Chaotic Discrete-Space Sampling With Metropolis-Hastings Acceptance

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Solution Overview

Problem

Classical digital computers are inefficient and energy-intensive for solving NP-hard combinatorial optimization problems, while existing physical systems-based computers face challenges in maintaining accuracy and fairness in sampling.

Innovation Solution

A hybrid computing approach using deterministic evolution with chaotic amplitude control and probabilistic sampling based on the Metropolis-Hastings criterion, which integrates digital and analog components to enhance speed and fairness in sampling.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Use of energy by moving object

If physical systems-based computers are used to solve combinatorial optimization problems, then energy efficiency is improved, but sampling accuracy and fairness deteriorate

Engineering Contradiction:

Improveenergy efficiencyVSAvoidsampling accuracy

Core Design Contradiction:

Use of energy by moving objectVSMeasurement precision

Solution Approach 1:

The patent implements a feedback mechanism where the Metropolis-Hastings acceptance criterion evaluates proposed state transitions based on energy differences. The system continuously monitors sampling outcomes and adjusts the acceptance probability accordingly, ensuring that only energetically favorable or probabilistically justified transitions are accepted. This feedback loop maintains sampling accuracy while preserving the energy efficiency of physical systems-based computation.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The patent dynamically adjusts the acceptance probability parameter in the Metropolis-Hastings criterion based on the energy difference between current and proposed states. By changing this parameter adaptively, the system ensures fair sampling across different energy landscapes while maintaining the inherent energy efficiency of physical systems. The acceptance probability is modified as a function of energy difference, allowing the system to explore the solution space effectively without sacrificing accuracy.

Inventive Principle:

Principle #35Parameter changes

2Reliability

If deterministic evolution is used in physical systems-based computing, then convergence to lowest energy state is improved, but ability to escape local minima deteriorates

Engineering Contradiction:

Improveconvergence reliabilityVSAvoidability to escape local minima

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent introduces dynamic behavior by combining deterministic evolution with probabilistic transitions. The system evolves deterministically toward lower energy states but incorporates random jumps that are accepted or rejected based on the Metropolis-Hastings criterion. This dynamic approach allows the system to occasionally escape local minima through probabilistic transitions while maintaining overall convergence reliability. The balance between deterministic and stochastic elements enables both reliable convergence and adaptability to escape suboptimal states.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The patent employs periodic alternating between deterministic evolution steps and probabilistic jump attempts. During deterministic phases, the system reliably converges toward lower energy states. Periodically, it introduces probabilistic jumps that can escape local minima if energetically favorable. This periodic alternation ensures both convergence reliability during deterministic phases and adaptability to escape local minima during probabilistic phases, resolving the contradiction between these two requirements.

Inventive Principle:

Principle #19Periodic action

3Productivity

If chaotic amplitude control is applied, then sampling speed is improved, but sampling fairness deteriorates

Engineering Contradiction:

Improvesampling speedVSAvoidsampling fairness

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent introduces the Metropolis-Hastings acceptance criterion as an intermediary mechanism between chaotic amplitude control and the physical system state. The chaotic control accelerates exploration of the solution space, but all proposed transitions are filtered through the Metropolis-Hastings criterion, which ensures fairness by accepting or rejecting jumps based on energy differences. This intermediary preserves the speed benefits of chaotic control while eliminating fairness violations, as the acceptance criterion enforces proper sampling distribution regardless of how rapidly states are proposed.

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS20250284762A1Metropolis-hastings adjusted chaotic discrete space sampling

Publication Date: 2025.09.11 NTT RESEARCH INC

AI summary

A system may be provided. The system may include one or more processors. The one or more processors may be configured to evolve a dynamic time system mapped to a combination of variables through a deterministic path for a predetermined time period. The one or more processors may further be configured to cause a probabilistic jump of the dynamic time system after the predetermined time period. The one or more processors may also be configured to accept or reject the probabilistic jump based on a Metropolis-Hastings criterion.