TH TRADING

[Tom Szwagier @tomszwagier]

Congrats Xavier!

[TH TRADING @th_trad]

@stefanhsommer GitHub repository https://t.co/2TFmdQPRI2

[TH TRADING @th_trad]

@stefanhsommer You can do parallel transport on Stiefel and Flag manifolds using JAX or numpy! Computing parallel transport is important in the geometric approach to optimization and computer vision. We give a new algorithm for a classical problem first raised in https://t.co/iiP1IpoVoT .

[Stefan Sommer @stefanhsommer]

Du @th_trad and I have a new preprint on arxiv: Parallel transport on matrix manifolds and Exponential Action https://t.co/zMpb1CDhpz

[arXiv math.NA Numerical Analysis @mathNAb]

Du Nguyen, Stefan Sommer: Parallel transport on matrix manifolds and Exponential Action https://t.co/0dOvXkFJgX https://t.co/oiTjo8MJrN

[Stefan Sommer @stefanhsommer]

Marcus Teller on Hyperiax at @CCEM_ucph workshop on Stochastic morphometry. Hyperiax is getting fast!

[TH TRADING @th_trad]

@stefanhsommer Package in JAX. While we often do not need automatic differentiation, we leverage vmap to accelerate the simulations. Common Riemannian manifolds in applications can be found in the package - and we hope to add more.

[TH TRADING @th_trad]

@stefanhsommer It has been great working with Professor Sommer! I believe this will find applications in diffusion models and sampling on Riemannian manifolds. Watch out for follow-up works!

[TH TRADING @th_trad]

@ninamiolane @SMataigne @geomstats Nice work! By the way, both original geodesic formulas of Stiefel manifolds in Edelman et. al. are generalized in https://t.co/kCPDipIPAK around the same time with Zimmermann - Huper's paper. Gradients of the Euclidan dist. func. for Stiefel and Flag manifolds are also in there.

[TH TRADING @th_trad]

@stefanhsommer Thank you!

[TH TRADING @th_trad]

@stefanhsommer You can double check your curvature formulas by evaluating the Bianchi identities on the flight!

[TH TRADING @th_trad]

@stefanhsommer You can also use it to compute the curvature of an embedded manifold or quotient of an embedded manifold. Examples are here https://t.co/g8MPsRpdoa based on https://t.co/56znLWkIVu . Lots of potential applications for geometric methods in applied mechanics.

[TH TRADING @th_trad]

@mathNAb Using Frechet derivatives to compute Riemannian logarithm for Stiefel and Flag manifolds are also in https://t.co/kCPDipIPAK
https://t.co/KmgQvFIM6n
https://t.co/aV6Avg3idh

[TH TRADING @th_trad]

@ejpatters It has been done implicitly. The space of fixed-rank matrices, ubiquitous in matrix completion is a fiber bundle. The fiber is a space of positive-definite matrices of size r=the rank, the base is the quotient by O(r) of two Stiefel manifolds from a USV^T decomposition.

[Seth Axen 🪓 @sethaxen]

🚨New package! PosteriorDB.jl is a @JuliaLang interface for posteriordb, which contains many @mcmc_stan models, data, and reference posterior draws. PosteriorDB makes comprehensively benchmarking new inference methods much easier! https://t.co/wAF5nj12I3

[TH TRADING @th_trad]

@ronnybergmann_ I have some logistic questions (whether to add methods to StiefelSubmersionMetric.jl or create new file, I implemented Frechet derivatives for exp based on scipy, may be of general interest) - probably best to discuss in a different setting. Is it OK to DM or email?

[Nick Higham @nhigham]

What Is a Fréchet Derivative? https://t.co/fPtlUzqrrP

[TH TRADING @th_trad]

@ronnybergmann_ I am very happy to! it probably will take a few weeks but will reach out when I have questions.

[TH TRADING @th_trad]

@ronnybergmann_ An alternative algorithm for Riemanniann logarithm for Stiefel and Flag manifold is in https://t.co/KmgQvFJjVV with Julia code for Stiefiel manifold in https://t.co/6AUyvCfJfJ