Recursive Dimensional Decomposition Convolution for High-Dimensional Tensors
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Solution Overview
Problem
Machine learning models, particularly convolutional neural networks, struggle to process datasets with more than three dimensions due to limitations in convolutional layers, leading to inefficiencies in computation, memory usage, and parallelization, especially in devices with limited memory resources.
Innovation Solution
The implementation of recursive dimensional decomposition (RDD) convolution, which iteratively 'peels off' dimensions from a tensor and processes them using lower-dimensional convolution functions, allowing datasets with higher dimensions to be processed efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a convolutional layer is configured to handle a specific number of dimensions (e.g., 2D or 3D), then the convolution operation can be performed efficiently with optimized computation and memory usage, but the system cannot process datasets with more dimensions than the convolutional layer is configured to handle
Solution Approach 1:
The patent segments the high-dimensional tensor processing into multiple sequential convolution operations. Each convolution operates on a specific dimension or subset of dimensions, breaking down the complex high-dimensional convolution into manageable lower-dimensional operations that can be processed efficiently by standard convolutional layers
Solution Approach 2:
The patent transforms the high-dimensional convolution problem into a sequence of lower-dimensional convolution operations. By processing dimensions sequentially and using batch processing to handle remaining dimensions, the system effectively converts a single high-dimensional operation into multiple lower-dimensional operations that fit within standard convolutional layer capabilities
2Adaptability or versatility
If a high-dimensional tensor is processed using multiple sequential convolution operations, then the system can handle datasets with more dimensions than a single convolutional layer supports, but the computation time and processing steps increase
Solution Approach 1:
The patent merges multiple convolution operations into a unified processing pipeline. By combining sequential convolutions with batch processing operations and using memory-efficient tensor manipulation techniques, the system reduces the overall computation time compared to naive sequential processing
3Productivity
If dimensions are grouped into a single dimension for processing, then the dimensionality of the tensor is reduced to match the convolution function requirements, but information from the grouped dimensions must be aggregated
Solution Approach 1:
The patent uses batch processing to give the batch dimension multiple functions: it serves as both a grouping mechanism for reducing dimensionality and as a container for preserving information from multiple original dimensions. The batch dimension effectively becomes a multi-functional space that handles both compression and information preservation
Data Source
AI summary
Dimensional decomposition convolution systems and techniques are described. A system receives a tensor including a first number of dimensions. The system processes a variant of the tensor using a convolution function including a second number of dimensions to generate a processed tensor. The first number of dimensions is greater than the second number of dimensions. A plurality of dimensions from the first number of dimensions of the tensor are grouped into a dimension of the variant of the tensor to reduce dimensionality of the variant of the tensor to the second number of dimensions.