CP Decomposition
A classical tensor decomposition method that represents a higher-order tensor as a sum of rank-one tensors. It is widely used for low-rank approximation and feature extraction from multi-dimensional data.
Timeline (last 90 days)
APTNN introduces the canonical polynomial (CP) decomposition structure of tensor neural networks (TNN) into the approximate representation of the solution, and the equation residual retains the CP decomposition form under this representation.
Because the residual retains the CP decomposition form, the high-dimensional loss integral can be decomposed into a combination of one-dimensional integrals for computation, reducing computation and storage cost from exponential growth with dimension to polynomial growth.
The choice of CP decomposition rank, the weighting balance of the augmented loss terms across different parameter regions, and extension to more complex geometries and boundary conditions are questions that have not yet been fully explored.
Commonly used tensor dimensionality reduction approaches include Tucker decomposition (each mode is reduced independently) and CP decomposition (all modes share the rank).
All Facts (4)
APTNN introduces the canonical polynomial (CP) decomposition structure of tensor neural networks (TNN) into the approximate representation of the solution, and the equation residual retains the CP decomposition form under this representation.
50%UnverifiedBecause the residual retains the CP decomposition form, the high-dimensional loss integral can be decomposed into a combination of one-dimensional integrals for computation, reducing computation and storage cost from exponential growth with dimension to polynomial growth.
50%UnverifiedThe choice of CP decomposition rank, the weighting balance of the augmented loss terms across different parameter regions, and extension to more complex geometries and boundary conditions are questions that have not yet been fully explored.
50%UnverifiedCommonly used tensor dimensionality reduction approaches include Tucker decomposition (each mode is reduced independently) and CP decomposition (all modes share the rank).
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