Apparatus and method for artificial intelligence neural network based on co-evolving neural ordinary differential equations

1. An apparatus for an artificial intelligence neural network based on co-evolving neural ordinary differential equations (NODEs), the apparatus comprising:

at least one processor and memory storing instructions performed by the at least one processor;

a main NODE module configured to provide a downstream machine learning task at an initial time; and

an attention NODE module configured to receive the downstream machine learning task from the main NODE module and provide attention to the main NODE module based on the downstream machine learning task,

wherein the main NODE module receives the attention provided from the attention NODE module and provides the downstream machine learning task at a next time after the initial time such that the main NODE module and the attention NODE module influence each other over time so that the main NODE module outputs a multivariate time-series value at a given time for an input sample x,

wherein the attention is used in a feature extraction layer before a NODE layer and does not introduce a new NODE model that is internally combined with the attention,

wherein Explainable Tensorized Neural (ETN)-ODE uses the attention to derive a correlation matrix in the feature extraction layer and then evolve the correlation matrix using the NODE layer, and

wherein the main NODE module and the attention NODE module are each implemented via the at least one processor.

2. The apparatus of claim 1 , further comprising: a feature extraction module configured to extract a feature for the input sample x to generate an initial feature vector at the initial time, and provide the initial feature vector to the main NODE module,

wherein the feature extraction module is implemented via the at least one processor.

3. The apparatus of claim 2 , further comprising: an initial attention generating module configured to receive the initial feature vector to generate initial attention, and provide the initial attention to the attention NODE module to support calculation of a multivariate time-series value at a next time,

wherein the initial attention generating module is implemented via the at least one processor.

4. The apparatus of claim 1 , wherein the main NODE module performs integration of an ordinary differential equation (ODE) function with respect to the ODE function for time, and the ODE function receives 1) the multivariate time-series value and 2) the attention at the given time.

5. The apparatus of claim 4 , wherein the attention NODE module performs element-wise multiplication between the multivariate time-series value and a sigmoid activation function of a time-evolving matrix as the ODE function.

6. The apparatus of claim 4 , wherein the attention NODE module performs integration of an attention generation function for the ODE function for time, and the attention generation function receives 1) a time evolution matrix representing a logit value of the attention and 2) the multivariate time-series value is input at the given time.

7. The apparatus of claim 1 , further comprising: a classification module configured to receive the multivariate time-series value at the given time and performs prediction on the input sample x,

wherein the classification module is implemented via the at least one processor.

8. A method for an artificial intelligence neural network based on co-evolving neural ordinary differential equations (NODEs), the method comprising:

providing, by a main NODE module, a downstream machine learning task at an initial time; and

receiving, by an attention NODE module, the downstream machine learning task from the main NODE module and providing attention to the main NODE module based on the downstream machine learning task,

wherein the main NODE module receives the attention provided from the attention NODE module and provides the downstream machine learning task at a next time such that the main NODE module and the attention NODE module influence each other over time so that the main NODE module outputs a multivariate time-series value at a given time for an input sample x,

wherein the attention is used in a feature extraction layer before a NODE layer and does not introduce a new NODE model that is internally combined with the attention,

wherein Explainable Tensorized Neural (ETN)-ODE uses the attention to derive a correlation matrix in the feature extraction layer and then evolve the correlation matrix using the NODE layer.

9. The method of claim 8 , further comprising:

extracting, by a feature extraction module, a feature for the input sample x to generate an initial feature vector at the initial time, and providing the initial feature vector to the main NODE module.

10. The method of claim 9 , further comprising:

receiving, by an initial attention generating module, the initial feature vector to generate initial attention, and providing the initial attention to the attention NODE module to support calculation of a multivariate time-series value at a next time.

11. The method of claim 8 , wherein the main NODE module performs integration of an ordinary differential equation (ODE) function with respect to adjoint times, and the ODE function receives 1) the multivariate time-series value and 2) the attention at the given time.

12. The method of claim 8 , further comprising:

receiving, by a classification module, the multivariate time-series value at the given time and performing prediction on the input sample x.