Volterra neural network and method

1. A computer-implemented neural network system comprising a processor and a memory configured to execute a memory structure comprising nodes connected via a plurality of layers, the memory structure comprising:

a plurality of kernels, a set of which being configured to execute an n th order filter, wherein the plurality of kernels of the n th order filters are repeatedly configured in a plurality of cascading layers of interconnected kernels to form a cascading hierarchical structure that approximates a high-order Volterra filter,

wherein the plurality of cascading layers include at least a first cascade layer and a second cascade layer, wherein the output features of the first cascade layer are overlapped to provide non-linearly cascading inputs into the second cascade layer.

2. The computer-implemented neural network system of claim 1 , wherein the n th order filters each comprise a 2 nd or 3 rd -order filter to form the cascading hierarchical structure and approximates a 4 th order filter or more.

3. The computer-implemented neural network system of claim 1 , wherein the n th order filters each includes a Volterra filter that models an input-output relationship of a nonlinear system.

4. The computer-implemented neural network system of claim 3 , wherein the Volterra filter is implemented as a product operator of two 3-dimensional matrices.

5. The computer-implemented neural network system of claim 1 , wherein the cascading hierarchical structure approximates a K th order filter from Z number of 2 nd order filters according to K=2 2 (Z−1) .

6. The computer-implemented neural network system of claim 1 , wherein the output features of the first cascade layer are overlapped to provide quadratic interactions between the first cascading layer and the second cascading layer.

7. The computer-implemented neural network system of claim 1 , wherein the set of the plurality of kernels each comprises a Volterra filter having an n th order filter and a filter length of at least 2.

8. The computer-implemented neural network system of claim 1 , wherein each cascading layer of the plurality of cascading layers has a same configuration.

9. The computer-implemented neural network system of claim 1 , wherein each kernel of a first cascade layer has a first configuration and each kernel of a second cascade layer has a second configuration, wherein the first configuration is different from the second configuration.

10. The computer-implemented neural network system of claim 1 , wherein the computer-implemented neural network is configured to output a plurality of predictor values each associated with a likelihood of a given recognized action being present or not present from among a set of evaluate-able recognized actions.

11. The computer-implemented neural network system of claim 1 ,

wherein the plurality of kernels of the cascading hierarchical structure are used to independently assess a first data set for first modality features,

wherein the memory structure further comprises:

a second plurality of kernels, a set of which being configured to execute an m th order Volterra filter, wherein the second plurality of kernels of the m th order filters are repeatedly configured in a plurality of cascading layer of interconnected kernels to form a second cascading hierarchical structure that approximates a high-order filter substantially greater than m, wherein the second plurality of kernels of the second cascading hierarchical structure are used to independently assess a second data set for second modality features, a fusion operator configured to fuse i) the first modality features of the first plurality of kernels in the first cascading hierarchical structure and ii) the second modality features of the second plurality of kernels in the second cascading hierarchical structure to generate output predictors.

12. The computer-implemented neural network system of claim 11 , wherein the fusion operator comprises a Volterra filter.

13. The computer-implemented neural network system of claim 11 , wherein the first and second modality features comprise spatial features and temporal features, respectively, wherein the computer-implemented neural network further comprises a classifier to output indication of presence or non-presence of a recognized action in a set of video frames or an image sequence having representations of one or more action therein based on the spatial features and temporal features.

14. The computer-implemented neural network system of claim 13 , wherein the set of video frames comprises red, green, and blue (RGB) data values.

15. The computer-implemented neural network system of claim 11 , wherein the first data set comprise a set of video frames.

16. The computer-implemented neural network system of claim 11 , wherein the second modality features are associated with an optical flow analysis.

17. The computer-implemented neural network system of claim 11 , wherein the fusion operator evaluate non-linear interactions between the first modality features and the second modality features.

18. The computer-implemented neural network system of claim 1 , wherein the plurality of kernels and cascading hierarchical structure are configured as a neural network auto-encoder.

19. The computer-implemented neural network system of claim 1 , wherein the plurality of kernels and cascading hierarchical structure are configured as a generative adversarial network.

20. The computer-implemented neural network system of claim 1 , wherein the output features of the first cascade layer additionally includes non-overlapping features to provide cascading inputs into the second cascade layer.

21. A method comprising:

training, via a computing system, a Volterra neural network comprising plurality of kernels each configured to execute an n th order filter, wherein the plurality of kernels of the n th order filters are repeatedly configured in a plurality of cascading layers of interconnected kernels to form a cascading hierarchical structure that approximates a high-order filter substantially greater than n, wherein the plurality of cascading layers include at least a first cascade layer and a second cascade layer, wherein the output features of the first cascade layer are overlapped to provide non-linearly cascading inputs into the second cascade layer; and

using the trained neural network in a video or image processing application.

22. A non-transitory computer readable medium comprising instructions, wherein execution of the instructions, by a processor, cause the processor to:

train a Volterra neural network comprising plurality of kernels each configured to execute an n th order filter, wherein the plurality of kernels of the n th order filters are repeatedly configured in a plurality of cascading layers of interconnected kernels to form a cascading hierarchical structure that approximates a high-order filter substantially greater than n, wherein the plurality of cascading layers include at least a first cascade layer and a second cascade layer, wherein the output features of the first cascade layer are overlapped to provide non-linearly cascading inputs into the second cascade layer; and

use the trained neural network in a video or image processing application.