arXiv:2510.09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based on this, we develop tools for a discrete Riemannian calculus approximating classical geometric operators. These tools are robust against inaccuracies of the implicit representation often occurring in practical examples. To obtain a suitable implicit representation, we propose to learn an approximate project
This paper represents a refinement in the mathematical understanding and practical application of latent spaces in AI, building on ongoing research in geometric deep learning.
Improved understanding and manipulation of latent manifolds could lead to more robust, interpretable, and efficient AI models, especially in areas requiring precise data representation and synthesis.
The development of discrete Riemannian calculus for implicitly defined latent manifolds provides new tools for analyzing and operating on complex data representations within AI.
- · AI researchers
- · Machine learning developers
- · Industries using generative AI
- · Robotics
- · Traditional data representation methods
- · AI models lacking geometric understanding
More sophisticated generative models and data compression techniques become possible.
Enhanced capabilities for AI agents to reason about and interact with complex environments.
Accelerated development of AI systems that can learn and adapt with human-like efficiency and intuition.
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Read at arXiv cs.LG