Related papers: Compositional Symmetry as Compression: Lie Pseudog…
Citation and coauthor networks offer an insight into the dynamics of scientific progress. We can also view them as representations of a causal structure, a logical process captured in a graph. From a causal perspective, we can ask questions…
Iterative LLM systems(self-refinement, chain-of-thought, autonomous agents) are increasingly deployed, yet their temporal dynamics remain uncharacterized. Prior work evaluates task performance at convergence but ignores the trajectory: how…
Compositional generalization, the ability of an agent to generalize to unseen combinations of latent factors, is easy for humans but hard for deep neural networks. A line of research in cognitive science has hypothesized a process,…
We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
Human intelligence relies in part on our brains' ability to create abstract mental models that succinctly capture the hidden blueprint of our reality. Such abstract world models notably allow us to rapidly navigate novel situations by…
Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…
As generative artificial intelligence evolves, autonomous agent networks present a powerful paradigm for interactive covert communication. However, because agents dynamically update internal memories via environmental interactions, existing…
The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…
Single-agent systems (SAS) have become the default pattern for LLM-driven scientific workflows, but routing planning, tool use, and synthesis through a single context window comes with a well-known cost: as tool specifications and…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
Approximating functions of a large number of variables poses particular challenges often subsumed under the term ``Curse of Dimensionality'' (CoD). Unless the approximated function exhibits a very high level of smoothness the CoD can be…
Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
Autoregressive language models achieve remarkable performance, yet a unified theory explaining their internal mechanisms, how training shapes representations, and why these representations support complex behavior remains incomplete. We…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…
We study generative nets which can control and modify observations, after being trained on real-life datasets. In order to zoom-in on an object, some spatial, color and other attributes are learned by classifiers in specialized attention…