arXiv:2606.01216v1 Announce Type: new Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors. In order to leverage the geometry of the space, we formulate the learning of such matrices as optimization on a Riemannian quotient manifold. We propose a novel block-diagonal Riemannian metric derived from the pullback of the Frobenius inner product. The metric is shown to be inv
The continuous drive for more efficient machine learning algorithms and methods for handling large datasets necessitates advancements in mathematical optimization techniques.
This research provides a more efficient approach to modeling complex data structures with fewer parameters, which is crucial for scalable AI and large-scale data analysis.
New mathematical tools for Riemannian optimization will improve the parameter efficiency and computational performance of machine learning models dealing with multiplicative data structures.
- · AI researchers
- · Machine learning startups
- · Big data analytics firms
- · Inefficient AI models
- · Computationally intensive data analysis methods
Improved efficiency in training certain types of AI models, especially those with multiplicative components.
Reduced computational demand and energy consumption for specific machine learning tasks, contributing to sustainability in AI.
Enables the development of more complex and robust AI systems that were previously unfeasible due to computational constraints.
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Read at arXiv cs.LG