Reentry and Recursion in Neuronal Network

Reentry and Recursion in Neuronal Network

Reentrant activity leading to recursion is a fundamental feature of thalamocortical activity, and indeed nearly all neural activity. Reentrant activity is not simple feedback but functions in a network as recursive multiple pathways, which update iteratively on a time scale of tens to hundreds of milliseconds, rapidly converging to the dynamic core’s synaptically connected neuronal network mediating an instantaneous thought. This iterative neural activity generates gamma (~40-Hz) oscillations in the normal waking state. The converged state of the dynamic core can change as individual thoughts change on an approximate 100 ms basis. This allows a few iterations of the recursive reentrant activity with the local synaptic loops at the gamma (~40 Hz) rate to converge to the dynamic core.

Comprehension is always accomplished by a "holistic" attempt to integrate the information from all sources that has arrived in the brain up until that point. When further information (from any semantic source) arrives that can disambiguate an earlier piece of information, the model is adjusted accordingly. (Hurley, Dennett, Adams; Inside Jokes, 99)

The binding principle made possible by reentry is repeated across many levels of brain organization, thereby leading to consciousness. (Edelman; Universe of Consciousness, 107)

Recursive Functionality

Recursive networks incorporate feedback loops to sustain iterative dynamical processes based on continuous update of network state. (Squire; Fundamental Neuroscience, 847)

The idea that an iterative algorithm is carried out in the thalamocortical loop has received experimental confirmation in observed oscillations. (Mumford; Thalamus, 982)

Recursion -- hierarchical tree structure of propositions inside propositions. (Pinker; How the Mind Works, 124)

Recursion is a looping design of iterative information processing implemented in neural networks. (Pinker; How the Mind Works, 125)

Unless neural networks are specifically assembled into a recursive processor, they cannot handle our recursive thoughts. (Pinker; How the Mind Works, 125)

My model of working memory, Working Memory Model (Covington), is based upon recursive functionality.

Link to — Working Memory Model (Covington)

Link to — Bayesian Inference in Brain Functionality

Research Study — Brain Regions Involved in Decision-Making

Research Study — Thalamocortical Signals Selectively Amplified via Recurrent Inputs

Nested hierarchy of reentry and recursion

The neural network likely functions as a nested hierarchy of recursive loops operating at perhaps ~20 ms for visual sensory circuits, maybe ~50 ms in association cortex areas for perception, and perhaps >1 second for decision circuits in frontal cortex.

Very fast oscillations (VFO) can occur nested with a slower oscillation, beta-2 (20-30 Hz). (Traub; Cortical Oscillations, 260)

There is considerable evidence that the processing time required in each cortical area for useful computation is of the order of 20-30 ms. (Rolls & Treves; Neural Networks, 177)

A metaphor may be helpful. My experience with the Apollo lunar guidance system in the 1960s may have some insightful parallels for the brain's neural circuitry. The lunar ascent guidance system had gyroscopes and accelerometers whose rapidly changing state variables were refreshed every 10 ms. The vehicle attitude orientation computations were refreshed every 20 ms, and the vehicle guidance equations of position and velocity were refreshed every 2 seconds. This hierarchy of computations provided rapid response for rapidly changing quantities but allowed more time for more complex, slowly changing quantities.

This nested hierarchy of recursive guidance computations may provide some insight for the neural circuitry in the brain. I suspect the visual sensory cortex operates on perhaps a ~20 ms recursive cycle, the multimodal association cortex on perhaps a ~50 ms cycle, and the frontal cortex, with back projections to the posterior cortical areas, may operate on a >1 second recursive cycle.

Neurons in the sensory areas of the brain typically fire at high rates (0-100 Hz), whereas neurons in the prefrontal cortex at a lesser rate (0-10 Hz). (Edelman; Universe of Consciousness, 169)

Research Study — Cortex Timescales of Population Coding

These recursive guidance computations can comprise a complex system organized at multiple timescales. Slow rhythms involve very large numbers of cells that can be "heard" over a long distance, whereas localized fast oscillations involving only a small fraction of neurons may be conveyed only to a few partners. Power spectrum of the EEG is a straight line on a log-log plot, showing amplitude increasing as frequency decreases. This inverse relationship is expressed as the "one over f" power spectrum (also called "pink" noise). (Buzsáki - Rhythms of the Brain, 119)

Research Study — Cortex Timescales of Population Coding

Link to — Hierarchies of Recursion Loops Diagram

Reentry and recursion and the thalamocortical system

Core consciousness is created in pulses, each pulse triggered by an object we interact with or that we recall. Each new object triggers the process of changing the proto-self. Proto-self modified by the first object becomes the inaugural proto-self for the new object. Continuity of consciousness is based on the steady generation of consciousness pulses, which correspond to the endless processing of myriad objects, whose interaction, actual or recalled, constantly modifies the proto-self. (Damasio; Feeling of What Happens, 176)

There is a ceaseless production of new activity states, in early sensory cortices and in motor cortices, across time. It is these successive neural states, one after the other, that can be said to constitute "regresses" for the previous state. Neural assemblies are activated (refreshed) in a pulse-like manner by reentrant signals circulating in the network hierarchy. It is the perpetually recursive property of corticocortical systems that permits this special form of regress. [recursion] [Bayesian inference] [Fuster's perception-action cycle] (Domasio; Convergence Zone, 70)

Link to — Convergence-Divergence Zones

Massive reentrant connections formed by the hippocampal system in the medial temporal lobe. Input comes mainly from the entorhinal cortex, and its output returns there, though to a different cortical layer. (Koch and Crick; Neuronal Basis, 107)

Strong reciprocity exists in thalamocortical connections. (Shepherd; Synaptic Organization of the Brain, 295)

As a result of corticothalamic iteration, the thalamic pattern of activity is sent back to the cortex as an enhanced view of the world. (Mumford; Thalamus, 983)

Prefrontal regions are reciprocally connected with temporal, parietal, and occipital cortices, where they receive higher-level visual, auditory, and somatosensory information. (Miller; Human Frontal Lobes, 49)

Experimental observations have concluded that sensory information is processed in discrete time segments as low as 12 ms. (Llinás & Paré; Brain Modulated by Senses, 12)

Whereas the 12.5 ms time for the quantum of cognition has been determined psychophysically, another very distinct measurement of the phase shift of 40-Hz oscillatory activity over the human cortex has a 12.5-ms duration as well. (Llinás & Paré; Brain Modulated by Senses, 12)

In alert subjects, continuous 40-Hz oscillations can be recorded over large areas of the surface of the head. These oscillations are not in phase, but exhibit a 12- to 13-ms phase shift between the rostral and caudal parts of the brain. (Llinás & Paré; Brain Modulated by Senses, 7)

The thalamocortical system, by its hublike organization, allows radial communication of the thalamic nuclei with all aspects of the cortex. These cortical regions include the sensory, motor, and associational areas. These areas subserve a feedforward/feedback, reverberating flow of information. (Llinás; I of the Vortex, 126)

Thalamic input from the cortex is far larger than from the peripheral sensory systems. This suggests that thalamocortical iterative activity is a main mechanism of brain function. (Llinás; I of the Vortex, 124)

Responses triggered by the reentrant dynamic core can also stimulate non-conscious responses through the basal ganglia network. These travel along parallel, polysynaptic, one-directional pathways that leave the cortex, reach the various components of the basal ganglia and certain thalamic nuclei, and finally return to the cortex. (Edelman; Wider than the Sky, 70)

Responses subserving consciousness can connect to activity patterns in unconscious areas, served mainly but not exclusively by the basal ganglia. (Edelman; Wider than the Sky, 70)

Connectivity between the thalamus and the cortex is bidirectional. Layer 6 pyramidal cells project back to the area of the thalamus where their specific input arises, and layer 5 cells project to the nonspecific thalamus. The number of corticothalamic fibers is about one order of magnitude larger than the number of thalamocortical axons. (Llinás; Perception as Oneiric-like, 113)

A large part of the thalamocortical connectivity is organized in what is presently known as reentrant activity (Edelman) or previously viewed as reverberating activity. Only a minor part of thalamocortical connectivity is devoted to the reception and transfer of sensory input. The number of cortical fibers projecting to the specific thalamic nuclei is much larger than the number of fibers conveying the sensory information to the thalamus. (Llinás; Perception as Oneiric-like, 114)

Reciprocal connections between hippocampus and neocortex

Reciprocal connections between hippocampus and neocortex, long-term storage of memories. (LeDoux; Synaptic Self, 104)

Through reentry, a number of the hippocampal groups would be repeatedly activated, allowing synaptic change involving long-term potentiation and an integrated response to perceptual input. (Edelman; Remembered Present, 131)

Unlike feedback, reentry is not a single-pathway transmission of an error signal in a simple loop. Instead, it simultaneously involves many parallel reciprocal paths and has no prescribed error function. (Edelman; Wider than the Sky, 41)

The brain is a mass of reentry loops. (Andreasen, Creating Brain, 62)

Some connections create short loops among neurons, and some have long loops that spread across longer spans of the brain. (Andreasen, Creating Brain, 59)

It is estimated that a large loop covering the entire brain takes only five or six synapses. (Andreasen, Creating Brain, 59)

Flow of communications between the levels from brainstem to prefrontal cortex is constant and reflective, feeding back on itself as each moment advances, so decisions and actions are as appropriate as they can be. (Ratey; User's Guide to Brain, 161)

Regenerative feedback can incorporate the past into the system's present state, and it threads the system through both time and space, thereby allowing input-induced perturbations to be compared with the effects the previous similar encounters. (Buzsáki; Rhythms of the Brain, 370)

The most striking, yet perhaps the least appreciated, behavior of cortical networks is their regenerative, spontaneous activity. Every spike, sensory evoked or spontaneous, in cortical principles cells can reach distant neurons. (Buzsáki; Rhythms of the Brain, 370)

Subjective Present and the Temporal Window

Each mental act is characterized by simultaneous neuronal activity in different brain areas. (Poppel; Time Perception, 987)

Successive events are integrated up to approximately 2 to 3 seconds to set up an operational temporal window. (Poppel; Time Perception, 987)

The temporal window can be referred to as a subjective present. (Poppel; Time Perception, 987)

Perception-Action Cycle uses Reentry and Recursion

Joaquin Fuster’s Perception-Action Cycle uses reentry and recursion on all hierarchical layers between the frontal motor cortical areas and the posterior sensory cortical areas.

Widespread cortical and subcortical activity constitutes an image

The prominent recurrent nature of lateral intracortical connections and relatively wide spatial distribution of cortical inputs mean that the cortical output at any one location must depend on both the input and output over relatively great expanses of cortex. That is, the output at any one point must be a functional, of both inputs and outputs. (Stevens; Cortical Theory, 243)

Reentrant processing -- higher-level associations are made by fibers that reenter the brain areas that processed the initial input. (Baars, Essential Sources, Posner, "Attention: The Mechanisms of Consciousness," 286)

Layer 5's orderly connections to subcortical structures (e.g., from visual cortex to the pulvinar and the superior colliculus, structures implicated in controlling attention and eye movements) that are reciprocally connected in turn in a topographic manner to multiple visual areas. (Ullman; Sequence Seeking Counterstreams, 265)

Pulvinar, a subcortical nucleus of the thalamus, makes reciprocal connections with all of these visual processing cortical areas. (Van Essen; Dynamic Routing Strategies, 285)

Signal phase shift between the rostral and caudal parts of the brain

Magnetoencephalographic recordings performed in awake humans revealed the presence of continuous and coherent 40-Hz oscillations over the entire cortical mantle. (Llinás; Perception as Oneiric-like, 115)

Phase comparison of the oscillatory activity recorded from different cortical regions revealed the presence of a 12- to 13-msec phase shift between the rostral and caudal pole of the brain. (Llinás; Perception as Oneiric-like, 115)

Front-to-back phase shift of the 40-Hz activity over the head during REM sleep; well-organized 12-msec phase shift for the 40-Hz oscillation. (Llinás; Perception as Oneiric-like, 120)

Overall speed of the rostrocaudal scan, which averaged approximately 12.5 msec, corresponded quite closely to half a 40-Hz period. This number is the same as that calculated for a quantum of consciousness in psychophysical studies in the auditory system. (Llinás; Perception as Oneiric-like, 120)

Memory regeneration utilizes reentry and recursion

Retroactivation process uses the rich connectional patterns of feed-forward and feedback that characterize the architecture of cortical regions and subcortical nuclei. (Damasio; Making Images, 20)

Reentrant connectivity between hippocampus and medial temporal lobe

Reentrant connectivity between basal ganglia and nuclei

Activity in the basal ganglia is running all the time, playing motor patterns and snippets of motor patterns amongst and between themselves. Because of the reentrant inhibitory connectivity among and between these nuclei, they seem to act as a continuous, random, motor pattern generator. (Llinás; I of the Vortex, 170)

Shape of the dendritic tree may affect spike output pattern

Theoretical work has suggested that the shape of the dendritic tree is a major factor in controlling the pattern of spike output from neurons, (Douglas; Neocortex, 465)

Counterstreams functional architecture for reentry and recursion

An attractive model for mental object search and matching is to apply bidirectional methods, using both bottom-up and top-down processing. This counterstreams notion fits well with the 1-to-6 layered architecture of the cortex. (Ullman; Sequence Seeking Counterstreams, 258)

The sequence-seeking model requires two streams going in opposite directions with the appropriate cross-connections. The counterstreams go up and down between layers 1 and 6 of the cortex, with lateral cross connections between nearby areas. (Ullman; Sequence Seeking Counterstreams, 264)

The ascending stream goes through layer 4 to a subpopulation of the superficial layers, and then projects to layer 4 of the next cortical area. (Ullman; Sequence Seeking Counterstreams, 264)

The descending stream goes through a different subpopulation of the superficial layers to a descending subpopulation of the infragranular layers (often in layer 6), and from there to descending superficial layers of a preceding area. (Ullman; Sequence Seeking Counterstreams, 264)

Layer 5 (or parts of it) may be involved in control functions. (Ullman; Sequence Seeking Counterstreams, 265)

Layer 5's orderly connections to subcortical structures (e.g., from visual cortex to the pulvinar and the superior colliculus, structures implicated in controlling attention and eye movements) that are reciprocally connected in a topographic manner to multiple visual areas. (Ullman; Sequence Seeking Counterstreams, 265)

Firing pattern of a population of pyramidal cells in Layer 5 can initiate synchronized rhythms and project them on neurons in all layers. (Ullman; Sequence Seeking Counterstreams, 265)

Connections between cortical areas can be classified as forward, backward, or lateral connections on the basis of the laminar distribution of their source and destination. Lateral connections terminate in all layers. (Ullman; Sequence Seeking Counterstreams, 268)

Counterstreams sequence-seeking model is a bidirectional search performed by top-down and bottom-up streams seeking to meet. (Ullman; Sequence Seeking Counterstreams, 270)

The counter streams functional architecture accounts for several basic features of cortical circuitry: the predominantly reciprocal connectivity between cortical areas; the forward, backward, and lateral connection types; the regularities in the distribution patterns of interarea connections; the organization in 5-6 main layers; the effects of back projections. (Ullman; Sequence Seeking Counterstreams, 270)