Tensor Decomposition for Machine Learning via Mode Segmentation
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Solution Overview
Problem
The amount of calculation for tensor decomposition increases exponentially with the number of modes, leading to significant computational and memory requirements, particularly in applications like chemical formulas with multiple modes.
Innovation Solution
A machine learning device identifies label and topology modes in tensor data, converting mode products to concatenations to reduce the number of nonzero elements, thereby linearizing the increase in calculation, and rearranges the processing order to minimize the number of nonzero elements in intermediate tensors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If standard mode product calculation is used for tensor decomposition, then the calculation is systematic and follows conventional algorithms, but the computational burden and memory requirements increase exponentially with the number of modes
Solution Approach 1:
The patent segments the tensor decomposition process by identifying and separating label modes from topology modes. This segmentation allows different calculation strategies to be applied to different mode types, reducing the overall computational burden while maintaining systematic processing.
Solution Approach 2:
The patent changes the calculation parameter from standard mode product to concatenation operation for label modes. This parameter change transforms the exponential computational complexity into linear complexity with respect to the number of nonzero elements, significantly reducing computational burden.
2Ease of manufacture
If standard mode product calculation is used for tensor decomposition, then the calculation follows conventional algorithms, but the memory requirements increase exponentially with the number of modes
Solution Approach 1:
The patent segments the tensor decomposition process by identifying and separating label modes from topology modes. This segmentation allows different calculation strategies to be applied to different mode types, reducing the overall memory requirements while maintaining systematic processing.
Solution Approach 2:
The patent changes the calculation parameter from standard mode product to concatenation operation for label modes. This parameter change transforms the exponential memory requirements into linear memory requirements with respect to the number of nonzero elements, significantly reducing memory consumption.
3Ease of operation
If mode product is used for all modes, then the calculation is uniform and simple to implement, but the number of nonzero elements in intermediate tensors increases unnecessarily
Solution Approach 1:
The patent applies different calculation operations to different modes based on their local characteristics. Label modes use concatenation operation to preserve sparsity, while topology modes use mode product operation. This local quality approach optimizes the number of nonzero elements in intermediate tensors.
Solution Approach 2:
The patent changes the calculation parameter from mode product to concatenation for label modes, which have the property of being represented by one-hot vectors. This parameter change is applied locally to specific modes rather than uniformly to all modes, reducing the number of nonzero elements.
Data Source
AI summary
A machine learning process including identifying a first axis including elements represented by one-hot vectors and a second axis including elements not represented by one-hot vectors, among a plurality of axes included in tensor-form data, when calculating a core tensor from the tensor-form data via a plurality of intermediate tensors, calculating the core tensor from the tensor-form data by a first process of concatenating elements included in a first element matrix corresponding to the first axis to elements included in a first intermediate tensor among the plurality of intermediate tensors and a second process of calculating a mode product between a second intermediate tensor among the plurality of intermediate tensors and a second element matrix corresponding to the second axis, and performing machine learning of a machine learning model with the core tensor as an input.