Related papers: Compositional Symmetry as Compression: Lie Pseudog…
A new paradigm in Sampling theory has been developed recently by Lu and Do. In this new approach the classical linear model is replaced by a non-linear, but structured model consisting of a union of subspaces. This is the natural approach…
In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
We study sketch-to-diagram generation: converting rough hand sketches into precise, compositional diagrams. Diffusion models excel at photorealism but struggle with the spatial precision, alignment, and symbolic structure required for…
We propose a fitness measure quantifying multi-scale complexity for cellular automaton states, using compressibility as a proxy for complexity. The use of compressibility is grounded in the concept of Kolmogorov complexity, which defines…
We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP,…
This paper presents the Artificial Agency Program (AAP), a position and research agenda for building AI systems as reality embedded, resource-bounded agents whose development is driven by curiosity-as-learning-progress under physical and…
There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation…
Monotone frameworks is one of the most successful frameworks for intraprocedural data flow analysis extending the traditional class of bitvector frameworks (like live variables and available expressions). Weighted pushdown systems is…
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…
For Agent Based Models, in particular the Voter Model (VM), a general framework of aggregation is developed which exploits the symmetries of the agent network $G$. Depending on the symmetry group $Aut_{\omega} (N)$ of the weighted agent…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed…
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra,…
We study synthesis problems with constraints in partially observable Markov decision processes (POMDPs), where the objective is to compute a strategy for an agent that is guaranteed to satisfy certain safety and performance specifications.…
There is growing evidence that independently trained AI systems come to represent the world in the same way. In other words, independently trained embeddings from text, vision, audio, and neural signals share an underlying geometry. We call…
In this paper we use retraction and discretization maps (see [Barbero Li\~n\'an and Mart\'in de Diego, 2022]) as a tool for deriving in a systematic way numerical integrators preserving geometric structures (such as symplecticity or…