New paper in PLoS Comp Bio

Shashaank Vattikuti , Phyllis Thangaraj, Hua W. Xie, Stephen J. Gotts, Alex Martin, Carson C. Chow. Canonical Cortical Circuit Model Explains Rivalry, Intermittent Rivalry, and Rivalry Memory. PLoS Computational Biology (2016).


It has been shown that the same canonical cortical circuit model with mutual inhibition and a fatigue process can explain perceptual rivalry and other neurophysiological responses to a range of static stimuli. However, it has been proposed that this model cannot explain responses to dynamic inputs such as found in intermittent rivalry and rivalry memory, where maintenance of a percept when the stimulus is absent is required. This challenges the universality of the basic canonical cortical circuit. Here, we show that by including an overlooked realistic small nonspecific background neural activity, the same basic model can reproduce intermittent rivalry and rivalry memory without compromising static rivalry and other cortical phenomena. The background activity induces a mutual-inhibition mechanism for short-term memory, which is robust to noise and where fine-tuning of recurrent excitation or inclusion of sub-threshold currents or synaptic facilitation is unnecessary. We prove existence conditions for the mechanism and show that it can explain experimental results from the quartet apparent motion illusion, which is a prototypical intermittent rivalry stimulus.

Author Summary

When the brain is presented with an ambiguous stimulus like the Necker cube or what is known as the quartet illusion, the perception will alternate or rival between the possible interpretations. There are neurons in the brain whose activity is correlated with the perception and not the stimulus. Hence, perceptual rivalry provides a unique probe of cortical function and could possibly serve as a diagnostic tool for cognitive disorders such as autism. A mathematical model based on the known biology of the brain has been developed to account for perceptual rivalry when the stimulus is static. The basic model also accounts for other neural responses to stimuli that do not elicit rivalry. However, these models cannot explain illusions where the stimulus is intermittently switched on and off and the same perception returns after an off period because there is no built-in mechanism to hold the memory. Here, we show that the inclusion of experimentally observed low-level background neural activity is sufficient to explain rivalry for static inputs, and rivalry for intermittent inputs. We validate the model with new experiments.


This paper is the latest of a continuing series of papers outlining how a canonical cortical circuit of excitatory and inhibitory cells can explain psychophysical and electrophysiological data of perceptual and cortical dynamics under a wide range of stimuli and conditions. I’ve summarized some of the work before (e.g. see here). In this particular paper, we show how the same circuit previously shown to explain winner-take-all behavior, normalization, and oscillations at various time scales, can also possess memory in the absence of input. Previous work has shown that if you have a circuit with effective mutual inhibition between two pools representing different percepts and include some type of fatigue process such as synaptic depression or spike frequency adaptation, then the circuit exhibits various dynamics depending on the parameters and input conditions. If the inhibition strength is relatively low and the two pools receive equal inputs then the model will have a symmetric fixed point where both pools are equally active. As the inhibition strength (or input strength) increases, then there can be a bifurcation to oscillations between the two pools with a frequency that is dependent on the strengths of inhibition, recurrent excitation, input, and the time constant of the fatigue process. A further increase in inhibition leads to a bifurcation to a winner-take-all (WTA) state where one of the pools dominates the others. However, the same circuit would be expected to not possess “rivalry memory”, where the same percept returns after the stimulus is completely removed for a duration that is long compared to the average oscillation period (dominance time). The reason is that during rivalry, the dominant pool is weakened while the suppressed pool is strengthened by the fatigue process. Thus when the stimulus is removed and returned, the suppressed pool would be expected to win the competition and become dominant. This reasoning had led people, including myself, to believe that rivalry memory could not be explained by this same model.

However, one thing Shashaank observed and that I hadn’t really noticed before was that the winner-take-all state can persist for arbitrarily low input strength. We prove a little theorem in the paper showing that if the gain function (or FI curve) is concave (i.e. does not bend up), then the winner-take-all will persist for arbitrarily low input if the inhibition is strong enough. Most importantly, the input does not need to be tuned and could be provided by the natural background activity known to exist in the brain. Even zero mean noise is sufficient to maintain the WTA state. This low-activity WTA state can then serve as a memory since whatever was active during a state with strong input can remain active when the input is turned off and the neurons just receive low level background activity. It is thus a purely mutual inhibition maintained memory. We dubbed this “topological memory” because it is like a kink in the carpet that never disappears and persists over a wide range of parameter values and input strengths. Although, we only consider rivalry memory in this paper, the mechanism could also apply in other contexts such as working memory. In this paper, we also focus on a specific rivalry illusion called the quartet illusion, which makes the model slightly more complicated but we show how it naturally reduces to a two pool model. We are currently finishing a paper quantifying precisely how excitatory and inhibitory strengths affect rivalry and other cortical phenomena so watch this space. We also have submitted an abstract to neuroscience demonstrating how you can get WTA and rivalry in a balanced-state network.


Update: link to paper is fixed.

3 thoughts on “New paper in PLoS Comp Bio

  1. I wouldn’t be surprised if someone in a few weeks writes a paper based on this but applied to social systems with rivalry, topological memory, etc. There are already similar such papers.

    i’d say they go back for the last 35 years, based on the ‘synergetics’ or ‘cooperative systems’ approach of Hermann Haken—based on lasers, but historically even further bqck the way a big river originates in little springs which are often hard to find.

    ( I once walked from DC on the C and O canal trail except at the end to its source in a marked spring in W Va. Its about 200 miles. Also quite cheap to walk, tho just in case i had my private jet flying above to make sure i’d make it and drop me supplies–i’d send them an orde to pick me up a veggie sub from subway when i couldnt find any plants to eat—one time i did the whole thing just eating rosehips. The Cand O canal’s current existence is attributed to supreme court justice William o Douglas, who i once met since we shared an interest in mountains—someone knew.his law clrek so they took me up there to supreme court and i shook his hand—sortuh shaky. I was going to give him my view on the proper interpretation of the Constution–not exactly the same as Scalia’s–but at that time i hadnt heard of the constitution.

    My view was closer to that of Gil Scott Heron -who played my high school graduation —who had a song saying the consitution is a Noble piece of paper (maybe deserves a prize). (he also wrote a song called ‘the bottle’—warning youth against using alochol and drugs. He later got arrested and prison time for possession of heroin and died of AIDS. Musicians seem to follow me around—saw one i know last nite at a music show ‘jogo’ (combination of jazz and gogo). Pete Seeger played my elementary school graduation. i didnt go to my college graduation, because i was busy preparing for higher education, with hope of getting higher degrees from high, junior high, and elementary schools. i work back in time—see Huw Price on ‘backreaction’—feynman-wheeler electrodynamics, or GFR Ellis and Paul Davires on ‘top-down causation— just as i was already dead before i was born ). I’ve also been to the origins of the north and south forks of the potomac.

    The ‘social physics’ approach originates in math biology, sociology and economics; the ‘general physics’ section of arxiv is loaded with these—societities as neural nets, genetic algorithms, PDP systems and just about any other formalism–a quantum field. I saw one paper in a Marketing journal which discovered solitons in consumer behavior under the influence of advertizing. Fisher viewed the fundamental thorem of population genetics as a version of the second law of thermodynamics (others view it as more like newton’s law—dynamics driven by a potential, but nowadays people talk about ‘entropic forces’ so they may be equivalent, or at least indistinguishable empirically—like attributing behavior to ‘choice’ versus ‘deterministic or stochastic dynamics’ which are also often indistinguishable–Ornstein and Weiss ’91 bull. AMS, or eugene slutsky—slutsky-yule effect, econometrica 1937). Tinbergen in economics studied under Gibbs.

    The details will differ–humans arent neurons (perhaps–some talk about ‘a global brain’)..

    .As a side note, i wonder why when dealing with ‘obesity’ (kevin hall) , why metabolism slows down as people lose weight. It would seem that if people lose weight but keep up the same level of physical activity but on a lower calorie budget appropriate for their current reduced weight , they would keep it off. Apparently they don’t—they have to eat fewer calories than somone of their same current weight who had never been obese to stay at their current weight. So there are some ‘nonlinear’ effects, assuming they keep the same level of physical activity.

    I guess i think of this like riding a biciycle. One can ride a bike a certain number of miles to burn calories. But if you clean the chain and pump up the tires, riding the same distance will be easy. Perhaps cleaning out your system via dieting is like cleaning your bike chain. Any calorie you eat will then be absorbed, so a calorie of intake is not a calorie. People who have never been fat use a different operating system—they always have a ‘clean chain’ and absorb every calorie. Fat people have had their whole system modified. This is why people say ‘fat cells have memory’, just like infections which may have been reduced to something which doesnt iinterfere with health but still exist (as i gather is the case for people with aids and other things) . People with modified circuitry have a different set of communication and absorption channels.

    (This likely applies to cognition—eg ‘trigger words’. If you say the same thing to two different people, they may respond very differently since they dont hear the same thing. F de Waal was on wamu today talking a bit about how animals respond to music. It may differ based on the animal and the music. I noticed last nite that at the show, where there were two bands—most people split after the first band; i had come mostly to see the second one. Now on WAMU they have the issue of the word ‘redskins’ —refers to a team in DC (whose owner lives next to C and O canal and cut down alot of trees on park service land—he viewed it as his own, and the trees obstructed his view of the potomac—a major hardship. he got a small fine for that. Some indigenous americans object to using the word rdskin, just as some object to having a confederate flag on a statehouse) .

    so far we live in something close to a winner take all system (pareto or power laws, though possibly its even more nonlinear than the standard -self-preferential attachement model in network theory (maybe barabasi—i’ve seen some heavy criticisms of those papers from someone at u c bekerekely, and met a phD physicist from notre dame—worked for nsa—who said barabasi worked at least one of his grad students ( a female) almost to death and didnt give her much credit either). that model leads to standard bose-einstein condensation—eg H Frolich ‘bose einstein condensation in biological systems’ also applied to income distribution via the ‘balls in bins’ model.Wm. Feller has this, as did H Simon (economics nobleaureate from cmu). .. .


  2. Mart, slowing down metabolism is an evolutionary adaptation. When the famines rolled through the land, the high-metabolism skinny folks starved. Those that could reduce their metabolism had an increased chance of survival. If the surviving people maintained their slower metabolism once food was plentiful again, then they could replenish their fat stores easier in time for the next famine.


  3. I admit i still don’t quite see how people can regulate metabolism—though i gather its true.
    i hear some bhuddist monks can spend hours in cold water in the himalayas without freezing—part myth, part true. stress may regulate metabolism even if one is at the same level of physical activity —certain mental cues may raise your blood pressure and heart rate (fight or flight reaction). some meditate, which may regulate metabolism.

    I think of a human as being somewhat like a car. A heavily loaded ‘obese’ car can only go so far on a tank of gas. If you unload alot of the weight it can go further. . Theoretically it would seem there is a linear relationship between how far a car can go and what its weight is. But the work by K Hall on people who lose alot of weight but will regain it even if they stay on a diet calibrated to keep people at that weight at a steady weight suggests its a nonlinear relationship. i.e. an unloaded car turns out to be able to travel much further than predicted on a tank of gas than a car of the same weight which had never been loaded. There’s either a hysterisis effect (gaining weight and losing it doesnt return you to your original state) or else people who are obese are wired differently from those who who aren’t—due to genetics, or experience.

    I guess i just dont see why a car which has been loaded heavily, and then unloaded, should have a different ‘miles per gallon’ metric than one which had never been loaded and unloaded. But, the research shows for the analogy to humans, its metabolism or fuel efficiency changes. I can see that—a heavily loaded car might have its ‘infrastructure modified’–its a used car. It has ‘memory’, hysterisis’, and path dependence. A used car is not a new car, a calorie is not a calorie, and a dollar is not a dollar (economics phrase).

    It seems like this might be a useful thing to know if they predict a famine. One could fatten up, and then lose the fat during the famine, and when you return to your original weight you dont need to eat as much as you did before to maintain your weight while still maintaining the same level of activity.

    (The article says the person who lost the most weight to get down to something reasonable, had to eat like 900 calories less per day to remain at that weight than is predicted by the standard formula.
    I forget the formulas i’ve seen, but i never found them accurate or believable.

    I have gone through periods of very low cal diets (when i was hiking in mountains in mexico and india and was basically wandering around with no supplies for weeks on end (i basically knew where i was going but had no map, tho i knew a bit about ‘hunting and gathering’ ) —i called this the low budget travel plan. I did notice after awhile the tendency was to lower activity level—ie basically stop hiking , so it may be the person was reducing activity and not ‘using all the fuel in the tank’ , but conserving it in fat cells. I had to force myself to maintain activity level-`from 10 to 30 miles/day. . Some of these areas have certain plants the local people know which allow you to maintain activity level without food; i generally would lose 25 lbs in .3 to 6 weeks. I lost that amount in 6 weeks once in a hospital when i went in for pneumonia—they said i’d be out in 3 days. but I had an allergic reaction to medication, got put on life support, got sepsis, and had to walk out carrying an oxygen tank. (I may start a weight loss group called ‘the sepsis diet’–which means you are unable to eat)..
    They told me that sitting up in that state was the equivalent of running 10 miles.

    They didnt even want to let me out since when i practiced walking again all the meters went off the scale so they would take me back to bed. The physical therapists didnt want to deal with me, perhaps because they were busy, lazy or knew my history . I had to get a nurse (from jamaica) to break some rules and let me show her i could walk at my own pace—that was not her job, so then they said they’d let me out. Also they wanted me to go—3500$/day and i had no health insurance, Also i told em maybe i’ll just stay here till i die , watch tv , order `10 coffees at a time, and read science magazines, and sleep. I complained once when by mistake they turned off my oxygen supply–i was wearing an oxygen mask. I had to jump off the bed with all my iv tubes in my arms and turn it back on. Interesting experience.)


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