Simulation of convolutional network behavior and visualizing internal states of a network

1. A computerized method for simulating a convolutional network behavior, wherein the convolutional network is defined by a set of layers, wherein each layer comprises a two-dimensional lattice of neurons, wherein each layer with the exception of a last layer of said set of layers represents a source layer for a respectively following target layer, wherein a plurality of neurons of each of said source layer called a source sub-area share the identical connectivity weight matrix type, comprising the steps of:

decomposing each connectivity weight matrix type in an encoding filter and a decoding filter wherein each connectivity weight matrix type is represented by a scalar product of an encoding filter and a decoding filter;

determining a source reconstruction image on the basis of the encoding filters and the activities of the source layer; and

outputting a first input of the target layer, wherein said first input is a convolution of the source reconstruction image and the decoding filters.

2. The method of claim 1 , wherein said calculating the source reconstruction image includes the steps of:

identifying a scalar product of each of the source sub-areas and the corresponding encoding filter, and

combining the results of said scalar products of all source sub-areas.

3. The method of claim 2 , wherein the encoding filters and decoding filters are preset or generated by a learning process.

4. The method of claim 3 , wherein the encoding filter step and the decoding filter step are performed using a Fast Fourier Transformation.

5. The method of claim 4 , wherein the encoding filters and decoding filters extend along an axis along which the corresponding connectivity weight matrix type presents a translational invariance.

6. The method of claim 5 , further comprising the step of identifying internal states of a network characterized in that the internal states of the network are identified by one source reconstruction image for each connection between a source layer and a following target layer, the source reconstruction images being calculated on the basis of the encoding filters and the activities of the corresponding source layer.

7. The method of claim 6 , further comprising the step of calculating each source reconstruction image, including the steps of:

determining the scalar product of each of the source sub-areas of the source layer and the corresponding encoding filter, and

combining the results of the scalar products of all source sub-areas.

8. The method of claim 7 , wherein said method is used to recognize a pattern.

9. The method of claim 1 , wherein the encoding filters and decoding filters are preset or generated by a learning process.

10. The method of claim 9 , wherein the encoding filter step and the decoding filter step are performed using a Fast Fourier Transformation.

11. The method of claim 10 , wherein the encoding filters and decoding filters extend along an axis along which the corresponding connectivity weight matrix type presents a translational invariance.

12. The method of claim 11 , further comprising the step of identifying internal states of a network characterized in that the internal states of the network are identified by one source reconstruction image for each connection between a source layer and a following target layer, the source reconstruction images being calculated on the basis of the encoding filters and the activities of the corresponding source layer.

13. The method of claim 12 , further comprising the step of calculating each source reconstruction image, including the steps of:

determining the scalar product of each of the source sub-areas of the source layer and the corresponding encoding filter, and

combining the results of the scalar products of all source sub-areas.

14. The method of claim 13 , wherein said method is used to recognize a pattern.

15. The method of claim 1 , wherein said method is used to recognize a pattern, wherein said pattern is a representation of at least one of an acoustical characteristic or a visual characteristic of a physical object, said method further comprising the step of outputting said recognized pattern.

16. A computer program stored in a computer readable medium for performing the method of claim 1 .

17. A computerized method for the determining activities of target layers in a convolutional network behavior, wherein the convolutional network is defined by a set of layers, wherein each layer comprises a two-dimensional lattice of neurons, wherein each layer, with the exception of the last layer of said set of layers, represents a source layer for a respectively following target layer, and wherein a plurality of neurons of a source layer, called a source sub-area, share the identical connectivity weight matrix type, the method comprising the steps of:

representing each connectivity weight matrix type by a scalar product of an encoding filter and a decoding filter,

determining a source reconstruction image on the basis of the corresponding encoding filters and the activities of the corresponding source sub-area, for each source layer;

determining the input of the target layer as a convolution of the source reconstruction image and the decoding filter, for each connectivity weight matrix type, for each target sub-area and for each target layer;

determining the activities of the target layer in response to the activities of the source layer by using a response function of the neurons of the target layer and the calculated input of the target layer, for each target area; and

outputting the activities of the target layer.

18. The method of claim 17 , wherein each source reconstruction image is calculated by the following steps:

determining the scalar product of each of the source sub-areas of the corresponding source layer and the corresponding encoding filter, and

combining the results of the scalar products of all source sub-areas.

19. A computer program stored in a computer readable medium for performing the method of claim 17 .

20. The method of claim 17 , wherein said method is used to recognize a pattern, wherein said pattern is a representation of at least one of an acoustical characteristic or a visual characteristic of a physical object, said method further comprising the step of outputting said recognized pattern.

21. A computerized method for simulating a convolutional network behavior, wherein the convolutional network consists of a set of layers, wherein each layer includes a two-dimensional lattice of neurons, wherein each layer with the exception of a last layer of said set of layers represents a source layer for a respectively following target layer, the method comprising the steps of:

applying a connectivity weight matrix on activities of the source layer to determine a plurality of neurons of each of a source layer neurons, having the steps of:

convolving the activities of the source layer with an encoding filter to generate a source reconstruction image, and

determining a target layer input to the target layer by convolving the source reconstruction image with a decoding filter; and

outputting said target layer input to said target layer.

22. The method of claim 21 , wherein said method is used to recognize a pattern, wherein said pattern is a representation of at least one of an acoustical characteristic or a visual characteristic of a physical object, said method further comprising the step of outputting said recognized pattern.

23. A computer program stored in a computer readable medium for performing the method of claim 21 .

24. A computerized method for determining activities of target layers in a convolutional network behavior,

wherein said convolutional network includes data representing a pattern wherein said pattern is a representation of at least one of an acoustic characteristic and a visual characteristic of a physical object;

wherein a convolutional network is defined by a set of layers, wherein each layer is made up by a two-dimensional lattice of neurons, wherein each layer, except for a last layer of said set of layers, represents the source layer for a respectively following target layer, wherein a plurality of neurons of each source layer called a source sub-area share an identical connectivity weight matrix type, the method comprising the steps of:

decomposing each connectivity weight matrix type into an encoding filter and a decoding filter,

determining a source reconstruction image based upon corresponding encoding filters and activities of at least one of the corresponding source sub-area or source layer,

determining an input of the target layer as a convolution of the source reconstruction image and the decoding filter, for each connectivity weight matrix type, for each target sub area and for each target layer;

determining activities of the target layer in response to the activities of the source layer by using a response function of the neurons of the target layer and the input of the target layer, for each target area; and

outputting said activities of the target layer.

25. The method of claim 24 , wherein said method is used to recognize a pattern, wherein said pattern is a representation of at least one of an acoustical characteristic or a visual characteristic of a physical object, said method further comprising the step of outputting said recognized pattern.

26. A computer program stored in a computer readable medium for performing the method of claim 24 .