Related papers: Reconstructing cellular automata rules from observ…
We numerically study the dynamics of elementary 1D cellular automata (CA), where the binary state $\sigma_i(t) \in \{0,1\}$ of a cell $i$ does not only depend on the states in its local neighborhood at time $t-1$, but also on the memory of…
We present an algorithm, NN2Rules, to convert a trained neural network into a rule list. Rule lists are more interpretable since they align better with the way humans make decisions. NN2Rules is a decompositional approach to rule…
Associative networks theory is increasingly providing tools to interpret update rules of artificial neural networks. At the same time, deriving neural learning rules from a solid theory remains a fundamental challenge. We make some steps in…
The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by…
We consider a networked linear dynamical system with $p$ agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval $T$. We present a…
The cellular automata with local permutation invariance are considered. We show that in the two-state case the set of such automata coincides with the generalized Game of Life family. We count the number of equivalence classes of the rules…
Sequences and time-series often arise in robot tasks, e.g., in activity recognition and imitation learning. In recent years, deep neural networks (DNNs) have emerged as an effective data-driven methodology for processing sequences given…
Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform…
The total activity of the single-seeded cellular rule 150 automaton does not follow a one-step iteration like other elementary cellular automata, but can be solved as a two-step vectorial, or string, iteration, which can be viewed as a…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Consider a natural language sentence describing a specific step in a food recipe. In such instructions, recognizing actions (such as press, bake, etc.) and the resulting changes in the state of the ingredients (shape molded, custard cooked,…
Probing the ability of automata networks to solve decision problems has received a continuous attention in the literature, and specially with the automata reaching the answer by distributed consensus, i.e., their all taking on a same state,…
This paper introduces a new approach to reconstruct cosmological functions using artificial neural networks based on observational measurements with minimal theoretical and statistical assumptions. By using neural networks, we can generate…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
Many aspects of human reasoning, including language, require learning rules from very little data. Humans can do this, often learning systematic rules from very few examples, and combining these rules to form compositional rule-based…
Conway's cellular automaton Game of LIFE has been conjectured to be a critical (or quasicritical) dynamical system. This criticality is generally seen as a continuous order-disorder transition in cellular automata (CA) rule space. LIFE's…
Established recurrent neural networks are well-suited to solve a wide variety of prediction tasks involving discrete sequences. However, they do not perform as well in the task of dynamical system identification, when dealing with…
In applications, an anticipated situation is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed from the limited observations without…
Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…
We consider a network of agents that aim to learn some unknown state of the world using private observations and exchange of beliefs. At each time, agents observe private signals generated based on the true unknown state. Each agent might…