Number Embedding Generation for Adaptive Numerical Analysis
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Solution Overview
Problem
Conventional numerical analysis systems rely on preprogrammed rules and approximation techniques, making them inflexible and unable to discover new numerical properties or relationships, as they require known properties and methods, limiting their adaptability to new applications and discoveries.
Innovation Solution
The system generates number embeddings using machine learning models, such as artificial neural networks, to encode properties of numbers, allowing for the analysis and comparison of numbers in a multi-dimensional space to identify patterns and similarities, enabling the discovery of new relationships and properties without prior knowledge.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If preprogrammed rules and approximation techniques are used for numerical analysis, then the system can perform known calculations, but the system lacks flexibility and cannot discover new numerical properties or relationships
Solution Approach 1:
The patent replaces conventional preprogrammed rule-based numerical analysis systems with machine learning models that automatically learn numerical properties and relationships from data. The ML models substitute traditional approximation techniques, enabling the system to discover new numerical patterns without manual programming while maintaining computational efficiency.
Solution Approach 2:
The system changes the fundamental parameter of numerical analysis from fixed preprogrammed rules to dynamic learned representations. By training ML models on numerical data, the system adapts its internal parameters (weights and biases) to capture new numerical properties, transforming the analysis approach from static to adaptive.
2Adaptability or versatility
If machine learning models are used to generate number embeddings, then the system can discover new numerical properties and relationships, but the computational complexity increases
Solution Approach 1:
The system performs preliminary training of machine learning models offline to generate number embeddings that capture numerical properties and relationships. Once trained, these embeddings can be reused for multiple analysis tasks without retraining, reducing computational complexity during actual numerical analysis operations while maintaining the ability to discover new properties.
Solution Approach 2:
The patent creates simplified representations (embeddings) of numerical data that capture essential properties without requiring complex computations. These embedded representations serve as efficient copies that can be analyzed using simpler operations, reducing computational complexity while preserving the ability to discover numerical relationships.
3Reliability
If conventional numerical analysis methods are used, then the system requires known properties and methods, but this limits adaptability to new applications
Solution Approach 1:
The system enables the numerical analysis model to self-improve by automatically learning from numerical data without requiring pre-programmed knowledge of specific properties or methods. The ML model serves itself by adapting to new applications and discovering new numerical relationships, eliminating the need for manual configuration while maintaining reliable calculations.
Data Source
AI summary
Systems and methods are provided for using encoded representations of numbers in various applications. The encoded representations of numbers, also referred to as number embeddings, may be multi-element data structures (e.g., multi-dimensional vectors) in which each element is a real-numbered value. The values of a given number embedding collectively encode information from which properties of the number represented by the number embedding may be derived. Number embeddings may be compared or otherwise analyzed with respect to each other to identify patterns or similarities in the numbers represented by each number embedding.