Author | Lightnews

Michael Bleher @subthaumic.bsky.social · Aug 28

Kudos to Cyril & Alex (@alexandr.bsky.social) for leading this! Glad to have been part of it. This is a sharp field guide to low-dimensional embeddings in the sciences. TL;DR: great for exploration; mind trade-offs; show your working; and run quantitative checks to validate what you see (& infer!)

Alex Diaz-Papkovich @alexandr.bsky.social · Aug 27

Last year I met a bunch of great researchers who work with high-dimensional data at a Dagstuhl seminar. This week we put out a preprint about the history and philosophy of low-dimensional embedding methods, their applications, their challenges, and their possible future arxiv.org/abs/2508.15929

The participants of Dagstuhl Seminar 24122 standing on steps outside (from https://www.dagstuhl.de/24122)

Multiple types of embeddings (UMAP, t-SNE, Laplacian Eigenmaps, PHATE, PCA, MDS) of Wikipedia text data labelled by a text summaries generated by an LLM. Methods like UMAP and t-SNE show cluster structure that reflect shared subject matter in text, whiel other methods show more continuous structure.

Multiple embedding methods (PCA, Laplacian Eigenmaps, t-SNE, MDS, PHATE, UMAP) of primate brain organoids at different time periods. Different methods highlight different aspects of development, such as clusters of similar cell types or time courses of cell development.

Multiple embedding methods (PCA, Laplacian Eigenmaps, t-SNE, MDS, PHATE, UMAP) of 1000 Genomes Project genotypes. Different methods reflect different aspects of demographic history of populations.

2

Reposted by Michael Bleher

Alex Diaz-Papkovich @alexandr.bsky.social · Aug 27

Last year I met a bunch of great researchers who work with high-dimensional data at a Dagstuhl seminar. This week we put out a preprint about the history and philosophy of low-dimensional embedding methods, their applications, their challenges, and their possible future arxiv.org/abs/2508.15929

1 7 14

Michael Bleher @subthaumic.bsky.social · Jul 1

Topology, causality, mechanistic interpretability, it's all in there.

open.substack.com/pub/subthaum...

Happy for any reactions, confused or otherwise.

The Tangled Web They Weave

Distributed Representations, Polysemantic Neurons, and Directed Simplicial Complexes

open.substack.com

1

Michael Bleher @subthaumic.bsky.social · Jul 1

New blog post about an exploratory project that’s been stuck in my head for a while.

Directed simplicial complexes from coherent counterfactual ablations ... as a way to trace superpostions of distributed feature representations on polysemantic neurons in artificial neural nets.

1/2

1 1

Reposted by Michael Bleher

STRUCTURES Cluster of Excellence Heidelberg @structures-hd.bsky.social · May 13

Join us for the kick-off meeting of the Persistent Seminar tomorrow at 2pm, with an inaugural talk by Freya Jensen (IWR) on "Persistent Spectral Sequences and Where to Find Them"

#heidelberg #STRUCTURES #Mathematics #Topology #Persistent #Homology #Computation

Announcement Poster with a text saying: Persistent Seminar. A Biweekly Forum on Persistent Homology, Computational Algebraic Topology & Applications. Where and When: Mathematikon SR00.200. Wednesdays 14 to 16h, every other week. Kick-off: May 14: organizational slot + inaugural talk by Freya Jensen: "Persistent Spectral Sequences and Where to Find Them"

2 3

Michael Bleher @subthaumic.bsky.social · Apr 15

Surely it's "A monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor."

3

Reposted by Michael Bleher

STRUCTURES Cluster of Excellence Heidelberg @structures-hd.bsky.social · Apr 15

Register now for the Workshop on Geometry, Topology & Machine Learning (Nov 10-14, 2025), jointly organized by MPI-MIS & STRUCTURES. The event brings together two rapidly evolving fields central to modern machine learning. (1/4)
www.mis.mpg.de/events/serie...
#science #topology #geometry #learning

1 3 9

Reposted by Michael Bleher

Adi Onus @somepineapple.bsky.social · Feb 28

Heard about TDA and want to learn more? Lots of cool videos here from the recent AATRN tutorial-a-thon (including a fun little clip from someone you might recognise 👀)

youtube.com/playlist?lis...

Tutorial-a-thon 2025 Spring - YouTube

These videos were created for the Spring 2021 Tutorial-a-thon hosted by AATRN and WinCompTop https://sites.google.com/view/aatrn-tutorial-a-thon.

youtube.com

1 3

Reposted by Michael Bleher

STRUCTURES Cluster of Excellence Heidelberg @structures-hd.bsky.social · Feb 13

In our series "YRC in", we take you along on the journeys of our #EarlyCareerScientists attending scientific events with STRUCTURES support. Last September, Michael Bleher (@subthaumic.bsky.social) and Freya Jensen attended the 4th Workshop on Computational Persistence in Graz, Austria. (1/3)

1 1 2

Michael Bleher @subthaumic.bsky.social · Jan 3

The second article:

Looks at adiabatic solutions of the Haydys-Witten equations and relates them to paths in the moduli space of EBE monopoles. This suggests a relation between Haydys-Witten instanton Floer homology and symplectic Khovanov homology.

https://arxiv.org/abs/2501.01365

Michael Bleher @subthaumic.bsky.social · Jan 3

The first article:

Introduces a one-parameter family of instanton Floer homology groups for four-manifolds, using the θ-Kapustin-Witten and Haydys-Witten equations. A conjecture by Witten links this to Khovanov homology for knots.

https://arxiv.org/abs/2412.13285

2/3

1

Michael Bleher @subthaumic.bsky.social · Jan 3

I've finally uploaded the remaining two parts of my PhD thesis to the arXiv! These papers hadn’t been on there before but are now available as self-contained articles for easier reference.

They’re about gauge theory, knot invariants, and a conjecture by Witten.

1/3

1 2