Annealing System Nonlinear Objective Function Conversion
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Solution Overview
Problem
Existing annealing machines face difficulties in optimizing strong nonlinear objective functions derived from machine learning, as they require a large number of additional spin variables to convert these functions into Ising models, exceeding the upper limit of spin variables that can be handled.
Innovation Solution
An information processing system that analyzes a training database to derive an unconstrained quadratic-form function or a linear-constraint linear-form function using machine learning, reducing the dimensionality of nonlinear terms by generating dummy variables and converting the objective function, allowing for optimization using annealing or other methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a strong nonlinear objective function derived from machine learning is converted into an Ising model using conventional methods, then the objective function can be optimized using annealing, but the number of additional spin variables required exceeds the upper limit that can be handled
Solution Approach 1:
The patent changes the parameter representation by introducing a dummy variable that transforms the objective function from a nonlinear form with high-order terms to a quadratic form. This parameter transformation allows the function to be represented with fewer and simpler spin variables, converting the optimization problem into a form that fits within the hardware constraints of annealing machines while preserving the ability to handle nonlinear relationships through the dummy variable construction
Solution Approach 2:
The dummy variable acts as an intermediary element that mediates between the original nonlinear objective function and the Ising model representation. By introducing this intermediate variable, the patent enables the conversion of high-order nonlinear terms into quadratic interactions, thereby reducing the complexity of the spin variable system while maintaining the optimization capability for the original nonlinear function
2Measurement precision
If the number of dummy variables is increased to convert strong nonlinear objective functions into Ising models, then the conversion accuracy is improved, but the upper limit of spin variables that can be handled is exceeded
Solution Approach 1:
The patent applies parameter changes by reformulating the objective function into a quadratic form through intelligent dummy variable construction. This transformation achieves accurate representation of the original nonlinear function with a minimized number of dummy variables, as the quadratic form naturally captures the essential relationships without requiring excessive variable expansion
Solution Approach 2:
The patent employs partial action by introducing dummy variables only where necessary to capture the nonlinear relationships in the objective function. Rather than systematically expanding all possible interactions, the method selectively introduces dummy variables to represent the essential nonlinear terms, achieving sufficient conversion accuracy without the excessive variable proliferation that would exceed hardware limits
Data Source
AI summary
An information processing system enables searching for an optimum solution through annealing by converting, into an Ising model, a strong nonlinear objective function derived from machine learning. An objective function derivation system performs machine learning on a training database; and a function conversion system converts the objective function. The objective function derivation system includes: a machine learning setting unit; and a learning unit configured to derive the objective function. The function conversion system includes a dummy variable setting unit and generation unit, and a function conversion unit that reduces, by deleting the explanatory variable appearing explicitly in the objective function by using the dummy variable, a dimension of a nonlinear term of the explanatory variable at an order higher than quadratic to the quadratic or lower, and convert the objective function to the unconstrained quadratic-form function or the linear-constraint linear-form function related to the dummy variable and the objective variable.