Related papers: X-Rule's Precursor is also Logically Universal
In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to…
Languages encode distinct abstractions and inductive priors, yet most large language models (LLMs) overlook this diversity by reasoning in a single dominant language. In this work, we introduce x1, a family of reasoning models that can…
In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of…
Achieving advanced machine intelligence remains a central challenge in AI research, often approached through scaling neural architectures and generative models. However, biological systems offer a broader repertoire of strategies for…
We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic…
Cellular automata (CA) are well-studied models of decentralized parallel computation, known for their ability to exhibit complex global behavior from simple local rules. While their dynamics have been widely explored through simulations, a…
Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem…
Gradual argumentation frameworks represent arguments and their relationships in a weighted graph. Their graphical structure and intuitive semantics makes them a potentially interesting tool for interpretable machine learning. It has been…
In this paper we explore the boundary between biology and the study of formal systems (logic). In the end, we arrive at a summary formalism, a chapter in "boundary mathematics" where there are not only containers <> but also extainers ><,…
Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis:…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…
Generating human-like behavior on robots is a great challenge especially in dexterous manipulation tasks with robotic hands. Scripting policies from scratch is intractable due to the high-dimensional control space, and training policies…
We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this *e-posterior* allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the…
The architecture of a neural network controlling an unknown environment is presented. It is based on a randomly connected recurrent neural network from which both perception and action are simultaneously read and fed back. There are two…
The need to explain predictive models is well-established in modern machine learning. However, beyond model interpretability, understanding pre-processing methods is equally essential. Understanding how data modifications impact model…
This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…
A simple gripper can solve more complex manipulation tasks if it can utilize the external environment such as pushing the object against the table or a vertical wall, known as "Extrinsic Dexterity." Previous work in extrinsic dexterity…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…