Related papers: On beta-skeleton automata with memory
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
In the mammalian brain, newly acquired memories depend on the hippocampus for maintenance and recall, but over time the neocortex takes over these functions, rendering memories hippocampus-independent. The process responsible for this…
Soft machines display shape adaptation to external circumstances due to their intrinsic compliance. To achieve increasingly more responsive behaviors upon interactions without relying on centralized computation, embodying memory directly in…
The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
MemComputing is a new model of computation that exploits the non-equilibrium property-we call 'memory'-of any physical system to respond to external perturbations by keeping track of how it has reacted at previous times. Its digital,…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper,…
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the…
Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…
For a group $G$ and a finite set $A$, a cellular automaton (CA) is a transformation $\tau : A^G \to A^G$ defined via a finite memory set $S \subseteq G$ and a local map $\mu : A^S \to A$. Although memory sets are not unique, every CA admits…