DE102021208877A1 - Training of neural networks for equivariance or invariance against changes in the input image - Google Patents

Abstract

Method (100) for training a neural network (1) which is designed to process input images (2) and comprises a plurality of convolution layers, each of these convolution layers being designed to filter the input f of the respective convolution layer by applying at least one filter kernel κ onto at least one feature map Φ(f,κ), with the steps:• a set T of transformations T is provided (110) with respect to which the neural network (1) is to be enabled during training when these are applied Transformations to the input f of at least one convolution layer to learn how to generate at least one equivariant or invariant feature map Φ(f,κ);• this feature map Φ(f, κ) is parameterized by an aggregation (5) of feature maps Φj with parameters (5a). (f, Tj[κ]) expressed (120), each obtained by applying transformations Tj∈ T to the at least one filter kernel κ;• L ern images (2a) and learning outputs (3a) to which the trained neural network (1) should ideally map these learning images (2a), provided (130); • the learning images (2a) are provided by the neural network (1) on outputs (3) mapped (140);• Deviations of these outputs (3) from the learning outputs (3a) are evaluated with a predetermined cost function (4) (150);• Parameters (5a) of the parameterized Aggregation (5) and other parameters (1a), which characterize the behavior of the neural network (1), are optimized (160) with the aim that, with further processing of learning images (2a), the evaluation (4a) by the Cost function (4) expected to improve.

Description

The present invention relates to the training of neural networks that process images and map them, for example, to classification scores in relation to classes of a given classification.

State of the art

Many driver assistance systems and systems for at least partially automated driving process the measurement data recorded by sensors of a vehicle with classifiers to form classification scores in relation to one or more classes of a specified classification. On the basis of these classification scores, for example, decisions are then made about interventions in the driving dynamics of the vehicle.

The training of such classifiers requires training data with a high degree of variability, so that the classifier can generalize well to measurement data previously unseen in the training. The recording of training data on test drives with the vehicle and especially the largely manual labeling of this training data with target classification scores are time-consuming and expensive.

Therefore, the training data is often enriched with synthetically generated training data. So reveals about the DE 10 2018 204 494 B3 a method with which radar signals can be generated synthetically in order to enrich physically recorded radar signals for training a classifier.

Disclosure of Invention

A method for training a neural network was developed as part of the invention. This neural network is designed to process input images and includes multiple layers of convolution. Here, each convolution layer is designed to map its respective input f to at least one feature map Φ(f,κ) by applying at least one filter kernel κ. Typically, this feature map Φ(f,κ) has a significantly reduced dimensionality compared to the input f.

For example, an image classifier that maps input images to classification scores related to one or more classes of a given classification can be chosen as the neural network. In particular, the feature maps supplied by the last convolutional layer in a sequence of convolutional layers can be evaluated with regard to the classification scores.

As part of the method, a set T of transformations T is provided, with respect to which the neural network is to be enabled during training, when these transformations are applied to the input f of at least one convolutional layer, the generation of at least one equivariant or invariant feature map Φ(f, k) to learn. This does not mean that the feature map Φ(f,κ) is always equivariant or invariant to all transformations T from the set T. Rather, the aim is to make the feature map Φ(f,κ) equivariant or invariant to transformations to the extent that such transformations occur in the learning images used during training.

For this purpose, the feature map Φ(f,κ) to be made equivariant or invariant is expressed by an aggregation of feature maps Φ _j (f,T _j [κ]) parameterized with parameters, which are each obtained by applying transformations T _j ∈ T can be obtained on the at least one filter kernel κ. These parameters are used as additional degrees of freedom when training the neural network.

Learning images and learning outputs, onto which the trained neural network should ideally map these learning images, are provided for the monitored training. The learning images are mapped onto outputs by the neural network, and deviations of these outputs from the learning outputs are evaluated using a predetermined cost function.

Parameters of the parameterized aggregation and other parameters that characterize the behavior of the neural network are now optimized with the aim that the evaluation by the cost function will probably improve with further processing of learning images. These further parameters can in particular be weights, for example, with which inputs that are fed to neurons or other processing units of the neural network are weighted and summed to result in an activation of this neuron or this processing unit.

The term "probably" in this context is to be understood in such a way that iterative numerical optimization algorithms select the new values of the parameters for the next iteration on the basis of the history of iterations in the expectation that this will improve the evaluation by the cost function. However, this expectation does not have to be fulfilled for every iteration, ie an iteration can also turn out to be a "step backwards". However, the optimization algorithm can also use this type of feedback to ultimately arrive at values of the parameters for which the evaluation by the cost function improves.

By using the parameters of the parameterized aggregation as additional degrees of freedom for training, the neural network learns to make feature maps equivariant or invariant to transformations of the input to exactly the extent that the neural network's performance with respect to the particular concrete application actually does is beneficial. This is somewhat analogous to the fitting process for glasses at an optician. The transformations T here correspond to the various corrective lenses for short-sightedness, long-sightedness, astigmatism and other imaging errors of the eye. Precisely those corrections are applied that allow the customer to best recognize the numbers and letters presented for testing.

The useful effect of the trained equivariances and invariances during training is, in particular, that the neural network recognizes as the same objects and facts in different input images that differ only by an application of the said transformations and are otherwise the same in content. The realization that, for example, a vehicle that has been rotated, scaled, or viewed from a different perspective is still a vehicle, therefore no longer has to be implicitly conveyed to the neural network by presenting it with a large number of such modified learning images and all of these learning images be labeled with the same learning output.

Accordingly, the variability of the learning images used can concentrate on those properties that are to be examined with the neural network. A certain quantitative measure of performance in relation to the task of the neural network, for example in the case of an image classifier measured by the classification accuracy on a set of test or validation data, can then be achieved overall with a smaller amount of training images. Learning images of traffic situations labeled with learning outputs are particularly expensive to obtain, since long test drives are required and the labeling requires manual work.

In this case, only approximate knowledge of those transformations, with respect to which learning an equivariance or invariance could be advantageous, is sufficient in order to be able to benefit from this in relation to the task assigned to the neural network. In this respect, the analogy to the optician also applies here, who initially only knows what type of aberrations can actually be and only finds out the type and strength of aberrations in a specific eye through the iterative adjustment process.

In a particularly advantageous embodiment, the filter kernel κ is expressed as a linear combination Σ _i w _i ψ _i of basis functions ψ _i parameterized with parameters w _i . The effect of the transformations T on the basis functions ψ _i can then be calculated in advance and used again and again. During training, only the parameters w _i are varied to fit the linear combination. Thus, each adjustment of the linear combination in the course of a training step entails a lower computational effort.

Applying a transformation T to the input f of the convolutional layer makes the feature map Φ(f,κ) a feature map Φ(T[f],κ). If K is a matrix representation of the filter kernel κ and f is a matrix representation of the input f, then Φ(f,κ) = K × f. Applying the transform T with the matrix representation T here causes T to be multiplied by f before the Filter core κ is applied. According to the associative law for multiplication: $$\mathrm{\Phi }\left(\text{T}\text{'}\left[ƒ\right],k\right)=\text{K}\times \left(\text{T}\times \text{f}\right)=\left(\text{K}\times \text{T}\right)\times \text{f}=\mathrm{\Phi }\left(ƒ,\text{T}\left[k\right]\right)$$

So transforming the input f is equivalent to transforming the filter kernel κ. The notations T'[f] on the one hand and T[κ] on the other hand express that the multiplication with the matrix T is not commutative. That is, multiplying by T from the left does not produce the same result as multiplying by T from the right.

da die Zusammensetzung κ = Σ_i w_iψ_i = w · ψ aus den Basisfunktionen sich unter der Transformation T_j nicht ändert.The feature map Φ _j (f,T _j [κ]) obtained by applying the transformation T _j to a filter kernel κ can be written as: $${\mathrm{\Phi }}_j\left(ƒ,T_j\left[k\right]\right)={\Phi }_j\left(ƒ,T_j\left[{\displaystyle \sum _i{w}_i{\psi }_i}\right]\right)={\Phi }_j\left(ƒ,{\displaystyle \sum _i{w}_i{T}_j\left[{\psi }_i\right]}\right)={\Phi }_j\left(ƒ,w\cdot T_j\left[\psi \right]\right),$$

since the composition κ = Σ _i w _i ψ _i = w · ψ from the basis functions does not change under the transformation T _j .

The feature maps can then be weighted among one another in the aggregation, for example with weights β _j (f) dependent on the input f. A feature map Φ(f, T[κ]), which is obtained by applying one or more transformations T _j ∈ T, can then be written as: $$\mathrm{\Phi }\left(ƒ,T\left[k\right]\right)=\sigma \left(\begin{array}{c}{\beta }_0\left(ƒ\right)\Phi \left(ƒ,w\cdot T_0\left[\psi \right]\right)\\ {\beta }_1\left(ƒ\right)\Phi \left(ƒ,w\cdot T_1\left[\psi \right]\right)\\ \cdots \\ {\beta }_k\left(ƒ\right)\Phi \left(ƒ,w\cdot T_k\left[\psi \right]\right)\end{array}\right)$$

Here σ is any aggregation function, and the T _j are the transformations from the set T. This set T can in particular also contain the identity as a transformation, for example. The training can then be initialized, for example, such that initially only the weight β _j (f) for the identity is equal to 1 and the weights β _j (f) for all other transformations T _j are equal to 0.

mit einer Normierungskonstanten A und dem Skalierungsfaktor π. Mit derartigen Basisfunktionen können insbesondere solche Filterkerne κ konstruiert werden, die für die Erkennung von Merkmalen in Bildern besonders geeignet sind.In particular, functions can be selected as basis functions ψ for the filter cores κ, which depend at least via Hermitian polynomials H _m , H _n on spatial coordinates x, y in the input f: $${\psi }_{\pi }\left(x,y\right)=A\cdot \frac{1}{{\pi }^2}\cdot H_n\left(\frac{x}{\pi }\right)\cdot Hm\left(\frac{y}{\pi }\right)\cdot \text{ex}\left(-\frac{x^2+y^2}{2{\pi }^2}\right)$$

with a normalization constant A and the scaling factor π. Such basic functions can be used in particular to construct filter cores κ that are particularly suitable for recognizing features in images.

In a particularly advantageous embodiment, at least one feature map Φ(f,κ) is selected, which contains a sum of the input f and a processing product that results from the successive application of a plurality of filter cores κ ₁ , κ ₂ , . . . to the input f . In this way, the adjustments learned for the different convolutional layers in a stack in a so-called “residual block” can be coordinated with each other. A feature map Φ(f, T[κ ₁ , κ ₂ , ... ]) obtained by applying one or more transformations T _j ∈ T can then be written as: $$\mathrm{\Phi }\left(ƒ,T\left[{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="DE102021208877A1\_0010.png"\; state="\{\{state\}\}">k</figure-callout>}}_1,k_2,...\right]\right)=ƒ+\sigma \left(\begin{array}{c}{\beta }_0\left(ƒ\right)\Phi \left(ƒ,{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DE102021208877A1\_0010.png"\; state="\{\{state\}\}">w</figure-callout>}}_1\cdot T_0\left[{\psi }_1\right],w_2\cdot T_0\left[{\psi }_2\right],...\right)\\ {\beta }_1\left(ƒ\right)\Phi \left(ƒ,{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DE102021208877A1\_0010.png"\; state="\{\{state\}\}">w</figure-callout>}}_1\cdot T_1\left[{\psi }_1\right],w_2\cdot T_1\left[{\psi }_2\right],...\right)\\ \cdots \\ {\beta }_k\left(ƒ\right)\Phi \left(ƒ,{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="DE102021208877A1\_0010.png"\; state="\{\{state\}\}">w</figure-callout>}}_1\cdot T_k\left[{\psi }_1\right],w_2\cdot T_k\left[{\psi }_2\right],...\right)\end{array}\right).$$

Here ψ ₁ , ψ ₂ , ... are the basis functions from which the filter kernels κ ₁ , κ ₂ , ... are formed.

The transformations can in particular be elastic transformations, for example. These are transformations that can be described at least approximately as a field of displacements τ in spatial coordinates x of the input image f with a strength ε: $$T\left[ƒ\left(x\right)\right]\left(e\right)\approx \left(x+e\tau \left(x\right)\right).$$

This can be used to approximate a large class of transformations that result when, for example, a camera used to take an image changes its perspective relative to the scenery.

The elastic transformations can in particular include, for example, linear stretching and/or rotational scaling. These are transformations that are caused, for example, by changing the perspective of a camera relative to an object.

aus den ursprünglichen Koordinaten x, y hervorgehen. Hierin ist γ = 1/(e^-6 + cos(α)), δ = θ - ϕ, ϕ = arctan(y/x), θ ist eine kleine Auslegung, und α ist ein Elastizitätskoeffizient. Hierin soll die sehr kleine positive, willkürlich gewählte Konstante e^-6 eine Division durch Null verhindern, wenn cos(α) = 0.Coordinates x', y' in the input image after a linear stretching can, for example, according to $$\begin{array}{c}x\text{'}=\sqrt{x^2+y^2}\cdot \left(\text{sin}\left(\theta \right)\text{sin}\left(\delta \right)+g\text{cos}\left(\theta \right)\text{cos}\left(\delta \right)\right),\\ y\text{'}=\sqrt{x^2+y^2}\cdot \left(-\text{cos}\left(\theta \right)\text{sin}\left(\delta \right)+g\text{sin}\left(\theta \right)\text{cos}\left(\delta \right)\right)\end{array}$$

from the original coordinates x, y. Here γ = 1/(e ^-6 + cos(α)), δ = θ - φ, φ = arctan(y/x), θ is a small design, and α is a coefficient of elasticity. Here the very small positive, arbitrarily chosen constant e ^-6 is intended to prevent division by zero when cos(α) = 0.

aus den ursprünglichen Koordinaten x, y hervorgehen.Coordinates x', y' in the input image after rotational scaling can be, for example, according to $$\begin{array}{c}x\text{'}=x+a\left(x\text{cos}\left(\theta \right)+y\text{sin}\left(\theta \right)\right),\\ y\text{'}=y+a\left(-x\text{sin}\left(\theta \right)+y\text{cos}\left(\theta \right)\right)\end{array}$$

from the original coordinates x, y.

In these transformations it is assumed that the center of the filter kernel κ is at the point (0, 0) and is a fixed point of the transformation.

• • ein elementweises Maximum,
• • ein geglättetes elementweises Maximum oder
• • ein elementweiser Mittelwert

entlang der Dimension j der Transformationen T_j ∈ T bilden.The aggregation function σ for the aggregation of the feature maps Φ _j (f,T _j [K]) can in particular, for example, for each element of the feature maps

• • an elementwise maximum,
• • a smoothed elementwise maximum or
• • an element-wise average

along dimension j of the transformations T _j ∈ T.

For example, if an input image f has height H, width W, and number C of color channels, it can exist as a tensor of the form C×H×W. The K transformations T from the set T add another dimension. The aggregation function σ can now, for example, map from a space of the dimension K×C×H×W back into the space of the dimension C×H×W and, in particular, select the transformation T _j that best matches the available training data. This can be measured, for example, by the level of activation of neurons that are responsible for certain transformations.

ermittelt werden.An element-by-element maximum or an element-by-element mean is understood in this context, for example, as meaning that a maximum or a mean is formed separately for each entry in the dimensions C×H×W along the dimension K of the transformations. For example, a smoothed maximum can be obtained using the Logsumexp function $$\sigma \left(x\right)=\text{log}{\displaystyle \sum _i\text{ex}}\left(x_i\right)$$

be determined.

In a further advantageous embodiment, the aggregation of feature maps Φ _j (f,T _j [κ]) includes forming a norm over one or more spatial dimensions of each feature map and selecting one or more feature maps based on this norm. For example, l _p -norms can be formed along the dimensions C, H×W, or C×H×W. It can then be determined along the K-dimension for which transformations the largest norms result. A feature map and thus also a transformation can be selected that best fits the existing data.

As previously discussed, training involving invariances and equivariances enables the neural network to do its usual job better. In the case of an image classifier, for example, this is reflected in a higher classification accuracy on test images or validation images.

Therefore, in a further advantageous embodiment, the trained neural network is supplied with input images that were recorded with at least one sensor, so that these input images are mapped onto outputs by the neural network. A control signal is determined from the outputs. A vehicle and/or a system for product quality control and/or a system for monitoring areas is controlled with this control signal.

Due to the correct output of the neural network, the probability that the action carried out by the respectively controlled system is appropriate to the situation detected by the sensor is then advantageously increased.

In particular, the method can be fully or partially computer-implemented. The invention therefore also relates to a computer program with machine-readable instructions which, when executed on one or more computers, cause the computer or computers to carry out the method described. In this sense, control devices for vehicles and embedded systems for technical devices that are also able to execute machine-readable instructions are also to be regarded as computers.

The invention also relates to a machine-readable data carrier and/or a download product with the computer program. A downloadable product is a digital product that can be transmitted over a data network, i.e. can be downloaded by a user of the data network and that can be offered for sale in an online shop for immediate download, for example.

Furthermore, a computer can be equipped with the computer program, with the machine-readable data carrier or with the downloadable product.

Further measures improving the invention are presented in more detail below together with the description of the preferred exemplary embodiments of the invention with the aid of figures.

exemplary embodiments

• 1 Ausführungsbeispiel des Verfahrens 100 zum Trainieren eines neuronalen Netzwerks 1;
• 2 Beispielhafte Wirkung des Trainings mit dem Verfahren 100 auf die Klassifikationsgenauigkeit eines Bildklassifikators.

It shows:

• 1 Embodiment of the method 100 for training a neural network 1;
• 2 Exemplary effect of training with the method 100 on the classification accuracy of an image classifier.

1 1 is a schematic flowchart of an exemplary embodiment of the method 100 for training a neural network 1. In particular, an image classifier can be selected as the neural network 1 in step 105, for example. The neural network 1 is designed to process input images 2 and comprises a number of convolution layers. Each of these convolutional layers is designed to map the input f of the respective convolutional layer to at least one feature map Φ(f,κ) by applying at least one filter kernel κ.

In step 110, a set T of transformations T is provided. As part of the training described here, the neural network 1 can learn how to generate at least one equivariant or invariant feature map Φ(f,κ) when applying one or more of these transformations T to the input f of at least one convolutional layer of the network 1 .

According to block 111, elastic transformations, for example, which can be described as a field of deflections in spatial coordinates of the input image, can be selected as transformations T∈T. In particular, these elastic transformations can include linear stretching and/or rotational scaling according to block 111a, for example.

In step 120, this feature map Φ(f,κ) is expressed 120 by an aggregation 5 of feature maps Φ _j (f,T _j [κ]) parameterized with parameters 5a, each obtained by applying Transformatio NEN T _j ∈ T on the at least one filter core κ can be obtained. That is, the output of the corresponding convolutional layer changes depending on the parameters 5a.

According to block 121, the filter kernel κ can be expressed as a linear combination Σ _i w _i ψ _i of basis functions ψ _i parameterized with parameters w _i . In this case, for example, according to block 121a, basic functions ψ _i can be selected, which depend at least on Hermitian polynomials on location coordinates x, y in the input f.

According to block 122, the feature maps Φ _j (f,T _j [κ]) in the aggregation 5 can be weighted among one another with weights β _j (f) dependent on the input f.

According to block 123, at least one feature map Φ(f, κ) can be selected for the parameterization with the parameters 5a, which is a sum of the input f and a processing product, which is obtained by successive application of several filter cores κ ₁ , κ ₂ , . . the input f arises. Such a feature map is the work result of a "residual block".

• • ein elementweises Maximum,
• • ein geglättetes elementweises Maximum oder
• • ein elementweiser Mittelwert

entlang der Dimension j der Transformationen T_j ∈ T zu bilden.Aggregating the feature maps may include Φ _j (f,T _j [κ]) according to block 124, for each element of these feature maps

• • an elementwise maximum,
• • a smoothed elementwise maximum or
• • an element-wise average

along the dimension j of the transformations T _j ∈ T.

Alternatively or in combination with this, the aggregation of the feature maps Φ _j (f,T _j [κ]) according to block 125 can include forming a norm over one or more spatial dimensions of each feature map and selecting one or more feature maps based on this norm.

In step 130, learning images 2a and learning outputs 3a, onto which the trained neural network 1 should ideally map these learning images 2a, are provided.

In step 140, the learning images 2a are mapped by the neural network 1 to outputs 3.

Deviations of these outputs 3 from the learning outputs 3a are evaluated in step 150 using a predetermined cost function 4 .

In step 160, parameters 5a of the parameterized aggregation 5 and other parameters 1a, which characterize the behavior of the neural network 1, are optimized with the aim that the evaluation 4a by the cost function 4 is expected to improve with further processing of learning images 2a. The completely trained states of the parameters 1a and 5a are denoted by the reference symbols 1a* and 5a*, respectively. The completely trained neural network 1, whose behavior is characterized by the parameters 1a* and 5a*, is denoted by the reference symbol 1*.

In step 170, input images 2 that were recorded with at least one sensor 51 are supplied to the trained neural network 1*. These input images 2 are mapped onto outputs 3 by the neural network 1 .

In step 180, a control signal 180a is determined from the outputs 3.

In step 190, a vehicle 50 and/or a system 60 for product quality control and/or a system 70 for monitoring areas is controlled with this control signal 180a.

In 2 For a neural network 1 of the WideResnet-18 architecture designed as an image classifier, the loss ΔA in classification accuracy is plotted, which occurs when the input images are noisy with a strength P. The curves a to e relate to states of the neural network 1 after different training sessions. The experiment was fed with the publicly accessible data set STL-10, which contains 5000 training images and 8000 test images with a size of 96x96 pixels from 10 different classes.

Curve a refers to conventional training. The curves b to e relate to different examples of training according to the method 100 described here. The loss of accuracy caused by the noisy input images can be at least partially compensated again by the improved training. For some configurations, even with noise-free input images, there is already a gain (curve above curve a).

QUOTES INCLUDED IN DESCRIPTION

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Patent Literature Cited

• DE 102018204494 B3 [0004]

Claims (14)

Method (100) for training a neural network (1) which is designed to process input images (2) and comprises a plurality of convolution layers, each of these convolution layers being designed to filter the input f of the respective convolution layer by applying at least one filter kernel κ onto at least one feature map Φ(f,κ), with the steps: • a set T of transformations T is provided (110) with respect to which the neural network (1) is to be enabled during training when these are applied transformations on the input f of at least one convolutional layer to learn the generation of at least one equivariant or invariant feature map Φ(f,κ); • this feature map Φ(f, κ) is expressed (120) by an aggregation (5) parameterized with parameters (5a) of feature maps Φ _j (f, T _j [κ]), each obtained by applying transformations T _j ∈ T can be obtained on the at least one filter kernel κ; • learning images (2a) and learning outputs (3a) onto which the trained neural network (1) should ideally map these learning images (2a) are provided (130); • the learning images (2a) are mapped (140) by the neural network (1) to outputs (3); • Deviations of these outputs (3) from the learning outputs (3a) are evaluated (150) using a predetermined cost function (4); • Parameters (5a) of the parameterized aggregation (5) and other parameters (1a) that characterize the behavior of the neural network (1) are optimized (160) with the aim that further processing of learning images (2a) the assessment (4a) by the cost function (4) is expected to improve. Method (100) according to claim 1 , where the filter kernel κ is expressed as a linear combination Σ _i w _i ψ _i of basis functions ψ _i parameterized with parameters w _i (121). Method (100) according to claim 2 , where basis functions ψ _i are chosen (121a) which depend at least on Hermitian polynomials on spatial coordinates x, y in the input f. Method (100) according to any one of Claims 1 until 3 , wherein the feature maps Φ _j (f, T _j [κ]) in the aggregation (5) are weighted (122) with one another with weights β _j (f) dependent on the input f. Method (100) according to any one of Claims 1 until 4 , where elastic transformations, which can be described as a field of displacements in spatial coordinates of the input image, are chosen as transformations T ∈ T (111) . Method (100) according to claim 5 , where linear stretching and/or rotational scaling are chosen as transformations T ∈ T (111a). Method (100) according to any one of Claims 1 until 6 , wherein at least one feature map Φ(f, κ) is chosen (123) containing a sum of the input f and a processing product resulting from the successive application of a plurality of filter kernels κ ₁ , κ ₂ , ... to the input f . Method (100) according to any one of Claims 1 until 7 , where the feature maps Φ _j (f,T _j [κ]) are aggregated by forming for each element of the feature map • an element-by-element maximum, • a smoothed element-by-element maximum or • an element-by-element mean value along the dimension j of the transformations T _j ∈ T becomes (124). Method (100) according to any one of Claims 1 until 7 , wherein aggregating feature maps Φ _j (f,T _j [κ]) includes forming a norm about one or more spatial dimensions of each feature map and selecting one or more feature maps based on that norm (125). Method (100) according to any one of Claims 1 until 9 wherein an image classifier that maps input images to classification scores related to one or more classes of a given classification is selected (105) as the neural network (1). Method (100) according to any one of Claims 1 until 10 , where • the trained neural network (1*) is supplied with input images (2) (170) which were recorded with at least one sensor (51), so that these input images (2) are received by the neural network (1) mapped to outputs (3); • a control signal (180a) is determined from the outputs (3) (180); and • a vehicle (50), and/or a system (60) for product quality control, and/or a system (70) for monitoring areas, is controlled (190) with this control signal (180a). Computer program containing machine-readable instructions which, when executed on one or more computers, cause the computer or computers to carry out a method according to one of Claims 1 until 11 to execute. Machine-readable data carrier with the computer program claim 12 . One or more computers with the computer program after claim 12 , and/or with the machine-readable data carrier Claim 13 .

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