Showing papers by "Hava T. Siegelmann published in 2014"

The super-turing computational power of plastic recurrent neural networks

Abstract: We study the computational capabilities of a biologically inspired neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve over time rather than stay static. Our study focuses on the mere concept of plasticity of the model so that the nature of the updates is assumed to be not constrained. In this context, we show that the so-called plastic recurrent neural networks (RNNs) are capable of the precise super-Turing computational power — as the static analog neural networks — irrespective of whether their synaptic weights are modeled by rational or real numbers, and moreover, irrespective of whether their patterns of plasticity are restricted to bi-valued updates or expressed by any other more general form of updating. Consequently, the incorporation of only bi-valued plastic capabilities in a basic model of RNNs suffices to break the Turing barrier and achieve the super-Turing level of computation. The consideration of more general mechanisms of architectural plasticity or of real synaptic weights does not further increase the capabilities of the networks. These results support the claim that the general mechanism of plasticity is crucially involved in the computational and dynamical capabilities of biological neural networks. They further show that the super-Turing level of computation reflects in a suitable way the capabilities of brain-like models of computation.

Probabilistic Control and Swarm Dynamics in Mobile Robots and Ants

Abstract: The chapter considers the method of probabilistic control of mobile robots navigating in random environments and mimicking the foraging activity of ants, which is widely accepted as optimal with respect to the environmental conditions. The control is based on the Tsetlin automaton, which is a minimal automaton demonstrating an expedient behavior in random environments. The suggested automaton implements probability-based aggregators, which form a complete algebraic system and support an activity of the automaton over non-Boolean variables. The considered mobile agents are based on the Braitenberg vehicles equipped with four types of sensors, which mimic the basic sensing abilities of ants: shortand long-distance sensing of environmental states, sensing of neighboring agents, and sensing the pheromone traces. Numerical simulations demonstrate that the foraging behavior of the suggested mobile agents, running both individually and in groups, is statistically indistinguishable from the foraging behavior of real ants observed in laboratory experiments.

Development of Physical Super-Turing Analog Hardware

Abstract: In the 1930s, mathematician Alan Turing proposed a mathematical model of computation now called a Turing Machine to describe how people follow repetitive procedures given to them in order to come up with final calculation result. This extraordinary computational model has been the foundation of all modern digital computers since the World War II. Turing also speculated that this model had some limits and that more powerful computing machines should exist. In 1993, Siegelmann and colleagues introduced a Super-Turing Computational Model that may be an answer to Turing’s call. Super-Turing computation models have no inherent problem to be realizable physically and biologically. This is unlike the general class of hyper-computer as introduced in 1999 to include the Super-Turing model and some others. This report is on research to design, develop and physically realize two prototypes of analog recurrent neural networks that are capable of solving problems in the Super-Turing complexity hierarchy, similar to the class BPP/log*. We present plans to test and characterize these prototypes on problems that demonstrate anticipated Super- Turing capabilities in modeling Chaotic Systems.

Honest signaling in the cooperative search

Abstract: We consider a foraging by a group of agents acting in heterogeneous environment, and suggest a new model of cooperative foraging, which implements biological signaling. In the model, the individual foraging follows Brownian walks and the Levy flights with the varying parameters with respect to the observed states of the environment, and communication between the agents and their aggregation is defined on the basis of the Sir Philip Sidney game, which models the honest communication between animals. In our simulation, we find that a group of Brownian foragers with signaling behaves similarly to the group of Levy flyers without signaling, and the resulting cooperative foraging outperforms the known models of foraging without signaling. We argue that it provides a simple yet competitive description of the observed behavior of the foraging animals.

Biologically inspired load balancing mechanism in neocortical competitive learning

Abstract: A unique delayed self-inhibitory pathway mediated by layer 5 Martinotti Cells was studied in a biologically inspired neural network simulation. Inclusion of this pathway along with layer 5 basket cell lateral inhibition caused balanced competitive learning, which led to the formation of neuronal clusters as were indeed reported in the same region. Martinotti pathway proves to act as a learning "conscience", causing overly successful regions in the network to restrict themselves and let others fire. It thus spreads connectivity more evenly throughout the net and solves the "dead unit" problem of clustering algorithms in a local and biologically plausible manner