Solving the Problem of Negative Synaptic Weights in Cortical Models

Abstract

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.

Population Models of Temporal Differentiation

“…This combination of direct excitation and indirect inhibition can closely approximate any set of mixed excitatory and inhibitory synaptic weights, as discussed extensively elsewhere (Parisien et al, 2008). This allows us to first specify an approximate model, with projections that consist of optimal unconstrained synaptic weights and then to transform each of these idealized projections into physiologically realistic projections that function in essentially the same way.…”

“…This subtraction is critical to the computation. As discussed in section 3, there are a number of biophysical mechanisms by which the abstract subtraction operation might be realized through inhibitory synapses; detailed network models will be developed assuming the mechanism described by Parisien, Anderson, and Eliasmith (2008). Finally, the variable y ≈ su at the right of the diagram corresponds to the scalar variable that is represented by the output ensemble.…”

“…The presynaptic neurons also project to a small group of inhibitory interneurons, which project in turn to the postsynaptic neurons, compensating for the bias current introduced by increasing the excitatory weights. In this way, the original mapping is approximately recovered (Parisien et al, 2008). Because the indirect component of each projection passes through interneurons, it lags slightly behind the direct component.…”

Review of advances in neural networks: Neural design technology stack

“…For instance, the neurons in the brain are either inhibitory or excitatory (Dale's principle), so a very common change of ANN weight polarity is, from a biological standpoint, a change of neuron type. In fact, such a change is not feasible in the brain, but this is considered allowable as it is possible to transform a neural network model with mixed synapses into a network with inhibitory or excitatory neurons only [55].…”

Output feedback bipartite consensus and consensus of linear multi-agent systems

“…However, oftentimes, both collaboration and antagonistic interactions coexist within a certain group. Such examples can be found in scenarios of social networks ( [1], [12]), predator-prey dynamics [6], biological systems [9], and so on. In cases like these, nonnegative graphs cease to be applicable.…”