Computation <--> Learning and Memory

The speed of thinking process gives us approximate range of time scale that we do real-time computation. And our very long-lasting memory tells us the time scale of the corresponding memory processes. The former computation is most likely performed by fast dynamical systems, and the latter is hypothesized to be based on long-term synaptic plasticity. The important question is "How are these time scales connected"?

Among the underlying biophysical systems, the spike-timing dependent plasticity (STDP) is one of the possible mechanisms. If learning and memory is trying to store and recall the fast dynamics that it is performing now, it is necessary to be able to do prediction of its own dynamics. Hence, mechanisms like STDP that enhances the causal connections would be a very good start.

Living neurons as liquid in LSM, why it makes sense

8am

LCN: living cortical network
LSM: liquid state machine

Advantage of using LCN for LSM

In the original LSM framework, any dynamical system that satisfies the separation property can be used as the liquid. However, how to choose a proper liquid for a specific problem is not yet well established. Although the details are unknown, the LCN has the capability to adapt to the signals that it is exposed, and self-organize itself. Therefore, the information processing through LCN could be interesting. In fact, well known phenomenological synaptic plasticity rules including spike-timing dependent plasticity turned out to have the power of self-organization and mutual information maximization. Being a biological system that is far from being fully understood, the LCN system has the power equivalent to the brain—neurons grow axon and dendrites, self-regulate ion channels, synapses grow, split and disappear, and more. The totality of LCN cannot be simulated in a computer as a traditional LSM would work with. Even if it is possible to simulate the system, it is always computationally cheaper to use the actual physical system rather than the complicated simulation.

Story of excitatory synapses to STDP

I am a tiny synapse, the excitatory kind. I have a simple life, like a traffic light - I propagate the action potential from the presynaptic neuron to the postsynaptic neuron, only one way.
Unlike other pathetic sentient beings in this universe, my primary goal is simple: transfer as much information as possible. Through a long time of evolution, I've been thinking how to do this in the most efficient way. I have limited knowledge at a given time. I can sense the membrane potential of the (postsynaptic) neuron, remember for a while the fact that there was an action potential in either presynaptic or postsynaptically. I can change the amount of excitation that I will bring to the (postsynaptic) neuron which in turn increases the probability of firing. I also know that there are many other synapses like me, but I cannot communicate with them.

So, I thought that increasing the amount I am exciting the neuron per presynaptic action potential would be the only way I would increase the information transfer. Any information transfer has to be supported by a physical link, and it would be stronger as I increase my action.
This strategy worked sometimes, but often didn't work. Due to the dynamics of the neuron, some other action potential that I didn't cause discouraged from my contribution to fire. I definitely increased the probability of the neuron to fire, so I was happy.

One day it just struck me. I realized that I was asking the wrong question. The question I should have asked is how to transfer maximal information from all synapses through the neuron, not just me. That means I'll have to communicate with other syanpses and find out how to work together. There's only one information that all the synapses share, the timing of the postsynaptic action potential. The membrane potential was quite local in the dendritic structure and highly noisy. I have to rely on the output train of action potentials to figure out how I can cooperate with other synapses.

Imagine a network of thousand roads and millions of cars trying to get from point A to B. If there were no coordination of traffic lights, and each road is trying to maximize the number of cars that goes through itself, all the intersections would be clogged by interference among incoming traffic. Of course, information is nothing like cars, it's an analogy! If they were, a car would clone itself and turn into two cars, and transform into different cars, and just disappear without a clue. Anyway, the point is that if somebody else is sending some information, I should not send mine at the moment. But, unlike cars, if somebody is sending information through this neuron, and I have a very similar information, I should send mine too, to reinforce the transfer. That way we collaborate to reduce the variability of the output spike train.

Yes, that's what I should do. I should find a group of other synapses that share some input features and collaborate. If I cannot find one, I should stay low profile and do not disturb others but still be open to chances of finding future opportunities of collaborations. How will I find a group by only observing the output spike train? I would like to see if I seem to be strongly causing the output. If I am, that means there is a group of synapses that are also causing the output spike train, because I am not strong enough to cause it myself. So I should also participate strongly to the information transfer process.

How would I know that I am strongly causing the output? The feature I am looking for should be in the spike trains and cannot be temporally too spread, because of my short memory. In the simplest case, I would just see the relation between one presynaptic action potential and one postsynpatic action potential in a small time window. If the presynaptic one occurs first, then I am somewhat causing the output, and if it is the opposite case, I might just be disturbing. Therefore, if I use spike-timing dependent plasticity (STDP), over time this instantaneous causality would accumulate and I would be collaborating with similar synapses or not.

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• One big advantage of point process over regular random process is that the causality is easy to detect.
• There could be other measures of causality that extends to more than a pair of input/output.
• Papers in the literature does not address spatial patterns so that the STDP synapses could collaborate.
  

Bad milk breakfast day

7am
Distributed synchrony in a cell assembly of spiking neurons
Nir Levy, David Horn, Isaac Meilijson, Eytan Ruppin
Neural Networks, Vol. 14, No. 6-7. (9 July 2001), pp. 815-824.

Experiment:
Step 1. Feed a strong common input to a population of spiking neurons (both excitatory and inhibitory)
Step 2. Let STDP do their job for excitatory-excitatory synapses
Step 3. Stop the input and observe the sustained activity

Observation:

• Oscillation of synchronous firing is observed
• The neurons formed subgroups that fired in sequence
• The frequency of oscillation was simply dependent on the synaptic delay and number of subgroups
• Over time the group formation can slightly change
  

They call this synchronous subgroup firing oscillation as "distributed synchrony" state.
This is an evidence that STDP can be used to make synchronously firing neural ensembles.

9am
Time independent Schrödinger equation and information potential
Aim: A potential field that would yield the Parzen estimated pdf as one of the solutions of a
finite energy time-independent Shrodinger equation. The solution (wave function) has a physical meaning of being a probability amplitude function (complex valued) of a particle. Therefore somehow linking the probability and potential.
Dr. P: The potential might act as a regularizer

10am
Discussion with Dr. D
Memming: STDP can do some computation with synchrony code. Suppose you have two ensembles A and B. I can train a third ensemble C with STDP to fire only when A and B fire.
Dr. D: Why not try the idea of association? Eliminate C and just make A and B fire even when only A fires.