Hypervector Bundling With Blockwise Weighted Mapping
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Solution Overview
Problem
Existing methods for processing hypervectors, particularly in high-dimensional spaces, face inefficiencies due to the resource-intensive nature of operations like binding and factorization, especially when dealing with sparse vectors and arbitrary sparsity levels, leading to inaccurate results and high computational complexity.
Innovation Solution
The method involves segmenting hypervectors into blocks for blockwise processing, using resonator networks to iteratively search for factorizations, and employing a share-based bundling approach that maps M-dimensional vectors to S-dimensional vectors, allowing for efficient weighted bundling with controlled sparsity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional binding and factorization operations are used on high-dimensional hypervectors, then the operations can be performed, but the computational complexity and resource consumption increase significantly
Solution Approach 1:
The patent segments high-dimensional hypervectors into multiple blocks of lower-dimensional sub-vectors. Instead of performing operations on the entire D-dimensional hypervector at once, the system divides it into S blocks where each block has dimension L (D=S×L). This segmentation allows factorization to be performed blockwise, reducing the computational complexity from O(M×D) to O(S×L) where S < M, thereby improving computational efficiency while handling high-dimensional data.
Solution Approach 2:
The patent transforms the problem from operating directly in the high-dimensional D-space to operating in a lower-dimensional L-space through blockwise processing. By mapping D-dimensional hypervectors to S-dimensional block structures, the system effectively changes the operational dimensionality, performing factorization in smaller L-dimensional subspaces that are computationally more efficient while preserving the essential information through the block structure.
2Measurement precision
If sparse vectors with arbitrary sparsity levels are processed using traditional methods, then the processing can be performed, but the accuracy deteriorates due to resource constraints
Solution Approach 1:
The patent applies local quality by treating different blocks of the hypervector with specialized processing tailored to their sparsity characteristics. Each block can be processed independently with operations optimized for its specific sparsity level, allowing the system to maintain high accuracy for dense blocks while efficiently handling sparse blocks. This localized processing ensures that factorization accuracy is maintained across varying sparsity levels without requiring uniform high-resource allocation throughout the entire hypervector.
3Adaptability or versatility
If larger problem sizes are handled, then the capacity increases, but the computational complexity and resource requirements increase
Solution Approach 1:
The patent enables handling of larger problem sizes by segmenting large D-dimensional hypervectors into S manageable blocks of dimension L. This segmentation allows the system to process larger datasets and more complex factorization problems by dividing them into smaller, independently processable units. The blockwise approach maintains scalability, as the system can increase problem capacity by adjusting S and L parameters without proportionally increasing computational resources, since each block is processed separately with reduced complexity.
Data Source
AI summary
Embodiments are disclosed for a method. The method includes bundling a set of M code hypervectors, each of dimension D, where M>1. The bundling includes receiving an M-dimensional vector comprising weights for weighting the set of code hypervectors. The bundling further includes mapping the M-dimensional vector to an S-dimensional vector, sk, such that each element of the S-dimensional vector, sk, indicates one of the set of code hypervectors, where S=D/L and L≥1. Additionally, the bundling includes building a hypervector such that an ith element of the built hypervector is an ith element of the code hypervector indicated in an ith element of the S-dimensional vector, sk.