Next week (on the 15th and 16th), with @yasserroudi.bsky.social and Federico Turkheimer we will organize a workshop on the "The Topology of Human and Synthetic Minds"

Please do join us!
(Registration is free but required for access/catering!)

lordgrilo.github.io/topology-nat...

3/3 Surprisingly, sometimes adding even a single datapoint from outside (e.g. human generated data) may prevent model collapse.

2/3 This is what we studied in our recent paper for the Exponential Family, analytically finding some of the important features observed in more complex models: importantly model-collapse where the model's representational power severely decreases.

1/3 What happens if one repeatedly retrains a machine on data primarily generated from itself? For example when students use LLMs to write their essays that they then put online. And then profs use LLMs to write a paper on that topic and so on 😎
arxiv.org/abs/2506.20623

🚀 Just released a new tool for the neuroscience and Topological Data Analysis communities!
🔗 github.com/gdisarra/top...

The topology-degree repository provides code and methods to quantify the topology in high-dimensional data using persistent homology.
🔗 doi.org/10.1371/jour...

5/5 I also think avoiding binarization/categorizations with hard boundaries will do good for biology.

4/5 I think these, combined with the recent discoveries about null hypothesis in TDA, provide a better quantitative insight into topological structure in high-d data and the processes that cause them.
nature.com/articles/s41...
arxiv.org/abs/2406.05553
Our paper is one example.

3/5 Giovanni has now also released an easy-to-use code that can measure the degree of toroidality, degree of sphericality, degree of circularity and can be further extended to other topological structures.

t.co/MWWXLcOjhP

2/5 Introducing a "degree of toroidality" we avoid binary categorisation (there is toroidal topology - there is no toroidal topology), and propose continuous measures quantifying the degree to which the topology of data resembles that of a reference structure, e.g. torus.

1/5 Imagine if Newton, Galileo etc divided objects to heavy ones and light ones instead of assigning mass to them: no Eq. of motion+endless arguments about what's heavy/light; likely in caves.

In a recent paper, we avoid binarization in Topol. Data Analysis
t.co/5LZ20S0DKw