Neural Network Parameter Updates Using Segmented Kronecker Matrices
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Solution Overview
Problem
Higher-order optimization algorithms for deep learning models, while providing better training precision, suffer from high time complexity due to the computational expense of inverting large higher-order information matrices, which is not efficiently addressed by existing methods like KFAC for large-scale models.
Innovation Solution
Segment the Kronecker factor matrices of higher-order information matrices into smaller square matrices, ensuring each diagonal element is included in a single square matrix, and adjust neural network parameters based on these matrices to reduce inversion complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If higher-order optimization algorithms are used to improve training precision, then training precision is improved, but time complexity increases
Solution Approach 1:
The patent segments the large higher-order information matrix into multiple smaller square matrices by dividing the parameter space into disjoint groups. Each group forms a separate square matrix that can be processed independently, reducing the computational complexity from O(n³) for the full matrix to O(k·m³) where k is the number of segments and m is the size of each segment, with m < n.
2Measurement precision
If higher-order information matrices are inverted to optimize parameters, then training precision is improved, but training time increases
Solution Approach 1:
The patent divides the parameter space into multiple disjoint groups, where each group corresponds to a subset of parameters. The higher-order information matrix is then segmented into multiple smaller square matrices based on these groups. Each smaller matrix can be inverted independently and in parallel, significantly reducing the total inversion time compared to inverting the full large matrix.
Solution Approach 2:
The patent applies partial action by inverting only the diagonal blocks (smaller square matrices) of the higher-order information matrix rather than the entire matrix. This partial inversion approach captures the essential curvature information needed for optimization while avoiding the computational burden of full matrix inversion, thus reducing training time while maintaining precision.
3Productivity
If Kronecker factor matrices are used to approximate higher-order information matrices, then computational efficiency is improved, but approximation accuracy may be reduced
Solution Approach 1:
The patent segments the Kronecker factor matrices into multiple smaller square matrices corresponding to different parameter groups. This segmentation allows each small matrix to be processed with higher numerical precision while maintaining the overall approximation structure. The disjoint grouping ensures that each segment captures specific parameter interactions without redundancy, balancing accuracy and efficiency.
Data Source
AI summary
Example parameter optimization methods and apparatus are described. In one example parameter optimization method, a data processing device obtains a Kronecker factor matrix that is used to indicate a higher-order information matrix of a neural network model, and segments the Kronecker factor matrix to obtain a plurality of square matrices. The obtained plurality of square matrices are submatrices of the Kronecker factor matrix, and main diagonal lines of the plurality of square matrices each are in a one-to-one correspondence with a part of a main diagonal line of the Kronecker factor matrix. Then, the data processing device adjusts a parameter of the neural network model based on the obtained plurality of square matrices.