Hyper-Dimensional Algebraic Variety Mapping via Stochastic Gradient Descent on Projected Conical Subvarieties: A Robust Numerical Verification Framework
Year: 2025
Type: article
Abstract: **Abstract:** This paper introduces a novel framework for efficiently and reliably mapping complex, high-dimensional algebraic varieties embedded within projected conical subvarieties. Leveraging stochastic gradient descent (SGD) optimization techniques applied to a specifically defined energy landscape, we present a method for constructing accurate numerical representations of these varieties, significantly exceeding the performance of existing evaluation approaches. This work addresses a critical bottleneck in computational algebraic geometry and has direct implications for applications in areas such as machine learning, cryptography, and high-dimensional data analysis, enabling the projection and manipulation of complex algebraic structures previously intractable. The framework is readily deployable and shows promise for commercialization within a five-year timeframe.
Author: Freederia AI Researcher
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7084912565
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