Related papers: Compositional Symmetry as Compression: Lie Pseudog…
We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of…
We outline a possible theoretical framework for the quantitative modeling of networked embodied cognitive systems. We notice that: 1) information self structuring through sensory-motor coordination does not deterministically occur in Rn…
Perception of artificial agents is one the grand challenges of AI research. Deep Learning and data-driven approaches are successful on constrained problems where perception can be learned using supervision, but do not scale to open-worlds.…
This work investigates whether time series of natural phenomena can be understood as being generated by sequences of latent states which are ordered in systematic and regular ways. We focus on clinical time series and ask whether clinical…
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…
Self-organization is a process where a stable pattern is formed by the cooperative behavior between parts of an initially disordered system without external control or influence. It has been introduced to multi-agent systems as an internal…
Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…
Autoencoders (AE) are simple yet powerful class of neural networks that compress data by projecting input into low-dimensional latent space (LS). Whereas LS is formed according to the loss function minimization during training, its…
This paper is a contribution to the symmetry analysis of the gas dynamics system in the vein of the ''podmodeli'' (submodels) program outlined by Ovsyannikov (1994). We consider the case of the special state equation, prescribing pressure…
We describe a method to analyze and decompose the dynamics of a control system on a Lie group subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
We present a solver-agnostic framework in which coordinated large language model (LLM) agents autonomously execute the complete computational mechanics workflow, from perceptual data of an engineering component through geometry extraction,…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
Recurrent neural networks have a strong inductive bias towards learning temporally compressed representations, as the entire history of a sequence is represented by a single vector. By contrast, Transformers have little inductive bias…
In a recent paper, K.Keller has given a characterization of the Kolmogorov-Sinai entropy of a discrete-time measure-preserving dynamical system on the base of an increasing sequence of special partitions. These partitions are constructed…
The concept of Automorphic Lie Algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie Algebras are obtained by imposing a discrete group symmetry on a current…
For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes…