Recursive Neural Network Checking for Alternating Specifications

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Solution Overview

Problem

Conventional methods struggle to check the behavior of systems controlled by recursive neural networks, particularly when specifications require alternating satisfaction and non-satisfaction of functions over time, which cannot be described using Linear Temporal Logic.

Innovation Solution

A checking device and method that utilize a calculating unit to determine whether a recursive neural network satisfies a specification by calculating a semantics set using universal modal μ-calculus expressions and constrained zonotopes, and a determining unit to verify the satisfaction based on the initial state, with a generating unit generating counterexamples if necessary.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If conventional checking methods using Linear Temporal Logic are applied, then checking is simple and straightforward, but they cannot check recursive neural networks with alternating satisfaction and non-satisfaction specifications

Engineering Contradiction:

Improvecapability to check alternating satisfaction specificationsVSAvoidchecking method complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent changes the logical framework parameter from Linear Temporal Logic to modal μ-calculus, which provides greater expressive power for specifying alternating satisfaction and non-satisfaction conditions. This parameter change enables the checking method to handle complex temporal specifications that were previously inexpressible, directly resolving the adaptability limitation while managing complexity through formal mathematical foundations.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces a semantics set as an intermediary mathematical construct that bridges the recursive neural network and the modal μ-calculus specification. This intermediary enables the translation of complex temporal specifications into set-theoretic operations, making the checking process tractable while maintaining full expressive power for alternating satisfaction conditions.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If the checking method uses modal μ-calculus and semantics sets, then it can handle complex alternating specifications, but the calculation and verification process becomes more complex

Engineering Contradiction:

Improvespecification satisfaction verification accuracyVSAvoidchecking process complexity

Core Design Contradiction:

ReliabilityVSDifficulty of detecting and measuring

Solution Approach 1:

The patent replaces traditional model checking mechanics with a semantics-based mathematical approach. Instead of performing complex state-space exploration and temporal logic model checking, the method uses set operations and mathematical relationships to verify specification satisfaction. This substitution maintains high reliability for detecting specification violations while reducing the computational complexity of the checking process.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent segments the verification process into distinct mathematical operations: calculating the semantics set, determining set relationships, and comparing against the initial state. This segmentation breaks down the complex verification task into manageable, well-defined mathematical steps, reducing the difficulty of implementation and analysis while maintaining verification accuracy.

Inventive Principle:

Principle #1Segmentation

3Adaptability or versatility

If conventional model checking is used for nonlinear recursive neural networks, then the checking process is straightforward, but it cannot properly verify systems with alternating satisfaction periods

Engineering Contradiction:

Improvehandling of nonlinear functions and alternating specificationsVSAvoidchecking time

Core Design Contradiction:

Adaptability or versatilityVSLoss of time

Solution Approach 1:

The patent performs preliminary calculation of the semantics set, which encapsulates all possible satisfaction patterns in advance. This preliminary action pre-computes the critical information needed for verification, allowing the actual checking process to proceed efficiently by simply comparing the initial state against the pre-computed semantics set, thereby reducing overall checking time while handling complex alternating specifications.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent creates a mathematical copy of the system's behavior through the semantics set, which represents all possible satisfaction patterns without requiring exhaustive simulation of actual system execution. This copying approach enables verification of alternating satisfaction conditions without the time cost of running complete system simulations, significantly reducing checking time while maintaining thoroughness.

Inventive Principle:

Principle #26Copying

Data Source

PatentUS12554968B2Checking device, checking method, and checking program

Publication Date: 2026.02.17 NT T INC

AI summary

A calculating unit calculates a semantics set relating to an entirety of state of a recursive neural network satisfying a specification. A determining unit determines whether or not the recursive neural network that is an object of checking satisfies the specification, on the basis of the semantics set and an initial state of the recursive neural network that is the object of checking.