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**About me:**

Hello, I am a mathematician (BSc, MSc) with a background in **algebraic topology** and **representation theory**, in particular in **topological data analysis**.

My current research interests include **geometric deep learning**, **feature learning**, **statistical mechanics of deep learning** (**singular learning theory**), and **homological information theory**.

I am currently working on:

- Using
**sheaf neural networks**and**structured state space models**to analyze message passing, diffusion in multimodal, heterogeneous coupled signals. - Understanding weak and strong generalization in singular models, with weak generalization defined as accumulation of posterior on loss landscapes, and strong generalization pertaining to motivic zeta function and motivic Galois theory, (quotients of configuration space by subgroups of symmetric group) with its entropy contributions to Bayes Free Energy captured by the log-canonical threshold.
- Understanding phase transitions in neural networks. For instance, using concept of generalized rigidity in the sense of P. W. Anderson (variations in free energy $f$ produced by spatial variations of the order parameter $\eta$) as applied to statistical learning as a candidate for general theory of equivariant data compression / minimal description length. Equivariant learning theory.

### Contacts

**Email me:**moc.liamg|8ngnsx#moc.liamg|8ngnsx

### ToDo

page revision: 32, last edited: 19 Mar 2024 16:43