Determination of condition or characteristic of a target

1 . A device or system comprising:

a communications module configured to receive data from and transmit data to other devices or systems; at least one processor; and

at least one memory comprising computer program code for one or more programs;

the at least one processor, the at least one memory, and the computer program code being configured to cause the device or system to at least carry out the following for training a neural network for determining a condition or characteristic of a monitored target:

inputting N features of each set of historical data of a plurality of sets of historical data associated with the monitored target into the neural network, the neural network at least having N inputs and one or more outputs, where N is a natural number greater than one, the neural network having one or more hidden layers, each hidden layer being a tensor network in the form of a matrix product operator, MPO, with a respective plurality of tensors and having a respective predetermined activation function per hidden layer or per tensor in the MPO; and one or more iterations of the following steps up until one or more predetermined criteria are fulfilled:

computing a predicted value of the neural network in a forward pass of the neural network; and

sequentially carrying out the following processing for each possible pair of adjacent tensors in the MPO of each hidden layer up until all possible pairs of adjacent tensors in the MPO of each hidden layer have been processed starting from one end of each MPO and arriving at the other end of each MPO:

grouping the pair of adjacent tensors thereby providing a grouped tensor;

computing a gradient for the grouped tensor with respect to a predetermined loss function in a backward pass of the neural network;

updating the grouped tensor by combining the grouped tensor with the computed gradient for the grouped tensor; and

ungrouping the updated grouped tensor with singular value decomposition; and

wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following after having trained the neural network:

receiving a set of data associated with the monitored target, the set of data having N features;

inputting the N features of the received set of data into the trained neural network;

after inputting the N features into the trained neural network, determining a condition or characteristic of the target by processing the one or more outputs; and

providing a predetermined command at least based on the determined condition or characteristic, wherein the predetermined command includes one or both of:

providing a notification indicative of the determined condition or characteristic to an electronic device; and

providing a command to a controlling device or system associated with the target, the command being for changing a behavior of the target.

2 . The device or system of claim 1 , wherein the one or more iterations comprises two or more iterations, and wherein, in each iteration, the sequential processing of all possible pairs of adjacent tensors in the MPO of each hidden layer starts from a different one of the two ends of the MPO of the respective hidden layer so that the grouping of pairs of adjacent tensors is reversed.

3 . The device or system of claim 1 , wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following: prior to computing the gradient, computing an environment tensor at each side of the grouped tensor having at least one tensor in the MPO.

4 . The device or system of claim 1 , wherein the singular value decomposition is carried out such that virtual bonds of the updated group tensor are truncated and only a predetermined number of singular values are kept, wherein the predetermined number of singular values kept are the largest singular values.

5 . The device or system of claim 1 , wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following prior to any inputting:

determining a degree of correlation between the N features of any set of historical data to be inputted into the neural network; and

when the degree of correlation is below a predetermined correlation threshold, decomposing the N features of each set of historical data to be inputted into the neural network by local contraction of each feature, and converting each tensor of the MPO of a first hidden layer connected with an input layer of the neural network into a matrix product state tensor based on the local contraction of the features.

6 . The device or system of claim 1 , wherein the at least one processor comprises one or more classical processors and one or more quantum processors.

7 . The device or system of claim 1 , wherein the target comprises: an electrical grid, an electricity network, a portfolio of financial assets or derivatives, a stock market, a set of patients of a hospital unit, or a system of devices and/or machines.

8 . A device or system comprising:

a communications module configured to receive data from and transmit data to other devices or systems;

at least one processor; and

at least one memory comprising computer program code for one or more programs;

the at least one processor, the at least one memory, and the computer program code being configured to cause the device or system to at least carry out the following for training a neural network for determining a condition or characteristic of a monitored target:

inputting N features of each set of historical data of a plurality of sets of historical data associated with the monitored target into the neural network, the neural network at least having N inputs and one or more outputs, where N is a natural number greater than one, the neural network having one or more hidden layers, each hidden layer being a tensor network in the form of a matrix product operator, MPO, with a respective plurality of tensors and having a respective predetermined activation function per hidden layer or per tensor in the MPO; and

one or more iterations of the following steps until one or more predetermined criteria are fulfilled:

computing a predicted value of the neural network in a forward pass of the neural network;

computing a gradient for each tensor in the MPO of each hidden layer with respect to a predetermined loss function in a backward pass of the neural network; and

updating values of each tensor in the MPO of each hidden layer with gradient descent;

and wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following after having trained the neural network:

receiving a set of data associated with the monitored target, the set of data having N features;

inputting the N features of the received set of data into the trained neural network;

after inputting the N features into the trained neural network, determining a condition or characteristic of the target by processing the one or more outputs; and

providing a predetermined command at least based on the determined condition or characteristic, wherein the predetermined command includes one or both of:

providing a notification indicative of the determined condition or characteristic to an electronic device; and

providing a command to a controlling device or system associated with the monitored target, the command being for changing a behavior of the target.

9 . The device or system of claim 8 , wherein the predicted value is computed as a contraction of the tensor network of all the hidden layers.

10 . The device or system of claim 8 , wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following prior to any inputting:

determining a degree of correlation between the N features of any set of historical data to be inputted into the neural network; and

when the degree of correlation is below a predetermined correlation threshold, decomposing the N features of each set of historical data to be inputted into the neural network by local contraction of each feature, and converting each tensor of the MPO of a first hidden layer connected with an input layer of the neural network into a matrix product state tensor based on the local contraction of the features.

11 . The device or system of claim 8 , wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to at least carry out the following after having trained the neural network:

receiving a set of data associated with a monitored target, the set of data having N features, where N is a natural number greater than one;

inputting the N features of the received set of data into a neural network, the neural network being for determining a condition or characteristic of the target with a plurality of sets of historical data associated with the target, each set of the plurality of sets of historical data having N features, the neural network at least having N inputs and one or more outputs, the neural network having one or more hidden layers, each hidden layer being a tensor network in the form of a matrix product operator, MPO, with a respective plurality of tensors and having a respective predetermined activation function per hidden layer or per tensor in the MPO; and

after inputting the N features into the neural network, determining a condition or characteristic of the target by processing the one or more outputs.

12 . The device or system of claim 8 , wherein the at least one processor comprises one or more classical processors and one or more quantum processors.

13 . The device or system of claim 8 , wherein the target comprises: an electrical grid, an electricity network, a portfolio of financial assets or derivatives, a stock market, a set of patients of a hospital unit, or a system of devices and/or machines.