Tuesday, April 19, 2011

The Hierarchy of Neural Complexity

Sporns says that "brain connectivity is organized on a hierarchy of scales from local circuits of neurons to modules of functional brain systems" (258). His use of the word hierarchy presents me with some problems as I have for the last few years contrasted hierarchical structures with network structures. In general, I have assumed that hierarchies were rigid, closed, traced, arboreal structures (to use terms from Deleuze and Guattari) while networks were flexible, scaleable, open, mapped, rhizomatic structures. Hierarchies admit only sanctioned, homogenous nodes within its structure and then fix them into a well-defined place with well-defined relationships to all other nodes; whereas,  networks admit heterogenous nodes within its open structure and allow nodes to develop relationships with any or all other nodes for any reason. For me, then, hierarchies and networks are not the same, and I cringe just a bit each time Sporns uses the term hierarchy to describe an aspect of neural networking.

But I think I have a resolution to my concern. I don't think Sporns is using hierarchy as I do; rather, he is describing various physical and functional layers of the brain and how they interact. As he says: "A recurrent theme in studies of collective behavior in complex networks, from epidemic to brain models, is its dependence on the network's multiscale architecture, its nested levels of clustered communities" (261). He is not so much describing a pyramidal structure as an onion structure. He's talking about layers enclosing layers enclosing layers and so on. This might be a mere quibble over visual metaphors but for his concepts of heterogenous coupling and multiscale dynamics, and some others like them. These principles prevent Sporns' neural hierarchies from calcifying into rigid hierarchies, as I have used the term. Indeed, heterogenous coupling in neurophysiology reminds me much of Deleuze and Guattari's first principle of the rhizome given in the first chapter of their book A Thousand Plateaus (1988): "any point of a rhizome can be connected to anything other, and must be. This is very different from the tree or root, which plots a point, fixes an order" (7). I think Deleuze and Guattari would be most comfortable with Sporns' concept of heterogenous coupling as very rhizomatic.

Sporns also talks about the brain's metastability, or tendency toward chaotic itinerancy:
the itinerant or roaming motion of the trajectory of a high-dimensional system among varieties of ordered states. Chaotic itineracy is found in a number of physical systems that are globally coupled, that are far from equilibrium, or that engage in turbulent flow. … It has also been observed in brain recordings … and neural network models … Over time, systems exhibiting chaotic itineracy alternate between ordered low-dimensional motion within a dynamically unstable "attractor ruin" and high-dimensional chaotic transitions. System variables are coherently coupled, their dynamics slow down during ordered motion, and they transiently lose coherence as the system trajectory rapidly moves between attractor ruins. (263, 264)
This chaotic itinerancy of neural networks with their roaming motions and trajectories and their constant transitions between coherent couplings and incoherent chaos is strongly reminiscent of another characteristic of rhizomes: the principle of asignifying rupture. Deleuze and Guattari say of asignifying ruptures:
Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees. There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome.
Rhizomatic structures, then, deterritorialize and reterritorialize only to deterritorialize again. If I understand what Sporns is saying, then it seems that neural networks have a chaotic itinerancy that is at least a Rorschach of asignifying ruptures. Perhaps, Deleuze and Guattari's asignifying ruptures have deterritorialized and reterritorialized as chaotic itinerancy.

Seems possible. Anyway, chaotic itinerancy seems to fit nicely with D&G's whole idea about nomadology and motion in reality. Anyone know for sure?


  1. "If I understand what Sporns is saying, then it seems that neural networks have a chaotic itinerancy that is at least a Rorschach of asignifying ruptures."

    Keith, years ago I visited a rural church once and after teaching Sunday school there in the presence of the minister he said, "Now, lets put it down for the children." I looked around, thinking, "There are no children here!" He proceeded to say everything I had said again. I have no idea whether those present understood it any more the second time than the first. But they seemed as interested the second time as the first.

    I read this as a child. There must be something wonderful here but I cannot yet understand it. My guess is that others reading this may feel the same way. Can you put it down for me, please? If others have my same need, can I help you put it down for others also, somehow?
    - Bruce

  2. Bruce, I think I was being too clever by far. I was trying to conjure a complex image, and didn't quite succeed.

    Here's what I mean: I see a self similarity in Sporns' concept of chaotic itinerancy and Deleuze and Guattari's asignifying ruptures. Both concepts seem to suggest a similar kind of movement or process in the patterns that emerge in complex network structures, but even emerge is a somewhat awkward term in this case, as it suggests a finished, completed emerged entity. Both chaotic itinerancy and asignifying ruptures refer to a continual, perhaps continuous, process of emerging, of being in that dynamic state poised between regularity and randomness, or as D&G would say: the constant deterritorializing of one form, rupturing, and then reterritorializing elsewhere/when as a self similar form or another form.

    Cognition, then, is not a single thing, a single event, or even a single pattern in our brains. Rather, it is a dynamic, though patterned, movement across neural space and time that unfolds both under its own dynamic and within the dynamic of the brain's ecosystem, which includes all sensory input at the time the cognitive pattern is unfolding, other brain processes, and so on. Cognition is more like the unfolding of a musical motif in a jazz band that expresses itself, submerges, and then re-emerges again in a slightly different expression.

    The Rorschach is the image I used to capture visually the self similarity between the two concepts: that one is the suggestive image of the other.

    At least, I think this is what I meant.

  3. Thank you, again, Keith. It seems that you are using words when some form of multidimensional dynamic art may be needed. I will study and perhaps someday understand.