different layers have a different number of neurons.

des ersten Netzes 30 senden. Der Index j bezeichnet einen Eingangsdatensatz aus einer möglichen Gesamtmenge an Eingangsdatensätzen. Die Neuronen 30₁₁ , 30₁₂ , 30_1i , 30_1m leiten diese Werte an einzelne Neuronen 30₂₁ , 30₂₂ , 30_2i , 30_2m der zweiten Schicht 32 weiter. Diese weitergeleiteten Werte können als jeweilige Eingangswerte für eine jeweilige Aktivierungsfunktion der einzelnen Neuronen der zweiten Schicht 32 verwendet werden.The first layer 31 works in that 4th shown example of the first network 30th preferably like an input layer. The control unit 2nd can be connected to a respective neuron 30 ₁₁ , 30 ₁₂ , 30 _1i , 30 _1m the first layer 31 prefers a corresponding single entry 35 ₁ , 35 ₂ , 35 _i , 35 _m an input data record ${\overrightarrow{\mu }}_j$

of the first network 30th send. The index j denotes an input data record from a possible total amount of input data records. The neurons 30 ₁₁ , 30 ₁₂ , 30 _1i , 30 _1m pass these values on to individual neurons 30 ₂₁ , 30 ₂₂ , 30 _2i , 30 _2m the second layer 32 further. These forwarded values can be used as respective input values for a respective activation function of the individual neurons of the second layer 32 be used.

With the help of the respective input values, the respective activation function of the individual neurons 30 ₂₁ , 30 ₂₂ , 30 _2i , 30 _2m the second layer 32 an initial value of the corresponding neuron 30 ₂₁ , 30 ₂₂ , 30 _2i , 30 _2m the second layer 32 to calculate. The respective output value of the corresponding neuron 30 ₂₁ , 30 ₂₂ , 30 _2i , 30 _2m the second layer 32 is preferably to a respective neuron of the subsequent layer, in this case the third layer 33 , and can be read by this neuron in the form of an input value.

In the 4th architecture of the first network shown 30th is only an exemplary embodiment, in which a single output value of a single neuron of a single layer in the form of a single input variable at a neuron in the first network 30th subsequent layer.

wobei b_ji einen Schwellwert des i-ten Neurons der j-ten Schicht bezeichnet. 4 zeigt eine erste Variante des reduzierten Netzes 40. Gemäß der ersten Variante hat das reduzierte Netz 40 hat eine erste Schicht 41 mit einem ersten Neuron 40₁₁ , einem zweiten Neuron 40₁₂ , einem i-ten Neuron 40_1i und einem m-ten Neuron 40_1m . Die erste Schicht 41 funktioniert wie eine Eingabeschicht, in der die einzelnen Werte 35₁ , 35₂ , 35_i und 35_m des Eingabevektors 35 eingelesen werden können. Die eingelesenen Werte werden von den jeweiligen Neuronen 40₁₁ , 40₁₂ , 40_1i , 40_1m an jeweils ein entsprechendes erstes Neuron 40₂₁ , ein zweites Neuron 40₂₂ , ein i-tes Neuron 40_2i und ein m-tes Neuron 40_2m der zweiten Schicht 42 gesendet. The index j denotes a jth layer of the first network 30th and the index i an i-th neuron of a respective layer of the first network 30th . The respective input variable of the i-th neuron of the j-th layer is shown below as a _ji be designated. Furthermore, a basic function of the i-th neuron in the j-th layer is to be referred to as ϕ _ji . An activation function of the i-th neuron in the j-th layer is described below α _ji declared. For that in 4th shown example of the first network 30th can accordingly an output value of the i-th neuron of the j-th layer, which at the same time is an input value a _{(j + 1) i} of the i-th neuron of the subsequent j + 1-th layer is calculated as follows: $$a_{\left(j+1\right)i}={\alpha }_{ji}\left(a_{ji}\right)\cdot {\varphi }_{ji}+b_{ji}\mathrm{.,}$$

in which b _ji denotes a threshold of the i-th neuron of the j-th layer. 4th shows a first variant of the reduced network 40 . According to the first variant, the reduced network 40 has a first layer 41 with a first neuron 40 ₁₁ , a second neuron 40 ₁₂ , an ith neuron 40 _1i and an mth neuron 40 _1m . The first layer 41 works like an input layer in which the individual values 35 ₁ , 35 ₂ , 35 _i and 35 _m of the input vector 35 can be read. The read values are from the respective neurons 40 ₁₁ , 40 ₁₂ , 40 _1i , 40 _1m to a respective first neuron 40 ₂₁ , a second neuron 40 ₂₂ , an ith neuron 40 _2i and an mth neuron 40 _2m the second layer 42 sent.

wobei a_{red ji} einen Eingangswert des i-ten Neurons der j-ten Schicht, a_{red (j+1)i} einen Ausgangswert des i-ten Neurons der j-ten Schicht und einen Eingangswert des i-ten Neurons der j+1-ten Schicht, ψ_ji eine jeweilige Basisfunktion des i-ten Neurons der j-ten Schicht, β_ji eine Aktivierungsfunktion des i-ten Neurons der j-ten Schicht und c_ji einen Schwellwert des i-ten Neurons der j-ten Schicht jeweils des reduzierten Netzes 40 bezeichnen.The forwarded input values are from the respective neurons of the second layer 42 read in in the form of an input value and processed into an output value within the respective neuron. Similarly, the rest of the neurons 40 _ji the jth layer 43 and the N _red layer 44 function. Analogous to the first network 30th For example, a calculated output value of an ith neuron in the jth layer can be passed on to the subsequent layer in the form of an input value of the ith neuron of the j + 1th layer. This can be expressed by the following formula: $$a_{re{d}_{\left(j+1\right)i}}={\beta }_{ji}\left(a_{re{d}_{ji}}\right){\psi }_{ji}+c_{ji},$$

where a _{red ji} an input value of the ith neuron of the jth layer, a _{red (j + 1) i} an output value of the i th neuron of the j th layer and an input value of the i th neuron of the j + 1 th layer, ψ _ji a respective basic function of the i-th neuron of the j-th layer, β _ji an activation function of the ith neuron of the jth layer and c _ji a threshold value of the i-th neuron of the j-th layer of the reduced network in each case 40 describe.

unabhängig ist.The respective internal logic of the first network 30th and the reduced network 40 can be at least partially or completely specified by terms that calculate a respective output value of the i-th neuron of the j-th layer of the corresponding network 30th , 41 depending on a corresponding input value of the ith neuron of the jth layer of the corresponding network 30th , 41 influence. For example, the respective entries in the first matrix 21 or the reduced matrix 51 individual threshold values b _ji respectively. c _ji or in another variant individual basic functions ϕ _ji or ψ _ji specify. A base function can be represented in particular with a fixed value in scalar form or with the aid of fixed values in vector form, whereby the base function cannot be changed and therefore from an input data record ${\overrightarrow{\mu }}_j$

is independent.

Are schematic in 3rd the individual entries 20 ₁₁ , 20 ₁₂ , 20 _1m , 20 _ji , 20 _n1 , 20 _nm where m is a total number of columns of the first matrix 21 and n is a total number of rows of the first matrix 21 designated. Analog are in 6 individual entries 50 ₁₁ , 50 ₁₂ , 50 _1m , 50 _{N red 1} , 50 _ji , 50 _{N red m} , where m is a number of columns of the reduced matrix 51 and N _red a number of rows of the reduced matrix 51 designated.

The reduced matrix 51 has fewer non-zero entries than the first matrix 21 . The reduced matrix 51 is preferably more compact than the first matrix 21 . In the in 3rd and 6 shown embodiment of the first matrix 21 and the reduced matrix 51 has the reduced matrix 51 fewer rows than the first matrix 51 , ie N _red is less than n.

The reduced matrix is particularly advantageous with the aid of at least one eigenvector or singular vector of the first matrix 21 constructed.

Using the eigenvalue or singular vector of the first matrix 21 can advantageously use the reduced matrix 51 are formed such that the number of lines N _red and / or the columns of the reduced matrix 51 smaller than the number of rows n or the columns of the first matrix 21 is. For this purpose, several eigenvectors or singular vectors of the first matrix are preferably used 21 certainly.

As with the eigenvalue or singular vector, the reduced network 40 can be generated will be described below. A reduced model of the internal logic of the first network can be used during the second step 30th can be estimated using a model order reduction method.

In the event that the first matrix is square, the reduced model can be approximated using eigenvalues and eigenvectors of the first matrix. In the event that the first matrix is not quadratic, it is possible to approximate the reduced model using a singular value decomposition and the singular values and singular vectors obtained from it. An example in which the first matrix is square is considered below.

des reduzierten Modells kann beispielsweise in Abhängigkeit zumindest von einer Basisfunktion, insbesondere von mehreren Basisfunktionen ϕ_i, und zumindest einem von einem Eingangsdatensatz ${\overrightarrow{\mu }}_j$

abhängigen Koeffizienten, insbesondere mehreren von dem Eingangsdatensatz ${\overrightarrow{\mu }}_j$

abhängigen Koeffizienten $u_{N_i}\left({\overrightarrow{\mu }}_j\right),$

folgendermaßen berechnet werden: $$\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)={\displaystyle \sum _{i=1}^N{\overrightarrow{u}}_{N_i}\left({\overrightarrow{\mu }}_j\right){\varphi }_i}$$

An initial value $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

of the reduced model can, for example, as a function of at least one basic function, in particular of several basic functions, _i , and at least one of an input data record ${\overrightarrow{\mu }}_j$

dependent coefficients, in particular several from the input data set ${\overrightarrow{\mu }}_j$

dependent coefficients $u_{N_i}\left({\overrightarrow{\mu }}_j\right),$

can be calculated as follows: $$\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)={\displaystyle \sum _{i=1}^N{\overrightarrow{u}}_{N_i}\left({\overrightarrow{\mu }}_j\right){\varphi }_i}$$

können vorzugsweise mit Hilfe zumindest eines Teils der zur Verfügung stehenden Eingangsdatensatz ${\overrightarrow{\mu }}_j$

berechnet werden. Dabei können jeweilige Fehler zwischen dem Ausgangswert des reduzierten Modells und einem Ausgangswert des ersten Netzes 30, die jeweils in Abhängigkeit eines selben Eingangsdatensatzes ${\overrightarrow{\mu }}_j$

berechnet werden, in die Berechnung der Koeffizienten $u_{N_i}\left({\overrightarrow{\mu }}_j\right)$

mit einfließen. Ist beispielsweise bei der Berechnung des Ausgangswertes $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

des reduzierten Modells N = 1, so weist das reduzierte Modell nur eine erste Basisfunktion ϕ₁ und einen ersten Koeffizienten ${\overrightarrow{u}}_{N_1}\left({\overrightarrow{\mu }}_j\right)$

auf. Die erste Basisfunktion kann derjenige Eigenvektor der ersten Matrix 21 sein, dessen korrespondierender Eigenwert der größte Eigenwert der ersten Matrix 21 ist.The basic functions ϕ _{i can} advantageously be eigenvectors of the first matrix 21 his. The coefficients ${\overrightarrow{u}}_{N_i}$

can preferably with the help of at least part of the available input data record ${\overrightarrow{\mu }}_j$

be calculated. In this case, respective errors can occur between the output value of the reduced model and an output value of the first network 30th , each depending on the same input data record ${\overrightarrow{\mu }}_j$

be calculated in the calculation of the coefficients $u_{N_i}\left({\overrightarrow{\mu }}_j\right)$

flow into. For example, when calculating the initial value $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

of the reduced model N = 1, the reduced model has only a first basic function ϕ ₁ and a first coefficient ${\overrightarrow{u}}_{N_1}\left({\overrightarrow{\mu }}_j\right)$

on. The first basic function can be that eigenvector of the first matrix 21 whose corresponding eigenvalue is the largest eigenvalue of the first matrix 21.

in Abhängigkeit von einem Eingangsdatensatz ${\overrightarrow{\mu }}_j$

wie folgt berechnet werden: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)=Z^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right),$$

wobei W die erste Matrix 21 bezeichnet und Z eine Matrix ist, deren Spalten jeweils Eigenvektoren der ersten Matrix 21 sein können, und $u\left({\overrightarrow{\mu }}_j\right)$

ein Ausgangswert des ersten Netzes 30 in Abhängigkeit von einem Eingangsdatensatz ${\overrightarrow{\mu }}_j$

ist.In order to enable a faster calculation, a respective output value of the reduced model can be used in an alternative embodiment $u_N\left({\overrightarrow{\mu }}_j\right)$

depending on an input data record ${\overrightarrow{\mu }}_j$

can be calculated as follows: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)={\mathrm{Z.}}^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right),$$

where W denotes the first matrix 21 and Z is a matrix whose columns can each be eigenvectors of the first matrix 21, and $u\left({\overrightarrow{\mu }}_j\right)$

an initial value of the first network 30th depending on an input data record ${\overrightarrow{\mu }}_j$

is.

des reduzierten Modells bestimmt.Preferably, each time after a further eigenvalue of the first matrix 21 has been determined, a further basic function ϕ _i and a further coefficient are obtained $u_{N_i}\left({\overrightarrow{\mu }}_j\right)$

of the reduced model.

Preferably referred to N a number N the largest eigenvalues of the first matrix 21 . To each of the N largest eigenvalues of the first matrix 21 can each have an associated eigenvector of the first matrix 21 be determined. Furthermore, the eigenvectors are preferably normalized and form an orthonormal basis. The normalized eigenvectors obtained in this way can be used as the respective basic function ϕ _i for the reduced model.

7 shows partial steps of the second step 12th to generate the reduced matrix 51 at least with the help of the eigenvalue or singular value and the eigenvalue or singular vector of the first matrix 21 . In a first step 61 of the second step 12th the largest eigenvalue or largest singular value of the first matrix is selected. In a second step 62 of the second step 12th an eigenvector or singular vector corresponding to the selected eigenvalue or selected singular value is determined.

In a third step 63 it is checked whether a first termination criterion is met. The second step 62 is repeated if the first termination criterion is not met, wherein a new eigenvalue or singular value is selected that is less than or equal to the previously selected eigenvalue or singular value. In a fourth step 64 of the second step 12th becomes the auxiliary matrix Z. expanded using the eigenvectors or singular vectors determined in the second sub-step. In a fifth step 65 of the second step 12th becomes the reduced matrix 51 using the auxiliary matrix Z. constructed.

According to a simple embodiment, the first termination criterion can be met if a predetermined number of eigenvectors or singular vectors of the first matrix 21 have been determined. The predetermined number is preferably less than half of a number of rows or columns of the first matrix 21 .

The naming of the sub-steps 61 to 65 should not specify a mandatory sequence of the sub-steps. For example, according to a further embodiment, the fourth sub-step 64 after the second step 62 and before the third step 63 respectively. In this case, the auxiliary matrix is repeated each time the second sub-step is repeated 62 expanded with a single eigenvector or singular vector. This has the advantage that a check as to whether the first termination criterion is fulfilled can be made using the after the second substep 62 extended auxiliary matrix can be carried out.

und mit Hilfe des ersten neuronalen Netzes 30 und jeweilige zweite korrespondierende Ausgangsdatensätze mit Hilfe der jeweiligen Eingangsdatensätze ${\overrightarrow{\mu }}_j$

und mit Hilfe des reduzierten Modells berechnet werden. Im Anschluss daran wird zu jedem Eingangsdatensatz ${\overrightarrow{\mu }}_j$

eine korrespondierende Abweichung zwischen dem jeweiligen korrespondierenden ersten Ausgangsdatensatz und dem jeweiligen korrespondierenden zweiten Ausgangsdatensatz ermittelt. Dabei kann ein einzelner zweiter korrespondierender Ausgangsdatensatz ${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)$

des reduzierten Modells in Abhängigkeit der Hilfsmatrix Z und des jeweiligen Eingangsdatensatzes ${\overrightarrow{\mu }}_j$

wie folgt berechnet werden: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)=Z^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right)$$

For example, the first termination criterion can be determined as a function of the auxiliary matrix as follows. First of all, respective first corresponding output data records can be used as a function of respective input data records ${\overrightarrow{\mu }}_j$

and with the help of the first neural network 30th and respective second corresponding output data sets with the aid of the respective input data sets ${\overrightarrow{\mu }}_j$

and be calculated using the reduced model. This is followed by each input data record ${\overrightarrow{\mu }}_j$

a corresponding deviation between the respective corresponding first output data record and the respective corresponding second output data record is determined. A single second corresponding output data record can be used ${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)$

of the reduced model depending on the auxiliary matrix Z. and the respective input data record ${\overrightarrow{\mu }}_j$

can be calculated as follows: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)={\mathrm{Z.}}^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right)$$

korrespondierende Abweichung $e_{N_j}\left({\overrightarrow{\mu }}_j\right)$

kann beispielsweise mithilfe einer Vektornorm wie folgt bestimmt werden: $$e_{N_j}\left({\overrightarrow{\mu }}_j\right)=\Vert {\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)-\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\Vert ,$$

wobei $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

der jeweilige erste Ausgangsdatensatz des ersten Netzes 30 ist und wie folgt mit Hilfe von Ausgangswerten des ersten Netzes 30 angegeben werden kann: $$\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)=\left(\begin{array}{c}{a}_{n1}\\ a_{n2}\\ ⋮\\ a_{ni}\\ ⋮\\ a_{nm}\end{array}\right),$$

wobei die jeweiligen Einträge des ersten korrespondierenden Ausgangsdatensatzes $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

den Ausgangswerten der entsprechenden Neuronen 30_n1 , 30_ni , 30_nm der n-ten Schicht 34 des ersten Netzes 30 entsprechen können.The for each input data record ${\overrightarrow{\mu }}_j$

corresponding deviation $e_{N_j}\left({\overrightarrow{\mu }}_j\right)$

can be determined, for example, using a vector standard as follows: $$e_{N_j}\left({\overrightarrow{\mu }}_j\right)=\Vert {\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)-\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\Vert ,$$

in which $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

the respective first output data record of the first network 30th is and as follows using output values of the first network 30th can be specified: $$\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)=\left(\begin{array}{c}{a}_{n1}\\ a_{n\mathrm{2nd}}\\ ⋮\\ a_{ni}\\ ⋮\\ a_{nm}\end{array}\right),$$

the respective entries of the first corresponding output data record $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

the initial values of the corresponding neurons 30 _n1 , 30 _ni , 30 _nm the nth layer 34 of the first network 30th can correspond.

wobei M die Anzahl aller zur Verfügung stehenden Eingangsdatensätze ${\overrightarrow{\mu }}_j$

der Gesamtmenge der Eingangsdatensätze bezeichnet.The partial steps 62 and 64 are preferably repeated until all the respective deviations, which correspond to the respective input data record, lie below a predetermined limit ε. The barrier can preferably be specified by a user. The first termination criterion for repeating the partial steps 62 , and preferred 64 , can then be specified as follows: $$\text{Max}{\left(e_{N_j}\right)}_{j=1...M}<\epsilon ,$$

where M is the number of all available input data sets ${\overrightarrow{\mu }}_j$

the total amount of input data records.

wobei W_N die reduzierte Matrix 51, W die erste Matrix 21, Z die Hilfsmatrix und Z^T die transponierte Hilfsmatrix bezeichnet. Eine Anzahl, mit welcher Häufigkeit der zweite Teilschritt 62 wiederholt wird, kann als Optimierungszahl bezeichnet werden. Die Hilfsmatrix weist bevorzugt eine Anzahl an Spalten auf, die gleich der Optimierungszahl ist. Die Optimierungszahl ist insbesondere kleiner als die Anzahl der Spalten der ersten Matrix 21, vorzugsweise mehr als zehn Mal so klein. Die reduzierte Matrix 51 kann eine Anzahl an Spalten und Zeilen haben, die gleich der Optimierungszahl ist.Preferably, the sub-steps are repeated each time 62 and 64 the eigenvector associated with the selected eigenvalue is added in the form of a further column of the auxiliary matrix Z. Before adding the further eigenvector, the columns already present in the auxiliary matrix Z are preferably orthogonalized with the eigenvector to be added. The reduced matrix 51 can advantageously be calculated using the auxiliary matrix as follows: $$W_N={\mathrm{Z.}}^{T}W\mathrm{Z.},$$

in which W _N the reduced matrix 51 , W the first matrix 21 , Z denotes the auxiliary matrix and Z ^T denotes the transposed auxiliary matrix. A number, with what frequency the second substep 62 repeated, can be called the optimization number. The auxiliary matrix preferably has a number of columns that is equal to the optimization number. The optimization number is in particular smaller than the number of columns in the first matrix 21 , preferably more than ten times smaller. The reduced matrix 51 can have a number of columns and rows equal to the optimization number.

In a further embodiment, the proposed method comprises a third step in which the above-described calculation of the respective first corresponding output data sets takes place, a fourth step in which the above-described calculation of the respective second corresponding output data sets takes place and a fifth step in which the above described calculation of the respective deviations between the first output data sets and the second output data sets corresponding to the first output data sets. Corresponding the respective first output data record with the respective second output data record means that these two output data records are calculated as a function of the same input data record.

A sixth step of this embodiment provides that those input data records which correspond to the greatest deviations are collected in the form of a first set of input data records. Corresponding the respective input data sets with the greatest deviations means that these greatest deviations were calculated with these input data sets. In a seventh step, the reduced neural network is adapted using the first set of input data sets. The adaptation can be carried out like an ordinary training of a neural network according to the state of the art. Steps three to six are advantageously repeated each time the second sub-step is carried out.

If the termination criterion is met, the first set contains the input data records that have the greatest influence on the previously calculated deviations. The first set of input data sets is smaller than the total set of input data sets, which contains all available input data sets. The advantage of collecting the input data records in the first set in this way is that the reduced network can be trained faster with the input data records of the first set. This applies in particular to a convergence rate when exercising.

des reduzierten Modells in Abhängigkeit der Hilfsmatrix Z und des jeweiligen Eingangsdatensatzes ${\overrightarrow{\mu }}_j$

wie folgt berechnet werden: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)=Z^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right)$$

According to a further embodiment, it is possible that, in an initial step of this embodiment, a predetermined number of the largest eigenvalues or singular values of the first matrix are determined and combined in a second set and the reduced matrix is constructed using the second set of the eigenvalue or singular values. Then the respective corresponding eigenvectors or singular vectors are determined and preferably orthogonalized on the basis of the largest eigenvalues or singular values. The auxiliary matrix Z can then be constructed using these, preferably orthogonalized, eigenvectors or singular vectors, for example in that the eigenvectors or singular vectors form columns of the auxiliary matrix Z. Subsequently, as described above, a single second corresponding output data record can ${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)$

of the reduced model depending on the auxiliary matrix Z. and the respective input data record ${\overrightarrow{\mu }}_j$

can be calculated as follows: $${\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)={\mathrm{Z.}}^T\left(W\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\right)$$

die korrespondierende Abweichung $e_{N_j}\left({\overrightarrow{\mu }}_j\right)$

mithilfe einer Vektornorm wie folgt bestimmt werden: $$e_{N_j}\left({\overrightarrow{\mu }}_j\right)=\Vert {\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)-\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\Vert ,$$

wobei $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

der jeweilige erste Ausgangsdatensatz des ersten Netzes 30 ist, der in Abhängigkeit des Eingangsdatensatzes ${\overrightarrow{\mu }}_j$

berechnet wird. Ist das erste Abbruchkriterium: $$\text{max}{\left(e_{N_j}\right)}_{j=1\dots M}<\epsilon ,$$

erfüllt, so kann die reduzierte Matrix 51 mithilfe der Hilfsmatrix vorteilhaft wie folgt berechnet werden: $$W_N=Z^{T}WZ,$$

Subsequent to this, each input data record ${\overrightarrow{\mu }}_j$

the corresponding deviation $e_{N_j}\left({\overrightarrow{\mu }}_j\right)$

can be determined using a vector standard as follows: $$e_{N_j}\left({\overrightarrow{\mu }}_j\right)=\Vert {\overrightarrow{u}}_N\left({\overrightarrow{\mu }}_j\right)-\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)\Vert ,$$

in which $\overrightarrow{u}\left({\overrightarrow{\mu }}_j\right)$

the respective first output data record of the first network 30th is dependent on the input data record ${\overrightarrow{\mu }}_j$

is calculated. The first termination criterion is: $$\text{Max}{\left(e_{N_j}\right)}_{j=1...M}<\epsilon ,$$

fulfilled, so the reduced matrix 51 can be advantageously calculated as follows using the auxiliary matrix: $$W_N={\mathrm{Z.}}^{T}W\mathrm{Z.},$$

If the first termination criterion is not met, the predetermined number of the largest eigenvalues or singular values of the first matrix is increased by one. This configuration of the method is repeated from the above-mentioned initial step until the first termination criterion is met. The predetermined number is advantageously greater than one, in particular greater than ten. This embodiment of the method can accelerate the generation of the auxiliary matrix.

The networks 30th , 40 are very simple examples of neural networks. In general, it is possible for a plurality of output values from neurons of a first exemplary layer to be linked to one another, for example added up, and for a value calculated using such a link to be an input value for an individual activation function of a single neuron in a second exemplary layer. In this, the first and the reduced matrix are preferably multidimensional, in particular three-dimensional. However, the eigenvalues or singular values of the first matrix can be calculated using the variants of the proposed method described above.

The project that gave rise to this patent application was funded by the joint company "Electronic Component Systems for European Leadership" in accordance with research funding agreement No. 737469. The joint company is supported by the research and innovation program of the European Union Horizon 2020 and Germany, Austria, Spain, Latvia, Belgium, Netherlands, Sweden, Lithuania, Czech Republic, Romania, Norway.

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Patent literature cited

• DE 102018103113 [0002]

Claims (10)

Method for generating a reduced neural network (40) for a control unit (2) of a vehicle (1) and / or a vehicle component (7, 8, 9), with the following steps: - reading in a first data field of a first neural network (30), the first data field having entries which in their entirety at least partially represent internal logic of the first neural network (30), in a first step (11), - Generating the reduced neural network (40) at least with the aid of the first data field in a second step (12), the reduced neural network having a reduced data field with entries which, in their entirety, at least partially have internal logic of the reduced neural network (40) represent and the reduced data field has fewer non-zero entries than the first data field. Procedure according to Claim 1 The first data field is in the form of a first matrix (21) and the reduced data field is in the form of a reduced matrix (51) and the reduced matrix (51) is constructed using at least one eigenvector or singular vector of the first matrix (21). Procedure according to Claim 2 , with the following further steps being carried out: - selecting a largest eigenvalue or largest singular value of the first matrix in a first substep (61) of the second step, - determining an eigenvector or singular vector corresponding to the selected eigenvalue or selected singular value in a second substep (62 ) the second step, - check whether a first termination criterion is met in a third sub-step (63) and repeat the second sub-step if the first termination criterion is not met, wherein a new eigenvalue or singular value is selected that is less than or equal to the previous one selected eigenvalue or singular value, - expanding an auxiliary matrix using the eigenvectors or singular vectors determined in the second sub-step in a fourth sub-step (64) of the second step, - constructing the reduced matrix (51) using the auxiliary matrix in a fifth substep (65) of the second step. Procedure according to one of the Claims 1 to 3rd The following steps are carried out: - Calculation of respective first corresponding output data sets using the first neural network (30) and depending on a respective input data set in a third step, - Calculation of respective second corresponding output data sets using a reduced model of the first neural network ( 30) and depending on the respective input data record in a fourth step, - determining respective deviations between the first output data records and the second output data records corresponding to the first output data records in a fifth step, - collecting those input data records that correspond to the greatest deviations in the form a first set of input data sets in a sixth step, - adapting the reduced neural network (40) using the first set of input data sets in a seventh step. Procedure according to Claim 4 , steps three to six being repeated each time the second step is carried out. Procedure according to Claim 2 , a predetermined number of the largest eigenvalues or singular values of the first matrix (21) being determined and combined in a second set, and the reduced matrix (51) being constructed using the second set of eigenvalues or singular values. Reduced neural network (40), established by a method according to one of the Claims 1 to 6 , wherein the reduced neural network (40) has the reduced matrix (51) with entries which each represent an internal logic of the reduced neural network (40), and the reduced matrix (51) has fewer non-zero entries than the first matrix ( 21) has. A computer program product (10) comprising a program that, when executed by a computer, causes the computer to perform a method according to one of the Claims 1 to 6 perform. Control device (2) for a vehicle (1) and / or a vehicle component (7, 8, 9), set up by a method and / or for carrying out a method according to one of the Claims 1 to 6 . Vehicle (1) comprising a control device (2) according to Claim 9 .

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