Confabulation theory (computational intelligence)
Confabulation theory offers a comprehensive detailed explanation of the mechanism of thought (i.e., “cognition”: vision, hearing, reasoning, language, planning, origination of movement and thought processes, etc.) in humans and other vertebrates (and possibly in invertebrates, such as octopi and bees). For expositional simplicity, only the human case is considered here.
A Universal Theory of Animal Cognition
Confabulation theory (Hecht-Nielsen 2005, 2006a, 2006b, 2006c, 2007) (Figure 1) proposes that cognition is a phylogenetic outgrowth of movement and that cognition utilizes the same neural circuitry that was originally developed for movement.
Movement relies on the deliberate, smooth, properly sequenced and coordinated, graded, contractions of selected ensembles of discrete muscles. Therefore, the neural circuitry of movement was specialized for this purpose. Soon, a new design possibility emerged: the elaborate neuronal machinery of movement control could be applied to brain tissue itself. In particular, discrete brain structures, modules, emerged that could be controlled exactly like individual muscles (the physical arrangement of the neurons involved in a single module differs considerably across taxa, e.g., see [Karten 1991], although module function is strongly conserved). By manipulating these modules in properly coordinated 'movements' (thought processes), valuable information processing (cognition) could be carried out – thereby further enhancing animal competitive success and diversity.
Confabulation theory postulates that the gray matter of human cerebral cortex is comprised of roughly 4,000 localized, largely mutually disjoint, modules (each of roughly 45 mm2 areal extent and including all cortical layers within this extent). Genetically selected pairs of these modules are connected by knowledge bases; of which humans have roughly 40,000. [Note: Specific parameter values cited in this article are crude estimates of means intended to fix ideas. These values surely vary significantly within each human brain and between human brains.] Each individual module and knowledge base also includes a small, uniquely dedicated, zone of thalamus. Modules and knowledge bases constitute the hardware of thought.
Modules and knowledge bases are postulated by confabulation theory to implement four key information processing functional elements that together make up the mechanism of thought. These four key elements (each a central hypothesis of confabulation theory) are described for the human case in the next four sections.
Each Module Describes One ''Attribute'' that a Mental World Object May Possess
A longstanding hypothesis (Martin 1994) regarding the function of cerebral cortex is that many cortical neurons function as feature detectors. This hypothesis has been confirmed widely across cortex.
The ubiquitous presence of feature detector neurons across cortex suggests that an important function of cortex is to have neurons which selectively respond to certain ‘aspects’ of objects in the mental world. Confabulation theory takes this much further by hypothesizing that each module is specialized for describing one and only one fixed attribute that a mental world object may possess. In other words, all of the 'feature detector' (or, as confabulation theory terms them, symbol) neurons within a module are devoted to describing one attribute.
Specifically, according to confabulation theory, a primary function of each thalamocortical module in Figure 2 is to describe exactly one attribute that an object of the mental universe (a sensory object, a motor process object, a thought process object, a plan object, a language object, etc.) may possess. To carry out this object attribute description function, each module implements a large collection of symbols, Figure 3. When utilized for describing an object, a module typically expresses one symbol chosen from its collection (primary sensory and motor modules usually express multiple symbols). [Note: Expression of a symbol by a module occurs as a result of a confabulation operation; which is described in the section after next.]
As shown in Figure 3, each symbol is represented by roughly 60 neurons selected (approximately uniformly at random) from a special population of roughly 400,000 symbol-representing neurons (shown as colored dots within the enlarged depiction of inset A of Figure 2 and again in Figure 3); which probably reside in layer III of the module. Inset B of Figure 2 illustrates that actual modules are probably somewhat irregularly shaped (each different colored area shown in the inset represents a different module). Unlike cortical columns (Mountcastle 1997) and other localized functional units of cortex which have been postulated previously, modules have a completely specified set of basic functional capabilities – which together explain how thinking works. These capabilities are described in this section and the following three.
In Figure 3, a module with 126,008 symbols is depicted. Each symbol's set of 60 symbol-representing pyramidal neurons (drawn essentially uniformly at random from the layer III population mentioned above) is shown schematically on the right.
Symbols are hypothesized to be mostly formed in childhood and then remain stable throughout life; they are the stable terms of reference that must exist if knowledge is to be accumulated across decades. Thalamocortical module symbol sets (the collection of different descriptive terms for representing the particular object attribute that the module is responsible for encoding) are the first of the four key functional elements of confabulation theory.
Knowledge Links Connect Pairs of Co-Occurring Symbols
Although the vague concept of human cognitive knowledge (something which is acquired, stored, and then used) has been in widespread use since at least the time of (Aristotle c.350 BC); until confabulation theory, there was no detailed hypothesis regarding the nature of knowledge or the neuronal mechanisms involved in its acquisition, storage, and use (other than the persistent vague suspicion that Hebbian co-occurrence-based synaptic modification [Hebb 1949] might somehow be involved). Confabulation theory specifies precisely what cognitive knowledge is, how it is acquired, how it is stored, and (see next section) how it is used in thinking. Figure 4 illustrates a single cognitive knowledge link. Here, a human subject is viewing and considering a red apple. A visual module is expressing a symbol for the color of the apple. At the same time, a language module is expressing a symbol for the name of the apple. Pairs of symbols which meaningfully co-occur in this manner are postulated by confabulation theory to have unidirectional axonal links, termed knowledge links (each considered a single item of knowledge), established between them via synaptic strengthening (assuming that the required axons are actually present; which is determined by genetics). A single knowledge link, therefore, is a connection between two populations(or portions thereof) of neurons.
The concept that the co-occurrence of pairs of items is the fundamental driver for the creation of knowledge was presciently envisioned by Aristotle ("When two things commonly occur together, the appearance of one will bring the other to mind." [Aristotle c.350 B.C.]). This associationist notion of the nature of animal cognitive knowledge was later progressively refined by many others, including Locke, Hume, Hartley, Mills, (Bain 1864), (James 1890), Pavlov, and (Hebb 1949). That all cognitive processing (seeing, hearing, reasoning, dancing, singing, conversing, writing, doing calculus, etc., etc.) can be based entirely upon pairwise knowledge links between meaningfully co-occurring symbols seems preposterous. But that is exactly what confabulation theory hypothesizes.
Confabulation theory postulates that the average adult human has billions of knowledge links; most of which are established in childhood. The sustained net average rate of human knowledge acquisition can probably sometimes exceed ten links per second for periods of days. Each knowledge link is hypothesized to be implemented via a two-stage synfire chain (Abeles 1991) connecting (via the fascicles of the cortical white matter) the collection of neurons that represent the source symbol of the link with a subset of the neuron collection which represents the target symbol of the link. Formation of knowledge links involves a complex process of instantaneous, but temporary, knowledge link establishment at time of first co-occurrence; followed by repeated evaluations and strengthenings (if the evaluation is favorable) of each such individual provisional knowledge link over the following hundred hours or so. Sejnowski and Destexhe (2000) propose that cortical activity during sleep is suited for consolidating information in neural assemblies. Thus, confabulation theory proposes that knowledge evaluation and solidification processes that strengthen knowledge links are largely carried out during sleep and involve entorhinal cortex, hippocampus, and many other brain nuclei. Given that many tens of thousands of provisional knowledge links are often formed daily, it is no wonder that we must sleep a third of the time (see Hecht-Nielsen 2006a, 2006c for more information).
The set of all knowledge links joining symbols belonging to one specific source module to symbols belonging to one specific target module is termed a knowledge base. In the human brain, knowledge bases are hypothesized by confabulation theory to essentially take the form of the huge bundles of axons (the classical fascicles), which together make up a large portion of each cerebral hemisphere's ipsilateral white matter. Each module also typically has a knowledge base to its contralateral twin module (and perhaps to a few others near its twin); which together constitute the corpus colossum fascicle coherently linking the two cerebral hemispheres topographically.
Figure 5 illustrates how billions of pairs of symbols end up being connected via knowledge links. Here, a human subject is considering an apple and reciprocal knowledge links (red arrows), only some of which are shown, connect each expressed symbol representing an attribute of the apple pairwise with other such symbols. When an apple is currently present in the mental world, it is its collection of knowledge-link-connected symbols which are currently being expressed. It is these strong links between the attribute descriptors of an object that probably explain the many experimentally observed pairings of mirror neurons (Aziz-Zadeh et al 2006). In confabulation theory there is no binding problem (von der Malsberg 1981) because many of these symbols are automatically mutually bound by their previously-established pairwise knowledge links.
Knowledge links are the second of the four key elements of confabulation theory.
Confabulation: The Information Processing Operation of Thought
The vague notion that cognition employs some sort of "information processing" also dates to at least the time of Aristotle. Yet, until confabulation theory, no detailed specification has been offered of what this information processing might be.
Confabulation theory hypothesizes that cognition involves one, and only one, information processing operation: confabulation, a specialized type of winners-take-all competition between the symbols of a module on the basis of the total input excitation each symbol is receiving from knowledge links.
Confabulation takes place only when the module receives a specific, deliberate, thought command signal axonal input (analogous to motorneuron input to a muscle). Each module has a separate and independent thought command input (for simplicity, the sources of these thought command signal axonal inputs are not discussed here -- see [Hecht-Nielsen 2006b, 2006a, 2006c] for further discussion). A confabulation in this sense can be thought of as a neural contraction, where the state of the contraction determines how many symbols are competing and the completion of the contraction results in a single symbol being expressed.
A concrete example of confabulation involving five thalamocortical modules is shown in Figure 6 (for simplicity, each module is illustrated as a dashed green oval with a list of that module's symbols inside it). The four modules on the left in Figure 6 are each describing attributes of one or more mental world objects by each expressing a single symbol (labeled \(\alpha\ ,\) \(\beta\ ,\) \(\gamma\ ,\) and \(\delta\ ,\) respectively). Each of these four expressed symbols (termed assumed facts of the confabulation) has a large number of knowledge links connecting it with symbols of the fifth module (of which, only four knowledge links, linking each expressed symbol on the first four modules to generic symbol \(\epsilon\) of the fifth module, are shown). The situation within this fifth module, which is about to undergo confabulation, is shown enlarged on the right. For illustration, symbol 4 of this module is receiving two knowledge links (one from symbol \(\alpha\ ,\) and one from symbol \(\delta\)); whereas symbols 9 and 126,007 are receiving knowledge links from all of \(\alpha\ ,\) \(\beta\ ,\) \(\gamma\ ,\) and \(\delta\ .\) Each knowledge link is delivering a certain quantity of input excitation to the neurons of its target symbol.
The knowledge link synaptic input excitations arriving at symbol k from the different knowledge links targeting that symbol from the assumed facts (if any there be) are simply summed to yield the total input excitation for symbol k: denoted by I(k) (this summation is noted in Figure 6 by the plus signs between the knowledge links in the enlarged illustration of module five). This additive knowledge combination property is one of the paramount reasons for the enormous information processing power and flexibility of thought. In effect, every item of knowledge being employed in a confabulation operation has equal status – no matter which attribute the module the symbol supplying the link is describing. By this means, knowledge emanating from visual, language, plan, or a multitude of other object attribute symbols can be freely combined. This interoperability of knowledge links is what lies behind the effortless ability of thought to combine arbitrary relevant assumed facts.
For example, if auditory and olfactory attribute information (in the form of assumed facts) is available regarding an object that is visually occluded, we can carry out a confabulation to determine the object’s name. If the object then suddenly becomes visible, we can repeat the confabulation; now with knowledge links from auditory, olfactory, AND visual assumed fact symbols regarding the object being employed. The second confabulation will be improved because of the availability of more assumed fact input. Yet, mathematically, all that happens is that the additional excitation from the newly available knowledge links from visual symbols is effectively just added in with that from the auditory and olfactory sources.
Upon being commanded to do so (by the deliberate externally-supplied thought command signal), the symbols of the fifth module compete with one another (via a special highly parallel, fast, neuronal attractor network function of the module [Willshaw et al 1969, Amari 1974, Anderson et al 1977, Hopfield 1982, Kosko 1988, Haines and Hecht-Nielsen 1988, Amit 1989, Sommer and Palm 1999, Xie, Hahnloser and Seung 2001], which is not discussed here); yielding a final module state in which all of the neurons representing that symbol \(\epsilon\) having the largest input intensity I (in this example, symbol 9) are highly active and all other symbol-representing neurons are not. This winners-take-all information processing operation is called confabulation, and the winning symbol is termed its conclusion.
In Figure 6, there is only one confabulation taking place. Ordinarily, confabulations on multiple modules take place together, with convergence to the winning symbol slowed somewhat, to allow mutual interaction between the sets of symbols (those with high levels of input excitation) which remain in consideration during the slow convergence to a final single conclusion symbol on each module. This 'comparing notes' process allows creation of a confabulation consensus of final conclusions which are mutually strongly linked by knowledge; ensuring their mutual logical consistency. In such a multiconfabulation, often millions of items of knowledge, each emanating from a viable candidate conclusion, are employed in parallel in a 'swirling' convergence process. This parallel application of (often) millions of relevant items of knowledge (knowledge links emanating from symbols on each module which are, at that particular stage of processing, still viable candidates to be selected as that module’s final conclusion) is a key strength of thinking.
An immediate question which arises in connection with confabulation is: what sort of mathematical principle underlies such a simple winner-take-all information processing operation? And how can this one mathematical principle apply universally to all cognitive information processing?
The mathematics underlying confabulation is termed maximization of cogency; the specific generalization of Aristotelian logic which confabulation theory claims all animal cognition is based. In the case of a single confabulation, e.g., that of Figure 6, confabulation selects that conclusion symbol \(\epsilon\) which, if assumed to be true, maximizes the probability, \(p(\alpha \beta \gamma \delta | \epsilon)\) (termed the cogency of symbol \(\epsilon\) in the context \(\alpha \beta \gamma \delta\)), that the set of assumed facts being used, symbols \(\alpha\ ,\) \(\beta\ ,\) \(\gamma\ ,\) and \(\delta\ ,\) are all true. One of many nice properties of cogency maximization is that when Aristotelian logic applies, it yields logical conclusions (see [Hecht-Nielsen 2005, 2006b] for details).
One of the reasons confabulation theory was probably not discovered long ago is that cogency maximization is NOT consistent with so-called 'Bayesian mathematics' (which essentially calls for choosing that conclusion which has the highest probability of being true, given the assumption that the assumed facts are true). The Bayesian mathematics juggernaut (a system of beliefs, not indisputable facts) has dominated many areas of information processing research for decades. This dominance probably strongly deterred researchers from considering other possibilities. For details of confabulation mathematics see (Hecht-Nielsen 2006b).
Confabulation is the third of the four key elements of confabulation theory.
The ''Conclusion-Action Principle'': The Origin of Behavior
Humans and other animals often launch many behaviors (thought processes and/or movement processes) every second they are awake. Most of these are microbehaviors (small amendments to ongoing behaviors); but typically many times per hour, major new behaviors are launched, predicated on newly emerged events. Beyond reflexes (e.g., knee jerk), autonomic reactions (e.g., digestion), and cerebellar sustainment of previously launched behaviors (walking down the street, cruising down a freeway lane), no understanding of how and why new behaviors originate currently exists.
Confabulation theory proposes the conclusion-action principle ( Figure 7); which states that every time a confabulation operation on a thalamocortical module reaches a conclusion, an associated set of action commands are launched from layer V neurons of the module (which proceed via axons of these neurons to subcortical brain nuclei). Often, these action commands lead to the initiation of behaviors (either immediately or after further evaluation). All non-reflexive and non-autonomic behaviors begin in this manner.
In Figure 7, a thalamocortical module (illustrated, in consonance with Figure 6, as an abstract 'oval' structure containing a list of the module's symbols) has successfully completed a confabulation operation (under control of its externally supplied thought command signal) and reached a conclusion (symbol number 9 as in Figure 6). Whenever a module completes a confabulation and reaches a conclusion it immediately causes a set of action command outputs to be launched. The specific action command outputs that are launched are those which have been previously associated from this specific conclusion symbol via a completely separate, subcortically managed, skill learning process.
Action commands can be regarded as suggested behaviors which subcortical structures either immediately execute, consider further for future execution, or (e.g., if the suggested behavior is not consistent with past successful reductions in currently-elevated goal or drive states) discard.
The associations between each symbol of a module and the specific action commands which are to be issued when that symbol wins a confabulation competition are termed skill knowledge. Skill knowledge is formed via selective strengthening of special synapses within cerebral cortex; but the involved skill learning process is controlled by subcortical structures; principally the basal ganglia.
Skill knowledge has a different neuroanatomical location, and very different properties, in comparison with cognitive knowledge links. For example, unlike a cognitive knowledge link (which, if solidified over the 100 hours or so following the initial symbol pair co-occurrence, is extremely durable, often lasting years even if unused), skill knowledge is often fragile and short-lived (this is essential for rehearsal learning of skills, wherein later, more competent, skill knowledge needs to 'supersede' and supplant earlier, less perfected, skill knowledge).
Behavioral triggering, skill knowledge, and skill learning are not parts of thinking (they come into play only after thinking has completed its job of reaching conclusions). Of course, thinking itself is utterly dependent upon the behavioral triggering thought command sequences which control the 'contractions' of the thalamocortical modules involved in a particular thought process.
Thought command sequences are learned, stored, and recalled in exactly the same manner as the movement command sequences (actually, postural goal sequences) employed in movement. So, via the conclusion-action principle, thought begets movement and thought (both termed actions) in an endless action-thought-action-thought-action-thought- sequence during wakefulness (thereby exorcising the need for a tiny wizard homunculus in the brain, hiding behind a curtain, pulling the control levers of the brain and body).
Actions have two aspects: the symbols which trigger them and the specific action commands which are associated from those symbols. Actions are typically stored using cognitive knowledge links arranged in nested spatiotemporal symbol hierarchies. Once learned, these cognitive action knowledge links are extremely durable.
However, the skill knowledge that connects each symbol to a set of action command outputs is fragile and subject to rapid loss without frequent practice of the action.
Thus, while the cognitive knowledge associated with riding a bicycle is permanent, the skill mappings from these action symbols to the requisite action command neurons are quickly lost – making it necessary for a person riding a bicycle after a long hiatus to be very careful at first.
The conclusion - action principle is the fourth and last of the key elements of confabulation theory.
Some Predictions of Confabulation Theory
Besides the specific functions described in the previous four sections, confabulation theory makes a number of neuroscience predictions that should be testable soon. Examples of these are presented in this section.
The requirement that knowledge links be established instantly between arbitrary pairs of symbols (for ordered pairs of symbols within modules genetically provided with a knowledge base) is very demanding. Initial analysis [Hecht-Nielsen 2006b] suggests that this will only be possible if each knowledge link is implemented via a two-stage synfire (Abeles 1991) (or polysynchrony [Izhikevich 2006, 2007]) chain. This analysis suggests that for this arrangement to work (i.e., for the required links to be available instantly with high probability), roughly 99% of all cortical synapses available for use in implementing knowledge links must be vestigial and unused. This tracks recent findings that the vast majority of cortical synapses are small, weak, unreliable, and of short life span. Confabulation theory also predicts that the small fraction of these available cortical synapses actually used for implementing knowledge links are strong, reliable, and essentially permanent (Hecht-Nielsen 2006a, 2006c).
Another prediction of confabulation theory is that the total number of knowledge links possessed by the average adult human is huge: often numbering in the billions. Some humans of the highest intellectual capacity and achievement might possess over 100 billion knowledge links. Since childhood only lasts about 7,670 days (birth to 21 years of age), a 21-year-old human with 2 billion knowledge links has accumulated them at the average rate of 260,748 knowledge links per day. Yet school children often return home after school and report that they "learned nothing" in school that day.
Current perceived cognitive knowledge learning rates are typically vastly below the rates predicted by confabulation theory. These vast underestimates permeate almost all disciplines concerned with human performance and its interpretation (philosophy, neuroscience, psychology, neurology, psychiatry, education, human factors, etc.). Confabulation theory may require reevaluations of the fundamentals of all of these fields. Perhaps the pedestals upon which human statues rest will need to be raised, as well.
Since cognitive knowledge is essentially permanent, it must be carefully evaluated and considered before being finally committed to storage. Erroneous knowledge cannot be erased and the mechanisms for working around it are often cumbersome and time consuming to set up. This applies to all of the new temporary knowledge links that are formed during the day. Every time two symbols that can be linked co-occur for the first time, one (unidirectional), or two (two links in opposite directions), temporary knowledge link(s) between them is(are) instantly formed. The axons linking the involved symbol neurons in layer III of the pair of modules involved must send axonal outputs to entorhinal cortex and hippocampus (these axons are known to exist) so that this new symbol pair can be ‘logged in’ to the memory consolidation system that, over the following 100 hours or so, carries out the evaluation process for this new knowledge link. Later (e.g., during the next few sleep periods), the level of drive and/or goal reduction that has become associated with this new symbol pair (this association is implemented by hippocampus and its associated entorhinal cortex – often after a considerable delay following the symbol pair’s first co-occurrence) is then used to decide if this knowledge is significant to the individual. In this way, the “Id” (e.g., the amygdala) ultimately controls what is learned.
If a new knowledge link is deemed worthy of retention, then the involved link synapses (those from the link’s transponder neurons to neurons representing the link's target symbol [Hecht-Nielsen, 2006a, 2006c]) are gradually made permanent (this probably takes multiple successful evaluations).
Scientific evaluation of confabulation theory is beginning. The rapidly improving spatial and temporal resolution of neuron activity monitoring techniques (fMRI, MEG, EEG, optical neuron state monitoring, etc.) will soon allow definitive testing of the theory to commence.
Of course, any detailed concrete theory of the mechanism of thought can also be tested using computer simulations of the involved neuronal tissue information processing. Results should demonstrate "intelligence"; and they do (Hecht-Nielsen 2007).
- Abeles M. (1991) Corticonics. Cambridge University Press.
- Amari, S.-I. (1974) A method of statistical neurodynamics. Biological Cybernetics 14:201-215.
- Amit, D. (1989) Modeling Brain Function: The World of Attractor Networks. Cambridge University Press.
- Anderson J.A., Silverstein J.W., Ritz S.A., Jones R.S. (1977) Distinctive features, categorical perception, and probability learning: Some applications of a neural model. Psychological Review 84:413-451.
- Aristotle (c. 350 B.C.) Collected Works. [English Translation: Barnes J. [Ed] (1984) Complete Works of Aristotle: The Revised Oxford Translation (in two volumes). Princeton University Press.]
- Aziz-Zadeh L., Wilson S.M., Rizzolatti G., Iacoboni M. (2006) Congruent embodied representations for visually presented actions and linguistic phrases describing actions. Current Biology 16:1818-1823.
- Bain A. (1864) The Senses and The Intellect. Longman et al: London.
- Duda R.O., Hart P.E., Stork D.G. (2000) Pattern Classification and Scene Analysis, 2nd ed. Wiley-Interscience: New York.
- Haines K., Hecht-Nielsen R. (1988) A BAM with increased information storage capacity. Proceedings of the 1988 International Conference on Neural Networks. IEEE Press: Piscataway NJ, Volume I:181-190.
- Hebb D. (1949) The Organization of Behavior. Wiley: New York.
- Hecht-Nielsen R. (2005) Cogent confabulation. Neural Networks 18:111-115.
- Hecht-Nielsen R. (2006a) Mechanization of Cognition. in: Bar-Cohen Y. [Ed] Biomimetics. CRC Press: Boca Raton FL, 57–128.
- Hecht-Nielsen R. (2006b) The Mathematics of Thought. in: Yen G.Y. & Fogel D.B. [Eds] Computational Intelligence. IEEE Computational Intelligence Society Press: Piscataway NJ 1–16.
- Hecht-Nielsen R. (2006c) The mechanism of thought. Proceedings of the World Congress on Computational Intelligence (CD). Vancouver BC, CANADA. 16-21 July IEEE Press: Piscataway NJ.
- Hecht-Nielsen R. (2007) Confabulation Theory. Springer-Verlag: Heidelberg.
- Hopfield J.J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings National Academy Science 79:2554–2558.
- Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT Press.
- Izhikevich E.M. (2006) Polychronization: Computation with spikes. Neural Computation 18:245-282.
- James W. (1890) The Principles of Psychology. Henry Holt and Company: New York.
- Karten H.J. (1991) Homology and evolutionary origins of the ‘Neocortex’. Brain, Behavior, and Evolution 38:264–272.
- Kosko B. (1988) Bidirectional associative memories. IEEE Transactions on Systems, Man and Cybernetics 18:49–60.
- von der Malsburg C. (1981) The Correlation Theory of Brain Function. Max Planck Institute for Biophysical Chemistry Internal Report 81-2, Göttingen, Germany.
- Martin K.A.C. (1994) A brief history of the “feature detector”. Cerebral Cortex 4:1-7.
- Mountcastle V.B. (1997) The columnar organization of the neocortex. Brain 120:701-722.
- Sagi B., Nemat-Nasser S.C., Kerr R., Hayek R., Downing C., Hecht-Nielsen R. (2001) A biologically motivated solution to the cocktail party problem. Neural Computation 13:1575-1602.
- Sommer F.T., Palm G. (1999) Improved bidirectional retrieval of sparse patterns stored by Hebbian learning. Neural Networks 12:281–297.
- Willshaw D.J., Buneman O.P., Longuet-Higgins H.C. (1969) Non-holographic associative memory. Nature 222:960-962.
- Xie X., Hahnloser R., Seung H.S. (2001) Learning winner-take-all competition between groups of neurons in lateral inhibitory networks. in: Proceedings of NIPS 2001, Neural Information Processing Systems: Natural and Synthetic. MIT Press, 350-356.
- Chris Eliasmith (2007) Attractor network. Scholarpedia, 2(10):1380.
- Peter Redgrave (2007) Basal ganglia. Scholarpedia, 2(6):1825.
- Valentino Braitenberg (2007) Brain. Scholarpedia, 2(11):2918.
- Paul L. Nunez and Ramesh Srinivasan (2007) Electroencephalogram. Scholarpedia, 2(2):1348.
- Seiji Ogawa and Yul-Wan Sung (2007) Functional magnetic resonance imaging. Scholarpedia, 2(10):3105.
- Mark Aronoff (2007) Language. Scholarpedia, 2(5):3175.
- Philip Holmes and Eric T. Shea-Brown (2006) Stability. Scholarpedia, 1(10):1838.
- S. Murray Sherman (2006) Thalamus. Scholarpedia, 1(9):1583.