Hyperbolic Perceptron Classification for Hierarchical Data
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Solution Overview
Problem
Existing machine learning algorithms for classification tasks in hyperbolic spaces lack theoretical guarantees on convergence and generalization, and existing methods in Euclidean spaces fail to effectively leverage the hierarchical structure of data, leading to inefficient and suboptimal performance.
Innovation Solution
A hyperbolic perceptron algorithm with a normalization step and the use of adversarial examples to efficiently learn a large-margin classifier in hyperbolic space, ensuring provable convergence and improved performance by aligning with the intrinsic geometry of hierarchical data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard Euclidean embedding and classifier are used, then implementation is simple and well-established, but performance is suboptimal and fails to leverage hierarchical structure
Solution Approach 1:
The patent changes the fundamental parameter of space from Euclidean to hyperbolic, transforming the embedding space to match the intrinsic geometry of hierarchical data. This parameter change enables the system to capture hierarchical relationships that are lost in Euclidean space, thereby improving classification performance while maintaining algorithmic simplicity through direct adaptation of perceptron algorithms to the hyperbolic setting.
2Reliability
If existing hyperbolic classification algorithms are used, then hierarchical structure is leveraged, but lack of theoretical guarantees on convergence and generalization
Solution Approach 1:
The patent introduces a feedback mechanism through the perceptron update rule that explicitly uses classification errors to drive weight adjustments. The algorithm incorporates a normalization step that provides feedback on the magnitude of weight updates, ensuring stable convergence. This feedback loop, combined with the geometric properties of hyperbolic space, establishes theoretical convergence guarantees while keeping the algorithm relatively simple to implement.
3Reliability
If adversarial training examples are added, then robustness and predictive accuracy improve, but training time and computational resources increase
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing adversarial training examples alongside the original training data. The adversarial examples are generated in advance and integrated into the training dataset, allowing the perceptron algorithm to process them during standard training iterations without adding separate computational overhead. This approach improves robustness and predictive accuracy while minimizing additional training time.
Data Source
AI summary
Generally, the present disclosure provides systems and methods for performing machine learning in hyperbolic space. Specifically, techniques are provided which enable the learning of a classifier (e.g., large-margin classifier) for data defined within a hyperbolic space (e.g., which may be particularly beneficial for data possessing a hierarchical structure).