New parallelogram rule extends proportional analogies to Riemannian manifolds

Researchers have introduced a new method for formalizing proportional analogies within Riemannian domains, extending the parallelogram rule traditionally used in Euclidean spaces. This novel approach is demonstrated on various non-Euclidean manifolds, including spheres, shape spaces, and manifolds of probability distributions. The work aims to broaden the application of proportional analogies beyond symbolic and vector-based domains. AI

IMPACT This research could enable more sophisticated analogical reasoning in AI systems operating in non-Euclidean data spaces.

RANK_REASON Academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• manifolds of probability distributions
• Pierre-Alexandre Murena
• Riemannian manifold
• shape spaces

• paper
• other

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