Related papers: Dynamic task delegation for hierarchical agents
We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…
Coordination of distributed agents is required for problems arising in many areas, including multi-robot systems, networking and e-commerce. As a formal framework for such problems, we use the decentralized partially observable Markov…
We study different algebraic structures associated to an operad and their relations: to any operad $\mathbf{P}$ is attached a bialgebra,the monoid of characters of this bialgebra, the underlying pre-Lie algebra and its enveloping algebra;…
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another.…
Interesting and efficient collective behavior observed in multi-robot or swarm systems emerges from the individual behavior of the robots. The functional space of individual robot behaviors is in turn shaped or constrained by the robot's…
Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word…
Large language models (LLMs) have achieved remarkable results across diverse downstream tasks, but their monolithic nature restricts scalability and efficiency in complex problem-solving. While recent research explores multi-agent…
Self-organization of complex morphological patterns from local interactions is a fascinating phenomenon in many natural and artificial systems. In the artificial world, typical examples of such morphogenetic systems are cellular automata.…
Two sets of mutually commuting $q-$difference operators $x_i$ and $y_j$, $i,j=1, ...,N$ such that $x_i$ and $y_i$ generate a homomorphic image of the $q-$Onsager algebra for each $i$ are introduced. The common polynomial eigenfunctions of…
The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum…
We develop an $\infty$-categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for $\infty$-operads, namely $\infty$-operads as…
We study the category of polynomial functors from finitely generated free groups to a stable infinity-category D. We show that this category is equivalent to the category of excisive functors from pointed animas to D, and also to truncated…
Human-autonomy teaming (HAT) scenarios feature humans and autonomous agents collaborating to meet a shared goal. For effective collaboration, the agents must be transparent and able to share important information about their operation with…
Multi-agent embodied systems hold promise for complex collaborative manipulation, yet face critical challenges in spatial coordination, temporal reasoning, and shared workspace awareness. Inspired by human collaboration where cognitive…
This work is focused on constructing space-time covariance functions through a hierarchical mixture approach that can serve as building blocks for capturing complex dependency structures. This hierarchical mixture approach provides a…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
The classical Eckmann-Hilton argument shows that two monoid structures on a set, such that one is a homomorphism for the other, coincide and, moreover, the resulting monoid is commutative. This argument immediately gives a proof of the…
Multi-agent large language model systems can tackle complex multi-step tasks by decomposing work and coordinating specialized behaviors. However, current coordination mechanisms typically rely on statically assigned roles and centralized…
in this paper we describe a method which allows agents to dynamically select protocols and roles when they need to execute collaborative tasks
In this paper we explore the mathematical structure of hierarchical organization in smooth dynamical systems. We start by making precise what we mean by a level in a hierarchy, and how the higher le vels need to respect the dynamics on the…