<p>While we don't entirely know how all aspects of working memory operate, experiments show that a subset of cells in the brain exhibit <em>persistent activity</em> during working memory tasks.</p>
<p>Here's an example from a review by <a href="https://www.sciencedirect.com/science/article/pii/S1364661303001979" rel="nofollow noreferrer">Curtis &amp; D'Esposito</a>:</p>
<p><a href="https://i.sstatic.net/QrplW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/QrplW.png" alt="enter image description here" /></a></p>
<p>This is a task in panel (a) where there is a cue presented briefly (marked by &quot;C&quot;), and then the monkey needs to remember the cue (during the time marked by &quot;D&quot;), and finally at time R the targets appear and the monkey can make a response.</p>
<p>We see in spiking recordings from monkeys that there are cells in dorsolateral prefrontal cortex that are activated not only by the cue and during the response, but they have persistent activity during the delay period. In human studies we can't ordinarily place electrodes but part (b) shows a similar study using fMRI, and the colored areas on the brain indicate brain areas that demonstrated more blood flow (marking metabolism) during the delay period, which includes areas of the same brain region as the monkey experiments.</p>
<p>The explanations are <strong>recurrent network activity</strong> and <strong>bistability</strong>: a population of cells that is excited can continue to excite each other and remain active until stopped (see for example <a href="https://en.wikipedia.org/wiki/Attractor_network" rel="nofollow noreferrer">attractor networks</a> for a conceptual idea), as well as bistability in individual neurons where a neuron that reaches threshold <em>continues to fire tonically</em> rather than firing a single action potential, until firing is ceased via inhibition. <a href="https://link.springer.com/content/pdf/10.1023/A:1008837311948.pdf" rel="nofollow noreferrer">Camperi and Wang 1998</a> is an excellent, clear review of these concepts with a straightforward mathematical approach to how you can model this <em>in silico</em>. It's probably more efficient to start from here rather than reinventing it on your own.</p>
<p>I also recommend other papers by XJ Wang who has done extensive work in this area. I also recommend you look at <a href="https://en.wikipedia.org/wiki/Phase_space" rel="nofollow noreferrer">phase-space diagrams</a> which can help conceptualize dynamic systems with stable properties (and which network parameters are necessary for stability), they come up a lot in theoretical neuroscience. Dayan and Abbott's <a href="https://mitpress.mit.edu/books/theoretical-neuroscience" rel="nofollow noreferrer">Theoretical Neuroscience</a> is also a good starting point if you can find a copy.</p>
<hr />
<p>Camperi, M., &amp; Wang, X. J. (1998). A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. Journal of computational neuroscience, 5(4), 383-405.</p>
<p>Curtis, C. E., &amp; D'Esposito, M. (2003). Persistent activity in the prefrontal cortex during working memory. Trends in cognitive sciences, 7(9), 415-423.</p>

CC BY-SA 4.0
2020-12-21T19:51:34.823Z
Thanks a lot for your reply! I was not aware of bistability. I have looked at several models of working memory before, but I have not seen anybody using it. It's not the same as bursting, is it? I'll read the literature by Wang you have recommended and get back to you. A small question if I may. The persistent activity in Esposito et al - it is persistent in every trial individually, or in trial-average picture? I have heard there is a large controversy between persistent and 'transient' activity, whatever the latter is
Aleksejs Fomins
CC BY-SA 4.0
2020-12-21T19:55:21.680Z
@AleksejsFomins It's a trial average. You can have persistent activity that's either relatively constant or persistent activity that comes in "waves"; this is true for sensory responses, too, see work by Ken Harris and Artur Luczak.
Bryan Krause
CC BY-SA 4.0
2020-12-21T19:56:35.133Z
If you're coming at it from ANNs I'm not sure what the motivations would be for directly modeling working memory, if any. It's a biological solution, not necessarily relevant to artificial networks that have other tools available.
Bryan Krause
CC BY-SA 4.0
2020-12-21T23:09:34.763Z
No no, I'm something in-between. I'm well aware that brain-inspired ANN have no chance of competing with digital hardware or known ML algorithms. I'm trying to solve credit assignment problem in the brain by means of reservoir/echo state networks. The idea is nice - reservoir does some generic space/time transform on incoming data, and a shallow readout can then learn whatever it needs. Bio-plausible and maybe in future can improve training cost of simple ANN. The main problem there is that most implementations to date forget input very fast, which makes them useless. Need to tune
Aleksejs Fomins
CC BY-SA 4.0
2020-12-21T23:30:50.710Z
@AleksejsFomins Gotcha. For learning you might also look into intracellular memory processes via second-messenger systems, if you haven't already. These are outside what is called "short term memory" but are still a trace of recent history that can be used for training biological networks. Not my area of expertise, though.
Bryan Krause
CC BY-SA 4.0
2020-12-21T23:36:41.833Z
Hmm, that's of course really cool but maybe deeper than I can afford to go. A compromise I have seen used includes storing several dynamic variables inside of a cell. For example, the firing threshold of a cell can adapt on a few different timescales due to processes like intrinsic homeostatic plasticity or increased excitability.
Aleksejs Fomins
CC BY-SA 4.0
2020-12-21T23:52:55.803Z
@AleksejsFomins Yes, if you propose some second messenger increases intracellularly when a spike fires (or a synapse is activated) and decays with some (relatively slow) time constant you need not model all the intracellular metabolic processes. In the biology you expect some nonlinearities but depending on your goals those may not be important (or, at least, can be compromised away).
Bryan Krause
CC BY-SA 4.0
2020-12-21T17:00:49.133Z
2020-12-21T17:08:07.647Z
2020-12-21T17:08:07.647Z
Bryan Krause
<p>So I close my eyes, turn around, open them for just a blink and close again. I have observed a chair. I can't tell you how the chair looks like in detail, but I can more or less tell its shape and color. What's more, if I'm not disturbed, I can remember that shape and color for at least a minute.</p>
<p>What if I wanted to construct a device that could repeat this process. With digital hardware its not too hard - take a digital camera and a solid state memory device. For every bit of info in my solid state drive, I can call the operation &quot;store&quot; and my bit will be stored, or &quot;erase&quot; and it will be erased. Don't know how reliably each physical bit works with current technology, but given sufficient number of physical bits per logical bit I can theoretically make a device that will store my picture for as long as I want.</p>
<p>What about building a spiking neuronal network to do the same thing? I have tried some naive approaches, and I arrive at a fundamental problem: spiking neuronal networks seem to have almost no inertia on the fast timescale. A neuron only fires while there is sufficient input. When input is gone, it no longer fires (besides some resting state activity). I can construct a network with recurrently-connected neurons, in which case, in principle, the activity of the network could sustain itself after the input is gone. However, depending on the parameters of the network I observe a rapid switch between two very extreme behaviours. In one case, the feedback strength of the network is too weak, and the activity drops as soon as the input is gone. In the other, the feedback weight is too strong, and the activity of the network quickly reaches some maximal firing state independently of which exact input the network has received. These transitions happen exponentially fast. Theoretically, there are adaptive control mechanisms in neuronal networks, such as inhibition and synaptic plasticity. However, I am struggling to understand how such mechanisms can ever be fast enough to compensate for the sudden increase or drop of input.</p>
<p><strong>TL;DR</strong>: Naively neuronal networks do not seem stable enough to implement robust short-term memory. What are the known mechanisms that nevertheless make it possible?</p>
<p>Note: I'm not asking how exactly short-term memory works. I am aware that nobody really knows. I'm asking for intuition to help disprove my argument that it should not work when implemented using neurons.</p>

<theoretical-neuroscience><working-memory><short-term-memory>
Is short-term memory theoretically possible to with spiking neurons?
Aleksejs Fomins
# Is short-term memory theoretically possible to with spiking neurons?

(Asked by: username_0 on 2020-12-21)

So I close my eyes, turn around, open them for just a blink and close again. I have observed a chair. I can't tell you how the chair looks like in detail, but I can more or less tell its shape and color. What's more, if I'm not disturbed, I can remember that shape and color for at least a minute.

What if I wanted to construct a device that could repeat this process. With digital hardware its not too hard - take a digital camera and a solid state memory device. For every bit of info in my solid state drive, I can call the operation "store" and my bit will be stored, or "erase" and it will be erased. Don't know how reliably each physical bit works with current technology, but given sufficient number of physical bits per logical bit I can theoretically make a device that will store my picture for as long as I want.

What about building a spiking neuronal network to do the same thing? I have tried some naive approaches, and I arrive at a fundamental problem: spiking neuronal networks seem to have almost no inertia on the fast timescale. A neuron only fires while there is sufficient input. When input is gone, it no longer fires (besides some resting state activity). I can construct a network with recurrently-connected neurons, in which case, in principle, the activity of the network could sustain itself after the input is gone. However, depending on the parameters of the network I observe a rapid switch between two very extreme behaviours. In one case, the feedback strength of the network is too weak, and the activity drops as soon as the input is gone. In the other, the feedback weight is too strong, and the activity of the network quickly reaches some maximal firing state independently of which exact input the network has received. These transitions happen exponentially fast. Theoretically, there are adaptive control mechanisms in neuronal networks, such as inhibition and synaptic plasticity. However, I am struggling to understand how such mechanisms can ever be fast enough to compensate for the sudden increase or drop of input.

**TL;DR**: Naively neuronal networks do not seem stable enough to implement robust short-term memory. What are the known mechanisms that nevertheless make it possible?

Note: I'm not asking how exactly short-term memory works. I am aware that nobody really knows. I'm asking for intuition to help disprove my argument that it should not work when implemented using neurons.

**Tags:** theoretical-neuroscience, working-memory, short-term-memory


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## 1 answers

### Answer by username_1 on 2020-12-21. Score: 1 | Accepted answer

While we don't entirely know how all aspects of working memory operate, experiments show that a subset of cells in the brain exhibit *persistent activity* during working memory tasks.

Here's an example from a review by [Curtis & D'Esposito](https://www.sciencedirect.com/science/article/pii/S1364661303001979):

[![enter image description here](https://i.sstatic.net/QrplW.png)](https://i.sstatic.net/QrplW.png)

This is a task in panel (a) where there is a cue presented briefly (marked by "C"), and then the monkey needs to remember the cue (during the time marked by "D"), and finally at time R the targets appear and the monkey can make a response.

We see in spiking recordings from monkeys that there are cells in dorsolateral prefrontal cortex that are activated not only by the cue and during the response, but they have persistent activity during the delay period. In human studies we can't ordinarily place electrodes but part (b) shows a similar study using fMRI, and the colored areas on the brain indicate brain areas that demonstrated more blood flow (marking metabolism) during the delay period, which includes areas of the same brain region as the monkey experiments.

The explanations are **recurrent network activity** and **bistability**: a population of cells that is excited can continue to excite each other and remain active until stopped (see for example [attractor networks](https://en.wikipedia.org/wiki/Attractor_network) for a conceptual idea), as well as bistability in individual neurons where a neuron that reaches threshold *continues to fire tonically* rather than firing a single action potential, until firing is ceased via inhibition. [Camperi and Wang 1998](https://link.springer.com/content/pdf/10.1023/A:1008837311948.pdf) is an excellent, clear review of these concepts with a straightforward mathematical approach to how you can model this *in silico*. It's probably more efficient to start from here rather than reinventing it on your own.

I also recommend other papers by XJ Wang who has done extensive work in this area. I also recommend you look at [phase-space diagrams](https://en.wikipedia.org/wiki/Phase_space) which can help conceptualize dynamic systems with stable properties (and which network parameters are necessary for stability), they come up a lot in theoretical neuroscience. Dayan and Abbott's [Theoretical Neuroscience](https://mitpress.mit.edu/books/theoretical-neuroscience) is also a good starting point if you can find a copy.

---

Camperi, M., & Wang, X. J. (1998). A model of visuospatial working memory in prefrontal cortex: recurrent network and cellular bistability. Journal of computational neuroscience, 5(4), 383-405.

Curtis, C. E., & D'Esposito, M. (2003). Persistent activity in the prefrontal cortex during working memory. Trends in cognitive sciences, 7(9), 415-423.

> **Comments:**
> **username_0**: Thanks a lot for your reply! I was not aware of bistability. I have looked at several models of working memory before, but I have not seen anybody using it. It's not the same as bursting, is it? I'll read the literature by Wang you have recommended and get back to you. A small question if I may. The persistent activity in Esposito et al - it is persistent in every trial individually, or in trial-average picture? I have heard there is a large controversy between persistent and 'transient' activity, whatever the latter is  
> **username_1**: @AleksejsFomins It's a trial average. You can have persistent activity that's either relatively constant or persistent activity that comes in "waves"; this is true for sensory responses, too, see work by Ken Harris and Artur Luczak.  
> **username_1**: If you're coming at it from ANNs I'm not sure what the motivations would be for directly modeling working memory, if any. It's a biological solution, not necessarily relevant to artificial networks that have other tools available.  
> **username_0**: No no, I'm something in-between. I'm well aware that brain-inspired ANN have no chance of competing with digital hardware or known ML algorithms. I'm trying to solve credit assignment problem in the brain by means of reservoir/echo state networks. The idea is nice - reservoir does some generic space/time transform on incoming data, and a shallow readout can then learn whatever it needs. Bio-plausible and maybe in future can improve training cost of simple ANN. The main problem there is that most implementations to date forget input very fast, which makes them useless. Need to tune  
> **username_1**: @AleksejsFomins Gotcha. For learning you might also look into intracellular memory processes via second-messenger systems, if you haven't already. These are outside what is called "short term memory" but are still a trace of recent history that can be used for training biological networks. Not my area of expertise, though.  
> **username_0**: Hmm, that's of course really cool but maybe deeper than I can afford to go. A compromise I have seen used includes storing several dynamic variables inside of a cell. For example, the firing threshold of a cell can adapt on a few different timescales due to processes like intrinsic homeostatic plasticity or increased excitability.  
> **username_1**: @AleksejsFomins Yes, if you propose some second messenger increases intracellularly when a spike fires (or a synapse is activated) and decays with some (relatively slow) time constant you need not model all the intracellular metabolic processes. In the biology you expect some nonlinearities but depending on your goals those may not be important (or, at least, can be compromised away).  

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