A method includes using a computational network to learn and predict time-series data. The computational network is configured to receive the time-series data and perform transformation-invariant encoding of the time-series data. The computational network includes one or more encoding layers. The method also includes feeding back future predictions of the time-series data through inertial adjustments of transformations. The inertial adjustments preserve the invariants in the computational network. The computational network could further include one or more pooling layers each configured to reduce dimensionality of data, where the one or more pooling layers provide the transformation invariance for the encoding.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method comprising: using a computational network to learn and predict time-series data, the computational network configured to receive the time-series data and perform transformation-invariant encoding of the time-series data, the computational network comprising one or more encoding layers; and feeding back future predictions of the time-series data through inertial adjustments of transformations, the inertial adjustments preserving the invariants in the computational network. 2. The method of claim 1, wherein the computational network further comprises one or more pooling layers each configured to reduce dimensionality of data, the one or more pooling layers providing the transformation invariance for the encoding. 3. The method of claim 2, wherein each pooling layer performs a pooling function, the pooling function representing a l2 norm. 4. The method of claim 1, wherein the inertial adjustments of the transformations are made based on a projection function that combines a current value of the time-series data with a previous value of the time-series data. 5. The method of claim 4, wherein the projection function represents an arc projection defined as: 2   y τ - 1 · y τ  y τ  2  y τ - y τ - 1 where yτ denotes the current value and yτ−1 denotes the previous value. 6. The method of claim 4, wherein the projection function represents a sequence projection yτ−1yτ→yτ+1 defined as: eiej→e2j-i(mod n) where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, and n denotes a dimension of y. 7. The method of claim 4, wherein the projection function represents a memory projection yτ−1yτ→yτ+1 defined as: eiej→ΣkPijkek where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, Pij denotes learned frequencies with a decaying distribution, and k denotes an index of a summation function Σ. 8. An apparatus comprising: at least one processing device; and at least one memory storing instructions that, when executed by the at least one processing device, cause the at least one processing device to: learn and predict time-series data using a computational network, the computational network configured to receive the time-series data and perform transformation-invariant encoding of the time-series data, the computational network comprising one or more encoding layers; and feed back future predictions of the time-series data through inertial adjustments of transformations, the inertial adjustments preserving the invariants in the computational network. 9. The apparatus of claim 8, wherein the computational network further comprises one or more pooling layers each configured to reduce dimensionality of data, the one or more pooling layers configured to provide the transformation invariance for the encoding. 10. The apparatus of claim 9, wherein each pooling layer is configured to perform a pooling function, the pooling function representing a l2 norm. 11. The apparatus of claim 8, wherein the at least one processing device is configured to make the inertial adjustments of the transformations based on a projection function that combines a current value of the time-series data with a previous value of the time-series data. 12. The apparatus of claim 11, wherein the projection function represents an arc projection defined as: 2   y τ - 1 · y τ  y τ  2  y τ - y τ - 1 where yτ denotes the current value and yτ−1 denotes the previous value. 13. The apparatus of claim 11, wherein the projection function represents a sequence projection yτ−1yτ→yτ+1 defined as: eiej→e2j-i(mod n) where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, and n denotes a dimension of y. 14. The apparatus of claim 11, wherein the projection function represents a memory projection yτ−1yτ→yτ+1 defined as: eiej→ΣkPijkek where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, Pij denotes learned frequencies with a decaying distribution, and k denotes an index of a summation function Σ. 15. A non-transitory computer readable medium containing instructions that, when executed by at least one processing device, cause the at least one processing device to: learn and predict time-series data using a computational network, the computational network configured to receive the time-series data and perform transformation-invariant encoding of the time-series data, the computational network comprising one or more encoding layers; and feed back future predictions of the time-series data through inertial adjustments of transformations, the inertial adjustments preserving the invariants in the computational network. 16. The non-transitory computer readable medium of claim 15, wherein the computational network further comprises one or more pooling layers each configured to reduce dimensionality of data, the one or more pooling layers configured to provide the transformation invariance for the encoding. 17. The non-transitory computer readable medium of claim 16, wherein each pooling layer is configured to perform a pooling function, the pooling function representing a l2 norm. 18. The non-transitory computer readable medium of claim 15, wherein the inertial adjustments of the transformations are based on a projection function that combines a current value of the time-series data with a previous value of the time-series data. 19. The non-transitory computer readable medium of claim 18, wherein the projection function represents an arc projection defined as: 2   y τ - 1 · y τ  y τ  2  y τ - y τ - 1 where yτ denotes the current value and yτ−1 denotes the previous value. 20. The non-transitory computer readable medium of claim 18, wherein the projection function represents a sequence projection yτ−1yτ→yτ+1 defined as: eiej→e2j-i(mod n) where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, and n denotes a dimension of y. 21. The non-transitory computer readable medium of claim 18, wherein the projection function represents a memory projection yτ−1yτ→yτ+1 defined as: eiej→ΣkPijkek where yτ denotes the current value, yτ−1 denotes the previous value, yτ+1 denotes a predicted future value, ei and ej respectively denote unit vectors in ith and jth directions, Pij denotes learned frequencies with a decaying distribution, and k denotes an index of a summation function Σ.