Tag: geometry
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The Geometry of Laziness: What Angles Reveal About AI Hallucinations
The Geometry of Laziness: What Angles Reveal About AI Hallucinations A story about failing forward, spheres you can’t visualize, and why sometimes the math knows things before we do The post The Geometry of Laziness: What Angles Reveal About AI Hallucinations appeared first on Towards Data Science. Javier Marin Go to original source
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Generalization Below the Edge of Stability: The Role of Data Geometry
Generalization Below the Edge of Stability: The Role of Data Geometry arXiv:2510.18120v1 Announce Type: new Abstract: Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we theoretically explore how data geometry controls this implicit bias. This paper presents theoretical results for overparameterized…
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From Universal Approximation Theorem to Tropical Geometry of Multi-Layer Perceptrons
From Universal Approximation Theorem to Tropical Geometry of Multi-Layer Perceptrons arXiv:2510.15012v1 Announce Type: new Abstract: We revisit the Universal Approximation Theorem(UAT) through the lens of the tropical geometry of neural networks and introduce a constructive, geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs). Tropical geometry shows that Rectified Linear Unit (ReLU) networks admit decision functions with…
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Learning over von Mises-Fisher Distributions via a Wasserstein-like Geometry
Learning over von Mises-Fisher Distributions via a Wasserstein-like Geometry arXiv:2504.14164v1 Announce Type: new Abstract: We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a variety of probabilistic learning tasks involving…