Hebbian theory
Hebbian theory is a
Let us assume that the persistence or repetition of a reverberatory activity (or "trace") tends to induce lasting cellular changes that add to its stability. ... When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.[1]
The theory is often summarized as "Cells that fire together wire together."[2] However, Hebb emphasized that cell A needs to "take part in firing" cell B, and such causality can occur only if cell A fires just before, not at the same time as, cell B. This aspect of causation in Hebb's work foreshadowed what is now known about spike-timing-dependent plasticity, which requires temporal precedence.[3]
The theory attempts to explain
Hebbian engrams and cell assembly theory
Hebbian theory concerns how neurons might connect themselves to become engrams. Hebb's theories on the form and function of cell assemblies can be understood from the following:[1]: 70
The general idea is an old one, that any two cells or systems of cells that are repeatedly active at the same time will tend to become 'associated' so that activity in one facilitates activity in the other.
Hebb also wrote:[1]: 63
When one cell repeatedly assists in firing another, the axon of the first cell develops synaptic knobs (or enlarges them if they already exist) in contact with the soma of the second cell.
[D. Alan Allport] posits additional ideas regarding cell assembly theory and its role in forming engrams, along the lines of the concept of auto-association, described as follows:
If the inputs to a system cause the same pattern of activity to occur repeatedly, the set of active elements constituting that pattern will become increasingly strongly inter-associated. That is, each element will tend to turn on every other element and (with negative weights) to turn off the elements that do not form part of the pattern. To put it another way, the pattern as a whole will become 'auto-associated'. We may call a learned (auto-associated) pattern an engram.[4]: 44
Work in the laboratory of
Principles
From the point of view of
The following is a formulaic description of Hebbian learning: (many other descriptions are possible)
where is the weight of the connection from neuron to neuron and the input for neuron . Note that this is pattern learning (weights updated after every training example). In a Hopfield network, connections are set to zero if (no reflexive connections allowed). With binary neurons (activations either 0 or 1), connections would be set to 1 if the connected neurons have the same activation for a pattern.
When several training patterns are used the expression becomes an average of individual ones:
where is the weight of the connection from neuron to neuron , is the number of training patterns and the -th input for neuron . This is learning by epoch (weights updated after all the training examples are presented), being last term applicable to both discrete and continuous training sets. Again, in a Hopfield network, connections are set to zero if (no reflexive connections).
A variation of Hebbian learning that takes into account phenomena such as blocking and many other neural learning phenomena is the mathematical model of Harry Klopf.[6] Klopf's model reproduces a great many biological phenomena, and is also simple to implement.
Relationship to unsupervised learning, stability, and generalization
Because of the simple nature of Hebbian learning, based only on the coincidence of pre- and post-synaptic activity, it may not be intuitively clear why this form of plasticity leads to meaningful learning. However, it can be shown that Hebbian plasticity does pick up the statistical properties of the input in a way that can be categorized as unsupervised learning.
This can be mathematically shown in a simplified example. Let us work under the simplifying assumption of a single rate-based neuron of rate , whose inputs have rates . The response of the neuron is usually described as a linear combination of its input, , followed by a
As defined in the previous sections, Hebbian plasticity describes the evolution in time of the synaptic weight :
Assuming, for simplicity, an identity response function , we can write
or in matrix form:
As in the previous chapter, if training by epoch is done an average over discrete or continuous (time) training set of can be done:
where are arbitrary constants, are the eigenvectors of and their corresponding eigen values. Since a correlation matrix is always a
Regardless, even for the unstable solution above, one can see that, when sufficient time has passed, one of the terms dominates over the others, and
where is the largest eigenvalue of . At this time, the postsynaptic neuron performs the following operation:
Because, again, is the eigenvector corresponding to the largest eigenvalue of the correlation matrix between the s, this corresponds exactly to computing the first
This mechanism can be extended to performing a full PCA (principal component analysis) of the input by adding further postsynaptic neurons, provided the postsynaptic neurons are prevented from all picking up the same principal component, for example by adding lateral inhibition in the postsynaptic layer. We have thus connected Hebbian learning to PCA, which is an elementary form of unsupervised learning, in the sense that the network can pick up useful statistical aspects of the input, and "describe" them in a distilled way in its output.[9]
Limitations
Despite the common use of Hebbian models for long-term potentiation, Hebb's principle does not cover all forms of synaptic long-term plasticity. Hebb did not postulate any rules for inhibitory synapses, nor did he make predictions for anti-causal spike sequences (presynaptic neuron fires after the postsynaptic neuron). Synaptic modification may not simply occur only between activated neurons A and B, but at neighboring synapses as well.[10] All forms of hetero synaptic and homeostatic plasticity are therefore considered non-Hebbian. An example is retrograde signaling to presynaptic terminals.[11] The compound most commonly identified as fulfilling this retrograde transmitter role is nitric oxide, which, due to its high solubility and diffusivity, often exerts effects on nearby neurons.[12] This type of diffuse synaptic modification, known as volume learning, is not included in the traditional Hebbian model.[13]
Hebbian learning account of mirror neurons
Hebbian learning and spike-timing-dependent plasticity have been used in an influential theory of how mirror neurons emerge.[14][15] Mirror neurons are neurons that fire both when an individual performs an action and when the individual sees[16] or hears[17] another perform a similar action. The discovery of these neurons has been very influential in explaining how individuals make sense of the actions of others, by showing that, when a person perceives the actions of others, the person activates the motor programs which they would use to perform similar actions. The activation of these motor programs then adds information to the perception and helps predict what the person will do next based on the perceiver's own motor program. A challenge has been to explain how individuals come to have neurons that respond both while performing an action and while hearing or seeing another perform similar actions.
Christian Keysers and David Perrett suggested that as an individual performs a particular action, the individual will see, hear, and feel the performing of the action. These re-afferent sensory signals will trigger activity in neurons responding to the sight, sound, and feel of the action. Because the activity of these sensory neurons will consistently overlap in time with those of the motor neurons that caused the action, Hebbian learning predicts that the synapses connecting neurons responding to the sight, sound, and feel of an action and those of the neurons triggering the action should be potentiated. The same is true while people look at themselves in the mirror, hear themselves babble, or are imitated by others. After repeated experience of this re-afference, the synapses connecting the sensory and motor representations of an action are so strong that the motor neurons start firing to the sound or the vision of the action, and a mirror neuron is created.
Evidence for that perspective comes from many experiments that show that motor programs can be triggered by novel auditory or visual stimuli after repeated pairing of the stimulus with the execution of the motor program (for a review of the evidence, see Giudice et al., 2009[18]). For instance, people who have never played the piano do not activate brain regions involved in playing the piano when listening to piano music. Five hours of piano lessons, in which the participant is exposed to the sound of the piano each time they press a key is proven sufficient to trigger activity in motor regions of the brain upon listening to piano music when heard at a later time.[19] Consistent with the fact that spike-timing-dependent plasticity occurs only if the presynaptic neuron's firing predicts the post-synaptic neuron's firing,[20] the link between sensory stimuli and motor programs also only seem to be potentiated if the stimulus is contingent on the motor program.
See also
References
- ^ a b c d Hebb, D.O. (1949). The Organization of Behavior. New York: Wiley & Sons.
- PMID 1372754.
- PMID 18275283.
- ISBN 978-0-443-03039-0.
- PMID 10753798.
- ^ Klopf, A. H. (1972). Brain function and adaptive systems—A heterostatic theory. Technical Report AFCRL-72-0164, Air Force Cambridge Research Laboratories, Bedford, MA.
- ^ Euliano, Neil R. (1999-12-21). "Neural and Adaptive Systems: Fundamentals Through Simulations" (PDF). Wiley. Archived from the original (PDF) on 2015-12-25. Retrieved 2016-03-16.
- ^ Shouval, Harel (2005-01-03). "The Physics of the Brain". The Synaptic basis for Learning and Memory: A theoretical approach. The University of Texas Health Science Center at Houston. Archived from the original on 2007-06-10. Retrieved 2007-11-14.
- )
- PMID 8197441.
- S2CID 11604896.
- ^ López, P; C.P. Araujo (2009). "A computational study of the diffuse neighbourhoods in biological and artificial neural networks" (PDF). International Joint Conference on Computational Intelligence.
- S2CID 2325474.
- S2CID 8039741.
- ^ Keysers, C. (2011). The Empathic Brain.
- PMID 8800951.
- S2CID 7704309.
- PMID 19143807.
- PMID 17215391.
- S2CID 33130204.
Further reading
- Hebb, D.O. (1961). "Distinctive features of learning in the higher animal". In J. F. Delafresnaye (ed.). Brain Mechanisms and Learning. London: Oxford University Press.
- Hebb, D. O. (1940). "Human Behavior After Extensive Bilateral Removal from the Frontal Lobes". Archives of Neurology and Psychiatry. 44 (2): 421–438. .
- Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford: Oxford University Press. ISBN 978-0-19-853849-3.
- Paulsen, O.; Sejnowski, T. J. (2000). "Natural patterns of activity and long-term synaptic plasticity". Current Opinion in Neurobiology. 10 (2): 172–179. PMID 10753798.
External links
- Overview Archived 2017-05-02 at the Wayback Machine
- Hebbian Learning tutorial (Part 1: Novelty Filtering, Part 2: PCA)