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Complexity Science | University Potsdam @complexityup.bsky.social · 16/06/2026

Grokking, as hysteresis. L2 regularization drives first-order phase transitions in deep linear networks and below the critical strength, the metastable phase coexists with the global one. Trapped a networks reproduce all hallmarks of grokking & noise-driven escape. openreview.net/forum?id=AkQ...

Delayed convergence in deep linear networks. (a) Random (blue), rank-1 trap (green), trivial-phase trap (orange). The convergence is strongly delayed when the model is initialized in the local minima of the lower accuracy phases. (b) Canonical grokking via sparse sub-sampling (25 training samples, β = 0.0025). Initialised in the rank-1 phase, train MSE (blue) drops quickly but only to a plateau while test MSE (red) plateaus higher; at ≈1500 epochs the model escapes the rank-1 phase and test MSE falls sharply, approaching train MSE to within a small residual gap set by the irreducible noise of the task.

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Complexity Science | University Potsdam @complexityup.bsky.social · 30/01/2026

Our work on practical insights into nonlinear dimensionality reduction with Diffusion Maps is now out! Parametrization, pitfalls & component selection 🚀 Great read for the weekend! Preprint on arXiv: arxiv.org/abs/2601.20428

An insect on a spiral transforms into an insect on a line thanks to diffusion map.

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Complexity Science | University Potsdam @complexityup.bsky.social · 18/11/2025

At this Scientific Machine Learning workshop we showed that strong regularization can cause phase transitions in neural networks. By linking these transitions to the geometric curvature of the training landscape, we reveal a new way to understand and optimize how neural networks learn.

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Complexity Science | University Potsdam @complexityup.bsky.social · 05/11/2025

A few weeks ago, our group spent a few days at Burg Hohenstein for our annual retreat — great discussions, beautiful surroundings, and a chance to recharge before the new semester! 🧠🏰

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Complexity Science | University Potsdam @complexityup.bsky.social · 18/06/2025

4/6 🧵 The Diffusion map that we've talked about here on Bluesky is one of them. It reveals that, apparently, political systems behave like physical systems. Countries, over time, form this well-defined map, and their movement across this map can tell a lot about the stability of the regime.

The manifold obtained by applying the Diffusion Map technique on the 25 variables from the V-Dem-Dataset. The three-dimensional curve contains every datapoint for each country in each year from 1900 up until 2021. Each datapoint is assigned an Electoral Democracy Index, represented in the color. The lighter the colour, the more democratic a country is considered in that year.

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Complexity Science | University Potsdam @complexityup.bsky.social · 18/06/2025

3/6 🧵Statistical analysis shows that there are states that differ in election quality, despite having a similar Electoral Democracy Index (EDI, @vdeminstitute.bsky.social). Differences between autocratic regimes can thus be uncovered.

Trade-off between election quality and civil liberties (Principal Component 2) versus EDI for all 12 296 data points, (a) with density lines and (b) with examples for 2011–2021 (small dot–large dot).

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Complexity Science | University Potsdam @complexityup.bsky.social · 18/06/2025

The #Complexity Science Research Group in Potsdam is specialised in two major fields. One of them is the analysis of politcal systems using tools from . 🧪 1/6 🧵Here's a thread on @karowiesner.bsky.social's research and the many papers she has published on this topic!

Illustration (by @dantalionart.bsky.social‬) of political science in context of complexity science. A diffusion map wraps around an abstract globe, representing international connections that can be modelled physically.

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Complexity Science | University Potsdam @complexityup.bsky.social · 26/05/2025

Living beings rely on one another. One species facing the threat of extinction affects other species as well. Understanding the extent of ecological damages helps take measures against them. With low computational costs, this model for the robustness of a #complex system can prove useful in future.

🧪 (a) An example plant–pollinator network and (b) its associated robustness curve. For this network, pollinators are treated as
primary species and plants as secondary species. Random primary extinctions are simulated repeatedly and the proportion of surviving
secondary species is recorded to generate the robustness curve. The greater the red area below the graph, the more robust is the system. Illustrations used in (a) are all available in the public domain under a
CC0 license.

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Complexity Science | University Potsdam @complexityup.bsky.social · 10/03/2025

6/10🧵 As a country goes through political change, it moves along this curve. Its development can be traced, and jumps and static phases linked to real life events and phases! Using tools from statistical physics, distinct types of behaviour have been identified in the data.

The development of three different countries (South Africa, Russia, USA, respectively from left to right) traced as they move along the manifold curve. South Africa, for instance, shows a large jump from 1993 to 1994, which can be linked to the changes at the end of the Apartheid regime.

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Complexity Science | University Potsdam @complexityup.bsky.social · 10/03/2025

5/10🧵 Taking 25 variables out of the V-Dem dataset describing the “democraticness” of each country every year and simplifying them using diffusion to fit in a three-dimensional space, the data forms a curve - not a cloud of points - summarising the whole dataset considered. Surprising, isn't it?

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Complexity Science | University Potsdam @complexityup.bsky.social · 10/03/2025

Meet Paula, one of the PhDs in our group! 🧪 Before joining us, she did her Bachelor's in Physics and Master's degree in Physics of Complex Systems and Biophysics at the University of Barcelona. Now, let's talk about her current #research! 1/10🧵 #WomenInSTEM #SciCom #Complexity

Paula, a PhD in our research group, in front of an illustration of the manifold explored in her paper called "Unraveling 20th-century political regime dynamics using the physics of diffusion", co-written by Matthew C. Wilson, Sönke Beier, Karoline Wiesner

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Complexity Science | University Potsdam @complexityup.bsky.social · 06/03/2025

5/6🧵 Sometimes, the emergent structure isn't obvious on first sight. However, when a system shows a certain regularity in its ongoing development, it is a case of emergence. Phase transitions in materials or the relationship between hunter and prey in nature are examples of this form of emergence.

A graph showing thermodynamic phase transition processes in a pressure to temperature diagram. A substance can take a solid, liquid or gaseous shape. This type of emergence cannot be directly concluded by a fixed state of the material, but rather by examining it's development under changing conditions.
https://theory.labster.com/phase-transition/

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Complexity Science | University Potsdam @complexityup.bsky.social · 06/03/2025

3/6🧵 Emergence can refer to the physical structures that arise at different physical scales. Proteins, for instance, can form more defined and diverse structures the larger they get, eventually forming enzymes with highly specific biochemical functions.

A graph showing protein folding as an example for structural emergence. The four different detail or property levels of proteins can be seen. The structure of a protein depends on the single amino acids that can form helical or planar structures that that fold in unice ways.
By Holger87 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=20899169

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Complexity Science | University Potsdam @complexityup.bsky.social · 13/02/2025

During his research on self-reproductive systems like those that can be found in nature, von Neumann defined the first cellular automata. Different dynamics can arise from the interaction of neighbouring cells that follow a set of behavioural rules, as can be seen in Conway's Game of Life.

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Complexity Science | University Potsdam @complexityup.bsky.social · 13/02/2025

A system expressing emergent behaviour is "more than the sum of its parts", as the biologist Bertalanffy determined in his studies of adaptive systems. By trying to find models or principles that would apply to any kind of system, biological or not, he made way for a new way of conducting science.

Karl Ludwig von Bertalanffy, Austrian researcher in theoretical #biology.
https://de.wikipedia.org/wiki/Ludwig_von_Bertalanffy#

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Complexity Science | University Potsdam @complexityup.bsky.social · 13/02/2025

In the 1940s, Wiener and Rosenblueth coined the term "cybernetics" as the theory of control and communication in living and non-living systems: machines and brains. Concepts of feedback and self-organization were introduced back then, and are still essential in the study of complex systems.

American physicist and pioneer of cybernetics, Norbert Wiener, in an MIT classroom. (https://monoskop.org/Norbert_Wiener)

Arturo Rosenblueth, another pioneer of cybernetics, Mexican physician and physiologist.
(https://en.wikipedia.org/wiki/Arturo_Rosenblueth)

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Complexity Science | University Potsdam @complexityup.bsky.social · 11/02/2025

Hello there! We're the Complexity Science group at the University of Potsdam, consisting of professor @karowiesner.bsky.social , post-docs, PhDs, as well as master's and bachelor's students and student assistants.

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Complexity Science | University Potsdam @complexityup.bsky.social · 06/02/2025

In their book "What Is a Complex System?", @karowiesner.bsky.social and James Ladyman explore the defining features of complexity and methods to measure them. Stay updated on the latest insights into complexity and Karoline Wiesner's research group by following us!

Book cover of James Ladyman and Karoline Wiesner's book titled "What Is A Complex System?"

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Complexity Science | University Potsdam @complexityup.bsky.social · 06/02/2025

What is a complex system? #Complexity can be found anywhere from neural networks and ant colonies, to climatic systems and governments. Here, at the University of Potsdam, the research group led by physicist @karowiesner.bsky.social explores ways to quantify and better understand complexity.

Abstract drawing of a complex system. Ants spiraling in a circle, converging in a dark mass, representing a "black box" with a human brain inside. This depiction contains different forms of complexity. The structural complexity of the movement, the interactions in an ant colony and neural networks are examples for complexity. Artwork by @dantalionart.bsky.social.

Photo of physicist Karoline Wieser during a talk. She is the person behind the group of this account.

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