Ultrahyperbolic Graph Representation for Neural Network Inference
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional latent spaces and graphs are inadequate for representing complex data structures like social networks and proteins, leading to inaccurate inferencing results due to their inability to capture hierarchical relationships with cycles.
Innovation Solution
The use of ultrahyperbolic graph representations, which map input graphs to a non-Riemannian manifold of constant nonzero curvature, allowing for more accurate classification and inferencing tasks by generalizing hyperbolic and elliptical geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional latent space or graph representation is used, then the data representation is simple, but the inferencing accuracy deteriorates due to inability to capture hierarchical relationships with cycles
Solution Approach 1:
The patent transitions from conventional Euclidean latent spaces to ultrahyperbolic geometry, adding temporal dimensions to the representation space. This dimensional extension enables the manifold to capture hierarchical relationships with cycles, resolving the contradiction by improving inferencing accuracy through enhanced representational capacity rather than complicating the base structure.
Solution Approach 2:
The patent changes the geometric parameters of the representation space by introducing ultrahhyperbolic curvature instead of flat Euclidean geometry. This parameter transformation allows the manifold to naturally encode hierarchical structures with cycles, achieving higher inferencing accuracy while maintaining a systematic representation framework.
2Measurement precision
If traditional hyperbolic embeddings are used, then the representation captures some hierarchical structure, but it fails to accurately represent graphs with cycles
Solution Approach 1:
The ultrahhyperbolic manifold serves multiple functions simultaneously: it captures hierarchical structures like traditional hyperbolic embeddings, while also accommodating cyclic relationships through its extended geometry. This multi-functionality resolves the contradiction by making the representation system universally applicable to both acyclic and cyclic graph structures.
Solution Approach 2:
The patent embeds traditional hyperbolic representations within the broader ultrahhyperbolic framework. The ultrahhyperbolic manifold can accommodate conventional hyperbolic structures as a subset, allowing it to inherit the ability to represent hierarchical data while adding the capability to handle cyclic relationships, thus resolving the limitation of traditional hyperbolic embeddings.
Data Source
AI summary
Approaches presented herein use ultrahyperbolic representations (e.g., non-Riemannian manifolds) in inferencing tasks—such as classification—performed by machine learning models (e.g., neural networks). For example, a machine learning model may receive, as input, a graph including data on which to perform an inferencing task. This input can be in the form of, for example, a set of nodes and an adjacency matrix, where the nodes can each correspond to a vector in the graph. The neural network can take this input and perform mapping in order to generate a representation of this graph using an ultrahyperbolic (e.g., non-parametric, pseudo- or semi-Riemannian) manifold. This manifold can be of constant non-zero curvature, generalizing to at least hyperbolic and elliptical geometries. Once such a manifold-based representation is obtained, the neural network can perform one or more inferencing tasks using this representation, such as for classification or animation.