Hyperbolic Embeddings Tutorial (DiffGeo4DL NeurIPS 2020)
ฝัง
- เผยแพร่เมื่อ 10 ก.ค. 2024
- This video gives a brief introduction to hyperbolic embeddings and their use in Machine Learning (ML) applications. We start by reviewing some basic concepts of Riemannian and Hyperbolic Geometry. We then motivate the use of hyperbolic embeddings in ML tasks and describe embedding methods to learn hyperbolic representations of hierarchical data.
Awesome work.
Great talk and amazing work! What exactly is the difference between the projection and the logarithmic map? Both map from the manifold to the tangent space? And how would these projections be computed in the Poincare disk?
Thanks :)
Thanks for the great tutorial. Is the slides available for download?
Fantastic talk! I learned a ton. Thank you for sharing! May I ask: you defined "g" (Riemannian Metric Tensor) on slide 10. On slide 15, you use g inverse. Does it invert the g? The first g takes 2 vectors and maps onto a scalar. The inverse is now taking a vector. How can g^-1 be computed? -- I am sorry if my question is novice... g(u, v) = _L ... And also, in general, is the g function invertible? I.e. if you fix "a" and "b" in "g(u, a) == b"; must there be at most one value of "u" that satisfies equality?
the g is considered as a matrix with i-j entries as [ e_i(p) . e_j(p)], the standard inner product of i-th and j-th local basis, with non-negative determinant, whose inverse is mentioned here.
What a great presentation! At minute 7pm the author explains how for binary trees, the number of nodes grows exponentially with depth. But in Euclidean space, the number of nodes grows polynomially with the tree radius. My disconnect with understanding this is about relating a "binary tree" to "Euclidean space". Is this "Euclidean space" referring to the adjacency matrix created for the nodes in the graph? If so, how does Hyperbolic Geometry offer an improvement? Thank you in advance. This is such an interesting topic.
Why is a hyperbolic space so much better for tree-like data, and how do you know how tree-like ones data is ?