CONFIGURING A NEURAL NETWORK FOR EQUIVARIANT OR INVARIANT BEHAVIOR

Abstract

A method for configuring a neural network which is designed to map measured data to one or more output variables. The method includes: transformation(s) of the measured data is/are specified which when applied to the measured data, is/are meant to induce the output variables supplied by the neural network to exhibit an invariant or equivariant behavior; at least one equation is set up which links a condition that the desired invariance or equivariance be given with the architecture of the neural network; by solving the at least one equation a feature is obtained that characterizes the desired architecture and/or a distribution of weights of the neural network in at least one location of this architecture; a neural network is configured in such a way that its architecture and/or its distribution of weights in at least one location of this architecture has/have all of the features ascertained in this way.

Claims

1. A method for configuring a neural network which is configured to map measured data to one or more output variables, the method comprising the following steps: specifying one or more transformations of the measured data which, when applied to the measured data, is meant to induce output variables supplied by the neural network to exhibit a desired invariant or equivariant behavior; setting up at least one equation which links a condition that the desired invariance or equivariance be given with an architecture of the neural network; obtaining, by solving the at least one equation, at least one feature that characterizes the architecture and/or a distribution of weights of the neural network in at least one location of the architecture; and configuring the neural network in such a way that its architecture and/or the distribution of weights in at least one location of the architecture, has all of the ascertained at least one feature.

2. The method as recited in claim 1, wherein the at least one equation includes: a function ϕ.sub.u, which describes a further development of features of layers of the neural network during a transition from one layer to the next, and/or a function ϕ.sub.m, which describes an information flow within the neural network as a function of the architecture of the neural network.

3. The method as recited in claim 2, wherein the neural network is a graph in which nodes occupied by features h.sub.i.sup.l are connected by edges e.sub.ij.

4. The method as recited in claim 3, wherein the function ϕ.sub.u links features h.sub.i.sup.l+1 of the i.sup.th node in a layer l+1 with features h.sub.i.sup.l of the i.sup.th node in a layer I and with the information flow m.sub.i.sup.l received in total by the node.

5. The method as recited in claim 4, wherein the function ϕ.sub.m links the information flow m.sub.j.fwdarw.i.sup.l from node j to node i in a layer l with an edge e.sub.ij between nodes I and j and also with features h.sub.j.sup.l of the j.sup.th node in the layer I.

6. The method as recited in claim 1, wherein, in the specifying step, at least one group of transformations is specified for which the desired invariance or equivariance of the output variables is to apply.

7. The method as recited in claim 1, wherein the at least one equation is expressed in hyperparameters which characterize the architecture of the neural network, and the solving of the at least one equation leads to values of the hyperparameters as features.

8. The method as recited in claim 1, wherein: observations of multiple agents of a centralized or decentralized Markov decision process are the measured data, and a reward to be expected when a predefined action is performed in a certain state of the Markov decision process and/or a policy for at least one agent mapping a predefined state to an action to be performed is selected as an output variable of the output variables.

9. The method as recited in claim 8, wherein the observations include positions of agents.

10. The method as recited in claim 8, further comprising: ascertaining, from the reward to be expected, a control signal for at least one robot and/or for at least one vehicle and/or for at least one unmanned flying device and/or from the policy; and controlling, using the control signal, the robot and/or the vehicle and/or the unmanned flying device (.

11. The method as recited in claim 1, wherein the neural network to be configured is a classifier network, which maps the measured data to classification scores with regard to one or more classes of a predefined classification.

12. The method as recited in claim 11, further comprising: ascertaining, from the classification scores, a control signal for at least one robot and/or for at least one vehicle and/or for at least one unmanned flying device; and controlling, using the control signal, the robot and/or the vehicle and/or the unmanned flying device.

13. A non-transitory machine-readable data carrier on which is stored a computer program for configuring a neural network which is configured to map measured data to one or more output variables, the computer program, when executed by one or more computers, causing the one or more computers to perform the following steps: specifying one or more transformations of the measured data which, when applied to the measured data, is meant to induce output variables supplied by the neural network to exhibit a desired invariant or equivariant behavior; setting up at least one equation which links a condition that the desired invariance or equivariance be given with an architecture of the neural network; obtaining, by solving the at least one equation, at least one feature that characterizes the architecture and/or a distribution of weights of the neural network in at least one location of the architecture; and configuring the neural network in such a way that its architecture and/or the distribution of weights in at least one location of the architecture, has all of the ascertained at least one feature.

14. One or more computers configured to configure a neural network which is configured to map measured data to one or more output variables, the one or more computers being configured to: specify one or more transformations of the measured data which, when applied to the measured data, is meant to induce output variables supplied by the neural network to exhibit a desired invariant or equivariant behavior; set up at least one equation which links a condition that the desired invariance or equivariance be given with an architecture of the neural network; obtain, by solving the at least one equation, at least one feature that characterizes the architecture and/or a distribution of weights of the neural network in at least one location of the architecture; and configure the neural network in such a way that its architecture and/or the distribution of weights in at least one location of the architecture, has all of the ascertained at least one feature.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0050] FIG. 1 shows an exemplary embodiment of method 100 for configuring a neural network 1, according to the present invention.

[0051] FIG. 2 shows a sketch of a Markov decision process for video monitoring with the aid of drones.

[0052] FIGS. 3A and 3B show the effect of method 100 for configuring a neural network 1 in the application shown in FIG. 2, according to the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0053] FIG. 1 shows a schematic flow diagram of an exemplary embodiment of method 100 for configuring a neural network 1 which maps measured data 2 to one or more output variable(s) 3.

[0054] In step 105, observations of multiple agents of a centralized or decentralized Markov decision process are able to be selected as measured data 2. A reward to be expected when carrying out a predefined action in a certain state of the Markov decision process and/or a policy for at least one agent, which maps a predefined state to an action to be performed, may then be selected as output variable 3 of neural network 1 in step 6.

[0055] In step 107, a classifier network which maps measured data 2 to classification scores with regard to one or more classes(s) of a predefined classification can then be selected as neural network 1 to be configured.

[0056] In step 110, one or more transformation(s) 2a of measured data 2 is/are specified, which when applied to measured data 2, are to induce output variables 3 supplied by neural network 1 to exhibit an invariant or equivariant response.

[0057] According to block 111, at least one group G of transformations 2a to which the desired invariance or equivariance of the output variables 3 is meant to apply may be specified in this context.

[0058] In step 120, at least one equation 4 is set up, which links a condition to the effect that the desired invariance or equivariance be given, with architecture la of neural network 1.

[0059] According to block 121, this at least one equation 4 may particularly include a function ϕ.sub.u, for example, which describes a further development of the features of layers of neural network 1 during the transition from one layer to the next.

[0060] Alternatively or in combination therewith, the at least one equation 4 according to block 122 may particularly include a function ϕ.sub.m which describes an information flow within neural network 1 as a function of architecture la of neural network 1, for example.

[0061] According to block 121a, if the neural network is developed as a graph in which nodes occupied by features h.sub.i.sup.l are linked by edges e.sub.ij, function ϕ.sub.u is able to link in particular features h.sub.i.sup.l+1 of the i.sup.th node in layer l+1 with features h.sub.i.sup.l of the i.sup.th node in layer I and also with the information flow m.sub.i.sup.l received in total by this node.

[0062] According to block 122a, alternatively or also in combination therewith, the function ϕ.sub.m is able to link information flow m.sub.j.fwdarw.i.sup.l from node j to node i in layer I with an edge e.sub.ij between nodes i and j and also with features h.sub.j.sup.l of the j.sup.th node in layer I.

[0063] According to block 123, the at least one equation 4 is able to be expressed in hyperparameters which characterize architecture 1a of neural network 1. For instance, the hyperparameters may include the number, size and types of layers of neural network 1 and/or of neurons or other processing units that make up these layers.

[0064] In step 130, at least one feature 5 is obtained by solving the at least one equation 4, which characterizes the desired architecture 1a and/or a distribution of weights of neural network 1 in at least one location in this architecture 1a.

[0065] If equation 4 depends on hyperparameters, then the solving of the at least one equation 4 may lead to values of the hyperparameters as features 5 according to block 131.

[0066] In step 140, at least one neural network 1 is configured in such a way that its architecture la and/or its distribution of weights has/have all of the features 5 ascertained in step 130 in at least one location in this architecture.

[0067] In step 150, following intermediate training of the configured neural network 1 and the populating of this network 1 with measured data 2, for example, a control signal 6 for at least one robot 50 and/or for at least one vehicle 60 and/or for at least one unmanned flying vehicle 11-13 is able to be ascertained as output variable 3 from a reward to be expected and/or from a policy within the framework of a Markov decision process.

[0068] In step 160, for instance following intermediate training of configured neural network 1 and the populating of this network 1 with measured data 2, it is likewise possible to ascertain a control signal 6 as output variables 3 for at least one robot 50 and/or for at least one vehicle 60 and/or for at least one unmanned flying device 11-13 from classification scores for measured data 2 ascertained by the neural network 1.

[0069] Regardless of the source from which control signal 6 is obtained, robot 50 and/or vehicle 60 and/or unmanned flying device 11-13 is/are able to be controlled by this control signal 6 in step 170.

[0070] In FIG. 2, a Markov decision process for the video monitoring with the aid of drones in which a neural network 1 configured by the previously described method 100 is able to be utilized is sketched by way of example. In the video monitoring, multiple (i.e., three in this example) drones 11-13 have to coordinate among one another in order to locate an offender 14. Each drone 11-13 has a downward-facing camera and records images of a monitored region 11a-13a. To allow for a reliable detection of offender 14, the offender must be acquired from two different perspectives. The offender must thus be located in the overlap region U of acquisition regions 11a, 12a of at least two drones 11, 12. Each drone 11-13 assisting in this way in a team of at least two drones and catching an offender is given a reward of +1 within the scope of the Markov decision process. No two drones 11-13 may be at the same location on the other side at any time. It is furthermore known that the selected actions of the drones should ideally be equivariant with regard to rotations. If the optimal action of two drones for a given image recording is the enlargement of their distance in the x-direction, then an enlargement of the distance in the y-direction should come about in a rotation of recorded images by 90°. This is an example of a possible specified transformation in step 110 of method 100.

[0071] Since the cameras are perpendicularly pointing down, drones 11-13 are unable to see one another. They can transmit merely their respective current observations from respective acquisition range 11a-13a. If the Markov decision process is controlled in a centralized manner, then these observations may conveyed to a central instance which coordinates the deployment of drones 11-13. If the Markov decision process is controlled in a decentralized manner, the observations of a drone 11-13 are able to be transmitted to other drones 11-13 in a limited physical environment.

[0072] FIG. 3A shows medium rewards R over time t, which were obtained within the framework of the Markov decision process sketched in FIG. 2. Curve a was obtained for a conventional neural network 1. Curve b was obtained for a network 1 configured with the aid of the previously described method 100, which right from the start is invariant with regard to certain transformations 2a of the observations (e.g., an adaptation of the brightness or contrast), and equivariant from the start with regard to other transformations 2a (e.g., rotations). It can be seen quite clearly that the performance of network 1 configured with the aid of method 100 increases very rapidly while the conventional neural network 1 must first expend a lot of energy to learn the desired invariances and equivariances.

[0073] FIG. 3B was prepared analogously to FIG. 3A, with the only difference that the Markov decision process was carried out in a decentralized manner in this instance. In the decentralized case, the performance of conventional neural network 1 is clearly better than in the centralized case, in particular at the start. Nevertheless, neural network 1 configured using method 100 is still much better.