Magnitude-based pruning is a standard #ML #AI technique to produce sparse models, but in our @ICMLConf paper https://www.arxiv.org/abs/2406.04934 we find it doesn’t work for #DynamicalSystems reconstruction.
Instead, via geometry-based pruning we find the *network topology* is far more important!

It turns out that even RNN weights small in relative size can have a dramatic impact on system dynamics as measured by attractor agreement. In fact, there is not much difference between small and large magnitude weights in contribution to DS reconstruction quality. (Fig. 1)

Following the lottery ticket hypothesis, we find that large RNNs still contain winning tickets that can be carved out by *geometry-based* pruning, but that these tickets are defined by *graph topology* with initial weight values hardly playing any role. (Fig. 4)

The ‘winning’ graph topology distilled from trained RNNs turns out to exhibit both hub-like and small world features. RNNs initialized with this topology perform significantly better than equally-sized RNNs with random, Watts-Strogatz or Barabási-Albert topology. (Fig. 6)

… and also train much faster. (Fig. 7)

This all makes sense: Natural and engineered DS often bear a specific sparse network topology that is crucial for shaping their dynamics!

Fantastic work lead by Christoph Hemmer with Manuel Brenner and Florian Hess!

My commentary on our 2023 LIDA paper just got published! In it, I explore the idea that the behavioral and cognitive dispositions our original paper was concerned with may be understood as topological features of cognitive subsystems:

https://journals.sagepub.com/doi/10.1177/00368504241245812

Excited to share that this July I will be hosting a symposium on network psychometrics at IMPS, Prague, where I will present with @liu_thorsten, Ria Hoekstra, @bsiepe, Tatiana Kvetnaya, and Kai Nehler about our latest work! #RStats #EMA #ExperienceSampling #statistics #IMPS
#Psychometrics #Networks #SEM #IRT
#DynamicalSystems #MultivariateStatistics

Dear fellow #control #engineers and #systemstheory nerds . I want to invite you on my little journey through the interesting lands of #nonlinear #DynamicalSystems.

My goal is to come up with some differential equations of dynamical systems which have some not-so-common step responses. How far and interesting this will be – I don't know, but it might get interesting.

We start with this little friend: It loads fast but unloads slow. I call it "leashed DT1 element".

Genuary Prompt 13: Wobbly Function Day #genuary #genuary2024 #genuary13 #dynamicalsystems

FOUND! thx @lilbatscholar
Dynamics: The Geometry of Behavior, by R. Abraham

I remember one time I ...found a book w/ pdf.
It was about displaying dynamical systems theory, showing manifolds and so on.
Plots were not made with any programming language, they were actual drawings, pastels, watercolors.
It's the type of book I literally have dreams about, but I think this one exists what was it?

Kindly boost my chances to find it

This week in our #DynamicalSystems course at #UPC we studied the effect of a hyperbolic saddle point in orbits of discrete maps. The periodically forced pendulum is a good example to simulate with #julialang ensemble simulations https://web.mat.upc.edu/joaquim.puig/J4DS/EnsembleParallel/EnsembleParallelPendulum.html

Fernando Rosas (unfortunately not on Mastodon) asked on bsky:

"Has anyone figured out what exactly is the relation between the ideas of feedback, recurrence, and self-reference?"

A really interesting question.

He pointed to this paper for ideas: https://arxiv.org/abs/1711.02456
"Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos"

I did some desk research and found this cool paper:
https://arxiv.org/abs/1112.2141
"Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic"
that argues there is no essential incompleteness in formal reasoning systems if you look closely enough (using a more elaborate formalism based on polynomial equations to represent and evaluate logical proposition).

I wonder if analogous construction could be created for related theorems like the halting problem in computability theory.

This week at our #DynamicalSystems course at #UPC we will learn how to compute the orbits of iterations of maps using DifferentialEquations.jl in #julialang see https://web.mat.upc.edu/joaquim.puig/J4DS/DiscreteMaps/DiscreteMaps.html

" we provide neural evidence that energy landscapes predict decision consistency, which reflects decision confidence."

https://www.nature.com/articles/s41593-023-01445-x

This week at our course on #DynamicalSystems at #FME #UPC we computed resonance tongues for Mahtieu Equations using #julialang The code can be found in https://web.mat.upc.edu/joaquim.puig/J4DS/

Triggy Trippy Dynamical System: Last one!

Full Length-Full Scale-Full Quality-Musical Version with annotated function: https://youtu.be/PAdEgArd5S8

I put up the code for my Dynamical Systems Project! (Including my handwriting )

https://github.com/NonEuclideanDreamer/DynamicalSystem