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I'm reading about mathematical models of biological neural networks, which can be grouped into two categories:

  1. The model accounts for the fact that a signal takes time to travel from the excitatory to excited neuron

  2. The signal is modeled as if it travels instantaneously between neurons

I'm trying to understand whether a signal delay is introduced for the purpose of realistically modelling a neural network, or whether it has other functional roles in the model. So by function I mean a role in the information-processing capacity of the network that extends mere physical limitations of axon signaling. I'm referring specifically to their function in biological neural networks

Here are three distinct cases that I expect the answer should fall under, to further illustrate what I mean by function:

  1. They don't, signal delays are a mere physical necessity of biological neural networks, irrelevant for the information-processing aspect of their operation. The differences between delay durations are primarily due to the fact that low reaction times are metabolically expensive and spatially-inefficient and are thus reserved for specialized purposes such as reflexes, instead of having a wider functional role as a parameter.

  2. They do, signal delays are fundamentally required for neural networks to process spatio-temporal patterns. However, the differences between the durations of delays are unnecessary to explain any fundamental internal property and are still due to external factors.

  3. They do, and the differing durations themselves are operational parameters, i.e. the function of a sub-network can only be fully understood if the ratios of the delays in signal transfers are taken into account.

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  • $\begingroup$ It's unclear from your question whether you are asking about the importance of timing delays in biological systems, or about the purpose of timing delays in artificial neural networks. $\endgroup$ – Bryan Krause Feb 7 '18 at 20:38
  • $\begingroup$ @BryanKrause I've edited in a clarification, this has to do with biological neural networks, and of course mathematical models of them, not the classical broader computer science concept but continuous-time numerical simulations $\endgroup$ – jcora Feb 7 '18 at 21:15
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Your point #1 is correct, signal propagation is not instantaneous in real physical world. But for some models it is "good enough" to approximate action potential to go through axon in an instance.

There is also biological role of signal propagation timing. One example, is classic Hebbian learning model. Based on "fire together - wire together" idea, connected neurons that become active relatively close in time, will increase synaptic connectivity, illustrated here:

Hebbian learning model

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  • $\begingroup$ General temporal dynamics are present in both models, and Hebbian learning is achieved via a simple rule dz(i, j)/dt = x(i)*x(j), where z is connection strength and x is the activation. That rule perfectly approximates Hebbian learning through time for neurons i and j without there being a need for a signal delay between them. Axonal delay is far from the only source of temporal dynamics in networks $\endgroup$ – jcora Feb 7 '18 at 19:36
  • $\begingroup$ @jcora i though that delay is driving learning, but source of the delay is unspecified. It can be regulated on different levels, including axonal propagation speed. $\endgroup$ – aaaaaa Feb 7 '18 at 19:43
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    $\begingroup$ See also this paper from Izhikevich in which he claims that the conduction delays can be instrumental in timing-based assembly formation, memory encoding and recall. $\endgroup$ – vkehayas Feb 7 '18 at 19:52
  • $\begingroup$ @aaaaaa that paper is likely exactly what I needed, will report back when I check it out:) $\endgroup$ – jcora Feb 7 '18 at 19:55
  • $\begingroup$ @jcora .paper was not my suggestion :) $\endgroup$ – aaaaaa Feb 7 '18 at 20:35

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