neuron spike computational capacity

The following is taken from this blog post. I’m posting it here now because of this argument between jacob_cannell and others including Eliezer Yudkowsky.

A neuron firing by opening sodium channels is all-or-nothing, so information must be transmitted in the timing. Neurons have no global absolute clock, so information must be contained in “time since last spike” rather than the absolute time of spikes, unless a spike means that something has just happened.

For some current theories of neuron firing, see this page.

From artificial neural network (ANN) research, we know that linear representations of activations are worse at low resolution than some nonlinear ones. I would expect a spike to typically represent an activation of approximately:

Formula 1: a + b * e^(-c * time_since_last_spike)

Each neuron is connected to many synapses, typically ~7000 in a human brain. When a neuron fires, at each connected synapse, some neurotransmitters are released. Most neurotransmitters have no immediate effect on neuron firing, and instead regulate slower processes, but let’s consider just the short-term behavior of neurons. A neuron N1 fires, it releases some neurotransmitters at a synapse, and they bind to receptors at neuron N2 which have some net effect on the electric potential of N2.

That net short-term effect on N2 potential is analogous to a “weight” in an ANN, but it’s not a constant, it’s a function: spike timing → change in potential. (Also, the neurotransmitter receptors at synapses can be disabled or added over a longer timescale.) The N2 potential is analogous to an ANN accumulator, but it decays towards a baseline over time.

The represented weights can be both positive and negative. It’s also common for a single synapse to have receptors with positive and negative effects on cell potential active at the same time.

I wrote above that I’d expect the activation represented by a spike to often approximately follow Formula 1. An obvious way to accomplish that is to have a synapse with a channel type with approximately constant value on firing, and another channel type transporting ions that, as time passes after a spike, are transported and asymptotically approach an approximately opposite value.

That being the case, I’d expect two spikes in rapid succession at the same synapse to usually represent a large activation value. Depending on the “weights” at that synapse, that could either strongly inhibit neuron firing, or lead to immediate firing. But of course, there’s no need for all synapses to use timing representations with the same shape. At some synapses, longer times between spikes probably represent larger values; that would be useful for making fast simple reactions, where you want a single pulse to propagage through some paths quickly.

When neurons modify receptors at synapses, how much internal data can they draw upon? Memories are partly stored by DNA methylation patterns, so potentially quite a bit.

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