In a learning system, a storage stores training data. At least one processor performs a plurality of processes. Each of the processes calculates, based on the at least one parameter at a present time and the training data, a differential value for updating the at least one parameter in accordance with backpropagation. Each of the processes calculates, based on the differential value and the at least one parameter at the present time, a transmission value to be transmitted to the other processes. Each of the processes updates, based on the transmission values transmitted from the other processes, the at least one parameter at the present time.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A learning system for updating at least one parameter for a neural network, the learning system comprising: a storage storing training data; and at least one processor configured to perform a plurality of processes, each of the processes being configured to: calculate, based on the at least one parameter at a present time and the training data, a differential value for updating the at least one parameter in accordance with backpropagation; calculate, based on the differential value and the at least one parameter at the present time, a transmission value to be transmitted to the other processes; and update, based on the transmission values transmitted from the other processes, the at least one parameter at the present time. 2. A learning system for updating at least one parameter for a neural network, the learning system comprising: a storage storing training data; and at least one processor configured to perform plural pairs of a differential process and a communication process, the differential process of each pair being configured to: calculate, based on the at least one parameter at a present time and the training data, a differential value for updating the at least one parameter in accordance with backpropagation; and calculate, based on the differential value and the at least one parameter at the present time, a transmission value to be transmitted to the communication processes of the other pairs, the communication process of each pair being configured to determine whether the differential process of the corresponding pair has completed calculation of the transmission value; transmit the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has completed calculation of the transmission value; transmit a part of the at least one parameter at the present time to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has not completed calculation of the transmission value; and update the at least one parameter at the present time based on: the transmission value transmitted from the communication process of at least one of the other pairs; and the part of the at least one parameter at the present time transmitted from the communication process of the remaining at least one of the other pairs. 3. The learning system according to claim 1, wherein: the communication process of each pair is configured to update the at least one parameter at the present time each time the communication process of the corresponding pair transmits the transmission value or the part of the at least one parameter at the present time to the communication processes of the other pairs independently of whether the differential process of the corresponding pair has completed calculation of the transmission value. 4. The learning system according to claim 2, wherein: the number of the plural pairs is defined based on: a number of pieces of the training data used by the differential process of each pair; an optimum number of pieces of the training data used for one updating of the at least one parameter at the present time; and time required for the differential process of each pair to calculate the transmission value. 5. The learning system according to claim 4, wherein: the number of pieces of the training data used by the differential process of each pair is represented as A; the optimum number of pieces of the training data used for one updating of the at least one parameter at the present time is represented as B; and the number of the plural pairs is defined such that an average of B/A differential processes in the differential processes of all the pairs have completed the transmission value when the communication process of each pair is about to perform the transmission, 6. A learning system for updating at least one parameter for a neural network, the learning system comprising: a storage storing training data; and at least one processor configured to perform a plurality of processes, each of the processes being configured to: calculate, as a difference value, a compressed value of a difference between a first value of the at least one parameter at a present time that is referred to a first time and a second value of the at least one parameter at a second time that is later than the first time; calculate, based on the at least one parameter at the first time, the difference value, and the training data, a differential value for updating the at least one parameter in accordance with backpropagation; compress the differential value; calculate, based on the encoded differential value and the difference value, a transmission value to be transmitted to the other processes; obtain the difference value based on the transmission values transmitted from the other processes and the transmission value calculated by the corresponding process; and update, based on a restored value of the difference value, the at least one parameter at the second time. 7. A learning system for updating at least one parameter for a neural network, the learning system comprising: a storage storing training data; and at least one processor configured to perform plural pairs of a differential process and a communication process, the differential process of each pair being configured to: calculate, as a difference value, a compressed value of a difference between a first value of the at least one parameter at a present time that is referred to a first time and a second value of the at least one parameter at a second time that is later than the first time; calculate, based on the at least one parameter at the first time, the difference value, and the training data, a differential value for updating the at least one parameter in accordance with backpropagation; compress the differential value; and calculate, based on the encoded differential value and the difference value, a transmission value to be transmitted to the other processes, the communication process of each pair being configured to: determine whether the differential process of the corresponding pair has completed calculation of the transmission value; transmit the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has completed calculation of the transmission value; transmit the difference value as the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has not completed calculation of the transmission value; obtain the difference value based on the transmission values transmitted from the other processes and the transmission value calculated by the differential process of the corresponding pair; and update, based on a restored value of the difference value, the at least one parameter at the second time. 8. The learning system according to claim 6, wherein: each of the processes is configured to select, as compressing of the encode the differential value, one of: calculating the product of the differential value and a predetermined matrix; encoding the differential value while satisfying a distributive law; and multiplying, by the predetermined matrix, a matrix comprised of the differential values generated by all the processes. 9. The learning system according to claim 8, wherein: each of the processes is configured to update the predetermined matrix during predetermined times of updating of the at least one parameter. 10. The learning system according to claim 9, wherein: each of the processes is configured to update the predetermined matrix based on at least one of the past differential values during the predetermined times of updating of the at least one parameter. 11. The learning system according to claim 10, wherein: each of the processes is configured to update the predetermined matrix based on a principal component analysis of the at least one of the past differential values during the predetermined times of updating of the at least one parameter. 12. The learning system according to claim 1, wherein: the at least one parameter comprises a plurality of parameters of the neural network; and a first part of the parameters is shared as a second part of the parameters, or the first part of the parameters has a predetermined relationship with respect to the second part of the parameters. 13. The learning system according to claim 1, wherein: the neural network comprises a plurality of filters; and at least one first filter in the filters is shared as at least one second filter in the filters, or the at least one first filter in the filters has a predetermined relationship with respect to the at least one second filter in the filters. 14. The learning system according to claim 13, wherein: the at least one first filter in the filters is a filter generated by at least one of: symmetrically converting the at least one second filter with respect to a point, horizontally reversing the at least one second filter, and vertically reversing the at least one second filter. 15. The learning system according to claim 1, further comprising: at least one second processor configured to deform prepared images to generate deformed images as the training data. 16. A program product usable for the learning system according to claim 2, the program product comprising: a non-transitory computer-readable medium; and a set of computer program instructions embedded in the computer-readable medium, the instructions causing the at least one processor to perform at least one of: the differential process of each pair; and the communication process of the corresponding pair. 17. A learning method for updating at least one parameter for a neural network based on a plurality of processes executed by at least one processor, the learning method, by each of the processes, comprising: calculating, based on the at least one parameter at a present time and training data stored in a storage, a differential value for updating the at least one parameter in accordance with backpropagation; calculating, based on the differential value and the at least one parameter at the present time, a transmission value to be transmitted to the other processes; and updating, based on the transmission values transmitted from the other processes, the at least one parameter at the present time. 18. A learning method for updating at least one parameter for a neural network based on plural pairs of a differential process and a communication process executed by at least one processor, the learning method comprising: calculating, by the differential process of each pair based on the at least one parameter at a present time and training data stored in a storage, a differential value for updating the at least one parameter in accordance with backpropagation; calculating, by the differential process of each pair based on the differential value and the at least one parameter at the present time, a transmission value to be transmitted to the communication processes of the other pairs; determining, by the communication process of each pair, whether the differential process of the corresponding pair has completed calculation of the transmission value; transmitting, by the communication process of each pair, the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has completed calculation of the transmission value; transmitting, by the communication process of each pair, a part of the at least one parameter at the present time to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has not completed calculation of the transmission value; and updating, by the communication process of each pair, the at least one parameter at the present time based on: the transmission value transmitted from the communication process of at least one of the other pairs; and the part of the at least one parameter at the present time transmitted from the communication process of the remaining at least one of the other pairs. 19. A learning method for updating at least one parameter for a neural network based on a plurality of processes executed by at least one processor, the learning method, by each of the processes, comprising: calculating, as a difference value, a compressed value of a difference between a first value of the at least one parameter at a present time that is referred to a first time and a second value of the at least one parameter at a second time that is later than the first time; calculating, based on the at least one parameter at the first time, the difference value, and training data stored in a storage, a differential value for updating the at least one parameter in accordance with backpropagation; compressing the differential value; calculating, based on the encoded differential value and the difference value, a transmission value to be transmitted to the other processes; obtaining the difference value based on the transmission values transmitted from the other processes and the transmission value calculated by the corresponding process; and updating, based on a restored value of the difference value, the at least one parameter at the second time. 20. A learning method for updating at least one parameter for a neural network based on plural pairs of a differential process and a communication process executed by at least one processor, the learning method comprising: calculating, by the differential process of each pair, a difference value indicative of a compressed value of a difference between a first value of the at least one parameter at a present time that is referred to a first time and a second value of the at least one parameter at a second time that is later than the first time; calculating, by the differential process of each pair based on the at least one parameter at the first time, the difference value, and training data stored in a storage, a differential value for updating the at least one parameter in accordance with backpropagation; compressing, by the differential process of each pair, the differential value; calculating, by the differential process of each pair based on the encoded differential value and the difference value, a transmission value to be transmitted to the other processes; determining, by the communication process of each pair, whether the differential process of the corresponding pair has completed calculation of the transmission value; transmitting, by the communication process of each pair, the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has completed calculation of the transmission value; transmitting, by the communication process of each pair, the difference value as the transmission value to the communication processes of the other pairs when it is determined that the differential process of the corresponding pair has not completed calculation of the transmission value; obtaining, by the communication process of each pair, the difference value based on the transmission values transmitted from the other processes and the transmission value calculated by the differential process of the corresponding pair; and updating, by the communication process of each pair based on a restored value of the difference value, the at least one parameter at the second time.