Ising Machine Auxiliary Variables for Higher-Order Optimization
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Solution Overview
Problem
The existing Ising machines face difficulties in solving discrete optimization problems represented by higher-order evaluation functions due to an increase in the number of independent variables, which complicates the solution space and reduces the size of solvable problems.
Innovation Solution
A data processing apparatus that calculates local fields for higher-order terms using auxiliary variables, allowing the evaluation function to reach local minima or maxima without increasing the number of independent variables, by employing a processor to determine value changes based on coefficients and local fields from storage devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a higher-order evaluation function is used to represent discrete optimization problems, then the problem-solving capability is improved, but the number of independent variables increases
Solution Approach 1:
The patent introduces auxiliary variables as intermediaries to represent higher-order terms in the evaluation function. These auxiliary variables act as mediators between the original state variables and the higher-order interactions, allowing the system to handle cubic and higher-order terms without directly increasing the number of independent state variables. The auxiliary variables are determined by the values of state variables through specific relationships defined in the patent.
Solution Approach 2:
The patent segments the evaluation function into quadratic terms and higher-order terms. The higher-order terms are separated and represented using auxiliary variables, while the state variables themselves remain unchanged. This segmentation allows the Ising machine to process the problem in a structured way, handling different order terms through appropriate computational mechanisms.
2Adaptability or versatility
If the number of independent variables increases to handle higher-order terms, then the evaluation function can represent more complex problems, but the solution space increases
Solution Approach 1:
By using auxiliary variables as intermediaries, the patent avoids directly expanding the solution space with additional independent state variables. The auxiliary variables are functionally dependent on the state variables, meaning they don't independently expand the search space but rather provide a computational mechanism to represent higher-order interactions within the existing variable framework.
Solution Approach 2:
The patent effectively adds a computational dimension by introducing auxiliary variables that are determined by relationships with state variables. This allows the system to handle higher-order terms without proportionally increasing the independent solution space, as the auxiliary variables operate in a dependent dimension rather than an independent one.
3Measurement precision
If auxiliary variables are introduced to calculate local fields for higher-order terms, then the calculation accuracy is improved, but the computational complexity increases
Solution Approach 1:
The patent segments the local field calculation into contributions from quadratic terms and higher-order terms. The auxiliary variables are specifically designed to handle the higher-order term contributions, allowing for precise calculation of each component separately. This segmentation enables accurate local field computation while organizing the computational complexity in a manageable structure.
Solution Approach 2:
The auxiliary variables are determined self-consistently from the state variables through predefined relationships. Once the state variables are set, the auxiliary variables automatically take on appropriate values that reflect the higher-order interactions, reducing the need for complex external computation and allowing the system to self-determine the necessary field contributions.
Data Source
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AI summary
A computer of searching for a combination of state variables with which an evaluation function including the state variables becomes a local minimum or maximum, the computer including: a memory storing a first coefficient indicating a magnitude of interaction between k state variables in a kth order term of the evaluation function; and a processor that performs: calculating a first local field indicating a change amount of the kth order term when a first state variable among the k state variables changes by the first coefficient and a first variable obtained by the k state variables and second coefficients; and determining whether to allow a change in the first state variable based on a result of comparison between a predetermined value and a product of a sum of the first local field and a second local field indicating a change amount of quadratic and lower-order terms of the evaluation function.