System theoretic approach of information processing in nested cellular automata

• URL: http://arxiv.org/abs/2210.06052v1
• Date: Wed, 12 Oct 2022 09:45:45 GMT
• Title: System theoretic approach of information processing in nested cellular automata
• Authors: Jerzy Szynka
• Abstract summary: The concept of information processing in regular structures based on multi-level processing in nested cellular automata is presented. In the model appear expressions similar to expressions used in the Special Relativity Theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The subject of this paper is the evolution of the concept of information processing in regular structures based on multi-level processing in nested cellular automata. The essence of the proposed model is a discrete space-time containing nested orthogonal space-times at its points. The factorization of the function describing the global behavior of a system is the key element of the mathematical description. Factorization describes the relations of physical connections, signal propagation times and signal processing to global behavior. In the model appear expressions similar to expressions used in the Special Relativity Theory.

Related papers

• Semantic Numeration Systems as Dynamical Systems [55.2480439325792]
  The cardinal abstract object (CAO) formed by them in a certain connectivity topology is proposed to be considered as a linear discrete dynamical system with nonlinear control.<n>The fundamental role of the configuration matrix, which combines information about the types of cardinal semantic operators in the CAO, their parameters and topology of connectivity, is demonstrated.
  arXiv  Detail & Related papers  (2025-07-28T19:29:36Z)
• A Free Probabilistic Framework for Analyzing the Transformer-based Language Models [19.78896931593813]
  We present a formal operator-theoretic framework for analyzing Transformer-based language models using free probability theory.<n>This work offers a principled, though theoretical, perspective on structural dynamics in large language models.
  arXiv  Detail & Related papers  (2025-06-19T19:13:02Z)
• Generalized Derangetropy Functionals for Modeling Cyclical Information Flow [11.095723123836965]
  This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such as Shannon entropy, these functionals act directly on probability densities and provide a topographical representation of information structure across the support of the distribution.
  arXiv  Detail & Related papers  (2025-04-20T13:09:21Z)
• EulerFormer: Sequential User Behavior Modeling with Complex Vector Attention [88.45459681677369]
  We propose a novel transformer variant with complex vector attention, named EulerFormer. It provides a unified theoretical framework to formulate both semantic difference and positional difference. It is more robust to semantic variations and possesses moresuperior theoretical properties in principle.
  arXiv  Detail & Related papers  (2024-03-26T14:18:43Z)
• Binding Dynamics in Rotating Features [72.80071820194273]
  We propose an alternative "cosine binding" mechanism, which explicitly computes the alignment between features and adjusts weights accordingly. This allows us to draw direct connections to self-attention and biological neural processes, and to shed light on the fundamental dynamics for object-centric representations to emerge in Rotating Features.
  arXiv  Detail & Related papers  (2024-02-08T12:31:08Z)
• Capturing long-range memory structures with tree-geometry process tensors [0.0]
  We introduce a class of quantum non-Markovian processes that exhibit decaying temporal correlations and memory distributed across time scales. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects. We show how it can efficiently approximate the strong memory dynamics of the paradigm spin-boson model.
  arXiv  Detail & Related papers  (2023-12-07T19:00:01Z)
• Discrete, compositional, and symbolic representations through attractor dynamics [51.20712945239422]
  We introduce a novel neural systems model that integrates attractor dynamics with symbolic representations to model cognitive processes akin to the probabilistic language of thought (PLoT) Our model segments the continuous representational space into discrete basins, with attractor states corresponding to symbolic sequences, that reflect the semanticity and compositionality characteristic of symbolic systems through unsupervised learning, rather than relying on pre-defined primitives. This approach establishes a unified framework that integrates both symbolic and sub-symbolic processing through neural dynamics, a neuroplausible substrate with proven expressivity in AI, offering a more comprehensive model that mirrors the complex duality of cognitive operations
  arXiv  Detail & Related papers  (2023-10-03T05:40:56Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems [3.9811842769009034]
  We outline the general framework of machine learning (ML) methods for multi-scale dynamical modeling of condensed matter systems. We focus on the group-theoretical method that offers a systematic and rigorous approach to compute invariants based on the bispectrum coefficients.
  arXiv  Detail & Related papers  (2022-01-03T18:38:26Z)
• Adapted projection operator technique for the treatment of initial correlations [0.0]
  We introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Our method is further illustrated by means of two cases study, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.
  arXiv  Detail & Related papers  (2021-07-28T18:01:12Z)
• A supervised learning algorithm for interacting topological insulators based on local curvature [6.281776745576886]
  We introduce a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We show that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality.
  arXiv  Detail & Related papers  (2021-04-22T18:00:00Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.