DE102019214546A1 - Computer-implemented method and device for optimizing an architecture of an artificial neural network - Google Patents

Abstract

Device and computer-implemented method for optimizing an architecture of an artificial neural network, an architecture of the artificial neural network being specified in which arithmetic operations of the artificial neural network are summarized in functional layers, with a reciprocal of a number of neurons of the artificial neural network depending on the architecture neural network in an output layer of one of the functional layers is determined (202), for this functional layer, depending on the architecture, a factor depending on a window size of a max-pooling window in one of the other functional layers following the functional layer. Layers is determined (204), a measure for a sensitivity of the architecture to hardware memory errors depending on a product of the reciprocal value with the factor is determined (208), it is checked whether the measure falls below a threshold value (210) and where a Hardware acceleration it (106) is configured with neurons, connections between neurons, weights and / or activation functions that are specified by the architecture if the measure falls below the threshold value (210) and otherwise the measure is determined for a different architecture.

Description

State of the art

The invention is based on a device and a method for optimizing an architecture of an artificial neural network.

It is desirable to provide artificial neural networks that are particularly robust against random hardware memory errors. Random hardware memory errors are, for example, bit-flip errors that are triggered by electromagnetic radiation acting on a memory. However, an assessment of an architecture of an artificial neural network with a large number of neurons against such errors is difficult to represent.

Disclosure of the invention

The device and the method according to the independent claims enable a particularly good assessment of the robustness of the architecture of artificial neural networks with respect to random hardware memory errors. Optimization of an architecture of the artificial neural network is thus possible in a particularly efficient manner.

In a computer-implemented method for optimizing an architecture of an artificial neural network, an architecture of the artificial neural network is specified in which arithmetic operations of the artificial neural network are summarized in functional layers, a reciprocal of a number of neurons of the artificial neural network depending on the architecture one of the functional layers is determined in an output layer, a factor being determined for this functional layer depending on the architecture depending on a window size of a max-pooling window in one of the other functional layers following the functional layer, wherein a measure for a sensitivity of the architecture to hardware memory errors depending on a product of the reciprocal value with the factor is determined, whereby it is checked whether the measure falls below a threshold value and wherein a hardware accelerator with neurons, connections between Neurons, weights and / or activation functions is configured, which are specified by the architecture, if the measure falls below the threshold value and otherwise the measure is determined for a different architecture. This measure represents a parameter for the robustness of the artificial neural network. For example, a functional layer is defined as follows, unlike in typical deep learning software tools: A functional layer contains all computing operations that a dedicated deep neural network hardware accelerator can be carried out one after the other before the result is stored in an output feature map for calculation by the next functional layer in a memory. The arithmetic operations are, for example, the partial arithmetic operations for a convolutional layer, a pooling layer, a batch normalization, or an activation function. In the example, the memory is a hardware memory. The last sub-arithmetic operation of the functional layer provides a result in the output layer. For the hardware memory, for example, a constant and uniformly distributed bit flip probability is used as the basis for the hardware memory. The bit flip probability indicates the probability with which a bit in the memory changes its value, e.g. in response to external influences. The measure is used to calculate an optimized architecture for an artificial neural network. This measure represents a parameter of the architecture that can be evaluated favorably in terms of computing time and computing resources. The parameter makes it possible to evaluate the robustness of neural networks against bit-flip errors and to increase it by optimizing the architecture in this regard. In order to maximize the robustness, in particular the error sensitivity of the architecture is minimized in that the architecture that is implemented in the memory falls below the threshold value. This automatically generates an optimized artificial neural network.

In one aspect, the factor for the functional layer is determined as a function of an in particular arithmetic mean value of the individual window sizes of max pooling windows for a plurality of the other subsequent functional layers. This enables a particularly efficient calculation for more complex architectures.

In one aspect, depending on the degree, an architecture for the artificial neural network is selected from a plurality of architectures for the artificial neural network. The measure can be used, for example, in a cost function for sampling architectures for evaluation, the architecture being selected which minimizes the cost function.

An architecture is preferably determined for the artificial neural network which minimizes a cost function, the cost function being defined as a function of the measure.

The cost function is preferably dependent on a number of arithmetic operations or a number of memory transfers required for the hardware accelerator to determine a result 106 Are defined. This automatically generates a particularly fast, efficient and robust artificial neural network.

In one aspect, the architecture defines an artificial neural network for recognizing or classifying objects as a function of sensor data, in particular video data, data for optical distance or speed measurement or radar data, an input variable for the artificial neural network being determined as a function of the sensor data, whereby depending on an output signal of the artificial neural network, a control signal for controlling an at least partially autonomous robot, an at least partially autonomous vehicle, an actuator, a machine, a household appliance or a do-it-yourself device is determined.

In one aspect, the architecture defines an artificial neural network for recognizing or classifying objects as a function of sensor data, in particular video data or radar data, an input variable for the artificial neural network being determined as a function of sensor data Information about a pedestrian and / or a traffic sign and / or a vehicle and / or their position relative to one another is determined.

In one aspect, the architecture defines an artificial neural network for segmenting sensor data, in particular video data, data for optical distance or speed measurement or radar data, an input variable for the artificial neural network being determined as a function of the sensor data, depending on segmented sensor data are determined from an output signal of the artificial neural network.

In a first phase, an architecture for the artificial neural network is preferably determined for which the measure falls below the threshold value, with training data being provided in a second phase and this architecture being trained as a function of the training data, and with the sensor data in a third phase the artificial neural network trained in this way.

A device comprises a processor and a memory for an artificial neural network, which are designed to carry out the method.

• 1 eine schematische Darstellung von Teilen einer Recheneinrichtung,
• 2 Schritte in einem Verfahren für die Recheneinrichtung,
• 3 ein Berechnungsschema für das Verfahren.

Further advantageous embodiments emerge from the following description and the drawing. In the drawing shows:

• 1 a schematic representation of parts of a computing device,
• 2 Steps in a method for the computing device,
• 3rd a calculation scheme for the process.

In 1 is a device 100 shown schematically.

The device 100 includes a processor 102 , a memory 104 , a hardware accelerator 106 for an artificial neural network, a sensor 108 and an output device 110 . The artificial neural network has a large number of neurons. The hardware accelerator 106 can be configured with neurons, connections between neurons, weights and / or activation functions according to an architecture for the artificial neural network.

The memory 104 can be used for storing the configurations of neural networks as well as for writing / reading input and output tensors of the artificial neural network. It doesn't necessarily have to be the same memory 104 can be used for storing the configurations of neural networks and for writing / reading input and output tensors of the artificial neural network. Different memories can be used for this.

The hardware accelerator 106 is designed in the example, results from an output layer of the artificial neural network in the memory 104 to write. Corresponding data can from Hardware accelerator 106 about the processor 102 to the store 104 flow. In 1 arrows are shown that represent data flows for this and other exemplary data flows. The hardware accelerator 106 is designed to output the result via the processor 102 to the output device 110 to spend.

A memory access for writing / reading input and output tensors not necessarily via the processor 102 respectively. It can be a direct access from the hardware accelerator 106 on the memory 104 , a so-called "direct memory access" can be provided. In this case, for example, a central data bus is provided on which the processor 102 , the memory 104 , the hardware accelerator 106 , the input device 108 and the output device 110 connected and that regulates the flow of data.

The sensor 108 is trained to deliver sensor data. The output device 110 is designed to output an output signal.

The device 100 is trained to carry out the procedure described below. The method evaluates the robustness of architectures for the artificial neural network and the artificial neural network in the memory 104 configured according to a particularly robust architecture determined in the process.

In particular, it is robust to random hardware memory errors, ie in particular bit-flip errors that occur in the memory 104 can occur, rated. These errors can be caused, for example, by an on a memory 104 acting electromagnetic radiation can be triggered. These errors occur, for example, with a bit flip probability that is assumed to be constant and uniformly distributed.

In the method, a measure f _ASI (N) for a sensitivity of an architecture of the artificial neural network with N functional layers is determined. A low sensitivity, in particular to the random hardware memory errors, in particular to the bit-flip errors caused by the memory 104 acting electromagnetic radiation is triggered, means a high level of robustness. In this context, sensitivity means that an output of a neural network provided with bit-flip errors deviates significantly from an uninfluenced variant of the network. A significant deviation occurs, for example, if other conclusions are drawn from the output, such as changed classification results.

In the example, the artificial neural network comprises at least one functional layer 1, which is defined by a large number of arithmetic operations of the artificial neural network, in particular by a hardware accelerator 106 to determine a result in an output layer of the functional layer 1 can be carried out one after the other. The result can be defined as an output tensor or an output feature map. The result is when using the artificial neural network in memory 104 saved. A function layer following this function layer 1 can take the result for the subsequent processing from the memory 104 load. A multiplicity of the functional layers 1 can be provided.

In the example, the method comprises three phases in which the artificial neural network is first determined, then trained and then used. These three phases can be carried out in the order described below or independently of one another.

The first phase is one step 202 a reciprocal of a number n ^(l) of neurons of the artificial neural network in the output layer of the functional layer l is determined for the functional layer l. If a plurality of the functional layers 1 is provided, an individual reciprocal value is determined for each of the layers.

The first phase is in one step 204 for the functional layer l a factor λ ^{(l) is determined as a} function of a window size of a max pooling window for the result in the subsequent functional layer. This factor λ ^(l) is also referred to below as the max pooling factor λ ^(l) .

If the result in the output layer of the functional layer 1 is determined for subsequent processing in a large number of functional layers following the functional layer 1, the max-pooling factor λ ^{(1) is determined as a} function of an in particular arithmetic mean value, the the max-pooling window for the majority of the subsequent functional layers is defined via individual window sizes.

If a multiplicity of the functional layers l is provided, an individual max-pooling factor λ ^{(l) is} determined for each of the layers.

The first phase can be an optional step 206 ^{a further factor l (l)} can be determined for the functional layer l, which is defined as a function of a number of functional layers, the result of which in the same subsequent functional layer, in particular by component-wise addition of input tensors from the memory 104 to be read, to be united. In the example, the input tensors correspond to the output tensors that were previously stored.

If a plurality of the functional layers l is provided, an individual factor ζ ^{(l) is} determined for each of the layers. For function layers l that are not included in a component-wise addition, ie if none of the following function layers carry out a component-wise addition, this factor is ζ ^(l) = 1.

The first phase is in one step 208 the measure f _ASI (N) for the sensitivity is determined as a function of a product of the reciprocal value with the max pooling factor λ ^(l) .

If a multiplicity of the functional layers 1 is provided, the measure f _ASI (N) is determined as a function of a sum of a multiplicity of the products which are determined for individual functional layers 1.

For a number N of functional layers I, the measure f _ASI (N) is determined, for example, as: $$f_{\mathrm{A.}\mathrm{S.}\mathrm{I.}}\left(N\right)={\displaystyle {\sum }_{l\in N}\frac{1}{n^l}{\lambda }^{\left(l\right)}{\varsigma }^{\left(l\right)}}$$

In one step 210 an architecture for the artificial neural network from a plurality of architectures for the artificial neural network is determined as a function of the measure f _{ASI (N).}

_{For example, an individual measure f ASI} (N) is determined for each architecture of a large number of architectures for the artificial neural network. The memory 104 is configured in this example with neurons, connections between neurons, weights and / or activation functions that are specified by the architecture with the smallest of the individual dimensions.

The hardware accelerator 106 will be in crotch 210 configured with neurons, connections between neurons, weights and / or activation functions according to an architecture for which the measure f _ASI (N) falls below a threshold value. The threshold value is, for example, in the range between 0 and 1 and is, for example, 0.1 or 0.2 or 0.5. For a comparison of an architecture with another architecture, the threshold value can also be defined by the measure f _ASI (N), which was determined for one of the two architectures to be compared. If the measure does not fall below the threshold value, these steps can be repeated, for example, until a certain number of architectures have been determined and evaluated with the measure. Provided that the dimension is not undershot, the architecture with the smallest dimension can be used. The architectures define a topology for an artificial neural network that includes neurons, connections between neurons, weights and / or activation functions.

The measure f _ASI (N) is used, for example, as a cost function in a calculation scheme for the architecture of artificial neural networks. An example of such a calculation scheme is in the pre-published DE 102017219282 A1 specified. In particular, an evaluation unit by means of the measure f _ASI (N) is used as a cost function for evaluating the performance of the artificial neural network or of further developments of the artificial neural network. In this the artificial neural network is defined by parameter p.

The artificial neural network or the further developments of the artificial neural network are optimized by varying the respective parameters p. The resulting measures f _ASI (N) in this example keep the artificial neural network or select that one of the developments of the artificial neural network whose measure f _ASI (N) is minimal compared to the other measures f _ASI (N) . For this purpose, a topology of a respective neural network N, for example a graph which defines the artificial neural network N and the parameterization of its layers as parameter p, can be transferred to a function for calculating the measure f _ASI (N). The return value of this function is a numerical value that indicates the architecture sensitivity. High sensitivity corresponds to in this example of poor robustness against bit-flip errors. In an example, this value is used for sampling parent architectures and child architectures and for calculating a Pareto front. In addition to the measure f _ASI (N), further cost functions, which for example an efficiency of the neural network for a given hardware accelerator, can be used 106 estimate, be used. This additional cost function takes into account, for example, a number of arithmetic operations or a number of required memory transfers for the determination of the result by this hardware accelerator 106 .

The hardware accelerator 106 can be or comprise a graphical processing unit, a digital signal processing unit, a programmable FPGA or a dedicated computing device.

A second phase will be in one step 212 Training data provided and this architecture trained depending on the training data.

In a first aspect, the architecture defines, for example, an artificial neural network for recognizing objects as a function of sensor data, in particular video data, data for optical distance or speed measurement or radar data. In this case, in the example, the sensor data are specified as training data, an input variable for the artificial neural network is determined as a function of the sensor data, and the artificial neural network is trained to recognize the objects. Instead of a recognition of objects, a classification of objects can also be provided.

In a second aspect, the architecture defines, for example, an artificial neural network for segmenting sensor data, in particular video data, data for optical distance or speed measurement or radar data. In this case, in the example, the sensor data are specified as training data, an input variable for the artificial neural network is determined as a function of the sensor data, and the artificial neural network is trained to segment the sensor data.

A third phase will be in one step 214 processes the sensor data with the artificial neural network trained in this way. In the example, an input variable for the artificial neural network is determined depending on the sensor data. In the example, the output signal is determined depending on the input variables.

In the first aspect it can be provided that a control signal for controlling an at least partially autonomous robot, an at least partially autonomous vehicle, an actuator, a machine, a household appliance or a do-it-yourself device is determined as the output signal depending on an output signal of the artificial neural network. In the first aspect, it can be provided that information about a pedestrian and / or a traffic sign and / or a vehicle and / or their position relative to one another is determined as the output signal as a function of an output signal of the artificial neural network.

In the second aspect, segmented sensor data are determined as an output signal as a function of an output signal of the artificial neural network.

In 3rd is a calculation scheme exemplary for an artificial neural network 300 with a network input on a first functional layer 302 with n = 1000 neurons in an output layer of the first functional layer 302 shown. The first functional layer 302 includes, for example, the arithmetic operations 2D Convolution and Activation. The first functional layer 302 a layer index l = 1 is assigned.

The first functional layer 302 immediately following is a hidden second functional layer 304 arranged. Arranged immediately below in this context means that an output tensor of the first functional layer 302 , for example in memory 104 is stored, the input tensor of the hidden second functional layer 304 , for example from memory 104 is read. The hidden second functional layer 304 comprises, for example, n = 1000 neurons in an output layer of the second functional layer 304 . The second functional layer 304 includes, for example, the arithmetic operations 2D Convolution and Activation. The hidden second functional layer 304 a layer index l = 2 is assigned.

The first functional layer 302 immediately following is a hidden third functional layer 306 arranged. Arranged immediately below in this context means that the output tensor of the first functional layer 302 the input tensor of the hidden third functional layer 306 , for example from memory 104 is read. The hidden third functional layer 306 comprises, for example, n = 100 neurons in an output layer of the third functional layer 306 . The hidden third functional layer is designed for 2x2 max pooling and, for example, 2D convolution and activation. The hidden third functional layer 304 a layer index l = 3 is assigned.

The hidden second functional layer 304 immediately following is a hidden fourth functional layer 308 arranged whose input tensor through an output tensor of the hidden second functional layer 304 is defined. The hidden fourth functional layer 308 comprises, for example, n = 100 neurons in an output layer of the fourth functional layer 308 . The hidden fourth functional layer 308 is trained for 2x2 max pooling as well as 2D convolution and activation, for example. The hidden fourth functional layer 308 a layer index l = 4 is assigned.

The hidden third functional layer 306 immediately following is a hidden fifth functional layer 310 arranged whose input tensor through an output tensor of the hidden third functional layer 306 is defined. The hidden fifth functional layer 310 comprises, for example, n = 100 neurons in an output layer of the fifth functional layer 310 . The fifth functional layer 310 includes, for example, the arithmetic operations 2D Convolution and Activation. The hidden fifth functional layer 310 a layer index l = 5 is assigned.

The hidden fourth functional layer 308 and the hidden fifth layer 310 is a hidden addition layer 312 immediately downstream. In the hidden addition layer 312 a component-wise addition of input tensors is carried out, for example from the memory 104 are read and dependent on the output tensors of the hidden fourth functional layer 308 and the hidden fifth functional layer 310 are defined. In the example these input tensors are added to a tensor.

The hidden addition layer 312 immediately following is a hidden sixth functional layer 314 arranged whose input tensor through an output tensor of the hidden addition layer 312 is defined. The hidden sixth functional layer 314 comprises, for example, n = 100 neurons in an output layer of the sixth functional layer 314 . The hidden sixth functional layer 314 is trained for 4x4 max pooling as well as 2D convolution and activation, for example. The hidden sixth functional layer 314 a layer index l = 6 is assigned.

The hidden sixth functional layer 314 immediately following is a seventh functional layer 316 arranged whose input tensor through an output tensor of the hidden sixth functional layer 314 is defined. The seventh functional layer 316 comprises, for example, n = 10 neurons in an output layer of the seventh functional layer 316 . The seventh functional layer 316 includes, for example, the computing operations Fully Connected and Activation. The seventh functional layer 316 Output layer provides a network output. The seventh functional layer 316 a layer index l = 7 is assigned.

The functional layers with the layer indices are general 1 - 7th each functional layer that can contain several arithmetic operations, eg 2D convolution, activation, max pooling, which are provided by the hardware accelerator 106 in one computing step of the hardware accelerator 106 be calculated. In this example it must be from the hardware accelerator 106 for everyone in 3rd function layers shown a result in the memory 104 to be written. The memory 104 is prone to errors. The value must be taken from the memory in a function layer that is arranged downstream of another function layer 104 reloaded. So each arrow in the figure goes with a load from memory 104 hand in hand. Due to these loading processes, the functional layers cannot share the hardware accelerator 106 be calculated. A layer could, however, also contain further arithmetic operations if the hardware accelerator is implemented 106 this without intermediate storage in a faulty memory 104 enables.

den Max-Pooling Faktor λ^(l), und den weiteren Faktor ζ^(l) sowie das daraus berechnete jeweilige Produkt $\frac{1}{n^{\left(l\right)}}{\lambda }^{\left(l\right)}{\varsigma }^{\left(l\right)}$

an, die sich für diese Architektur ergeben. Die Additions-Schicht 312 geht in diesem Beispiel nicht direkt in die Berechnung des Maßes f_ASI(N) ein. Der Einfluss der Additions-Schicht 312 wird durch weitere Faktoren in den Schichten mit Layer Index l = 4 und l = 5 modelliert. Dadurch geht die Additions-Schicht 312 indirekt das Maß f_ASI(N) ein. I $\frac{1}{n^{\left(l\right)}}$

λ^(l) ζ^(l) Produkt 1 0,001 2,5 1 0,0025 2 0,001 4 1 0,004 3 0,01 1 1 0,01 4 0,01 16 2 0,32 5 0,01 16 2 0,32 6 0,01 1 1 0,01 7 0,1 1 1 0,1 The following table gives the values for the reciprocal value for each of the layers I individually $\frac{1}{n^{\left(l\right)}},$

the max pooling factor λ ^(l) , and the further factor ζ ^(l) as well as the respective product calculated from it $\frac{1}{n^{\left(l\right)}}{\lambda }^{\left(l\right)}{\varsigma }^{\left(l\right)}$

resulting for this architecture. The addition layer 312 is not directly included in the calculation of the dimension f _ASI (N) in this example. The influence of the addition layer 312 is influenced by other factors in the Layers modeled with layer index l = 4 and l = 5. This goes through the addition layer 312 indirectly the measure f _ASI (N). I. $\frac{1}{n^{\left(l\right)}}$

λ ^(l) ζ ^(l) product 1 0.001 2.5 1 0.0025 2 0.001 4th 1 0.004 3rd 0.01 1 1 0.01 4th 0.01 16 2 0.32 5 0.01 16 2 0.32 6th 0.01 1 1 0.01 7th 0.1 1 1 0.1

The resulting value of the measure f _ASI (N) is f _ASI (N) = 0.7665 in this example.

The artificial neural network is, for example, a deep neural network that runs on the hardware accelerator 106 is performed. The artificial neural network is designed, for example, to process sensor data. For example, the network input is determined depending on the sensor data. The artificial neural network determined in this way is particularly robust against hardware errors and is particularly suitable for use in safety-critical applications, for example in automobiles, in which very high robustness is to be achieved with small or limited hardware resources. Hardware resources are, for example, power consumption, latency or memory bandwidth for the processing of data by the artificial neural network. Applications in medical or industrial environments in which radiation is used can also be designed to be very robust. Other applications relate to the use for robots, machine tools, production machines or control systems.

QUOTES INCLUDED IN THE DESCRIPTION

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Patent literature cited

• DE 102017219282 A1 [0038]

Claims (12)

Computer-implemented method for optimizing an architecture of an artificial neural network, characterized in that an architecture of the artificial neural network is specified, in which arithmetic operations of the artificial neural network are summarized in functional layers, with a reciprocal of a number of neurons depending on the architecture artificial neural network in an output layer of one of the functional layers is determined (202), for this functional layer, depending on the architecture, a factor depending on a window size of a max-pooling window in one of the other functional layers following the functional layer Layers is determined (204), a measure for a sensitivity of the architecture to hardware memory errors being determined as a function of a product of the reciprocal value with the factor (208), it being checked whether the measure falls below a threshold value (210) and where a hardware bes Accelerator (106) is configured with neurons, connections between neurons, weights and / or activation functions that are specified by the architecture if the measure falls below the threshold value (210) and otherwise the measure is determined for a different architecture. Procedure according to Claim 1 , characterized in that the factor for the functional layer is determined as a function of an in particular arithmetic mean value of the individual window sizes of max pooling windows for a plurality of the other subsequent functional layers (204). Method according to one of the preceding claims, characterized in that, depending on the measure, an architecture for the artificial neural network is selected from a plurality of architectures for the artificial neural network (210). Method according to one of the preceding claims, characterized in that an architecture is determined for the artificial neural network which minimizes a cost function, the cost function being defined as a function of the measure. Procedure according to Claim 4 , characterized in that the cost function is defined as a function of a number of arithmetic operations or a number of required memory transfers for a determination of a result by the hardware accelerator (106). Method according to one of the preceding claims, characterized in that the architecture defines an artificial neural network for recognizing or classifying objects depending on sensor data, in particular video data, data for optical distance or speed measurement or radar data, with an input variable depending on the sensor data is determined for the artificial neural network, a control signal for controlling an at least partially autonomous robot, an at least partially autonomous vehicle, an actuator, a machine, a household appliance or a do-it-yourself device is determined as a function of an output signal of the artificial neural network (214). Method according to one of the Claims 1 to 5 , characterized in that the architecture defines an artificial neural network for the detection or classification of objects depending on sensor data, in particular video data or radar data, an input variable for the artificial neural network being determined depending on sensor data, and depending on an output signal of the artificial neural network Network information about a pedestrian and / or a traffic sign and / or a vehicle and / or their position relative to one another is determined (214). Method according to one of the Claims 1 to 5 , characterized in that the architecture defines an artificial neural network for segmenting sensor data, in particular video data, data for optical distance or speed measurement or radar data, with an input variable for the artificial neural network being determined depending on the sensor data, with depending sensor data segmented by an output signal of the artificial neural network is determined (214). Method according to one of the Claims 6 to 8th , characterized in that in a first phase (202, 204, 206, 208, 210) an architecture for the artificial neural network is determined for which the measure falls below the threshold value, with training data being provided in a second phase (212) and this architecture is trained as a function of the training data, and in a third phase (214) the sensor data are processed with the artificial neural network trained in this way. Device (100) for optimizing an architecture of an artificial neural network, characterized in that the device (100) comprises a processor (102) and a memory (104) for the artificial neural network, which are designed according to one of the Claims 1 to 9 to execute. Computer program, characterized in that the computer program comprises computer-readable instructions, when they are executed on a computer, a method according to one of the Claims 1 to 9 expires. Computer program product, characterized by a machine-readable storage medium on which the computer program is based Claim 11 is stored.

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