Related papers: On Factor Universality in Symbolic Spaces
Neuro-symbolic artificial intelligence (neuro-symbolic AI) excels in logical analysis and reasoning. Hyperdimensional Computing (HDC), a promising brain-inspired computational model, is integral to neuro-symbolic AI. Various HDC models have…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…
We present ongoing work on a tool that consists of two parts: (i) A raw micro-level abstract world simulator with an interface to (ii) a 3D game engine, translator of raw abstract simulator data to photorealistic graphics. Part (i)…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
A new formulation of special relativity is described. It is based on a postulate that the universe is a vast Cellular Automata (CA). We show that any CA model automatically leads to a maximum speed limit for the transfer of information from…
We investigate expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically…
This paper introduces a new formalism for quantum cellular automata (QCAs), based on evolving tensor products of qubits using local unitary operators. It subsequently uses this formalism to analyze and validate several conjectures, stemming…
To study potential limitations of controllability of physical systems I have earlier proposed physically universal cellular automata and Hamiltonians. These are translation invariant interactions for which any control operation on a finite…
Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of…
The study of subshifts on groups different from $\mathbb{Z}$, such as $\mathbb{Z}^d$, $d\geq 2$, has been a subject of intense research in recent years. These investigations have unveiled aremarkable connection between dynamics and…
The objective of transfer reinforcement learning is to generalize from a set of previous tasks to unseen new tasks. In this work, we focus on the transfer scenario where the dynamics among tasks are the same, but their goals differ.…
Representation learning is a central challenge across a range of machine learning areas. In reinforcement learning, effective and functional representations have the potential to tremendously accelerate learning progress and solve more…
Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern…
The ability to learn and act in novel situations is still a prerogative of animate intelligence, as current machine learning methods mostly fail when moving beyond the standard i.i.d. setting. What is the reason for this discrepancy? Most…
This paper proposes a generalized framework for cellular automata using the language of category theory, extending the classical definition beyond set-theoretic constraints. For an arbitrary category $\mathscr{C}$ with products, we define…