Practical Solutions for Enhancing Tensor Contraction Paths
Introduction
Tensor contradictions are crucial in various research fields, including model counting, quantum circuits, graph problems, and machine learning. However, minimizing computational cost is essential. The computational cost varies based on matrix dimensions and the number of tensors, making it important to find efficient contraction paths.
Efficient Contraction Paths
Earlier methods focused on finding efficient contraction paths for tensor hypernetworks. These methods include simulated annealing, genetic algorithms, graph decomposition, reinforcement learning, and graph neural networks. A novel method has been introduced to enhance tensor contraction paths using a modified standard greedy algorithm with an improved cost function, outperforming existing approaches.
Computing Contraction Paths
The computation of contraction paths involves three phases: computation of Hadamard products, contraction of remaining tensors, and computation of outer products. The modified greedy algorithm uses multiple cost functions as parameters, selecting the most appropriate cost function at runtime for generating efficient contraction paths.
Experimental Results
Researchers conducted experiments to compare various algorithms and measure flops for different problem examples. The proposed method demonstrated the ability to find efficient contraction paths in less time and solve complex problems, outperforming other methods.
Conclusion
The proposed method offers a novel approach to enhance tensor contraction paths, using a multiple-cost-functions approach and a modified standard greedy algorithm. It provides efficient solutions for practical scenarios, outperforming existing algorithms.
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