Synfire waves in small balanced networks
Introduction
In a balanced network (BN) the mean inhibitory input to a neuron cancels the mean excitatory input [8]. BNs of integrate-and-fire (IF) neurons with sparse random connectivity have been shown [3] to have stable asynchronous states (AS). The statistics of the AS is closely related to that of cortical tissue. In addition, it has been shown on another model [9] of BN that the AS performs well in transferring rate code via population activity.
In this work, we seek a system that conveys information using both temporal and rate codes, perhaps even simultaneously. We adopt the BN model as the framework for rate coding, and the synfire [1] model as a framework for temporal coding.
In the synfire model, pools of excitatory neurons are connected in a consecutive manner to form a chain. All neurons in a pool project their output to all neurons in the consecutive pool. Diesmann et al. [5], and more recently [4], [7], have shown that above a critical pool size, pool activity ignited at the first pool propagates from one pool to the next, forming a synfire wave. The successful propagation is due to exact timing of the excitatory input, hence it reflects temporal coding.
Here, we embed a chain in the excitatory-to-excitatory connectivity matrix of the BN, and we look for conditions under which the AS of a BN is stable and, on top of it, a synchronized wave of activity can propagate along a chain. Since the connectivity matrix is not random anymore, and since there is feedback between the network activity and the chain (which is part of the network), it is not clear if such conditions exist. In a previous work [2], we have demonstrated that these conditions can be met by very large networks. Here, we will demonstrate that an additional modification allows them to be met in small networks too.
Section snippets
The problem: too much excitement, the balance is broken
The idea underlying the synfire model is that a stable and reproducible wave can propagate under noisy conditions, if strong excitatory input overcomes the noise and drives the correct neuron across threshold at the right time. The strong correlated excitatory input is obtained through converging connections from one pool of neurons to the next.
On the other hand, rate coding in general and BN in particular, requires random connectivity. Randomness is required for desynchronizing neurons,
A solution: casting shadows
We define a modified synfire chain as follows: A pool of randomly chosen inhibitory neurons, a ‘shadow’ pool, is attached to each excitatory pool in a synfire chain. A neuron in an excitatory pool projects its output, not only to the next pool in the chain, but also to all neurons in its shadow pool. A neuron in the shadow pool, does not project it output in any ordered manner, but diffuses its output randomly to the rest of the network, as is in a completely random network. Similar
Summary
To allow temporal coding on top of a rate-coding system, we introduced a double-balance requirement: at the macroscopic level, inhibitory input cancels mean excitatory input, providing a global asynchronous state. At the microscopic level, inhibitory pools counteract synchronized excitatory synfire pools.
Acknowledgements
This work was supported in part by Grants from GIF.
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