Related papers: Generalization over different cellular automata ru…
Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such…
In this work, we propose a notion of practical learnability grounded in finite sample settings, and develop a conjugate learning theoretical framework based on convex conjugate duality to characterize this learnability property. Building on…
Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…
A deep generative model such as a GAN learns to model a rich set of semantic and physical rules about the target distribution, but up to now, it has been obscure how such rules are encoded in the network, or how a rule could be changed. In…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
Existing defects in software components is unavoidable and leads to not only a waste of time and money but also many serious consequences. To build predictive models, previous studies focus on manually extracting features or using tree…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…
Machine learning (ML) formalizes the problem of getting computers to learn from experience as optimization of performance according to some metric(s) on a set of data examples. This is in contrast to requiring behaviour specified in advance…
While deep neural networks take loose inspiration from neuroscience, it is an open question how seriously to take the analogies between artificial deep networks and biological neuronal systems. Interestingly, recent work has shown that deep…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…
The emergence of complex structures in the systems governed by a simple set of rules is among the most fascinating aspects of Nature. The particularly powerful and versatile model suitable for investigating this phenomenon is provided by…
In this paper a method is proposed which uses data mining techniques based on rough sets theory to select neighborhood and determine update rule for cellular automata (CA). According to the proposed approach, neighborhood is detected by…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
Deep reinforcement-learning methods have achieved remarkable performance on challenging control tasks. Observations of the resulting behavior give the impression that the agent has constructed a generalized representation that supports…
Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…
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…
In this paper, we introduce a new type of generalized neural network where neurons and synapses maintain multiple states. We show that classical gradient-based backpropagation in neural networks can be seen as a special case of a two-state…
We present a probabilistic 3D generative model, named Generative Cellular Automata, which is able to produce diverse and high quality shapes. We formulate the shape generation process as sampling from the transition kernel of a Markov…