Related papers: Polynomial Life: the Structure of Adaptive Systems
The multifarious internal workings of organisms are difficult to reconcile with a single feature defining a state of being alive. Indeed, definitions of life rely on emergent properties (growth, capacity to evolve, agency) only symptomatic…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
Organizing physics has been a long-standing preoccupation of applied category theory, going back at least to Lawvere. We contribute to this research thread by noticing that Hamiltonian mechanics and gradient descent depend crucially on a…
In psychology and neuroscience it is common to describe cognitive systems as input/output devices where perceptual and motor functions are implemented in a purely feedforward, open-loop fashion. On this view, perception and action are often…
We introduce structured active inference, a large generalization and formalization of active inference using the tools of categorical systems theory. We cast generative models formally as systems "on an interface", with the latter being a…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Active inference is an ambitious theory that treats perception, inference and action selection of autonomous agents under the heading of a single principle. It suggests biologically plausible explanations for many cognitive phenomena,…
This paper explores the idea that information is an essential and distinctive feature of living systems. Unlike non-living systems, living systems actively acquire, process, and use information about their environments to respond to…
Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often…
Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy…
This paper proposes a structural and dynamical framework for modeling cognitive processes within a cybernetic perspective. Cognitive states are represented as elements of a state space evolving through an iterative update rule of the form…
We establish a correspondence between equivalence classes of agent-state policies for deterministic POMDPs and one-input process functions (the classical-deterministic limit of higher-order quantum operations). We use this correspondence to…
Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. Their work presented these ideas clearly but ultimately led…
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…
Building autonomous -- i.e., choosing goals based on one's needs -- and adaptive -- i.e., surviving in ever-changing environments -- agents has been a holy grail of artificial intelligence (AI). A living organism is a prime example of such…
Social agents both internalize collective norms and reshape them through creative action, yet computational models have not captured this bidirectional process within a unified framework. We propose a multi-agent simulation model grounded…