DOI 10.1007/s11063-006-9029-2Neural Processing Letters (2007) 25:31–47 © Springer 2006

Neuronal spatial learning

DORIAN AUR� and MANDAR S. JOGDepartment of Clinical Neurological Sciences, Movement Disorders Program, London, ON,Canada e-mail: daur2@uwo.ca

Abstract. Neurons are electrically active structures determined by the evolution ofion-specific pumps and channels that allow the transfer of charges under the influence ofelectric fields and concentration gradients. Extensive studies of spike timing of neurons andthe relationship to learning exist. However, the properties of spatial activations during actionpotential in the context of learning have to our knowledge not been consistently studied. Weexamined spatial propagation of electrical signal for many consecutive spikes using recordedinformation from tetrodes in freely behaving rats before and during rewarded T-maze learn-ing tasks. Analyzing spatial spike propagation in expert medium spiny neurons with thecharge movement model we show that electrical flow has directionality which becomes orga-nized with behavioral learning. This implies that neurons within a network may behaveas “weak learners” attending to preferred spatial directions in the probably approximatelycorrect sense. Importantly, the organization of spatial electrical activity within the neuro-nal network could be interpreted as representing a change in spatial activation of neuronalensemble termed “strong learning.” Together, the subtle yet critical modulations of electricalflow directivity during weak and strong learning represent the dynamics of what happens inthe neuronal network during acquisition of a behavioral task.

Key words. action potential, computation, information theory, machine learning, tetroderecordings, weak learning

1. Introduction

The electrical properties of neurons are well recognized as their ability to generateaction potentials (APs). These APs depend on the evolution of ion-specific pumpsand channels that allow the transfer of charges under the influence of electricfields and concentration gradients that causes the generation of a voltage differ-ence within the membrane. Electrophysiological recordings in the brain show thatthis voltage difference is measurable in the extracellular milieu as a series of APs,termed the spike train.

The presence of the so called expert neurons in the striatum has been advancedfor some time [2, 24, 27]. Their temporal spiking activity was revealed recently dur-ing T-maze experiments [7]. Tremendous amount of effort has been concentratedon understanding the patterns of these APs on a temporal basis either in single ormultiple neuronal recordings [15, 17, 23, 24, 32, 41]. However, the voltage changein the extracellular space during AP can be seen as an effect of spatial charge flow

� Author for correspondence.

32 DORIAN AUR AND MANDAR S. JOG

in the neuron [4]. Therefore, the recorded signals from each AP contain informa-tion about electrical events and propagation of electrical phenomena within theneuron and outside the neuron within certain vicinity.

During the AP, a massive charge flux occurs and results in electrical flow withinthe neuron. Any extracellular recording device will see an induced voltage in it,which is a direct result of the electrical phenomenon occurring within the neu-ron and its surroundings. This surge of voltage that occurs with an action poten-tial can have a substantial impact on the sensitivity of the membrane, especiallywithin the dendrites which receive the bulk of the incoming information. Quirkand Wilson, demonstrated that the action potential amplitude of neurons variessystematically depending on behavioral time scales [36] and later they showed thatAP attenuation during bursts is NMDA-dependent [37]. The experiments done byOesch et al., [33] in rabbit retina shed a new light on this directed electrophysio-logical communication in neuron. Using patch-clamp recordings and two-photoncalcium imaging they demonstrated that dendrites are selective to AP directivity.They showed that somatic spike generation is sharpened by directional tuning ofdendritic spikes, i.e., the direction from which dendritic spikes are received. It istherefore likely that a critical reciprocal relationship exists between activated den-dritic spikes and the generated AP that provides remarkable tuning within theneuron.

Electrical mechanisms of communication are quite similar in different brainareas. At chemical synapses, electrical activity in a presynaptic neuron causes therelease of a chemical messenger and implicitly elicits changes in the electrical activ-ity on the postsynaptic neuron. Electrical synapses, for example gap junctions arepresent almost everywhere: neocortex, [8, 13], hippocampus [22], thalamic reticularnucleus [31]. Recently, a mechanism that involves ephaptic communication withinchemical synapses has also been discovered [9]. In striatal neurons in addition tothe electrico-chemical inputs, electrical couplings by gap junctions are seen on theirdendrites [28, 30]. The coupling allows a rapid propagation of voltage changes [14].This connectivity has been used to explain some electrophysiological behavior ofthe striatal medium spiny neurons [11].

This mechanism of AP generation offers a deeper physiological relevance forobserved changes within the directivity of electrical flow within the charge move-ment model during several spikes of the same neuron.

The role of the dendritic tree was minimized by early work of Ramon andCajal that assumed that AP travels only along axons. For example, the role of fastprepotentials was still unclear until the simultaneous application of optical tech-niques and direct dendritic measurements [25, 35]. Similarly, the active back propa-gation of somatic action potentials into dendrites is highly regulated and mediatedby voltage-gated Na+ and/or Ca2+ channels [19, 26].

Dendrites and soma are equipped with several voltage-gated ion channels thatgreatly enrich the observed charge flow. Several studies have pointed out thatgated ion channels interact with plastic changes in the synaptic strength to

NEURONAL SPATIAL LEARNING 33

influence behavior [34]. Similarly, synaptic activity may lead to changes in ionchannel function in dendrites. Subtle manipulations of the distribution of eithersodium or potassium channels in the dendrites have several effects influencing theinduction of synaptic plasticity [16]. These changes are reflected during each APin charge densities within the cell and their outward flux and evidenced by direc-tivity changes provided by charge movement model (CMM). Spatial and temporalpatterns measured in extracellular space reveal much about the location and tim-ing of currents in the cell [21]. Therefore, the propagation of charge fluxes withineach AP can be analyzed using signals recorded by tetrodes in extracellular space.Further, using computational techniques one can reveal information about currentsin the cell from the extracellular tetrode recordings.

Our prior work has demonstrated that extracellular recordings can reveal elec-trical processes within the neuron during AP. Second, we have shown that theinduced voltage during AP obtained from extracellular tetrode recordings is areflection of spatial electrical flow mostly within the neuron. Seen as a charge flowmovement, each AP has a resultant which consists of a directivity of electric flow[4]. The directional electric flow may indicate in which direction the dendritic treeis being activated therefore reflecting the spatial activation pattern of the neuron.Such measurements would have been impossible prior to the multichannel tetrodestyle recording techniques developed in the late 1990s.

In the present paper, the calculation of directionality of electric flow withinneurons is based upon the established CMM and addresses several importantissues.

First, we demonstrate that this directional pattern of activation are modulatedover time as training completes and hence reveals that there is a spatial tuning pro-cess within neurons and implicitly in the network as learning progresses.

Second, and most importantly since spatial vector variables can in general notbe completely described by timing scalar component, theoretically this type of cod-ing in space provides a much richer outcome than the time coding paradigm.

2. Methods

We analyzed recordings from the dorsolateral striatum of three Sprague–Dawleyrats. All animals were maintained on feeding restriction not less than 80% of base-line weight. The animals were anesthetized, a burr hole was drilled for the pur-poses of tetrode penetration (for striatum: AP 9.2 mm, DV 5.9 mm, L 3.5 mm)and dura was removed. The headstage drive was lowered such that the cannulaholding the tetrodes just touched the surface of the brain [23,24]. Upon the ratawakening postoperatively, the tetrodes were lowered out of the cannula. Tetrodeswere advanced partially on each day so as to allow the brain to settle. The braintargets were reached by day 3 or 4 operatively. Recordings commenced after thiswas achieved. All procedures were approved by the animal care facilities at theUniversity of Western Ontario, London, ON, Canada.

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Tetrode recordings were obtained with well established methods [23] and datawas captured at an acquisition rate of about 25 KHz per channel so that eachAP recorded had 25 A-D ticks per channel using a Neuralynx@ data acquisitionsystem. The impedance for every channel of the tetrode was similar at between 200and 400 k�. On average, six tetrodes were available for analysis in each animal.Subsequent processing included clustering into putative neurons and de-noising ofthe data [23]. Each tetrode yielded up to three or four well separated and low-noiseunits (Figure 1).

After sorting spikes into putative units, spike assignments to individual unitsneeded to be confirmed to assess whether units were well separated from eachother. Measures of unit isolation quality, Lratio and Isolation Distance (ID), wereused to evaluate the performance of the sorting technique [42].

The spike profiles did not change significantly within a recording session andthus the location of the cells relative to the tetrode can be considered stable. Thereare cases when improper fixing of the head stage allows certain movement. How-ever, this type of drift can be easily seen in waveform amplitudes and revealedduring spike sorting procedure.

The data were collected in a two stage experiment, namely exploratorymovement on the T-maze before learning and during the performance of a T-mazeprocedural learning task. Tetrodes were not moved during this time of data acqui-sition. All animals performed the pre-learning free exploratory movement prior tothe subsequent T-maze learning. The animals were free to explore and no spe-cific task or reward was required. Recordings were carried out for 3 days duringthe free exploratory portion. Data were recorded continuously for periods of time

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of 20 seconds, giving approximately 400 ± 50 spikes for analysis yielding a spikerate of around (17.5±2.5) Hz/neuron/tetrode/day. Three such 20 second periodswere randomly chosen in time for each day. Four hundred sequential spikes wereanalysed serially from approximately each 60 neurons recorded from 18 tetrodesfor the free movement task per day in all animals combined.

Data from the three Sprague–Dawley rats performing a T-maze procedurallearning task were analysed for the effect of learning on the spatial directivity. Fol-lowing the free exploratory movement, animals were trained over a period of 7–10days to make a left or right turn based on an auditory cue [23]. Although datawere recorded during the entire period of task acquisition for the 7–10 days, theanalysis presented here is at the point when the animal had achieved a stable 75%correct turn response for 2 days in a row. Data from 20 ± 4 trials, each lastingapproximately 1 second from after start to turn completion, were analyzed fromthe third day after reaching this behavioral goal. Approximately the same num-ber of spikes (average 400 ± 50) for each of the three animals were analyzed perneuron/tetrode.

All diverse electrical phenomena are reflected in the CCM. The charge flowdescribes electrical propagation of spikes in dendrites, soma axon and externalmilieu. The corresponding estimated directivity has to be seen as a resultant ofthese electric effects during each AP. Several electrical processes that interfere havebeen presented above. The fact that there is a flow of charges in the milieu has ofcourse its value but this phenomenon does not minimize the importance of otherelectrical mechanisms within neuron. CMM approach offers a global perceptionover spatial electrical activity during AP.

The computational details of the directivity calculations for each spike recordedand the resulting charge flow were then performed using already published tech-niques [4]. Briefly, the following steps were utilized. Using the triangulationmethod and the point charge model, the trajectory of charge flow was calculatedfor each spike. Based on obtained trajectory, estimation of spike directivity in “tet-rode space” was achieved. The trajectory in “tetrode space” for every spike wasanalyzed using singular value decomposition (SVD) in order to find the best lin-ear approximation of the spike direction [43]. The tetrode space acts as an “imagein mirror” of the real 3D space.

A model of electrical spatial distribution is obtained by utilizing the largest sin-gular value and the corresponding right singular vector that represents directioncosines of the best linear approximation in tetrode space [4]. This SVD techniquegenerates three cosines (v1, v2, v3) for the largest singular value. Higher singularvalues of the decomposition indicate dimensions with higher energy within thedata.

At this stage, the probability density function was estimated for each of the threecosines, separately. This calculation was performed for each of the 20-second timeperiods for every tetrode in all animals during free exploration and for all trialsper tetrode for each neuron in the behavioral period described above. This level of

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spatial randomness within the spike train directivity was quantified by analyzingthe values of cosine angles using Shannon information theory. Shannon introducedthe notion of the entropy for a random discrete variable x, as the average of thequantity of information brought by it. Shannon information entropy is a functionof the probability distribution p [41]:

HS(p)=−∑

p(xi) log p(xi). (1)

Shannon entropy HS is a measure of uncertainty about the outcome of the randomvariables and the value HS does not depend on the state values x1,x2, . . . ,xn.

Estimations of probability density functions and entropies [10] were imple-mented using a PC computer (Pentium 4, 2.8 GHz, 512 MB RAM) and Mat-lab - MathWorks, Inc. All routines were custom developed or were already imple-mented within Matlab. In order to assess the quality of entropy estimation usingthe histogram method we have conducted a series of empirical studies on uniform,Gaussian and Poisson distributions. The histogram construction was made usingdirectly the statistics toolbox from Matlab.

The computed entropy value is considered, for a given bin size value, to bethe “relatively true” value of entropy. By maintaining a constant bin size duringentropy estimations, the error in entropy estimations remain bounded under 0.1bits for Gaussian, Poisson and uniform distributions for bin sizes ranging from 25to 60. These results are obtained even when the data size was doubled (from 200to 400), even though the variation in data size from experimental recordings usedin this paper remains between 400 ± 50. In the paper, the bin size used for allcomputations is 30.

Maintaining a constant bin size in computations provides tiny variability in theentropy estimations when the data size varies from 200 to 400 across various distri-butions (Figure 1). Since the variation in estimated entropy after learning is morethan 10 times this error the presented technique provides a robust estimate ofthe entropy variations over different distributions. Figure 1 shows that estimationsare consistently robust in case of transitions between several different distributionswith the variation in data width. The statistics for Gaussian, Poisson and uniformdistribution is exceedingly different while the errors show a consistent lower boundand this fact leads us to believe that these estimations are consistently free ofdistributional assumptions if the bin size is maintained constant.

3. Results

These expert neurons show an increase in spiking activity visibly correlatedwith behavioral events (tone cue, turning on T-maze, etc.) The percentage oftask-responsive units increased to a maximum of 85% units corresponding to aχ2-value (p<0.001).The number of units that respond to more than one task eventrose from 40 to 60%. Initially 27% of task-related units responded during turns(p <0.001) while by the end of training only 14% (p <0.001) responded.

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3.1. spatial propagation

Each AP provides four waveforms measured by the channels of a tetrode (Fig-ure 2). As discussed above, trajectories were obtained for each individual spike inthe “tetrode space.” Figure 3 demonstrates the trajectory (in magenta) and the esti-mated directivity (bold blue line) for a single representative spike. Figure 4 showsthe same neuron with two consecutive spikes, each spike showing the trajectoryand the estimated directivity of charge flow resulting from the spike. By analyz-ing SVD [4], during each spike about 70–80% from the AP energy has a preferreddirection for propagation (blue bold line Figure 2).

In order to see the predominance of the orientation of directivity in tetrodespace, a principal component analysis (PCA) was performed on the directioncosines of all spikes from individual neurons. Analyzing the distribution of direc-tion cosines of the best linear approximation using PCA for several spikes fromevery neuron, we found specific spatial directionality for this spike propagationduring the entire time period (20 seconds for this analysis). The plot of the PCAcomponents for approximately 400 spikes for one of the analyzed neurons is rep-resented in Figure 5. In this plot, high density in clusters of the PCA compo-nents can be seen in two locations in PCA space represented in red and blue color.This indicates a predominance of the directivity of charge flow during spiking inneurons.

3.2. calculation of probability density function

The PCA is carried out on selected cosine angles of directivity for all spikes ineach neuron in free exploration and during behavior. This generates the PCAdistributions, a representation of which is shown in Figure 5 with two clusters.

38 DORIAN AUR AND MANDAR S. JOG

Figure 3. Spike trajectory – (magenta curve) and estimated directivity – (bold blue line) duringone selected spike in free exploration. Each division is approximately 20 µ. For display purposesapproximately 60 µ of charge movement is shown.

Figure 4. An example of “bottom up” and “top-down” computed directivity for a neuron during twospikes in free exploration.

Subsequently, the probability density function is estimated for each cosine anglev1, v2, v3, separately within each of clusters. This is done in order to understandthe randomness or lack thereof of the distributions of the cosine angles. This anal-ysis is carried out on computed directivity for each and every neuron both beforelearning (free exploration) and after the learning stage is completed. The analysisof spike directivity before and after learning in the selected neuron reveals sub-stantial changes in the probability density function of cosine angles. The record-ings used for this analysis have been selected for the same neuron prior to andafter rewarded learning on the T-maze task. Only the v3 cosine angle is shown inFigures 6 and 7. The two clusters are obtained similarly to those from Figure 5.

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Figure 5. Principal component representations of selected direction cosines of the best linear approxima-tion for about 400 spikes from a single neuron during free exploration.

The blue color represents the probability density function (pdf) for the firstcluster and the red color the second cluster. A clear difference between pdf shapesfor both clustered spikes is visible in Figures 6 and 7. The two graphs in Figure 6(free exploration) show a higher level of randomness than those in Figure 7 (afterlearning). This difference in randomness can be quantified using Shannon informa-tion entropy that has almost double the value before learning than after T-mazelearning. In the presented pdf examples before T-maze learning the mean estimatedinformation entropy for v3cosine angle is HS = 4.2 ± 0.1 bits, while after learningthe information entropy decreases substantially around the mean of HS =2.7±0.1bits for about the same number of points in the data. This important decrease inthe Shannon information entropy although visible in the shape of pdf reflects the

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Figure 6. An example of the probability density of v3 cosine angle in selected expert neuron. Thespiking activity was recorded before T-maze learning. (a) The probability density of v3 cosine angle ina neuron for the first cluster from Figure 5 in blue color. (b) The probability density of v3 cosine anglein a neuron for the first cluster from Figure 5 in red color.

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Figure 7. The probability density function (pdf) for the v3 cosine angle in selected expert neuron afterthe animal had achieved a stable 75% correct turn response. The neuron performs better than randomin choosing spiking directivity. (a) An example of pdf for the v3 cosine angle after learning for the cor-responding cluster in blue. (b) An example of pdf for the v3 cosine angle after when the animal hadacieved a stable 75% correct turn response cluster in red.

random nature of spiking directivity before learning and substantial organizationin “charge flow” after learning.

Global and local maxima are computed next for the probability densityfunction for each cosine angle. In the free exploration phase, the probability den-sity function shapes for every cosine angles v1, v2, v3 yields predominantly threeglobal maxima and less visible local maxima. The directivity for the correspond-ing cosine angles of the three global maxima in pdf is plotted for both clustersin red and in blue color (Figure 8(a)). A similar analysis for after T-maze learn-ing shows in pdf not only three global maxima for each cosine angle but numer-ous substantial local maxima. Their corresponding directivity in tetrode space isplotted in Figure 8(b).

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Figure 8. Example of spatial directivity in tetrode space before and after the animal had achieved astable 75% correct turn response. (a) An example of directivity in neuron before training. The directiv-ity was computed for the global maximum. (b) Example of spatial directivity for one neuron after train-ing. Directivity was computed for the global and visible local maxima values detected in the probabilitydensity function.

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Figure 9. Spatial directions of all spikes between tone and turn starts for several trials during a session.Direction for spikes during left turn is represented by yellow and blue arrows. Spikes during right turnare represented in red and magenta arrows.

This organization of spike directivity during T-maze behavioral task displayssmall changes in directivity associated to external cues and behavioral data. Dur-ing a session spikes between signal tone and turn starts are merged and plottedin a single 3D image. Rotating this image, one may observe that there is a clearseparation for spikes associated to left turn and spikes that define right turn onT-maze. In Figure 9 the plotted upward red and yellow arrows are well separated.Selecting the arm to go on is based on the received cue tone.

4. Discussion

This paper demonstrates that with behavioral learning, the electrical flow withinspikes becomes organized. Three things are important to note here. First, theexistence of directionality of charge flow is a new observation and not an obvi-ous extension of the changes demonstrated before, in the spike timing approach.Second, to our knowledge, modulation of directionality of charge flow with behav-ioral learning has never been shown before. This is an important, stand aloneobservation. Third, this observation brings forward the importance of informa-tional richness within each spike. It is not only that the system information is rep-resented in time but also in space. Such an approach expands the dynamic range ofthe neuronal system substantially. Theoretically, coding in space provides a muchricher outcome than the time coding since spatial vector variables can in generalnot be completely described by a scalar component.

We have recently shown using ICA techniques, that pattern of activations can beevidenced within each spike [6]. These electrical patterns of activation are revealedin that manuscript within spike directivity in a simplified manner. We suppose thation channels are responsible for spatial modulation due to subtle changes that

42 DORIAN AUR AND MANDAR S. JOG

occur during learning in their opening and closing dynamics. Since we have provedthat information is linked to ionic currents [5] a spatial modulation of APs direc-tivity makes sense since information also travels in space [4].

The changes in the time of spiking (perceived as modulation of the firing rate)as well as subtle changes in the directivity of the charge flow with learning areobservable and measurable quantities and indeed correlated with the same behav-ior. In single electrode recordings, the spikes within a neuron do not have the sameshape (width, height). These observations could have been perceived earlier as anindication of changes in ionic flow “directivity.” The modulation of firing rate aftertraining completion was easily observed within single electrode recordings, whiledirectional modulation required the recording device to provide spatial resolutionwhich was not possible to obtain before developing the multi-electrode type ofrecording.

Inspired by biological learning [20] many machine learning algorithms haveproven to be of great practical value. One of the most recent models of learn-ing the “weak learning” theory was introduced by Schapire [39]. A weak learnershould perform at least slightly better than random guessing.

4.1. the neuron a “weak learner”

Changes in spike directivity observed during each spike reveal clearly a spatialcoding phenomenon that reflects in fact the physics of neuronal computationexpressed by ionic flow. Computation is processing of information based on a finiteset of operations and is mathematically defined by inputs, set of rules and outputs.In a simple computation, such as an arithmetic operation, the inputs, the rule andthe output are well defined. However, to obtain the output value in a computereach quantity needs to have a physical correspondence (e.g, current, voltage, etc.).We know that electron fluxes are responsible for fluctuations in voltage or currents.Therefore, the physical essence of classical computation is based on electron move-ment that obeys the laws of physics. Such an approach in this field began in the1960s with Landauer theory regarding information principles and was continuedwith Feynman lectures in computation.

In similitude, in each spike a physical correspondence for inputs, set of rulesand output can be revealed. We understood this issue after we performed severalsimulations on the Hodgkin–Huxley (HH) model while computing mutual infor-mation. Our analysis showed that mutual information between input signal andsodium flux is about two times that between input signal and output spikes duringeach spike [5]. Since mutual information between input stimuli and sodium fluxeshas these high values, then the incoming sodium fluxes can be considered duringeach spike to be the inputs. The set of rules in each AP are described by physicallaws of motion that govern the movement of charges. Finally, the outputs can beconsidered to be in the form of outward K+ fluxes.

NEURONAL SPATIAL LEARNING 43

For simplicity, in the above discussion we only considered the fluxes of sodiumand potassium. However, in each spike several charges of Na+, K+, Cl−, andeventually Ca2+perform complex computation obeying physical laws.

Physical computation within each spike is very efficient. A simple analysisregarding energy consumption per transferred bit shows that spikes are more effi-cient than actual processors. The energy associated with a single ATP molecule isabout 10−19 J. It is estimated that for a single spike, about 10+6 ATP moleculesare required [1]. If one spike transfers on average more than 3 bits of information[5] , that is equivalent to about 10−13 J per spike. In the current processors the dis-sipation per transferred bit is about 10−8 J [38], which is more than ten thousandtimes higher.

The APs are generated by the opening and closing of channels that allowthe flow of several charges. Channels are stochastic in nature and their conduc-tances can also be reflected as a probability of their opening. Since information-processing is based on ionic fluxes the “code” within each spike can be extremelycomplex and our approach is a step forward in understanding this computa-tional mechanism. This modulation of the spatial pattern of activation during APrevealed by changes in measured directivity is named “weak learning.”

4.2. strong learning in the network

Within a network, weak learning can be transformed into an algorithm whichlearns strongly [12,39]. In this context, once the system has generated a techniquefor weak learning, the algorithm is repeated on slightly different distributions ofinstances and generates different weak hypotheses. By combining these hypothe-ses a “strong” accurate hypothesis is generated. This process is termed “stronglearning.” For a correct or incorrect machine prediction, utility measures assign“rewards” or “penalties” representing unsupervised learning [40].

Instead of “hypothesis” as in machine learning, the spike spatial directional-ity can be seen to organize during T-maze trials pointing to certain directions inspace. Using similarity with machine learning theory for

→n1,

→n2, . . .,

→nN a set of

neuronal spike directions on a volume V, the preferred direction for output σp canbe computed by:

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N∑

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directionality at the neuron level gives, for groups of neurons, a strong direction-ality for the energy wave flux decided by the “majority vote” as a resultant. Bysimilitude strong learning effect is supported in the neuronal ensemble by a waveresponse:

�(r, t)=�(σpr +vt), (3)

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where r ∈R3 is the spatial component, v is the wave speed and σp ∈R3 representsthe direction of motion for the wave. A strong learning algorithm corresponds inour model to wave generation that may achieve any level of performance in theprobably approximately correct sense (PAC) [44].

In a dispersive medium, brain wave structure generally varies slowly in space andtime as a result of interference. An important characteristic of the learning algo-rithm is its generalizability and many attempts have been made in combining wellknown unsupervised techniques of learning with boosting procedures before know-ing their biological foundation [3,45].

The examination of spatial electrical flow during learning shows spatial specific-ity of charge flow within APs as demonstrated by our results provided by CMM.Indeed the preferential directional activation seen may be most highly representedwithin the dendritic tree and underestimated by previous theories.

Based on the charge movement model we show that electrical spatial pattern ofactivation within a neuron during the occurrence of each AP is important. Thisoccurrence of directed charge flow in the CMM becomes less random with pre-ferred directions during rewarded T-maze learning tasks. The phenomenon provesthat besides spike time or spike rate adaptation, learning effect is represented ineach neuron as a modulation of the spatial pattern of activation during AP. Thisis named “weak learning.” Groups of neighboring neurons could be expected toreceive similar afferent information, although the exact inputs are undefined tothe external observer. Each neighboring neuron probably receives a slightly differ-ent dataset of information. Over time, activation of each of the neurons withinthis group will have its own preferential directional electric flow for the dataset ithas received. Such an effect may be akin to the phenomenon of “weak learning”within a neuron while the larger scale alterations in the network are equivalent to“strong learning.”

This paper shows clearly that biological learning has a real, measurable electricalspatial representation within each neuron. The strength of this approach, termedspatial learning viewed in the context of machine learning algorithms, is clearlydemonstrated in showing that every neuron is a “weak learner.” Further extrap-olation of this data allows, based on Shapire machine learning mechanism, thedemonstration of ensembles of neurons as showing strong network level learn-ing in the form of electrical “waves.” Having slight randomness and differentialspatially preferred directions at different moments of time allows the biologicalneuron richer plasticity and higher information transfer than the well known com-putational models of neurons [18,29,33]. In the long term, these analyses withcharge movement model reflect spatial organization of the neuronal activity thatoccurs in neuron and network with learning.

This paper shows clearly that biological learning has a real, measurable outcomewithin expert neurons from the striatum. These spatial modulations correlated with

NEURONAL SPATIAL LEARNING 45

neuronal computations generate with learning a spatial organization of electricalflow that is complementary to modulations in firing rate or spiking time.

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