On the Electrodynamics of Neural Networks

We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction. Starting from a full-fledged three-compartment model of a single pyramidal neuron, including shunting and dendritic propagation, we derive an observation model for dendritic dipole currents in extracellular space and thereby for the dendritic field potential that contributes to the local field potential of a neural population. Under reasonable simplifications, we then derive a leaky integrate-and-fire model for the dynamics of a neural network, which facilitates comparison with existing neural network and observation models. In particular, we compare our results with a related model by means of numerical simulations. Performing a continuum limit, neural activity becomes represented by a neural field equation, while an observation model for electric field potentials is obtained from the interaction of cortical dipole currents with charge density in non-resistive extracellular space as described by the Nernst-Planck equation. Our work consistently satisfies the widespread dipole assumption discussed in the neuroscientific literature

Turing Computation with Recurrent Artifcial Neural Networks

We improve the results by Siegelmann & Sontag (1995) by providing a novel and parsimonious constructive mapping between Turing Machines and Recurrent Artificial Neural Networks, based on recent developments of Nonlinear Dynamical Automata. The architecture of the resulting R-ANNs is simple and elegant, stemming from its transparent relation with the underlying NDAs. These characteristics yield promise for developments in machine learning methods and symbolic computation with continuous time dynamical systems. A framework is provided to directly program the R-ANNs from Turing Machine descriptions, in absence of network training. At the same time, the network can potentially be trained to perform algorithmic tasks, with exciting possibilities in the integration of approaches akin to Google DeepMind's Neural Turing Machines.Comment: 11 pages, 3 figure

An integrated neural model of semantic memory, lexical retrieval and category formation, based on a distributed feature representation

This work presents a connectionist model of the semantic-lexical system. Model assumes that the lexical and semantic aspects of language are memorized in two distinct stores, and are then linked together on the basis of previous experience, using physiological learning mechanisms. Particular characteristics of the model are: (1) the semantic aspects of an object are described by a collection of features, whose number may vary between objects. (2) Individual features are topologically organized to implement a similarity principle. (3) Gamma-band synchronization is used to segment different objects simultaneously. (4) The model is able to simulate the formation of categories, assuming that objects belong to the same category if they share some features. (5) Homosynaptic potentiation and homosynaptic depression are used within the semantic network, to create an asymmetric pattern of synapses; this allows a different role to be assigned to shared and distinctive features during object reconstruction. (6) Features which frequently occurred together, and the corresponding word-forms, become linked via reciprocal excitatory synapses. (7) Features in the semantic network tend to inhibit words not associated with them during the previous learning phase. Simulations show that, after learning, presentation of a cue can evoke the overall object and the corresponding word in the lexical area. Word presentation, in turn, activates the corresponding features in the sensory-motor areas, recreating the same conditions occurred during learning, according to a grounded cognition viewpoint. Several words and their conceptual description can coexist in the lexical-semantic system exploiting gamma-band time division. Schematic exempla are shown, to illustrate the possibility to distinguish between words representing a category, and words representing individual members and to evaluate the role of gamma-band synchronization in priming. Finally, the model is used to simulate patients with focalized lesions, assuming a damage of synaptic strength in specific feature areas. Results are critically discussed in view of future model extensions and application to real objects. The model represents an original effort to incorporate many basic ideas, found in recent conceptual theories, within a single quantitative scaffold