Information space dynamics for neural networks

Increasing memory capacity and reducing spurious states in neural networks by introducing coherent and collective firing

It is well known that higher-order Hopfield nets called multispin models can increase memory capacity to some extent by extending the direct product of spin states to more than second order. However, a group of neurons can then respond degenerately to different loaded patterns, resulting in many spurious states due to cross-talk effects. We present an idea to increase the number of attracting basins for patterns while suppressing the associated spurious states, by introducing coherent and collective firing in multispin groups. We numerically implement the method and test the number, stability, and basin size of the attractors thus created. Increasing the size of a group of coherent excitation suppresses spurious states, stabilizes loaded patterns, and dramatically increases the number of pattern attractors.

Concatenated retrieval of correlated stored information in neural networks

We consider a coupled map lattice defined on a hypercube in M dimensions, taken here as the information space, to model memory retrieval and information association by a neural network. We assume that both neuronal activity and spike timing may carry information. In this model the state of the network at a given time t is completely determined by the intensity y(sigma,t) with which the information pattern represented by the integer sigma is being expressed by the network. Logistic maps, coupled in the information space, are used to describe the evolution of the intensity function y(sigma(upper arrow),t) with the intent to model memory retrieval in neural systems. We calculate the phase diagram of the system regarding the model ability to work as an associative memory. We show that this model is capable of retrieving simultaneously a correlated set of memories, after a relatively long transient that may be associated to the retrieving of concatenated memorized patterns that lead to a final attractor.

Synchronous neural oscillations and cognitive processes

The central problem for cognitive neuroscience is to describe how cognitive processes arise from brain processes. This review summarizes the recent evidence that synchronous neural oscillations reveal much about the origin and nature of cognitive processes such as memory, attention and consciousness. Memory processes are most closely related to theta and gamma rhythms, whereas attention seems closely associated with alpha and gamma rhythms. Conscious awareness may arise from synchronous neural oscillations occurring globally throughout the brain rather than from the locally synchronous oscillations that occur when a sensory area encodes a stimulus. These associations between the dynamics of the brain and cognitive processes indicate progress towards a unified theory of brain and cognition.