Sampling Apparatus Offset Feedback for Boltzmann Distribution
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Solution Overview
Problem
The optimization apparatus using digital circuitry speeds up computation by parallel search processing and adding an offset value, leading to a deviation from the Boltzmann distribution, resulting in lower sampling accuracy compared to the ordinary MCMC method.
Innovation Solution
A sampling apparatus that computes an expected value of the number of trials where a state remains unchanged, using an offset value to ensure each state remains unchanged for one trial, thereby reproducing the probability process of the ordinary MCMC method and maintaining high-speed computation processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If parallel search processing and offset value addition are used to speed up computation, then computation speed is improved, but sampling accuracy deteriorates due to deviation from Boltzmann distribution
Solution Approach 1:
The patent introduces a feedback mechanism where the system monitors the number of trials where state transitions occur and adjusts the offset value accordingly. By counting the frequency of state changes and comparing it against expected values from Boltzmann distribution, the system dynamically tunes the offset parameter to maintain distribution accuracy while preserving computational speedup benefits
Solution Approach 2:
The patent modifies the offset parameter based on observed state transition patterns. By changing the offset value in response to measured deviations from expected Boltzmann distribution characteristics, the system corrects accuracy issues while maintaining the parallel search computational advantage
2Productivity
If offset value is added to speed up computation, then computation efficiency is improved, but probability process accuracy deteriorates
Solution Approach 1:
The system implements feedback by monitoring the actual probability distribution generated during parallel search and comparing it against the theoretical Boltzmann distribution. Based on this comparison, the offset value is adjusted to ensure the probability process maintains mathematical correctness while benefiting from computational acceleration
3Measurement precision
If ordinary MCMC method is used to maintain sampling accuracy, then sampling accuracy is improved, but computation speed deteriorates
Solution Approach 1:
The patent segments the computation into two parts: parallel search processing that generates candidate states quickly, followed by a correction step that adjusts the offset value based on observed state transitions. This segmentation allows the system to benefit from both fast parallel exploration and accurate Boltzmann distribution sampling
Solution Approach 2:
The offset value acts as an intermediary parameter that bridges the gap between fast parallel search and accurate Boltzmann sampling. By tuning this intermediate parameter based on observed state transitions, the system reconciles the conflict between computational speed and sampling accuracy
Data Source
AI summary
An information processing apparatus includes: a memory; and a processor coupled to the memory and configured to: hold values of a plurality of state variables included in an evaluation function representing energy, and outputs, every certain number of trials, the values of the plurality of state variables; compute, when a state transition occurs in response to changing of one of the values of the plurality of state variables, an energy change value for each state transition based on a weight value selected based on an update index value; and determine a first offset value based on a plurality of the energy change values such that at least one of the state transitions is allowed, outputs a plurality of first evaluation values obtained by adding the first offset value to the plurality of energy change values, and outputs, every certain number of trials, the first offset value.