Training of a function that responds predictably to differences

Abstract

To provide a computer mounting method for training a function capable of machine learning and a corresponding system, and a computer readable medium including an instruction and / or a function parameter.SOLUTION: A system 100 for training a function capable of machine learning includes a data interface 120 and a processor sub-system 140. The data interface 120 accesses a training data set 030 of a data storage 021 including a plurality of training input observations. The data interface 120 accesses a set of parameters 040 having a function capable of machine learning to be trained. At a learned point in time, the parameter 040 is used to apply the function capable of machine learning to the observations. The processor sub-system 140 learns the set of the parameters having the function capable of machine learning by optimizing an object function during operation.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a computer-implemented method for training a machine-learnable function and a corresponding system. Further, the present invention relates to a computer-readable medium containing instructions and / or function parameters.

Background Art

[0002] Background of the Invention Machine-learnable functions have the potential to perform tasks much more accurately than manually designed algorithms. For example, machine-learnable functions have been shown to achieve a high level of accuracy for various image classification tasks, such as digit recognition, discrimination between cats and dogs, etc., based on, for example, convolutional neural networks or similar technologies. Typically, such machine-learnable functions are trained based on a training dataset that includes, for example, labeled images according to the desired classification. Generally, the more training examples there are, the higher the accuracy of the results of the trained function.

[0003] In many practical situations, the feasibility of obtaining training data that guarantees a sufficiently broad input is a major obstacle, preventing the adoption of machine learning solutions in practice. For example, in the field of (semi-)autonomous vehicles, machine-learnable functions have the potential to perform various tasks required to control or monitor a vehicle, such as image analysis of camera images of the vehicle environment, in order to, for example, warn of dangerous traffic situations. However, obtaining training data for such tasks requires driving the vehicle around, which is costly and can even be dangerous. Further, the images of the vehicle environment can vary widely not only with respect to, for example, the general configuration of the scene (whether there are other vehicles ahead, whether there are pedestrians in the vicinity, etc.), but also with respect to many other aspects (for example, the section of the road on which the vehicle is traveling, the style of traffic signs that vary from country to country, the weather conditions, etc.).

[0004] Thus, it is almost impossible to obtain a training data set that guarantees all combinations of situations that a vehicle may face, especially in the case of boundary conditions. On the other hand, especially when used for making decisions in autonomous driving, especially in such cases of boundary conditions, it is essential for machine-learnable functions to reliably handle them. Therefore, it is desirable to use a function that has a high level of generalization ability and provides accurate results for inputs that are not directly guaranteed in the training data set, for example.

[0005] One machine learning technique known to contribute to generalization ability is, for example, the so-called group equivariant convolutional network, as described in “Group Equivariant Convolutional Networks” by T. Cohen et al. (incorporated herein by reference and available at https: / / arxiv.org / abs / 1602.07576). A group equivariant convolutional network is a deep neural network or function that processes by passing an input, in this case an image, through a plurality of respective parameterized layers. In a group equivariant convolutional network, the representations in each of these layers are modeled as a linear G-space. G is a given mathematical group representing a set of applicable transformations (i.e., a set using a binary operation that satisfies closure, associativity, identity element, and invertibility). Equivariance means that given a transformation T g of the layer input and a transformation

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[0006] Unfortunately, existing techniques for making functions equivariant have several drawbacks. A complex analytical formulation of the transformation group G is required, and furthermore, these transformations must be known in advance and hard-coded into the model architecture. Also, when the function is used, the transformation group is used, and the model architecture becomes dependent on the type of transformation used for training, which makes it incompatible with standard tools for applying machine learning techniques, such as convolutional neural networks with a standard configuration. Also, the transformation must conform to the group axioms of the transformation group G. Therefore, only a limited set of (geometric-type) transformations can be specified.

Prior Art Documents

Non-Patent Documents

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] Summary of the Invention It is desirable to train machine-learnable functions, such as image classifiers or image feature extractors, so that generalizability is improved without the need to incorporate transformations into the model architecture. In particular, it is desirable to reward the predictability of the amount of change in input observations that do not operate according to a mathematical group structure. Also, it is desirable that the generalizability of machine-learnable functions is improved without affecting the model architecture, such that the trained function becomes, for example, a standard convolutional neural network.

Means for Solving the Problems

[0009] According to one aspect of the present invention, there is provided a computer-implemented method and a corresponding system for training a machine-learnable function as defined in claims 1 and 14 respectively. According to one aspect of the present invention, a computer-readable medium is described as defined in claim 15.

[0010] Various aspects relate to the training of a machine-learnable function by optimizing an objective function (in other words, the learning of a set of parameters that parameterize the machine-learnable function). Many types of machine-learnable functions and objective functions suitable for training these machine-learnable functions are known. For example, the learning task may be considered as classification or regression. The training may be supervised, for example, based on a labeled dataset of training input observations and corresponding training outputs, and the objective function may be configured to minimize the difference between the functional output of the machine-learnable function and the corresponding training output. The training may also be unsupervised, for example, of a feature extractor (feature extraction is also known as representation learning). In any case, a convolutional objective function may be used.

[0011] Interestingly, in order to improve generalizability, a machine-learnable function that predictably responds to a set of differences between input observations in a layer of machine-learnable functions may be rewarded. This is similar to a group-equivariant convolutional neural network that, by applying a given G-action to input observations, effects the application of the corresponding G-action to the output of the layer. However, interestingly, the inventors considered rewarding predictability not by hard-coding a particular set of transformations into the model architecture, but by including a regularization objective in the objective function used to train the machine-learnable function. For example, a regularization objective that reduces the level of predictability may be included in the loss function to be minimized, or a regularization objective that increases predictability may be included in the objective function to be maximized.

[0012] In particular, the objective function may be based on pairs of a first input observation and a second input observation, and a difference label indicating the difference between these first and second observations. For example, the first and second observations may be, as a whole, images of corresponding scenes, for example both may be in an environment of vehicles stopped at a traffic signal. The difference label may select a specific difference between the first and second observations from viewpoints such as, for example, weather conditions, the type of vehicle in front of the vehicle, the country where the image was acquired (and thus the types of traffic signals and / or traffic signs present). Apart from the difference indicated by the difference label, the pairs of observations are preferably selected such that the pairs of observations correspond to each other as much as possible.

[0013] In particular, the difference label may represent a transformation according to the extent to which the second observation can be (at least approximately) obtained from the first observation. Thus, typically, exchanging the first and second observations results in another difference label. However, interestingly, the set of differences for which the difference label is selected need not have any particular mathematical structure, and in particular need not be a group in the mathematical sense.

[0014] To evaluate a regularization objective that promotes predictability in a particular layer, a machine-learnable function can be applied to the first and second observations to obtain respective representations in that layer. Next, the regularization objective can reward predictability by promoting the mutual statistical dependence between these representations given the difference label. In other words, given the difference label, the amount of information that one representation provides about the other representation may be maximized by the objective function. Such mutual statistical dependence can be calculated, for example, from the perspective of conditional mutual information or interaction information, as will be considered in more detail below.

[0015] By promoting the mutual statistical dependence of representations given a differential label, a regularizer is obtained that improves the generalization ability and robustness of the trained function. That is, a function that learns how the difference between a pair of input observations affects the function output is effectively rewarded. Therefore, if the same difference is applied to unobserved observations, the function can better cope with this difference.

[0016] This is similar, from the perspective of the achieved results, to the improved generalization ability provided by group-equivariant convolutional networks, and the inventors were indeed able to show that, from the perspective of conditional mutual information, group-equivariant convolutional networks provide an optimal solution for regularization purposes. However, interestingly, the provided technique offers much more flexibility than group-equivariant convolutional networks and brings several practical advantages.

[0017] By using differences based on mutual statistical dependence, a measure applicable to a wide set of differences is obtained, and for example, it is not necessary to assume a specific mathematical group structure. This makes it possible to capture various types of differences that occur in practical situations, such as differences in weather conditions in the country where the observation was made. It is also not necessary to clearly define how the difference transforms one input into another. It is sufficient to have pairs of input observations and the accompanying differential labels, and even the differential labels can be learned from the data. Also, the pairs do not have to be completely different, but only follow the type of difference. For example, (although the training will be more effective if there is a closer correspondence) other differences between the observations may be considered. For the representation to which the regularization objective is applied, no transformation is given as input, and thus the function itself can learn the optimal way to represent the input.

[0018] Furthermore, by being included in the objective function, it becomes possible to balance the predictability with other training objectives. Substantially, the mutual statistical dependencies may be regarded as a continuum between unpredictability and predictability. Since the regularization term is typically weighted compared to the other terms of the objective function, the function itself is not forced to strictly enforce equivariance in any case and can reach an amount of statistical dependence suitable for the current learning task. This also improves the applicability of this function to situations where the performance deteriorates by enforcing equivariance too strictly.

[0019] (For example, rather than the model architecture) Another advantage of promoting predictability by adapting the objective function is that a trained function can be obtained that is independent of the type of differences considered during training. For example, the hardware / software used to apply the trained function does not depend on or need to support the various types of transformations that provide such differences. Thus, the compatibility with convolutional software / hardware for applying machine learning functions, such as convolutional neural network evaluation software / hardware, is improved.

[0020] Regarding the layer to which the regularization objective is applied, several options can be considered. Regardless of the type of machine-learnable function, this objective may be applied to the output layer. This also applies to, for example, non-neural networks when the machine-learnable function does not follow a layer structure. The output layer is a particularly good option when the machine-learnable function is a feature extractor, such as an image feature extractor. This is because the predictability provided by the regularization objective in this case can be fully utilized by other components that use the predictability. Instead of or in addition to this, for machine-learnable functions with internal layers such as neural networks and deep Gaussian processes, it is possible to apply the regularization objective to the internal layers of the function or apply each regularization objective to a plurality of respective internal layers. The beneficial option of regularizing machine-learnable functions and / or layers is considered throughout.

[0021] Optionally, the machine-learnable function may be an image classifier or an image feature extractor. Such an image processing model must particularly address the problem of input variation and thus obtains a particular benefit from having improved generalizability. In general, an image classifier may map an input image to one or more classification outputs. For example, the image classifier may be a detection model, e.g., a function that provides a classification output indicating whether an object is present in the entire image or within a segment of the image. The image classifier may be a semantic segmentation model, e.g., a function that provides a plurality of classification outputs indicating the presence of objects within each pixel or segment of the image. The image feature extractor may, for example, map an input image to a vector of image features for use in classification or other downstream applications. Using the training techniques to be described, a more effective and robust image processing model can be obtained.

[0022] Optionally, the machine-learnable function may be an image feature extractor used in a comprehensive image classifier. In this case, image features can be trained based on an unlabeled training dataset (i.e., the training does not use any available classification labels), and then, it is possible to train the comprehensive image classifier based on a labeled training dataset. The labeled dataset may be, for example, a subset of the unlabeled training dataset for which labels are available or may be a separate dataset. Typically, unlabeled data is much easier to obtain than labeled data. By separating the training of the feature extractor from the training of the classifier, the feature extractor can be trained using data without labels. When training the feature extractor separately, it is particularly important to learn generalizable features, and thus, the provided regularization objectives are advantageous. The regularization objectives are typically applied to the output layer of the feature extractor in this example. When training the classifier, the feature extractor may also be fine-tuned (which may or may not include the use of regularization objectives), but this is not essential.

[0023] Optionally, the objective function may include multiple respective regularization objectives for multiple respective layers of the machine-learnable function. Different layers of a function, such as a neural network, tend to represent input observations at different levels of abstraction. Thus, by applying regularization objectives to some layers, rewards can be given to the generalizability at the levels of abstraction of some layers. For example, during training in each layer, the regularization objective may be included in the objective function or removed from the objective function to determine whether it has an advantageous effect in that layer.

[0024] Optionally, the first input observation and the second input observation are images representing scenes of the same kind, for example, scenes including similar objects or similar arrangements of a plurality of objects. As an example, both images may represent, for example, a vehicle environment used in a visual model of a (semi-)autonomous vehicle. For example, both paired images may represent scenes such as a vehicle running on a highway, a vehicle stopped at a traffic signal, or a pedestrian unexpectedly crossing a road. However, other application fields where robustness against conversion is required are also conceivable.

[0025] In such a case, the difference label may indicate the difference in the characteristics of the objects in the scene or the scene itself (for example, the brand of the car, the type of the car, whether the car should drive on the left or on the right, or the country where the image was taken. These may be regarded as proxies for the characteristics of some scenes). The difference label may also indicate the difference in the observation conditions of the scene, for example, differences such as weather conditions, the occlusion level of the objects captured by the image, the position or orientation of the objects in the image. By including regularization purposes for such semantically important differences, rewards are given to the function so that these differences and the effects of the differences on the functional output can be logically considered, resulting in a function that generalizes better for these differences.

[0026] Optionally, the machine-learnable function may be a convolutional network. The convolutional network, also known as a convolutional neural network (CNN), has been found to be effective in various learning tasks, particularly in image analysis. Each layer of the convolutional neural network typically represents the input observation at each level of abstraction. By selecting the internal layers of the CNN, various types of differences between the input observations can be appropriately considered for regularization purposes. [[ID=,10]]

[0027] Optionally, the evaluation for regularization purposes may include estimating the mutual information between the first representation and the second representation given the differential label. This so-called conditional mutual information is suitable for determining the mutual statistical dependence between the representations of the input observations and provides a method motivated by information theory. However, other mutual information quantities regarding these three variables may also be estimated, for example, the mutual information between the first representation and the differential label given the second representation, or the mutual information between the second representation and the differential label given the first representation. For example, the regularization purpose may include the interaction information quantity, which will also be described below, based on these mutual information quantities. Instead of using a measure based on mutual information, other measures of mutual statistical dependence may also be considered, for example, the conditional entropy of the second observation given the first representation and the differential label, i.e., the amount of change in information.

[0028] (Conditional) mutual information is particularly advantageous to use for one reason that it can be efficiently estimated according to a trainable mutual information estimation model. Although it is also possible to directly calculate or estimate the (conditional) mutual information or related physical quantities, such as conditional entropy, using a trainable estimation model can greatly improve performance. Interestingly, for example, by including the learning objective of the mutual information estimation model in the objective function, a known mutual information estimation model can be trained simultaneously with a machine-learnable function. In this way, the function for estimating mutual information does not need to be learned from scratch every time the machine-learnable function is changed and can be gradually updated as the training of the machine-learnable function progresses.

[0029] Optionally, the regularization objective can be further configured to suppress the interdependence between the first representation and the second representation, e.g., the interdependence measured by the mutual information between the first representation and the second representation (without conditioning on the differential label), without conditioning on the differential label. In this way, the function can be suppressed to provide similar representations for both input observations. In other words, the function can be suppressed in terms of determining a representation that is not only equivariant but also invariant. Such an invariant representation may be a local optimum of the regularization objective. However, invariance may not be favorable for the generalization ability of the function. This is because invariance effectively rewards the function without learning how to respond non-trivially to labeled differences, discarding information about the labeled differences. This is because in the function of the network structure, the transformation information propagates deeper within the network and is structured in an orderly manner, and an invariant network may discard the transformation information. Therefore, it may be appropriate to achieve better generalization ability by penalizing invariance in this way, especially when there is little training data in the case of boundary conditions.

[0030] In particular, the regularization objective may include the difference between the mutual information conditioned on the differential label and the mutual information not conditioned on the differential label. This difference is also known as the interaction information amount between the first representation, the second representation, and the differential label. Note that the interaction information amount can be calculated without explicitly calculating the above mutual information amount. However, no matter how the interaction information amount is calculated, it is usually understood that both methods reward the mutual statistical dependence between the first representation and the second representation with the differential label given, and suppress the interdependence between the representations without conditioning on the differential label.

[0031] Several options exist for obtaining pairs of input observations and corresponding difference labels. Typically, the first input observation results from a training dataset. Optionally, the second input observation may be generated from the first input observation and the difference label, given the difference label. For example, a transformation according to the difference label may be applied, for example, an object in an image may be partially occluded, and differences in weather conditions may be simulated, for example, by adding snow or rain. It is also possible to determine the difference label given pairs of observations using a machine-learnable labeling function. For example, a labeling function that labels other pairs using the labels of some pairs of observations can be trained, thereby reducing the labeling effort required. Alternatively, the labeling function may be trained without a teacher, so that no labels may be specified manually at all.

[0032] The techniques described herein can be applied to various types of input observations. This includes various types of sensor data, including not only images but also radar data, ultrasonic data, LiDAR data, motion data, etc. For example, in the context of a computer control system, the sensor data may serve to provide observations of the computer control system and / or its environment. In such cases, the computer control system may be monitored and / or controlled based on the output of a machine-learnable function. Examples of computer control systems include robots, (semi- or fully) autonomous vehicles, household appliances, power tools, manufacturing machines, personal assistants, and access control systems. Systems that can be monitored include, for example, surveillance systems and medical (imaging) systems.

[0033] Those skilled in the art will understand that any two or more of the above-described embodiments, implementations, and / or any aspects of the present invention can be combined in any useful way.

[0034] Variations and modifications of any system and / or any computer-readable medium correspond to variations and modifications of the description of the corresponding computer-implemented method and are implementable by those skilled in the art based on this specification.

[0035] These and other aspects of the invention will become apparent and be better understood by referring to the embodiments described by way of example in the following description and the accompanying drawings.

Brief Description of the Drawings

[0036]

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[0037] Note that these drawings are for illustrative purposes only and are not drawn to scale. In the drawings, elements corresponding to elements already described may sometimes be given the same reference numerals.

Modes for Carrying Out the Invention

[0038] Detailed Description of Embodiments FIG. 1 shows a system 100 for training a machine-learnable function. The machine-learnable function may map an input observation to a function output. The machine-learnable function may include one or more internal layers and / or one output layer. This function is trained for use by a system that applies the machine-learnable function, such as system 200 of FIG. 2, and may in particular enable monitoring and / or control of a computer control system based on the output of the machine-learnable function.

[0039] System 100 may include a data interface 120. The data interface 120 may be for accessing a training data set 030 that includes a plurality of training input observations. Also, the data interface 120 may be for accessing a set of parameters 040 of a machine-learnable function to be trained. As discussed with reference to FIG. 2, at the time of learning, the parameters 040 can be used to apply the machine-learnable function to the observations. For example, as shown in FIG. 1, the data interface may be configured by a data storage interface 120 that can access data 030, 040 from a data storage 021 via a data communication 122. For example, the data storage interface 120 may be not only a memory interface or a persistent storage interface, such as a hard disk or SSD interface, but also a personal interface such as a Bluetooth interface, Zigbee interface or Wi-Fi interface, a local network interface or a wide area network interface, or an ethernet interface or an optical fiber interface. The data storage 021 may be not only an internal data storage of the system 100, such as a hard drive or SSD, but also an external data storage, such as a network-accessible data storage. In some embodiments, for example, via different subsystems of the data storage interface 120, the data 030, 040 can be respectively accessed from different data storages. Each subsystem may be of the types described above with respect to the data storage interface 120.

[0040] System 100 may further include a processor subsystem 140 configured to learn a set of parameters of a machine-learnable function by optimizing an objective function during operation of the system 100. The optimization may include rewarding a machine-learnable function that predictably responds to a set of differences between input observations in a layer of the machine-learnable function (e.g., an inner layer or an output layer). Here, the optimization can reward the predictability using a regularization objective included in the objective function.

[0041] To perform the optimization, the processor subsystem 140 can obtain a first input observation from a training data set, a corresponding second input observation, and a difference label of a set of differences indicating the difference between the first input observation and the second input observation. Further, the processor subsystem 140 can apply a machine-learnable function and determine a first representation of the first input observation and a second representation of the second input observation in a layer of the machine-learnable function, respectively. Further, the processor subsystem 140 can evaluate a regularization objective. The regularization objective may be configured to reward the mutual statistical dependence between the first representation and the second representation given the difference label between the first input observation and the second input observation. The system 100 can output a learned set of parameters via an output interface, such as by updating a set of parameters in the storage 021 via the data interface 120 and providing the set of parameters to a third party via a communication interface.

[0042] For example, FIG. 2 shows a system 200 that applies a machine-learnable function trained as described herein by the system 100 of FIG. 1 or the computer-implemented method 600 of FIG. 6. For example, the system 200 may be a vehicle control system, a robot control system, a manufacturing control system, or a building control system. Also, the system 200 can optionally perform training. For example, the system 200 can be combined with the system 100.

[0043] System 200 may include a data interface 220 that accesses a set of parameters 040 of a trained machine - learnable function. Similar considerations and configuration options apply to the data interface 120 of FIG. 1. Similar to the storage 021 and data communication 122 of FIG. 1, a data interface 220 that accesses parameters 040 from storage 022 via data communication 222 is shown in the figure.

[0044] During operation of system 200, system 200 may further include a processor subsystem 240 configured to apply a machine - learnable function parameterized by parameters 040 to the observation of the computer - control system and / or its environment. Based on the output of the machine - learnable function, the computer - control system may be monitored and / or controlled by conventional methods. Similar considerations and configuration options apply to the processor subsystem 140 of FIG. 1.

[0045] FIG. 2 further shows various optional components of system 200. For example, in some embodiments, system 200 may include a sensor interface 260 that directly accesses sensor data 224 that provides observation of the computer - control system and / or its environment. For example, sensor data 224 can be obtained by a sensor 072 within environment 082. The sensor may be disposed within environment 082, but may also be disposed remotely from environment 082, for example, if quantities can be measured remotely. However, sensor 072 may not be part of system 200 in some cases. Sensor 072 may have any suitable form, such as an image sensor, a LiDAR sensor, a radar sensor, a pressure sensor, a built - in temperature sensor, etc. Sensor interface 260 may have any suitable form corresponding to sensors of types including, but not limited to, low - level communication interfaces based on I2C data communication or SPI data communication, or data storage interfaces of the types described in relation to data interface 220.

[0046] In some embodiments, system 200 may include an actuator interface 280 that provides control data 226 to an actuator 092 within environment 082. The control data 226 can be generated by a processor subsystem 240 to control the actuator based on the output of a machine-learnable function. The actuator may or may not be part of system 200. For example, the actuator may be an electric actuator, a hydraulic actuator, a pneumatic actuator, a thermal actuator, a magnetic actuator, and / or a mechanical actuator. Specific but non-limiting examples include an electric motor, an electroactive polymer, a hydraulic cylinder, a piezoelectric actuator, a pneumatic actuator, a servo mechanism, a solenoid, a stepper motor, etc. This type of control will be described in relation to a (semi) autonomous vehicle with reference to FIG. 3.

[0047] In other embodiments (not shown in FIG. 2), system 200 includes an output interface connected to a rendering device such as a display, a light source, a loudspeaker, a vibration motor, etc. that can be used to generate a sensor-responsive output signal that can be generated based on the functional output. The sensor-responsive output signal can directly indicate the functional output, but can also represent a derived sensor-responsive output signal used, for example, in the guidance, navigation, or other types of control of a computer control system.

[0048] In general, each system including, but not limited to, the system 100 of FIG. 1 and the system 200 of FIG. 2 described herein may be embodied as a single device or apparatus such as a workstation or a server, or within a single device or apparatus. The device may be an embedded device. The device or apparatus may include one or more microprocessors that execute appropriate software. For example, the processor subsystem of each system may be embodied not only by a single central processing unit (CPU), but also by a combination or system of such a CPU and / or other types of processing devices. The software may be downloaded and / or stored in a corresponding memory, such as volatile memory like RAM or non-volatile memory like flash memory. Alternatively, the processor subsystem of each system may be implemented in the form of programmable logic within the device or apparatus, for example, as a field programmable gate array (FPGA). Generally, each functional device of each system can be implemented in the form of a circuit. Each system may be implemented in a distributed form involving different devices or apparatuses, such as a distributed local server or a cloud-based server. In some embodiments, the system 200 may be part of a vehicle, a robot, or a similar computer control system, and / or may represent a control system configured to control such a system.

[0049] FIG. 3 shows the above example. The system 200 is shown as a control system of a (semi)-autonomous vehicle 62 operating within an environment 50. The autonomous vehicle 62 may be autonomous in that it may include an autonomous driving system or a driving assistance system, the latter also being referred to as a semi-autonomous driving system. In this example, the input observations used by the system 200 may be images of the vehicle environment. The differential labels used in training can indicate, for example, differences in weather conditions and / or occlusion levels and / or positions and / or orientations of objects within the environment.

[0050] For example, the autonomous vehicle 62 incorporates the system 200 and can control the operation and braking of the autonomous vehicle based on sensor data obtained from a video camera 22 integrated within the vehicle 62. For example, when it is expected that the autonomous vehicle 62 will collide with a traffic participant, the system 200 can control the electric motor 42 and perform (regenerative) braking. The system 200 can control the operation and / or braking to avoid a collision with a traffic participant. For this purpose, the system 200 can acquire an image of the traffic situation around the vehicle 62 from the camera 22 and classify the image according to whether the traffic situation is safe. If the traffic situation is considered unsafe, the system 200 can take corresponding measures. Since images of unsafe traffic situations are usually difficult to obtain, generalizability is particularly important when learning image recognition.

[0051] Various embodiments include rewarding a machine-learnable function that predictably responds to a set of differences between input observations in a particular layer of a function using a regularization objective. Specifically, the regularization objective can include an evaluation of the mutual information between the representations of the input observations in the layer given a difference label between the input observations, and / or an evaluation of the interaction information between the representation and the difference label. Here, with reference to the concept of equivariance described in "Group Equivariant Convolutional Networks" by T. Cohen et al., in particular, the rationale for the validity of these options for the regularization objective is shown from a mathematical perspective.

[0052] As described in Cohen's reference, a mapping Φ that maps one space to another space, i.e., Φ: X → Z, in a group element g in the group G and a group action ·, when the mapping and the transformation are commutative, i.e., Φ(g·x) = g·Φ(x), the mapping Φ can be called G-equivariant or equivariant with respect to the action of the group G. In particular, when the action of the transformation in the Z space is the identity transformation, i.e., Φ(g·x) = Φ(x), the mapping Φ can be called G-invariant. Therefore, an equivariant mapping is an example of a mapping that predictably responds to a known difference in its input, in which case the inputs are related to each other by the application of a known transformation of the input.

[0053] However, interestingly, the inventors have considered statistically defining such predictability, for example, from the perspective of the relationship between random variables. In this way, a more general definition is obtained that is less strict and does not require a transformation that follows a group structure. This definition based on the statistics of predictability can be called "information-theoretic equivariance". This definition can be motivated by the following.

[0054] Using a similar notation for equivariance, the input observations for a machine-learnable function by a random variable x in the space X are shown. The random variable

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[0055] Using known identities and assuming that g is independent of x and z and therefore shares no mutual information with them, the conditional mutual entropy is

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[0056] Furthermore, note that the possible degenerate optimal solutions are invariant mappings with respect to the differences indicated by g, e.g., Φ(g·x)=Φ(x). The fact that such a solution becomes a global optimal solution can [Number] be prevented by maximizing the entropy of, but there is still a possibility of obtaining a local optimal solution, especially when estimating the mutual information using a mutual information estimation model. Also, since only invariance is required to solve various discrimination learning tasks, the occurrence of such a local optimal solution can be expected. However, such a local optimal solution is not desirable from the perspective of generalization ability.

[0057] To suppress the invariance in the trained machine-learnable function and thus further improve the generalization ability, an additional term that suppresses the interdependence between the first representation and the second representation without conditioning on the differential label may be included for regularization purposes. Specifically, [Number] the mutual information between and z (without conditioning on g) can be minimized. For example, the following regularization objective, i.e.,

Mathematics

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[0058] FIG. 4 shows a machine-learnable function MLF040, a non-limiting example in detail of a convolutional network in this case. Such a convolutional network is also referred to as a convolutional neural network (CNN). A convolutional network is a special type of neural network. A neural network is also known as an artificial neural network. A neural network typically comprises nodes in a plurality of successive layers. The parameters of a neural network typically include the weights of the nodes of the neural network. For example, the number of layers of the network may be at least 5 or at least 10, and the number of nodes and / or weights may be at least 1000 or at least 10000.

[0059] Generally speaking, a convolutional network is a neural network in which at least one layer is a convolutional layer, as will be considered below. Various convolutional network architectures are known, including so-called fully convolutional networks in which each layer of the network is a convolutional layer. In many cases, this architecture is used for semantic segmentation tasks, for example, in image classification. Another known architecture is shown in the figure, and the CNN comprises two components, namely, a convolutional part with at least one convolutional layer and a dense (e.g., fully connected) part with at least one dense layer. In many cases, this architecture is used for detection tasks, for example, in image classification.

[0060] For purposes of illustration, it will now be explained how a functional output FO230 for an input observation IO210 can be obtained using such a CNN. Typically, the input to a CNN is represented spatially as a volume, for example, of size M×N×d. Here, the dimension d = 1 is used, for example, for grayscale images, and the dimension d = 3 is used, in many cases, for color images. Similarly, the dimension d is known to represent volumes of other types of data, for example, audio data.

[0061] As shown in the figure, the input observation IO can be input to a machine-learnable function MLF, more specifically, the first layer CL1,212-1 of a plurality of filters (or in some cases a single filter). Each of these filters can convolve the input observation IO and cooperate to generate an activation volume, i.e., a "latent representation". Each "slice" of the activation volume can be the output of one of the plurality of filters. The latent representation can have a size different from the size M×N of the input observation IO, for example, a spatial resolution. Next, the latent representation can be used as an input to a subsequent layer CL2,212-2. Next, the filters of CL2 can convolve the latent representation output by the first layer CL1 to generate a second latent representation. This process can continue for further layers 212. By this convolutional part of the CNN, the spatial relationship of the latent representation with respect to the input observation is usually maintained, but the spatial dimension of the latent representation may be different from the spatial dimension of the input observation for each latent representation.

[0062] The latent representation LRk222 that occurs after the last layer CLk,212-k of the convolutional part of the CNN (often referred to as the last convolutional layer, but in some embodiments, the last layer CLk of the convolutional part may not necessarily be a convolutional layer. However, the last layer CLk maintains the spatial relationship as discussed above) is, in this example, input to the first dense layer DL1,214-1 of a plurality of dense layers. The dense layer 214 can be a fully connected layer, and the neurons of each fully connected layer are connected to all of the neurons of other layers. After passing through the dense part of the CNN, a function output FO, for example, a single classification score or a set of classification scores, can be input.

[0063] Figure 5a shows a detailed and non-limiting example of training a machine-learnable function using regularization purposes.

[0064] Shows a machine - learnable function Mlf,520. The machine - learnable function Mlf can map input observations to functional outputs. Generally, the machine - learnable function Mlf may be a deterministic function (e.g., a convolutional neural network), but the machine - learnable function may also be a statistical one (e.g., a Bayesian neural network).

[0065] For example, the input observation may be an image, or other types of sensor data represented as an image or sensor data represented in different ways. For example, the input observation may include one time - series of (direct or indirect) measurement values of a specific physical quantity, or a plurality of such time - series. Various features regarding images will be described below, but they are equally applicable to other types of sensor data.

[0066] The functional output may be of various types. For example, the functional output may include an image classification input indicating whether an image or one or more segments of an image belong to one or more given classes. The machine - learnable function Mlf may be an image classifier, e.g., a detection model or a semantic segmentation model. For a detection model, the output may include one or more classification scores. For a semantic segmentation model, the output may include a classification output of a dimension similar to the input representing the presence information of each segment of the input image. Also, the machine - learnable function Mlf may be, for example, an image feature extractor, in which case the functional output may be a vector of the extracted features.

[0067] The functional output of the machine-learnable function Mlf is referred to as the "output layer" of the machine-learnable function in this specification, and this functional output is the representation of the input observation in the output layer. For example, the representation of the input observation in the output layer may include at least 10, at least 100, or at least 1000 features. The input observation may also include at least 100, at least 1000, or at least 10000 features. In some embodiments, for example, in an object detection model, the output representation has fewer features than the input observation, but in the case of, for example, a semantic segmentation model, the number of features and / or the spatial dimension of the output representation may be the same as the spatial dimension of the input observation.

[0068] Separate from the output layer, the machine-learnable function Mlf may have one or more internal layers. That is, the evaluation of the machine-learnable function Mlf may include continuously evaluating one or more layers, and the output of the previous layer is used as the input of the next layer. Machine-learnable functions having layers include neural networks (especially deep neural networks) and deep Gaussian processes. For example, the machine-learnable function Mlf may be, for example, the convolutional network described in relation to FIG. 4, especially a fully convolutional network. However, it is not necessary for the machine-learnable function Mlf to have a layer structure. For example, the machine-learnable function may be a support vector machine or the like.

[0069] The machine-learnable function Mlf can be parameterized by a set of parameters (not shown in the drawings) that can be learned when training the machine-learnable function. For example, the parameters may include the weights of a neural network and the like. The number of parameters may be, for example, at least 1000 or at least 10000.

[0070] The parameters may be learned in the optimization operation Opt570 by optimizing the objective function. Various objective functions suitable for each learning task, such as classification, regression, feature extraction, autoencoding, etc. are known and can be used here. Convolutional training techniques including iterative optimization of the objective function can be used. For example, stochastic optimization techniques such as stochastic gradient descent using the Adam optimizer disclosed in Kingma and Ba, "Adam: A Method for Stochastic Optimization" (available at https: / / arxiv.org / abs / 1412.6980 and incorporated herein by reference) can be used. As is known, such optimization methods may be inductive and / or may reach local optima. Training can be performed for each instance or, for example, by batches of at least 64 instances or at least 256 instances or at most 64 instances or at most 256 instances.

[0071] The figure shows supervised learning based on a training data set of a plurality of input observations and corresponding training outputs. In this case, the objective function evaluated by the optimization Opt is typically the training loss (which may be referred to as the reconstruction loss) to be minimized based on the difference between the functional output of a machine-learnable function and the corresponding training output. The figure shows the input observation IO1,511 input to the machine-learnable function to obtain the corresponding functional output FO1,531'. The optimization Opt can compare the functional output FO1 of the input observation with the training output TO1,531 and adjust the parameters of the machine-learnable function Mlf based on this comparison. The optimization Opt can perform unsupervised learning. In this case, the machine-learnable function is typically adapted to the training instances, but the objective function is not based on the training output. Regardless of whether the training is supervised or unsupervised, the number of training input observations is, for example, at least 1000, at least 10000 or at least 100000.

[0072] Interestingly, for the purpose of rewarding a machine - learnable function Mlf that predictably responds to a set of differences between input observations in a layer of machine - learnable functions, a regularization objective Reg,560 can be included in the objective function to be optimized. The layer to which the regularization objective is applied may be an output layer or an internal layer. It is also possible to include a plurality of respective regularization objectives for each of a plurality of layers of machine - learnable functions (e.g., internal layers or output layers). For ease of explanation, here, a single regularization objective is considered. By repeating the operations described for each regularization objective used, a plurality of regularization objectives can be configured.

[0073] The regularization objective Reg may be defined from the perspective of the result of applying a machine - learnable function to a pair of different input observations IO1,511 and IO2,512 according to a given difference label DIF,513. Options for obtaining the pair IO1, IO2 and the corresponding difference label DIF are considered elsewhere. The set of difference labels is typically selected to be discrete and includes, for example, a maximum or at least 5, a maximum or at least 10, or a maximum or at least 25 possible differences. However, in principle, the use of continuous difference labels is also possible. Given the input observations IO1 and IO2, the machine - learnable function Mlf is (at least partially) applicable to obtain the corresponding representations R1,541 and R2,542 of the input observations in the layer where the regularization objective Reg is defined. Based on the representations R1 and R2 and the difference label DIF (typically, based on such a plurality of triplets of R1, R2, DIF), the regularization objective Reg can be evaluated.

[0074] The regularization objective Reg can be configured to reward the mutual statistical dependence between a first representation R1 and a second representation R2 given a difference label DIF. As described elsewhere, by minimizing the conditional entropy of R2 given R1 and DIF, and by maximizing the mutual information between R1 and R2 given DIF, for example,

Equation

Number

Number

Number

Number

[0075] To evaluate the regularization objective Reg, various convolution techniques for calculating or estimating each statistic can be used. However, this figure shows a regularization objective based on the (conditional) mutual information. The (conditional) mutual information is estimated according to a trainable mutual information estimation model Mie550. An example of such a trainable mutual information estimation model is disclosed in "MINE: Mutual Information Neural Estimation" by M. Belghazi et al. (available at https: / / arxiv.org / abs / 1801.04062 and incorporated herein by reference). Using each mutual information estimation model, the mutual information conditioned on the differential label DIF, for example,

Number

[0076] Considering the identity of mutual information I(X;Y|Z) - I(X;Y) = I(X;Z|Y) - I(X;Z) = I(Y;Z|X) - I(Y;Z), the interaction information can be estimated, for example, using the above mutual information estimation model, [Number] or [Number] and can also be estimated as.

[0077] Here, we proceed to the acquisition of the triplet IO1, IO2, DIF of the input observations and the corresponding differential labels, and several possibilities can be considered. In some embodiments, such a triplet may be available as part of a training dataset. This can be referred to as a supervised setting. Another possibility shown in FIG. 5b is that the input observation IO2 is generated from the input observation IO1 and the differential type DIF in the generation operation Gen580. This can be referred to as a self-supervised setting. Any generation operation Gen suitable for current applications may be used. The differential type DIF may indicate the transformation to be applied to the input observation IO1. The transformation may be, for example, not only a geometric transformation such as rotation and / or translation, but also a comprehensive change to the input observation IO1 that changes the characteristics of the objects in the scene or changes the observation conditions. For example, an image of a vehicle environment can be adapted such as introducing snow or rain, changing a daytime scene to a nighttime scene, etc.

[0078] Although not shown in the figure, a third option is to determine the differential label DIF from the input observations IO1 and IO2 using a machine-learnable labeling function. The function can be trained before performing the optimization Opt, but it is generally preferred to learn this function simultaneously with the function Mlf (e.g., using multi-task learning). The training of the labeling function may be supervised. For example, if the differential labels are available for a subset of the input observations, the labeling function is learned for that subset and can be applied to pairs where the labels are not available. Interestingly, the training may also be unsupervised, making it possible to completely eliminate the labeling effort. For example, the labeling function can be trained as described in M. Caron et al., “Deep Clustering for Unsupervised Learning of Visual Features” (available at https: / / arxiv.org / abs / 1807.05520 and incorporated herein by reference).

[0079] Figure 5c shows a detailed but non-limiting example where the machine-learnable function to be trained is an image feature extractor used in the comprehensive image classifier Cl590. That is, the comprehensive image classifier Cl obtains a functional output FO that provides a vector of features extracted from the input observation IO by applying the machine-learnable function Mlf, and classifies Cl using a further machine-learnable function on the resulting extracted features FO, thereby classifying the input observation IO, such as an input image. In this case, in order to train the comprehensive image classifier, the machine-learnable function can first be trained without using classification labels as described herein. Therefore, input observations IO for which classification labels are not available can also be used.

[0080] Thereafter, in the optimization operation Opt2,579, the comprehensive image classifier can be trained based on training examples IO labeled with the desired training classification output TCO595’. The optimization operation Opt2 at least learns the parameters of a further machine-learnable function Cl that outputs a classification. Optionally, the optimization Opt2 may also fine-tune the machine-learnable function Mlf. For this purpose, optionally, the regularization objective Reg of the machine-learnable function Mlf may be included in the objective function for training the comprehensive classifier.

[0081] Figure 6 shows a block diagram of a computer-implemented method 600 for training a machine-learnable function. The machine-learnable function can map an input observation to a functional output. The machine-learnable function may comprise one or more internal layers and / or output layers. The method 600 may correspond to the operation of the system 100 of FIG. 1. However, this is not limiting in that the method 600 may be implemented using other systems, devices or apparatuses.

[0082] Method 600 may include, in an operation titled "access training data, parameters", accessing 610 a training data set that includes a plurality of training input observations and a set of parameters of a machine-learnable function.

[0083] Method 600 may include, in an operation titled "learn parameters", learning 620 a set of parameters of a machine-learnable function by optimizing an objective function. The optimization may include providing a reward to a machine-learnable function that predictably responds to a set of differences between input observations in a layer of machine-learnable functions. The optimization can provide a reward to the above predictability by a regularization objective included in the objective function.

[0084] The optimization performed in learning operation 620 may include, in an operation titled "obtain observations, difference labels", obtaining 622 a first input observation of a training data set, a corresponding second input observation, and a difference label of a set of differences indicating the difference between the first input observation and the second input observation. The optimization may further include, in an operation titled "apply function to determine representations", applying a machine-learnable function to determine 624 a first representation of the first input observation and a second representation of the second input observation in a layer of machine-learnable functions, respectively. The optimization may further include, in an operation titled "provide reward to representation dependency given difference label", evaluating 626 a regularization objective. The regularization objective may be configured to provide a reward to the mutual statistical dependency between the first representation and the second representation given the difference label between the first input observation and the second input observation.

[0085] Generally, it will be understood that the operations of method 600 of FIG. 6 may be performed in any suitable order, for example, sequentially, simultaneously, or a combination thereof, depending on a particular order required, for example, by an input / output relationship, when applicable.

[0086] The method can be implemented on a computer as a computer-implemented method, dedicated hardware, or a combination of both. Also, as shown in FIG. 7, computer instructions, such as executable code, may be stored on a computer-readable medium 700 in the form of a series of machine-readable physical marks 710 and / or a series of elements having different electrical characteristics, such as magnetic or optical characteristics or values. The executable code may be stored temporarily or non-temporarily. Examples of computer-readable media include memory devices, optical storage devices, integrated circuits, servers, online software, and the like. FIG. 7 shows an optical disk 700. Alternatively, the computer-readable medium 700 may include temporary or non-temporary data 710 representing a set of parameters of a machine-learnable function trained by the computer-implemented method provided herein.

[0087] Whether or not non-limiting, e.g., embodiments, or any feature should not be understood as limiting the claimed invention.

[0088] The above embodiments are illustrative rather than restrictive, and it should be noted that those skilled in the art can design many alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claims. The use of the verb "comprise" and its conjugations does not exclude the presence of elements or steps other than those recited in the claims. The article "a" preceding an element does not exclude the presence of a plurality of such elements. When preceding a list or group of elements, expressions such as "at least one of" represent a selection of all or any subset of the list or group of elements. For example, the expression "at least one of A, B, and C" should be understood to include only A, only B, only C, both A and B, both A and C, both B and C, or all of A, B, and C. The present invention may be implemented by hardware including several individual elements and a suitably programmed computer. In the claims of a device listing several means, some of these means may be embodied by the hardware of a single and same product. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

1. A computer-implemented method (600) for training a machine-learnable function, wherein the machine-learnable function maps an input observation to a function output, the machine-learnable function comprises one or more internal layers and / or an output layer, and the method comprises: - accessing a training data set including a plurality of training input observations and a set of parameters of the machine-learnable function (610); - learning the set of parameters of the machine-learnable function by optimizing an objective function (620), wherein the optimization includes providing a reward to the machine-learnable function that predictably responds to a difference set between input observations in a layer of the machine-learnable function, and the optimization provides a reward to predictability by a regularization objective included in the objective function (620); including, the optimization: - obtaining a difference label of the difference set indicating a first input observation of the training data set, a corresponding second input observation, and a difference between the first input observation and the second input observation (622); - applying the machine-learnable function to determine a first representation of the first input observation and a second representation of the second input observation in the layer of the machine-learnable function, respectively (624); - evaluating the regularization objective configured to provide a reward to a mutual statistical dependency between the first representation and the second representation given the difference label between the first input observation and the second input observation (626); A method (600) including.

2. The method (600) according to claim 1, wherein the machine-learnable function is an image classifier or an image feature extractor.

3. The method (600) according to claim 2, wherein the machine-learnable function is an image feature extractor used in a comprehensive image classifier, the image feature extractor is trained based on an unlabeled training data set, and the method further includes training the comprehensive image classifier based on a labeled training data set.

4. The method (600) according to claim 2 or 3, wherein the objective function includes a plurality of respective regularization objectives for a plurality of respective layers.

5. The first input observation and the second input observation are a first image and a second image representing scenes of the same kind, and the difference label indicates a difference in characteristics of objects in the scene and / or a difference in observation conditions in the scene, the method (600) according to any one of claims 2 to 4. **Claim 6** The first image and the second image represent the environment around a vehicle, and the difference label is - a difference in weather conditions, - a difference in the occlusion level of an object in the environment, - a difference in the position of an object in the environment, and - a difference in the orientation of an object in the environment, indicating at least one of the group, the method (600) according to claim 5. **Claim 7** The machine-learnable function is a convolutional neural network, the method (600) according to any one of claims 1 to 6. **Claim 8** Evaluating the regularization objective includes estimating a conditional mutual information based on the first representation, the second representation, and the difference label, the method (600) according to any one of claims 1 to 7. **Claim 9** The mutual information is estimated according to a trainable mutual information estimation model, and the method further includes training the mutual information estimation model simultaneously with the machine-learnable function, the method (600) according to claim 8. **Claim 10** The regularization objective is further configured to suppress the interdependence between the first representation and the second representation without conditioning on the difference label, the method (600) according to any one of claims 1 to 9. **Claim 11** including generating the second input observation from the first input observation and the difference label, the method (600) according to any one of claims 1 to 10. **Claim 12** determining the difference label by applying a machine-learnable labeling function to the first input observation and the second input observation, the method (600) according to any one of claims 1 to 11. **Claim 13** Obtaining sensor data that provides observations of a computer control system and / or an environment of the computer control system via a sensor interface; applying the machine-learnable function to the observations; and monitoring and / or controlling the computer control system based on the output of the machine-learnable function. The method (600) according to any one of claims 1 to 12 further includes this.

14. A system (100) for training a machine-learnable function, wherein the machine-learnable function maps input observations to function outputs, the machine-learnable function includes one or more internal layers and / or output layers, and the system includes - A training data set (030) including a plurality of training input observations, and a data interface (120) for accessing a set of parameters (040) of the machine-learnable function - A processor subsystem (140) configured to learn the set of parameters of the machine-learnable function by optimizing an objective function, the optimization including rewarding the machine-learnable function that predictably responds to a difference set between input observations in the layer of the machine-learnable function, and the optimization rewarding predictability by a regularization objective included in the objective function. Processor subsystem (140) Comprising, the optimization is - Obtaining a first input observation of the training data set, a corresponding second input observation, and a difference label of the difference set indicating a difference between the first input observation and the second input observation - Applying the machine-learnable function to determine a first representation of the first input observation and a second representation of the second input observation in the layer of the machine-learnable function, respectively - Evaluating the regularization objective configured to reward the mutual statistical dependence between the first representation and the second representation given the difference label between the first input observation and the second input observation Including, system (100).

15. A computer-readable medium (700) including non-transitory data (710) representing instructions for causing the processor system to perform the computer-implemented method according to claim 1 when executed by the processor system.

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