▶️ Blackholes & Hyperspheres

What are the relationships between #Blackholes / #Whiteholes / #Wormholes
and #Cones / #Spheres / #Hypercones / #Hyperspheres?

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[Comment: this is neat!]

We additionally show that on the encoder side, the conceptual dimensions generate Part-of-Speech (PoS) clusters.

On the decoder side, we show that a di-gram approach helps to reveal the PoS clusters of the next token. Our approach paves a way to elucidate the processing of information through the deep layers of an NLP Transformer.

#hyperspheres #semantics #SemanticHyperspheres #hyperspace #hyperbolic #HyperbolicEmbeddings #embeddings

Sobolev Spaces, Kernels and Discrepancies over Hyperspheres

Simon Hubbert, Emilio Porcu, Chris J. Oates, Mark Girolami

https://openreview.net/forum?id=82hRiAbnnm

#kernels #hyperspheres #kernel

Sobolev Spaces, Kernels and Discrepancies over Hyperspheres

This work extends analytical foundations for kernel methods beyond the usual Euclidean manifold. Specifically, we characterise the smoothness of the native spaces (reproducing kernel Hilbert...

OpenReview