How grid cells could code memories of episodes, and more, in the brain.

In my prior post, I wrote about Professor Michael Hasselmo’s book on grid cells in the brain, which create a type of GPS grid as we walk through a space.   But the main point of the book is that grid cells plus ‘place cells’ can be part of a circuit for storing episodic memory.
Professor Hasselmo gives a scenario of one of his work days where he parks his car in one of many spots in the college garage, and then walks down Cummington street, passes one of his students, and then continues to his office where he speaks with his wife, and so forth.   The memory of this set of episodes involves a trajectory through space.   It also involves a point of view – for instance, which direction on Cummington street was he walking and what was he looking at.   The point of view can be thought of as a directional component of a vector.   Memory also involves time – such as how fast he was walking down the street.   When he is sitting in a chair in his office and talks on the phone his position in space doesn’t change, but time does.
You and I normally remember in sequence, but we can relive one segment and then jump back in time to remember an earlier segment.
In his model, Grid cells are the inputs to ‘place cells’, where place cells indicate your position in a space (grid cells fire at every point in an imaginary grid stretched across the space, but a place cell might fire if, for example, you were in the center of a room (or the corner of a farmer’s field).  You also have ‘head direction’ cells, which code for where your gaze is pointing.   If we combine head direction with speed information, we have velocity (speed plus direction, though one problem with this theory is that you could be walking sideways while your gaze is straight up).  We will assume that ‘head direction’ cells don’t just code direction, they also code speed, and therefore are really ‘velocity’ cells.   Hasselmo sometimes uses a more general term “action” to describe what ‘head direction’ cells do, as if they are responsible for your movement.
In his model you could have grid cell activations leading to place cell activations which in turn lead to velocity cell activation and then the velocity updates the grid cells, altering their frequency and relative phase, and that then leads in a loop back to place cells.   It takes a while for the information to propagate in each step. So you can have a simulation of you going through space, at the speed in which you originally traversed it.
Lets examine in more depth:
The ‘velocity’ cells are driven by your senses that tell you how fast and what direction you are going.
The velocity in turn, causes frequency differences between two cells that normally fire at the same frequency  and this also implies that those cells will probably be out of phase when the creature stops moving.
Grid cells differ in their response to velocity.   Some have a frequency that changes only gradually with velocity, others have a more dramatic dependence on velocity.   Grid cells can also start at different initial phases.   The result is that each grid cell corresponds to a different grid – maybe the spacing between the gridlines is different, or the difference is in the orientation in which the grid overlays space, or both.
When you learn a trajectory, your movements and behavior drive head direction cells, which then drive grid cells which in turn drive place cells which have synapses on the original head direction cells.  Learning the trajectory involves strengthening some of the links between the place cells and the head direction cells.
In contrast, when you remember a trajectory, the main driver of the head cells is not sensory inputs and not behavior, rather, it is the place cells.   The cue for retrieval could be your current location as coded by place cells, or it could be environmental stimuli that were previously associated with a particular pattern of place cells.   For instance, a sight of the  Art Museum in New York’s Central Park could send signals to a particular place-cell vector. The velocity cells have to fire in recollection just as long as they did in the real event, because their firing at the correct rate for the correct amount the time creates the phase differences in the grid cells that existed in the original real-life scenario.
You are able to distinguish actually having an experience from remembering it, and Prof Hasselmo speculates that the different drivers of the head direction cells in two cases give you a way of knowing the difference.
Professor Hasselmo cautions that this mechanism is not the only possible one, for instance, you could have time-interval cells that fire at steady intervals and independently fire cells for place and for action.
If you model this mechanism with a neural net, you would have one weight matrix from place cells to head direction cells (WHP) and another matrix between the grid cells and the place cells (WPG).


There are objections to chaining models based on experimental data showing that participants can  retrieve the end of a sequence after missing one or more items, or they can retrieve the wrong order of items in a sequence.   Hasselmo gives alternatives, where for instance a cue activates time cells, or as the creature moves it activates ‘arc length’ cells.   The latter measure one dimensional distance, and are useful, oddly enough, because they are missing the direction information.   Imagine you are riding a bicycle with a device that measures your distance from the start of your ride.   You also have a list of directions.   One direction says, “at 5 miles, turn left on Magpie road.”   The route then makes a loop and comes back to the same point, at which point your set of directions says  “at 10 miles, don’t repeat your loop on Magpie road, but go up to Crawfish Hill Road.   Since you have been keeping track of your distance, you know what to do.   If you just had 2 dimensional information, such as where you currently are on a map, and no memory of other than that, you would not know which road to take.   You need to know how far you’ve gone so far.   That is what the firing of arc-length cells would tell you.  ‘Place’ cells alone could not tell you which ‘head direction’ cell should fire next, in the case of a loop like this.
Another alternative might be ‘time cells’   (“after 1 hour of biking, take Magpie road, after two hours take Crawfish Hill Road”.)

In the prior examples, the phase differences that make grid cells fire are driven by arc cells or ‘time cells’, and not head-direction (velocity) cells.   (A velocity cell minus direction information is essentially an arc cell)

In the example of remembering at what parking spot you parked your car in the garage next to your workplace, you don’t want yesterday’s parking spot to interfere with today’s.    As  you walk into the garage, a trajectory would fire, and perhaps at ambiguous points the arc-cells or the time-cells would lead you in the correct direction.   The cue that resets the arc cells has to be some difference between today and yesterday.
To remember what you saw at different parts of your day – walking away from your car, and then along the street, and then into your building, and who you talked to, there would be a learned association between specific ‘place cell vectors’ and the sensory patterns that you experienced.   One advantage of this two-way association is that remembering a particular sensory cue can activate the place cells that were firing when you first were at that spot and the memory sequence could start in mid-trajectory.
If  you see the same room only at rare intervals, it has been found that grid cells and place cells show the same (stable) firing each time.   In the model, this requires sensory cues to set the phase of firing of grid cells to the same starting point.
The associations for this type of memory requires associations between the code for space and time with the coding of actions, items, or events. The code for space and time comes in the form of place cells, arc length cells, and time cells.   These are associated with actions in the form of speed cells and head direction cells.  The model also uses bidirectional associations between the code for space and time with cells coding features of individual events.   So a trajectory can cue the retrieval of an event (remembering what happened when you opened the door to the tiger cage in the zoo) or conversely, seeing a picture of a tiger can remind you of your quick trajectory out of the tiger cage and out of the Zoo.   In addition, an association of one item can lead to a trajectory of other items and events.


We could start speculating here.   Any “train of thought” is a sequence where one item leads to another.   Could grid cells and place cells be involved?   Hasselmo also has a chapter on goal directed behavior where place cells propagate signals along a path back from a goal, which meet grid cells signals propagating forward.   This sounds like problem solving – not just remembering a path.
When we look at any part of a room, we are focussed on only a small part of the room – at any moment, we assume the rest of the room is as we recently saw it.   Perhaps our experience of a room is a trajectory around the room associated at various positions with objects such as book shelves, chests of drawers, and lamps.  In fact, researchers at Numenta, a company that attempts to understand the cortex, hypothesize that every object in that room is itself represented by some type of grid cell trajectory and that these grid cells are in every column of the cortex.   They also believe that objects are ‘recursive’ – so for instance when you look at a cup with a handle, the handle itself has its own grid cell trajectory.
How We Remember – Michael Hasselmo (2012 – MIT)

Representing Space and Time by Neural Phase Shifts

An interesting way to represent information in neurons is explained in the book “How We Remember” by Michael Hasselmo. We have a type of GPS system – a grid that appears in our head whenever we go into a room, for instance. In fact, we have multiple spatial grids that vary in their spacing and in their orientation relative to the walls of the room.
To simplify, lets assume there is just one neuron per grid. As an additional simplification think of the grid as a series of vertical lines intersected by horizontal lines. Each intersection is a vertex. As you move through the room, every time you cross a vertex, the neuron will fire. For example, if the room has a square shape, then if you moved diagonally across the room, assuming the grid origin is at a corner of the room, you would intersect vertices as you crossed each square of the grid diagonally. This might not seem all that helpful in pinpointing your position since the neuron fires at many places in the room – in other words at every vertex of the grid.
In the top half of Figure 1 above, you see on the left the areas in space that fire one single grid cell.   All grid cells in a particular module have the same orientation and scale (scale means distance between areas that it will fire at).  At the top right, you see the firing areas of 2 cells in a module (green for one, blue for another).   The problem is that even though the cells are somewhat displaced from each other, the patterns repeat, and so if the two cells fire, you still can’t tell where in the room the creature is.   You can rule out some areas (the white areas), but the result is still ambiguous.
The saving grace is that you have several grids with different scales / spacing, and different orientations. If three different neurons, each for a different grid with different properties, fire at the same time the ambiguity in position is reduced.   At some point the combinations do repeat, but it will take much more space for that to happen. (see bottom half of figure 1)
To simplify  we will assume that there is just one dimension. (Your room has no width, only length.) Start with two cells that fire at the same frequency and the same phase. If a third cell fires when the spikes of the two cells impinge on it within a narrow time frame, then not surprisingly it will fire when they do. Now lets suppose the two neurons get out of phase. In that case the third cell will not fire (if they are sufficiently out of phase).
Suppose that one of the neurons will fire faster when you walk through the room. (The neuron that doesn’t change is called the ‘baseline’ neuron) The neuron that does change speeds up its spike rate the faster you walk. Not surprisingly, the baseline neuron will no longer be in phase with the speedup neuron. The third neuron that detects the coincidence of the other two will not fire during this period.

You can see the two neurons (B and C) start in phase, but neuron B speeds up its frequency for a short time, and then is in no longer in phase with neuron C (C is the baseline)
If you keep moving, at some point the spikes of the neurons are in phase again. You can think of this as two runners traveling around a circular track at different speeds. The faster runner catches up with the slower one, at which point their positions coincide, but then he runs past and the positions no longer coincide (until he overtakes again).
The first period of movement put the neurons out of phase, but the second period of movement was just long enough to get them into phase again.

So the third neuron (which is active when the spikes from the other 2 coincide) fires at regular intervals as you cross the room, if you cross the room at a steady speed.
This works at any speed. If you walk slowly then the non-baseline neuron is still firing faster than the baseline neuron, but not as much faster as in the prior case. So its frequency increment vs baseline is slower, and it takes more time for the two neurons to coincide.
The baseline neuron and the speedup neuron will still fire a spike simultaneously at the vertex, because the extra time to get to the peaks to coincide matches the extra time for you to reach the point in the room at your slower pace. So the grid, as expressed by the firing of a neuron, is not altered by how fast you move between vertices.

Moving quickly (upper example) vs moving slowly (lower example).  The frequency of the speedup neuron is faster in the first example, so the neurons get back in phase quicker.

The above example was for one dimension, and required three neurons. Suppose we want to extend the model to two dimensions. To do that we add another neuron. Its normal frequency is the same as the others, but like the other non-baseline neuron, it is also fires faster when you move, but only when you move south. As the angle deviates from due south, it fires less strongly (it falls off as the cosine of the angle). The other original non-baseline neuron will fire strongly as you go due east, and its firing will also fall off, as the cosine of the deviation from due east. (In practice these neurons don’t fire much at all after a deviation of 45 degrees off their preferred direction.)
Lets assume that the summing neuron now sums up the baseline neuron and the two directional neurons, and will only fire when they all are close to their peaks at the same time. In that case, it will fire at the vertices of a two dimensional grid. This summing neuron that fires when the spikes of all its inputs coincide is a grid cell .
To make several grid cells with different spacing, we could repeat several groups of four neurons, each group with a different innate base frequency. For example a group with a high frequency baseline results in its three input neurons firing together at vertices that were spatially closer – the summing neuron would correspond to a grid with small spacing between the vertices.
In the brain, the grids are hexagonal, or you can think of them as tiled triangles, so instead of having a neuron that fires when you go due south and another when you go due east, you would have three neurons that fire maximally at directions 120 degrees apart (3 * 120 = 360 – a complete revolution in direction back to the starting point).

We described intervals for space, but you can use neurons for time intervals as well.  If you have two neurons firing at the same frequency but with different phases, they will coincide at regular time intervals.   If you add a third neuron firing out of phase with the other two, then you have the coincidence of all three neurons repeating at a  longer time interval.If you have several grid cells, and they don’t have the same spacing, then, as I said earlier, you can disambiguate your location (one grid cell could mean you were at any vertex of the imaginary GPS grid overlaying the room).   This next illustration shows the one dimensional example again.   Each grid cell has a different spacing (the top one has the widest) and the sum of the top three grid cells peaks in only one place on the x-axis.   It is true that eventually there will be another peak, but if your room is small enough, you will run into a wall before that happens. You can always add cells that repeat at even larger spacings.


The next image shows the two dimensional case. When the 120 degree and the 240 degree and the 360 degree neurons coincide, you have the intersections of the 3 angled lines in the image.


The hippocampus has “place cells” that fire when you are at a particular place in a room. It is possible to model such cells by taking three grid cells at random as inputs to the place cell.  Prof. Hasselmo has an algorithm where the connections from those grid cells to the place cell are strengthened if they correspond to only one location, but I must confess that I did not understand his method from the text.

His model allows place cells of different ranges, so you could have a place cell that fires only when you are walking under the lamp in a room, and another that fires when you are walking anywhere in the town square but changes when you walk out of it.Michael Hasselmo also has a theory of how we remember, based on grid cells and place cells. I will describe his theory when I write the next post.   Numenta, which is a company in California that is attempting to model the cortex, also has a theory that the entire cortex uses a grid cell mechanism for general thinking.   I’ll describe that theory in another post as well.

How We Remember – Brain Mechanisms of Episodic Memory – by Michael E Hasselmo (2012 MIT Press)

Eric Kandel tells us what unusual Brains tell us about ourselves in his new book.

Prof. Kandel

Eric Kandel wrote the standard textbook of Neural Science (in which he was a pioneer) and just published a book titled The Disordered Mind – What Unusual Brains Tell Us About Ourselves.. I will just select a few interesting points from the book about the pre-frontal cortex, since that is a part of the brain that gives us all sorts of desirable characteristics, such as will-power, concentration, decision making, judgment, and planning for the future. The pre-frontal cortex has neurons that are key to working memory too. Plus it is important in what we call the moral emotions–indignation, compassion, shame, and embarrassment.

If you are under a lot of stress, your adrenal gland releases cortisol, which heightens vigilance. Unfortunately, over time it destroys synaptic connections in your prefrontal cortex. The mental disease of depression also causes a flood of Cortisol, and interestingly, various drugs that treat depression, such as Imipramine and Iproniazid and Ketamine, increase the number of synapses in the prefrontal cortex.
Ketamine works faster than traditional antidepressants, so it is prescribed for the first two weeks, until the other antidepressants take effect. The idea is to prevent suicide in those two weeks. It would be used for more than two weeks, but the problem is it has side effects. Ketamine works faster because it latches onto receptors on the target cell and keeps an excitatory neurotransmitter (Glutamate) from occupying that receptor and over-exciting the neuron. This is a direct effect. Other drugs usually target Serotonin, whose effects are indirect, they somehow fine tune the action of other neurotransmitters, whether excitatory or inhibitory. And the effects are slower.
(Ketamine is not always used wisely, in fact, drug dealers sell it and their customers often use it along with other drugs such as Ecstasy or cocaine or sprinkle it on marijuana blunts.  You can’t save people from themselves.   But I digress.)
A really interesting fact is that children have many more synapses than adults. Beginning about puberty, synaptic pruning removes the dendritic spines that the brain isn’t using, including spines that are not actually helping working memory. (Each incoming neural dendrite has spines on it, and those spines are where other neurons connect.) In Schizophrenia, synaptic pruning appears to go haywire during adolescence, snipping off far too many dendritic spines. So if you are a parent who has Schizophrenia in the family tree, you can’t breathe easy about the risk to your children until they get past adolescence.
There is actually a gene named C4 that produces a protein involved in tagging synapses for removal, and a variant of it named C4-A facilitates over-aggressive pruning.

Kandel’s subtitle for the book indicates that he is interested on what the various abnormalities he describes in the book, including Autism, Alzheimer’s, Gender behavior that doesn’t match external appearance, reveal about those of us without brain disorders.

One question raised in my mind was sparked by the section on Bipolar disorder. Bipolar disorder is characterized by extreme changes in mood, thought, and energy. Manic episodes include racing thoughts and decreased need for sleep. These episodes can be associated with high-risk behaviors such as excessive spending. Patients may get in trouble with the law. Later, a depressive episode will occur.
Kandel writes: “Once the first manic episode is initiated—usually at the age of seventeen or eighteen–the brain is changed in ways we do not yet understand, such that even minor events can trigger a later manic episode.”
The question that occurred to me is – are the rest of us feeling the appropriate mood for our situation?. Are we too much into optimism and risk taking? Are we too depressed and pessimistic? What is the right balance?

As you get old, you may develop Frontotemporal Dementia, which begins in the frontal lobe. Your moral reasoning degenerates, and you may end up being arrested for acts such as shoplifting. You may spend yourself into bankruptcy, or regularly overeat. So lets not be too judgmental on old people who start acting in an anti-social way.

In psychopaths, there is more gray matter (cell bodies) in and around the limbic system (which is involved in emotion), but the neural circuitry that connects the emotional areas to the frontal lobes is disrupted. I don’t know what this really means, but maybe we should not be too judgmental about psychopaths either!
More than 3 million Americans have bipolar disorder. About 20 million Americans suffer from major depression. Much suffering is caused by disorders of the brain. There is hope for  these disorders (if they are not caused by early miswiring in development, as Schizophrenia often is). Scientists are already finding genes involved in these diseases, and relevant proteins that are either overactive, or under-active, or malformed in some way. Perhaps as well some day researchers will find a way to make neurons divide and fill wounded areas.

Kandel’s book gives you a different way at looking at human behavior – and is worth reading.

How we use coherence of concepts to build ideologies and make sense of our world.

Much of human cognition can be though of as ‘constraint satisfaction’ according to philosopher Paul Thagard. For example, think of applying to a university. One college is in a beautiful setting, but another college has a professor who is an expert in your desired major. The first college is in a quaint town with a low crime rate, the second one is in an city with a high crime rate. You have a scholarship to the first college, but the second college charges less for tuition. And so forth.
Or suppose you are a detective in a murder case where the prime suspect is the daughter of the victim, a rich industrialist. The daughter was in line to inherit the family fortune. You interview the daughter, and find out she dedicates her spare time to helping the needy. Then you find out that her boyfriend is a fellow she rescued from jail. So again, there is information that leads you in conflicting directions.
One way to manage all the conflicts (or even just priorities) is by constraint satisfaction.

The following is a diagram of a simple situation. You are thinking of hiring a local carpenter named Karl, but you need to know whether you can trust him alone in your house. You know he’s a gypsy, and that the gypsy culture has allowed thievery from outsiders. So that knowledge would push you in one direction. But then you hear that he returned a lost wallet to your neighbor. So that pushes you in another direction. (I scanned the next figure, which illustrates the Karl scenario) from a small paperback, so the orientation is disturbing my coherence, but here it is)


The dotted lines are inhibitory, and connect incompatible nodes or hypotheses. The normal lines are excitatory. All connections are bidirectional – so that if node-A reinforces node-B, then node-B reinforces node-A also.

In this picture, the hypothesis of being honest is incompatible with being dishonest, so there is a dotted line between them. The action of returning the wallet is compatible – in fact is evidence for – honesty, and so there is a full line – an excitatory connection between them.

But decisions aren’t just made based on evidence, there is often an emotional component. Another diagram, a cognitive affective map, can show the influence of emotions:


Ovals are used for positive valences (a positive emotion) so in this example the oval around ‘food’ indicates that food is a desirable concept’. Hexagons have negative valences (and so the shape used in the diagram for hunger is a hexagon). Rectangles are neutral – you are not pro-or anti-broccoli in this example.

The diagrams can apply to political attitudes. For instance, in Canada, the law says you should refer to ‘trans’ people by their preferred pronoun (which might be neither ‘he’ nor ‘she’). Some Canadian libertarians, notably Jordan Peterson, have objected to this. Here are two diagrams from a 2018 article by Paul Thagard showing how a liberal, for whom equality ia a paramount value, might look at the issue, versus how a libertarian might look at the issue..


The green ovals with the strong borders show what the liberal prioritizes (equality) versus what the libertarian prizes (freedom).  In the lower diagram, the libertarian considers freedom as somewhat incompatible with regulation, and with taxation, but compatible with private property and economic development.    As a libertarian, you may take it as inevitable that economic development will result in income inequality, which is why the desirable value of ‘economic development’ has a inhibitory link with ‘income equality’ in the second diagram.   As a liberal, prioritizing equality, you might see the positive links between capitalism and the negative nodes of ‘exploitation’ and ‘inequality’, so even though there is a positive link between ‘capitalism’ and ‘freedom’ in the first diagram, you might, after the various constraints interact and settle down on a solution, want to modify Capitalism.

One way of learning about an opponent’s perspective is to draw the diagrams of how you believe your opponent he thinks -and then have him critique it and redraw it.

One advantage of such diagrams is that you can use an iterative (repetitive) process to spread the activations and find out, after the dust settles, which nodes are strongly activated.

You start by assigning activations to each node. We can assign all of the nodes an initial activation of .01, for example, except for nodes such as ‘evidence nodes’ that could be clamped at the maximum value (which is 1, the minimum value it can take is -1 ).  Evidence might be an experimental finding, or an item in the newspaper or an experience you had.

The next step is to construct a symmetric excitatory link for every positive constraint between two nodes (they are compatible) . For every negative constraint, construct a symmetric inhibitory link.

Then update every node’s activations based on the weights on links to other units, the activations of those other units, and the current activation of the node itself. Here is an equation to do that:


Here d is a decay parameter (say 0.05) that decrements each unit at every cycle, min is a minimum activation (-1) and max is (1). ‘net’ is the net input to a unit, it is a sum of the product of weights * activations of the nodes that the unit links to.

The net updates for several cycles, and after enough cycles have occurred, we can say that all nodes with an activation above a certain threshold are accepted. You could end up with the net telling you to go to that urban college, or the net telling you that the daughter of the industrialist is innocent, or that a diagnosis of Lyme disease is unwarranted, or that you should not trust Karl.

There are several types of coherence, and they often interact. Professor Thagard gives an example:

In 1997 my wife and I needed to find someone to drive our six-year-old son, Adam, from morning kindergarten to afternoon day care. One solution recommended to us was to send him by taxi every day, but our mental associations for taxi drivers, largely shaped by some bizarre experiences in New York City, put a very negative emotional appraisal on this option. We did not feel that we could trust an unknown taxi driver, even though I have several times trusted perfectly nice Waterloo taxi drivers to drive me around town.
So I asked around my department to see if there were any graduate students who might be interested in a part-time job. The department secretary suggested a student, Christine, who was looking for work, and I arranged an interview with her. Very quickly, I felt that Christine was someone whom I could trust with Adam. She was intelligent, enthusiastic, interested in children, and motivated to be reliable, and she reminded me of a good baby-sitter, Jennifer, who had worked for us some years before. My wife also met her and had a similar reaction. Explanatory, conceptual, and analogical coherence all supported a positive emotional appraisal, as shown in this figure:


Conceptual coherence encouraged such inferences as from smiles to friendly, from articulate to intelligent, and from philosophy graduate student to responsible. Explanatory coherence evaluated competing explanations of why she says she likes children, comparing the hypothesis that she is a friendly person who really does like kids with the hypothesis that she has sinister motives for wanting the job. Finally, analogical coherence enters the picture because of her similarity with our former baby-sitter Jennifer with respect to enthusiasm and similar dimensions. A fuller version of the figure would show the features of Jennifer that were transferred analogically to Christine, along with the positive valence associated with Jennifer.

If we leave out ’emotion’ then we just spread activations and compute new ones. To include emotions, we assign a ‘valence’ (positive or negative) to the nodes as well, and those valences are like the activations, in that they can spread over links, but with a difference – their spread is partly dependent on the activation spread.

Take a look at this diagram:


There is now a valence node at the top, that sends positive valence to honest’ and ‘negative’ valence to ‘dishonest’. When the net is run, first the Karl node is activated, which then passes activations to the two facts about him, that he is a gypsy, and he also returned a wallet. If ‘honest’ ends up with a large activation, then it will spread its positive valence to ‘returned wallet’ and then to Karl.

The equation for updating valences is just like updating activations, plus the inclusion of multiplying by valence.

Some interesting ideas emerge from this. One is the concept of ‘meta-coherence’. You could get a result with a high positive valence, but it is just above threshold, and you therefore not sure of it, which could cause you distress. You might have to make a decision that is momentous, which you really can’t fully be confident is the right one.
Another emotion, surprise, could result from many nodes switching from accepted to rejected or vice versa as the cycles progress. You may find that you had to revise many assumptions.
Humor is often based on a joke leading you toward one interpretation, and then ending up with a different one at the punch line. Professor Thagard says that the punch line of the joke shifts the system into another stable state distant from the original one.

In an actual brain, concepts are not likely to be represented by a single neuron, it is more likely that population codes (such as semantic pointers) would be used. So an implementation of the above relationships between concepts would be more complicated. Moreover, the model doesn’t explain how the original constraints between concepts are learned. I would guess that implementation details might modify the model somewhat. Coherence doesn’t ‘mean that multiple rational people will come to the same conclusions on issues – even scientists who prize rationality often disagree with each other. Sometimes, even the evidence you will accept depends on a large network of assumptions and beliefs. What nodes do you include? What weights to you assign to the constraints?

Still, the model is intuitive and makes sense.

You can get a link to the various programs mentioned at   There is also  more info at

Coherence in thought and action – Paul thagard 2000 MIT press
Emotional Consciousness: A neural model of how cognitive appraisal and somatic perception interact to produce qualitative experience
Thagard, P. (2018). Social equality: Cognitive modeling based on emotional coherence explains attitude change. Policy Insights from Behavioral and Brain Sciences., 5(2), 247-256.


Aha Moments, Creative Insight, and the Brain

In “The Eureka Factor – Aha Moments, Creative Insight, and the Brain”, authors John Kounios and Mark Beeman discuss insight – the kind of insight that might occur to you when taking a walk or taking a shower as opposed to trying to force a solution to a problem in your office under a deadline. (One creative inventor that they mention sets up his environment to encourage insights – at night he will sit on his armchair on his porch looking at the stars, with nondescript music in the background to drown out distracting noises.)
MRI experiments have shown that insight really does happen suddenly, its not just an illusion. (when it happens, there is a ‘gamma’ burst of activity in a part of the brain in the right hemisphere). While ‘analytical thinking’ is a process that builds systematically to a conclusion, insight doesn’t work that way, though it benefits from the thinker having looked at the problem from all angles.

Here are a few conclusions by the authors:

  1. …perceptual attention is closely linked to conceptual attention. Factors that broaden your attention to your surroundings, such as positive mood, have the same effect on the scope of your thinking. Besides taking in lots of seemingly unrelated things, the diffuse mind also entertains seemingly unrelated ideas.

  2. if you question people, you’ll find that some see meaning everywhere, in events like the Japanese tsunami and in cryptic sayings like those above. They will give you impassioned explanations of the significance of such things. Other people deny any inherent meaning. “Stuff just happens. Live with it.

    It was found that people who see meaning in so many life events are also people who trust their hunches and their intuition. Intuition is related to creative thought.

  3. Creative people can be odd:
    The book contains a quote by Ed Catmull, president of Walt Disney Animation Studios and Pixar Animation Studios. He said:

    “There’s very high tolerance for eccentricity; there are some people who are very much out there, very creative, to the point where some are strange.” He values that creative eccentricity and is willing to tolerate a lot of the weirdness that often accompanies it. But movies are made by teams of people and not by a single person, so he has to draw a line. “There are a small number of people who are, I would say, socially dysfunctional, very creative,” he said. “We get rid of them.”

So what are the neural underpinnings to the creative – insightful type?

The authors think there is a reduced inhibition.

Inhibition, as a cognitive psychologist thinks of it, regulates emotion, thought, and attention. It’s a basic property of the brain.
…when you purposely ignore something, even briefly, it’s difficult to immediately shift mental gears and pay full attention to it, a phenomenon called “negative priming.” This can sometimes be a minor inconvenience, but it occurs for a reason. When you ignore something, it’s because you deemed it to be unimportant. By inhibiting something that you’ve already labeled as irrelevant, you don’t have to waste time or energy reconsidering it. More generally, inhibition protects you from unimportant, distracting stimuli.

To me, (the blogger), it doesn’t make much sense that creative people would be more distractible. Or at least, I would think that creativity is not just a matter of casting a wide net to gather associations of little relevance to the problem at hand. That could be a part of it, of course.

Supporting that idea is the fact that insightfuls, in a resting state (when not solving problems) have more right-hemisphere activity and less left-hemisphere activity than normals. The right hemisphere differs from the left in that in many of its association areas, the neurons have larger input fields than do left hemisphere neurons. Specifically, right hemisphere pyramidal neurons have more synapses overall and especially more synapses far from the cell body. This indicates that they have larger input fields than corresponding left hemisphere pyramidal neurons. Because cortical connections are spatially organized, the right hemisphere’s larger input fields collect more differentiated inputs, perhaps requiring a variety of inputs to fire. The left hemisphere’s smaller input fields collect similar inputs, likely causing the neuron to respond best to somewhat redundant inputs.

Even the axons in the right hemisphere are longer, suggesting that more far-flung information is used.

Both hemispheres can work together to solve a problem, so you can have the best of the both worlds – a narrow focused approach, and a diffuser, more creative approach.

If you want to increase your own insights, the authors have various suggestions.

  1. Expansive surroundings will help you to induce the creative state. The sense of psychological distance conveyed by spaciousness not only broadens thought to include remote associations, it also weakens the prevention orientation resulting from a feeling of confinement. Even high ceilings have been shown to broaden attention. Small, windowless offices, low ceilings, and narrow corridors may reduce expenses, but if your goal is flexible, creative thought, then you get what you pay for.

  2. You should interact with diverse individuals, including some (nonthreatening) nonconformists.
  3. You should periodically consider your larger goals and how to accomplish them, merely thinking about this will induce a promotion mind-set. Reserve time for long-range planning. Thinking about the distant future stimulates broad, creative thought.
  4. Cultivate a positive mood…To put a twist on Pasteur’s famous saying, chance favors the happy mind.

So if you are tired of working at your desk, wave “The Eureka Factor” at your boss, and tell him that you need to hike in an alpine meadow with your eccentric friend with the guitar who never graduated high school, and maybe he’ll let you do it!

The Cognitive Neuroscience of Insight – John Kounios and Mark Beeman
The Eureka Factor – John Kounios and Mark Beeman (2015)

The frustrating insula – or why Brain Books can’t match Shakespeare

Often popular books on the brain will tell you that a particular part of the brain is responsible for various human attributes, but there is no common thread that jumps out at you. You learn more about people reading a good novel than you do after reading 100 pages of bewildering functions of grey matter..

The Insula (see diagram below) is an example. I’ll list a few tantalizing conclusions from various studies, and if you find a common thread, add a comment and let me know.


According to neuroscientists who study it, the insula is crucial to understanding what it feels like to be human.

They say it is the wellspring of social emotions, things like lust and disgust, pride and humiliation, guilt and atonement. It helps give rise to moral intuition, empathy and the capacity to respond emotionally to music.

So here are a few findings on this part of the brain:

  1. A conservative or left-wing brain? – liberals have higher insula activation:
    Researchers have long wondered if some people can’t help but be an extreme left-winger or right-winger, based on innate biology. To an extent, studies of the brains of self-identified liberals and conservatives have yielded some consistent trends.Two of these trends are that liberals tend to have more the insula and anterior cingulate cortex. Among other functions, the two regions overlap to an extent by dealing with cognitive conflict, in the insula’s case, while the anterior cingulate cortex helps in processing conflicting information.Conservatives, on the other hand, have demonstrated more activity in the amygdala, known as the brain’s “fear center.” “If you see a snake or a picture of a snake, the amygdala will light up.
  2. Higher insula activation when thinking about risk is associated with criminality. In fact criminals think about risk in an opposite way to law-abiding citizens:
    A study has shown a distinction between how risk is cognitively processed by law-abiding citizens and how that differs from lawbreakers, allowing researchers to better understand the criminal mind.“We have found that criminal behavior is associated with a particular kind of thinking about risk,” said Valerie Reyna, the Lois and Melvin Tukman Professor of Human Development and director of the Cornell University Magnetic Resonance Imaging Facility. “And we have found, through our fMRI capabilities, that there is a correlate in the brain that corresponds to it.”In the study, published recently in the Journal of Experimental Psychology, Reyna and her team took a new approach. They applied fuzzy-trace theory, originally developed by Reyna to help explain memory and reasoning, to examine neural substrates of risk preferences and criminality. They extended ideas about gist (simple meaning) and verbatim (precise risk-reward tradeoffs), both core aspects of the theory, to uncover neural correlates of risk-taking in adults.

    Participants who anonymously self-reported criminal or noncriminal tendencies were offered two choices: $20 guaranteed, or to gamble on a coin flip for double or nothing. Prior research shows that the vast majority of people would chose the $20 – the sure thing. This study found that individuals who are higher in criminal tendencies choose the gamble. Even though they know there is a risk of getting nothing, they delve into verbatim-based decision-making and the details around how $40 is more than $20.

    The same thing happens with losses, but in reverse.

    Given the option to lose $20 or flip a coin and either lose $40 or lose nothing, the majority of people this time would actually choose the gamble because losing nothing is better than losing something. This is the “gist” that determines most people’s preferences.

    Those who have self-reported criminal tendencies do the opposite through a calculating verbatim mindset, taking a sure loss over the gamble.

    “This is different because it is cognitive,” Reyna said. “It tells us that the way people think is different, and that is a very new and kind of revolutionary approach – helping to add to other factors that help explain the criminal brain.

    As these tasks were being completed, the researchers looked at brain activation through fMRI to see any correlations. They found that criminal behavior was associated with greater activation in temporal and parietal cortices, their junction and insula – brain areas involved in cognitive analysis and reasoning.

    “When participants made reverse-framing choices, which is the opposite of what you and I would do, their brain activation correlated or covaried with the score on the self-reported criminal activity,” said Reyna. “The higher the self-reported criminal behavior, the more activation we saw in the reasoning areas of the brain when they were making these decisions.”

    Noncriminal risk-taking was different: Ordinary risk-taking that did not break the law was associated with emotional reactivity (amygdala) and reward motivation (striatal) areas, she said.

    Not all criminals are psychopaths, but psychopaths show differences as well.
    A study of 80 prisoners used functional MRI technology to determine their responses to a series of scenarios depicting intentional harm or faces expressing pain. It found that psychopaths showed no activity in areas of the brain linked to empathic concern. The participants in the high psychopathy group exhibited significantly less activation in the ventromedial prefrontal cortex, lateral orbitofrontal cortex, amygdala and periaqueductal gray parts of the brain, but more activity in the striatum and the insula when compared to control participants, the study found.The high response in the insula in psychopaths was an unexpected finding, as this region is critically involved in emotion and somatic resonance. Conversely, the diminished response in the ventromedial prefrontal cortex and amygdala is consistent with the affective neuroscience literature on psychopathy. (This latter region is important for monitoring ongoing behavior, estimating consequences and incorporating emotional learning into moral decision-making, and plays a fundamental role in empathic concern and valuing the well-being of others.)

  3. Damaging the insula can cure addiction:
    The recent news about smoking was sensational: some people with damage to a prune-size slab of brain tissue called the insula were able to give up cigarettes instantly.
  4. The insula is responsible for the feeling of disgust:
    Insula activation was only significantly correlated with ratings of disgust, pointing to a specific role of this brain structure in the processing of disgust. This ties in somehow to what I cited before on political leanings. In one study, people of differing political persuasions were shown disgusting images in a brain scanner. In conservatives, the basal ganglia and amygdala and several other regions showed increased activity, while in liberals other regions of the brain increased in activity. Both groups reported similar conscious reactions to the images. The difference in activity patterns was large: the reaction to a single image could predict a person’s political leanings with 95% accuracy (this may be hard to believe, but it is according to Neuroscientist Read Montague, who works at Virginia Tech in Roanoke. It is reported in which in turn cites his research article).

I’ve listed all these items, many very interesting, but at the end of the day, what is going on?


Structural and Functional Cerebral Correlates of Hypnotic Suggestibility – Alexa Huber, Fausta Lui, Davide Duzzi, Giuseppe Pagnoni, Carlo Adolfo Porro

Neural Arithmetic Logic Units – getting backpropagation nets to extrapolate

Backpropagation nets have a problem doing math. You can get them to learn a multiplication table, but when you try to use the net on problems where the answers are higher or lower than the ones used in training, they fail. In theory, they should be able to extrapolate, but in practice, they memorize, instead of learning the principles behind addition, multiplication, division, etc.

A group at Google DeepMind in England solved this problem.
They did this by modifying the typical backprop neuron as follows:

  1. They removed the bias input
  2. They removed the nonlinear activation function
  3. Instead of just using one weight on each incoming connection to the neuron, they use two. Both weights are learned by gradient descent, but a sigmoid function is applied to one, a hypertangent function is applied to the other, and then they are multiplied together. In standard nets, a sigmoid or hypertangent function is not used on weights at all, instead these types of functions are used on activation.  The opposite is true here.

Here is the equation for computing the weight matrix.  W is the final weight, and the variables M and W with the hat symbols are values that are combined to create that final composite weight:


So what is the rationale behind all this?

First lets look at what a sigmoid function looks like:


And now a hypertangent function (also known as ‘tanh’):


We see that the sigmoid function ranges (on the Y axis) between 0 and 1. The hypertangent ranges from -1 to 1. Both functions have a high rate of change when their x-values are fairly close to zero, but that rate of change flattens out the farther they get from that point.

So if you multiply these two functions together, the most the product can be is 1, the least is -1, and there is a bias to the composite weight result – its less likely to be fractional, and more likely to be -1, 1, or zero.
Why the bias?
The reason is that near x = zero, the derivative being large actually indicates that the neuron would be biased to learn numbers other than that point (because it will take the biggest step sizes when the derivative is highest). Thus, tanh is biased to learn its saturation points (-1 and 1) and sigmoid is biased to learn its saturation points (0 and 1). The elementwise product of them thus has saturation points at -1, 1, and 0.

So why have a bias? As they explain:

Our first model is the neural accumulator (NAC), which is a special case of a linear (affine) layer whose transformation matrix W consists just of -1’s, 0’s, and 1’s; that is, its outputs are additions or subtractions (rather than arbitrary rescalings) of rows in the input vector. This prevents the layer from changing the scale of the representations of the numbers when mapping the input to the output, meaning that they are consistent throughout the model, no matter how many operations are chained together.

As an example, if you want the neuron to realize it has to add 5 and -7, you don’t want those numbers multiplied by fractions, rather in this case, you prefer 1 and -1. Likewise, the result of this neuron’s addition could be fed into another neuron, and again, you don’t want it multiplied by a fraction before it is combined with that neuron’s other inputs.

This isn’t always true though, one of their experiments was learning to calculate the square root, which required a weight training to the value of 0.5.

On my first read of the paper, I was sure of why the net worked, and so I asked one author: Andrew Trask, who replied that it works because:


  1. because it encodes numbers as real values (instead of as distributed representations)
  2. because the functions it learns over numbers extrapolate inherently (aka… addition/multiplication/division/subtraction) – so learning an attention mechanism over these functions leads to neural nets which extrapolate


The first point is important because many models assume that any particular number is coded by many neurons, each with different weights. In this model, one neuron, without any nonlinear function applied to its result, does math such as addition and subtraction.

It is true that real neurons are limited in the values they can represent. In fact, neurons fire at a constant, fixed amplitude and its just the frequency of pulses that increase when they get a higher input.

But ignoring that point, the units they have can extrapolate, because they do simple addition and subtraction (point #2).

But wait a minute – what about multiplication and division?

For those operations they make use of a mathematical property of logarithms. The log of (X * Y) is equal to log(X) + log(Y). So if you take logarithms of values before you feed them into an addition neuron, and then the inverse of the log of the result, you have the equivalent of multiplication.

The log is differentiable, so the net can still learn by gradient descent.

So they now need to combine the addition/subtraction neurons with the multiplication/division neurons, and this diagram shows their method:



This fairly simple but clever idea is a breakthrough:

Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.

Neural Arithmetic Logic Units – Andrew Trask, Felix Hill, Scott Reed, Jack Rae, Chris Dyer, Phil Blunsom – Google DeepMind