Tensor Contraction Tree Optimization for Speed-Memory Balance
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Solution Overview
Problem
Existing tensor network contraction schemes are inefficient in finding optimal contraction trees, leading to high computation time and memory usage, and are not adaptive to dynamic changes in tensor networks.
Innovation Solution
A method that iteratively decomposes and reconstructs contraction trees using multi-partite and bipartition decomposition algorithms, optimizing parameters to find a local optimal sub-graph, reducing computation and storage costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If standard matrix product contraction scheme is used, then the tensor network contraction can be performed, but it occupies large communication bandwidths and memory capacity
Solution Approach 1:
The patent segments the tensor network into multiple sub-networks and decomposes the contraction tree into smaller sub-trees. By processing contractions in divided segments rather than as a whole, the method reduces peak memory requirements while maintaining contraction speed through parallel processing of segments.
Solution Approach 2:
The patent transforms the traditional single-dimension contraction approach into a multi-dimensional optimization by considering both computation cost and memory footprint as separate optimization dimensions. The contraction tree is optimized to balance these two dimensions simultaneously, achieving high speed with reduced memory usage.
2Adaptability or versatility
If handcrafted contraction orders are used, then the contraction process is simplified, but it is not adaptive to dynamic changes in the tensor network
Solution Approach 1:
The patent implements a dynamic optimization approach where the contraction tree is constructed and optimized based on the actual structure and characteristics of the given tensor network. Rather than using fixed handcrafted orders, the system adapts the contraction sequence to the specific problem instance, enabling adaptability to dynamic changes while managing complexity through efficient algorithms.
Solution Approach 2:
The patent changes the optimization parameters from fixed handcrafted sequences to dynamically determined contraction orders based on tensor network characteristics. By adjusting contraction parameters according to the specific problem structure, the system achieves adaptability without excessive complexity through guided optimization strategies.
3Productivity
If decomposition into low-rank subnetworks is performed without parameter optimization, then the computation is simplified, but the contraction cost is not minimized
Solution Approach 1:
The patent employs feedback mechanisms where the optimization process evaluates contraction costs at each step and adjusts the contraction tree structure accordingly. By incorporating cost evaluation feedback into the tree construction process, the system minimizes total contraction cost while managing complexity through iterative refinement rather than exhaustive search.
Solution Approach 2:
The patent performs preliminary optimization of the contraction tree structure before executing the actual contractions. By pre-optimizing the tree topology and contraction sequence based on tensor network characteristics, the system reduces total contraction cost without requiring complex real-time optimization during execution.
Data Source
AI summary
Methods and systems for tensor network contraction are provided. A method implemented by a computing host comprises obtaining a contraction tree associated with a tensor network, wherein a plurality of vertices and edges of the contraction tree correspond to a set of tensor nodes and indices of the tensor network, respectively; iteratively performing operations until a termination condition is satisfied, the operations including selecting a sub-graph of the contraction tree; replacing the sub-graph with a local optimal sub-graph; and obtaining an optimized contraction tree including the local optimal sub-graph; and outputting the optimized contraction tree.