We study the problem of memory capacity in balanced networks of spiking neurons. Associative memories are represented by either synfire chains (SFC) or Hebbian cell assemblies (HCA). Both can be embedded in these balanced networks by a proper choice of the architecture of the network. The size w(E) of a pool in an SFC or of an HCA is limited from below and from above by dynamical considerations. Proper scaling of w(E) by radicalK, where K is the total excitatory synaptic connectivity, allows us to obtain a uniform description of our system for any given K. Using combinatorial arguments, we derive an upper limit on memory capacity. The capacity allowed by the dynamics of the system, alpha(c), is measured by simulations. For HCA, we obtain alpha(c) of order 0.1, and for SFC, we find values of order 0.065. The capacity can be improved by introducing shadow patterns, inhibitory cell assemblies that are fed by the excitatory assemblies in both memory models. This leads to a doubly balanced network, where, in addition to the usual global balancing of excitation and inhibition, there exists specific balance between the effects of both types of assemblies on the background activity of the network. For each of the memory models and for each network architecture, we obtain an allowed region (phase space) for w(E)/ radicalK in which the model is viable.

A balanced network leads to contradictory constraints on memory models, as exemplified in previous work on accommodation of synfire chains. Here we show that these constraints can be overcome by introducing a 'shadow' inhibitory pattern for each excitatory pattern of the model. This is interpreted as a double- balance principle, whereby there exists both global balance between average excitatory and inhibitory currents and local balance between the currents carrying coherent activity at any given time frame. This principle can be applied to networks with Hebbian cell assemblies, leading to a high capacity of the associative memory. The number of possible patterns is limited by a combinatorial constraint that turns out to be P=0.06N within the specific model that we employ. This limit is reached by the Hebbian cell assembly network. To the best of our knowledge this is the first time that such high memory capacities are demonstrated in the asynchronous state of models of spiking neurons.

We investigate the formation of synfire waves in a balanced network of integrate-and-fire neurons. The synaptic connectivity of this network embodies synfire chains within a sparse random connectivity. This network can exhibit global oscillations but can also operate in an asynchronous activity mode. We analyze the correlations of two neurons in a pool as convenient indicators for the state of the network. We find, using different models, that these indicators depend on a scaling variable. Beyond a critical point, strong correlations and large network oscillations are obtained. We looked for the conditions under which a synfire wave could be propagated on top of an otherwise asynchronous state of the network. This condition was found to be highly restrictive, requiring a large number of neurons for its implementation in our network. The results are based on analytic derivations and simulations.