317 
PARTITIONING OF SENSORY DATA BY A COPTICAI, NETWOPK  
Richard Granger, Jos Ambros-Ingerson, Howard Henry, Gary Lynch 
Center for the Neurobiology of Learning and Memory 
University of California 
Irvine, CA, 91717 
SUMMARY 
To process sensory data, sensory brain areas must preserve information about both 
the similarities and differences among learned cues: without the latter, acuity would 
be lost, whereas without the former, degraded versions of a cue would be erroneously 
thought to be distinct cues, and would not be recognized. We have constructed a 
model of piriform cortex incorporating a large number of biophysical, anatomical and 
physiological parameters, such as two-step excitatory firing thresholds, necessary and 
suicient conditions for long-term potentiation (LTP) of synapses, three distinct types 
of inhibitory currents (short IPSPs, long hyperpolarizing currents (LHP) and long cell- 
specific afterhyperpolarization (AHP)), sparse connectivity between bulb and layer-II 
cortex, caudally-fiowing excitatory collateral fibers, nonlinear dendritic summation, etc. 
We have tested the model for its ability to learn similarity- and difference-preserving 
encodings of incoming sensory cues; the biological characteristics of the model enable it 
to produce multiple encodings of each input cue in such a way that different readouts of 
the cell firing activity of the model preserve both similarity and difference-iuiormation. 
In particular, probabilistic quant al transmitter-release properties of pitiform synapses 
give rise to probabilistic postsynaptic voltage levels which, in combination with the ac- 
tivity of local patches of inhibitory interneurons in layer H, differentially select bursting 
rs. single-pulsing layer-II cells. Time-locked firing to the theta rhythm (Larson and 
Lynch, 1986) enables distinct spatial patterns to be read out against a relatively quies- 
cent background firing rate. raining trials using the physiological rules for induction of 
LTP yield stable layer-II-cell spatial firing patterns for learned cues. Multiple simulated 
olfactory input patterns (i.e., those that share many chemical features) will give rise 
to strongly-overlapping bulb firing patterns, activating many shared lateral olfactory 
tract (LOT) axons innervating layer Ia of pitiform cortex, which in turn yields highly 
overlapping layer-H-cell excitatory potentials, enabling this spatial layer-II-cell encod- 
ing to preserve the overlap (similarity) among similar inputs. At the same time, those 
synapses that are enhanced by the learning process cause stronger cell firing, yielding 
strong, cell-specific afterhyperpolarizing (AHP) currents. Local inhibitory interneurons 
effectively select alternate cells to fire once strongly-firing cells have undergone AHP. 
These alternate cells then activate their caudally-fiowing recurrent collaterals, activat- 
ing distinct populations of synapses in caudal layer Ib. Potentiation of these synapses 
in combination with those of still-active LOT axons selectively enhance the response of 
caudal cells that tend to accentuate the differences among even very-similar cues. 
Empirical tests of the computer simulation have shown that, after training, the 
initial spatial layer II cell firing responses to similar cues enhance the similarity of 
the cues, such that the overlap in response is equal to or greater than the overlap in 
Thls research was supported in part by the Otce of Naval lesearch under grants N00014-84-K-0391 
and N00014-87-K-0838 and by the National Science Foundation under grant IST-85-12419. 
 American Institute of Physics 1988 
318 
input cell firing (in the bulb): e.g., two cues that overlap by 65% give rise to response 
patterns that overlap by 80% or more. Reciprocally, later cell firing patterns (after 
AHP), increasingly enhance the differences among even very-similar patterns, so that 
cues with 90% input overlap give rise to output responses that overlap by less than 10%. 
This difference-enhancing response can be measured with respect to its acuity; since 90% 
input overlaps are reduced to near zero response overlaps, it enables the structure to 
distinguish between even very-similar cues. On the other hand, the similarity-enhancing 
response is properly viewed as a partitioning mechanism, mapping quite-distinct input 
cues onto nearly-identical response patterns (or category indicators). We therefore use 
a statistical metric for the information value of categorizations to measure the value of 
partitionings produced by the pitiform simulation network. 
INTRODUCTION 
The three primary dimensions along which network processing models vary are their 
learning rules, their performance rules and their architectural structures. In practice, 
perfornxance rules are much the same across different models, usually being some variant 
of a 'weighted-sum' rule (in which a unit's output is calculated as some function of the 
sum of its inputs multiplied by their 'synaptic' weights). Perfornxance rules are usually 
either 'static' rules (calculating unit outputs and halting) or 'settling' rules (iteratively 
calculating outputs until a convergent solution is reached). Most learning rules are 
either variants of a 'correlation' rule, loosely based on Hebb's (1949) postulate; or a 
'delta' rule, e.g., the perceptron rule (Rosenblatt, 1962), the adaline rule (Widrow and 
Hoff, 1960) or the generalized delta or 'backpropagation' rule (Parker, 1985; Rumelhart 
et al., 1986). Finally, architectures vary by and large with learning rules: e.g., multi- 
layered feedforward nets require a generalized delta rule for convergence; bidirectional 
connections usually imply a variant of a Hebbian or correlation rule, etc. 
Architectures and learning and performance rules are typically arrived at for reasons 
of their convenient computational properties and analytical tractability. These rules 
are sometimes based in part on some results borrowed from neurobiology: e.g., 'units' 
in some network models are intended to correspond loosely to neurons, and 'weights' 
loosely to synapses; the notions of parallelism and distributed processing are based on 
metaphors derived from neural processes. 
An open question is how much of the rest of the rich literature of neurobiological 
results should or could profitably be incorporated into a network model. lrom the 
point of view of constructing mechanisms to perform certain pre-specified computatonal 
functions (e.g., correlation, optimization), there are varying answers to this question. 
However, the goal of understanding brain circuit function introduces a fundamental 
problem: there are no known, pre-specifled functions of any given cortical structures. 
We have constructed and studied a physiologically- and anatomically-accurate model of 
a particular brain structure, olfactory cortex, that is strictly based on biological data, 
with the goal of elucidating the local function of this circuit from its perforinance in a 
bottom-up' fashion. We measure our progress by the accuracy with which the model 
corresponds to known data, and predicts novel physiological results (see, e.g., Lynch 
and Granger, 1988; Lynch et al., 1988). 
Our initial analysis of the circuit reveals a mechanism consisting of a learning rule 
that is notably simple and restricted compared to most network models, a relatively 
novel architecture with some unusual properties, and a performance rule that is ex- 
319 
traordinarily complex compared to typical network-model performance rules. Taken 
together, these rules, derived directly from the known biology of the olfactory cortex, 
generate a coherent mechanism that has interesting computational properties. This pa- 
per describes the learning and performance rules and the architecture of the model; the 
relevant physiology and anatomy underlying these rules and structures, respectively; 
and an analysis of the coherent mechanism that results. 
LEARNING RULES DERIVED FROM LONG-TERM POTENTIATION 
Long-term potentiation (LTP) of synapses is a phenomenon in which a brief series 
of biochemical events gives rise to an enhancement of synaptic efficacy that is extraordi- 
narily long-lasting (Bliss and Lzmo, 1973; Lynch and Baudry, 1984; Staubli and Lynch, 
1987); it is therefore a candidate mechanism underlying certain forms of learning, in 
which few triniug trials are required for long-lasting memory. The physiological char- 
acteristics of LTP form the basis for a straightforward network learning rule. 
It is known that simultaneous pre- and post-synaptic activity (i.e., intense depolar- 
ization) result in LTP (e.g., WigstrZm et al., 1986). Since excitatory cells are embedded 
in a meshwork of inhibitory interneurons, the requisite induction of adequate levels of 
pre- and postsynaptic activity is achieved by stimulation of large numbers of afferents 
for prolonged periods, by voltage clamping the postsynaptic cell, or by chemically block- 
ing the activity of inhibitory interneurons. In the intact animal, however, the question 
of how simultaneous pre- and postsynaptic activity rnght be induced has been an open 
question. Recent work (Larson and Lynch, 1986) has shown that when hippocampal 
afferents are subjected to patterned stimulation with particular temporal and frequency 
parameters, inhibition is naturally eliminated within a specific time window, and LTP 
can arise as a result. Figure I shows that LTP naturally occurs using short (3-4 pulse) 
bursts of high-frequency (100Hz) stimulation with a 200ms interburst interval; only the 
second of a pair of two such bursts causes potentiation. This occurs because the normal 
short inhibitory currents (IPSPs), which prevent the first burst from depolarizing the 
postsynaptic cell sufficiently to produce LTP, are maximally refractory at 200ms after 
being stimulated, and therefore, although the second burst arrives against a hyperpolar- 
ized background resulting from the long hyperpolarizing currents (LHP) initiated by the 
first burst, the second burst does not initiate its own IPSPs, since they are then refrac- 
tory. The studies leading to these conclusions were performed in in vitro hippocampal 
slices; LTP induced by this patterned stimulation technique in intact animals shows no 
measurable decrement prior to the time at which recording arrangements deteriorate: 
more than a month in some cases (see Staubli and Lynch, 1987). 
PERFORMANCE RULES DERIVED FROM 
OLFACTORY PHYSIOLOGY AND BEHAVIOR 
From the above data we may infer that LTP itself depends on simultaneous pre- and 
postsynaptic activity, as Hebb postulated, but that a sufficient degree of the latter occurs 
only under particular conditions. Those conditions (patterned stimulation) suggest the 
beginnings of a performance rule for the network. Drawing this out requires a review 
of the inhibitory currents active in hippocampus and in pitiform cortex. Three classes 
of such currents are known to be present: short IPSPs, long LHPs and extremely long, 
cell-specific afterhyperpolarization, or AHP (see Figure 2). Short IPSPs arise from both 
feedforward and feedback activation of inhibitory interneurons which in turn synapse 
320 
on excitatory cells (e.g., layer II cells, which are primary excitatory cells in pitiform). 
IPgPs develop more slowly than excitatory postsynaptic potentials (EP SPs) But quickly 
shunt the EPSP, thus reversing the depolarization that arises from EPSPs, and bringing 
the cell voltage down below its original resting potential. IPSPs last approximately 50- 
lOOms, and then enter a refractory period during which they cannot be reactivated 
from about 100-300ms after they have been once activated. Longer hyperpolarization 
(LHP) is presumably dependent on a distinct type of inhibitory interneuron or inhibitory 
receptor, and arises in much the same way; however, these cells are apparently not 
refractory once hctivated. LHP lasts for 300-500ms. 
Taken together, IPSPs and LHP constitute a form of high-pass frequency filter: 
200ms after an input burst, a subsequent input will arrive against a background of 
hyperpolarization due to LHP, yet this input will not initiate its own IPSP due to 
the refractory period. If the input is a single pulse, its EPSP will fail to trigger the 
postsynaptic cell, since it will not be able to overcome the LHP-induced hyperpolarized 
potential of the cell. Yet if the input is a high-frequency burst, the pulses comprising 
the burst will give rise to different behavior. Ordinarily, the first EPSP would have Been 
driven back to resting potentialby its accompanying IPSP, before the second pulse in the 
burst could arrive. But when the IPSP is absent, the first EPSP is not driven rapidly 
down to resting potential, and the second pulse sums with it, raising the voltage of 
the postsynaptic cell and allowing voltage-dependent channels to open, thereby further 
alepolarizing the cell, and causing it to spike (Figure 3). Hence these high-frequency 
bursts fire the cell, while single pulses or lower-frequency bursts would not do so. When 
these cells fire, then active synapses can be potentiated. 
The third inhibitory mechanism, AHP, is a current that causes an excitatory cell 
to become refractory after it has fired strongly or rapidly. This mechanism is therefore 
specific to those cells that have fired, unlike the first two mechanisms. AHP can prevent 
a cell from firing again for as long as 1000ms (1 second). 
It has long been observed that EEG waves in the hippocampi of learning animals are 
dominated By the theta rhythm, i.e., activity occuring at about 4-SHz. This is now seen 
to correspond to the optimal rate for firing postsynaptic cells and for enhancing synapses 
via LTP; i.e., this rhythmic aspect of the performance rules of these networks is suggested 
by the physiology of LTP. The resulting activation patterns may take the following form: 
relatively synchronized cell firing occurring approximately once every 200ms, i.e., spatial 
patterns of induced activity occurring at the rate of one new spatial cell-firing pattern 
every 200ms. The cells most strongly participating in any one firing pattern will not 
participate in subsequent patterns (at least the next 4-5 patterns, i.e., 800-1000ms), 
due to AHP. This raises the interesting possibility that different spatial patterns (at 
different times) may be conveying different information about their inputs. In summary, 
postsynaptic cells fire in pulses or bursts depending on the synaptically-weighted sums 
of their active axonal inputs; this firing is synchronized across the cells in a structure, 
giving rise to a spatial pattern of activity across these cells; once cells fire they will 
not fire again in subsequent patterns; each pattern (occuring at the theta rhythm, i.e., 
approrrately once every 200ms) will therefore consist of extremely different spatial 
patterns of cell activity. Hence the 'output' of such a network is a sequence of spatial 
patterns. 
In an animal engaged in an olfactory discrimination learning task, the theta rhythm 
321 
dominates the animals behavior: the animals literally sniff at theta. We have been 
able to sustitute direct stimulation (in theta-burst mode) of the lateral olfactory tract 
(LOT), which is the input to the olfactory cortex, for odors: these 'electrical odors' 
are learned and discrimbtated by the animals, either from other electrical odors (via 
different stimulating electrodes) or from real odors. Furthermore, behavioral learning 
in this paradigm is accompanied by LTP of pitiform synapses (Roman et al., 1987). 
This experimental paradigm thus provides us with a known set of behaviorally-relevant 
inputs to the olfactory cortex that give rise to synaptic potentiation that apparently 
underlies the learnlng of the stimuli. 
ARCHITECTURE OF OLFACTORY CORTEX 
Nasal receptor cells respond differentially to different chemicals; these cells topo- 
graphically innervate the olfactory bulb, which is arranged such that combinations of 
specific spatial 'patches' of bulb characteristically respond to specific odors. Bulb also 
receives a number of centrifugal afferents from brain, most of which terminate on the 
inhibitory granule cells. The excitatory mitral cells in bulb send out axons that fornx 
the lateral olfactory tract (LOT), which constitutes the only major input to olfactory 
(pitiform) cortex. This cortex in turn has some feedback connections to bulb via the 
anterior olfactory nucleus. 
Figure 4 illustrates the anatomy of the superficial layers of olfactory cortex: the 
LOT axons flow across layer Ia, synapsing with the dendrites of pitiform layer-H cells. 
Those cells in turn give rise to collateral axon outputs which flow, in layer Ib, parallel 
and subjacent to the LOT, in a predominantly rostral-to-caudal direction, eventually 
terminating in entorhinal cortex. Layer Ia is very sparsely connected; the probability 
of synapses between LOT axons and layer-H cell dendrites is less than 0.10 (Lynch, 
1986), and decreases candally. Layer Ib (where collaterals synapse with dendrites) is 
also sparse, but its density increases caudally, as the number of collaterals increases; the 
overall connectivity density on layer-H-cell dendrites is approximately constant through- 
out most of pitiform. Layer II also contains, in addition to the principal excitatory cells 
(modified stellates), inhibitory interneurons which synapse on excitatory cells within a 
specified radius, forming a 'patchwork' of cells affected by a particular inhibitory cell; 
the spheres of influence of inhibitory cells almost certainly overlap somewhat. There are 
approximately 50,000 LOT axons, 500,000 pitiform layer H cells, and a much smaller 
number of inhibitory cells that divide layer II roughly into functional patches. (See 
Price, 1973; Luskin and Price, 1983; Krettek and Price, 1977; Price and Slotnick, 1983; 
Haberly and Price, 1977, 1978a, 1978b). 
The layer II cell collateral axons flow through layer II-I for a distance before rising 
up to layer Ib (Haberly, 1985); taken in combination with the predominantly caudal 
directionality of these collaterals, this means that rostral pitiform will be dominated by 
LOT inputs. Extreme caudal pitiform (and all of lateral entorhinal cortex) is dominated 
by collaterals from more rostral cells; moving from rostral to caudal pitiform, cells 
increasingly can be thought of as 'hybrid cells': cells receiving inputs from both the 
bulb (via the LOT) and from rostral pitiform (via collateral axons). The architectural 
characteristics of rostral pitiform is therefore quite different from that of caudal pirifornx, 
and differential analysis must be performed of rostral cells vs. hybrid cells, as will be 
seen later in the paper. 
322 
SIMULATION AND FORMAL ANALYSIS: INTRODUCTION 
We have conducted several simulations of olfactory cortex incorporating many of 
the physiological features discussed earlier. Two hundred layer H cells are used with 
100 input (LOT) lines and 200 collateral axons; both the LOT and collateral axons 
flow caudally. LOT axons connect with rostral dendrites with a probability of 0.2, 
which decreases linearly to 0.05 by the caudal end of the model. The connectivity is 
arranged randomly, subject to the constraint that the number of contacts for axons and 
dendrites is fixed within certain narrow boundaries (in the most severe case, each axon 
forms 20 synapses and each dendrite receives 20 contacts). The resulting matrix is thus 
hypergeometric in both dimensions. There are 20 simulated inhibitory interneurons, 
such that the layer H cells are arranged in 20 overlapping patches, each within the 
influence of one such inldbitory cell. Inhibition rules are approximately as discussed 
above; i.e., the short IPSP is longer than an EPSP but only one fifth the length of the 
LHP; cell-specific AHP in turn is twice as long as LHP. 
Synaptic activity in the model is probabilistic and quantal: for any presynaptic 
activation, there is a fixed probability that the synapse will allow a certain amount 
of conductance to be contributed to the postsynaptic cell. Long-term potentiation 
was represented by a 40% increase in contact strength, as well as an increase in the 
probability of conductance being transmitted. These effects would be expected to arise, 
in sit, from modifying existing synapses as well as adding new ones (Lynch, 1986), 
two results obtained in electron microscopic studies (Lee et al., 1980). Only excitatory 
cell synapses are subject to LTP. LTP occurred when a cell was activated twice at a 
simulated 200ms interval: the first input 'primes' the synapse so that a subsequent 
burst input can drive it past a threshold value; following from the physiological results, 
previously potentiated synapses were much less different from "naive" synapses when 
driven at high frequency (see Lynch et al., 1988). The simulation used theta burst 
activation (i.e., bursts of pulses with the bursts occurring at 5Hz) of inputs during 
learning, and operated according to these synchronized fixed time steps, as discussed 
above. 
The network was trained on sets of "odors", each of which was represented as a group 
of active LOT lines, as in the "electric odor" experiments already described. Usually 
three or four "components" were used in an odor, with each component consisting of a 
group of contiguous LOT lines. We assumed that the bulb normalized the output signal 
to about 20% of all LOT fibers. In some cases, more specific bulb rules were used and 
in particular inhibition was assumed to be greatest in areas surrounding an active bulb 
"patch". 
The network exhibited several interesting behaviors. Learning, as expected, in- 
creased the robustness of the response to specific vectors; thus adding or subtracting 
LOT lines from a previously learned input did not, within limits, greatly change the 
response. The model, like most network simulations, dealt reasonably well with de- 
graded or noisy known signals. An unexpected result developed after the network had 
learned a succession of cues. In experiments of this type, the simulation would begin to 
generate two quite distinct output signals within a given sampling episode; that is, a sin- 
gle previously learned cue would generate two successive responses in successive 'sniffs' 
presented to an "experienced" network. The first of these response patterns proved to 
be common to several signals while the second was specific to each learned signal. The 
323 
common signal was found to occur when the network had learned 3-5 inputs which 
had substantial overlap in their components (e.g., four odors that shared 70% of their 
components). It appeared then that the network had begun to produce "category" or 
"clustering" responses, on the first sniff of a simulated odor, and "individual" or "dif- 
ferentiation" responses on subsequent sniffs of that same odor. When presented with a 
novel cue which contained elements shared with other, previously learned signals, the 
network produced the cluster response but no subsequent individual or specific output 
signal. Four to five cluster response patterns and 20 - 25 individual responses were 
produced in the network without distortion. 
In retrospect, it was clear that the model accomplished two necessary and in some 
senses opposing operations: 1) it detected similarities in the members of a cue category 
or cluster, and, 2) it nonetheless distinguished between cues that were quite similar. Its 
first response was to the similarity-based category and its second to the specific signal. 
ANALYSIS OF CATEGOPIZATION IN POSTRAL PIRIFOPM 
Assume that a set of input cues (or 'simulated odors') X a, Xt... X  differ from each 
other in the firing of dx LOT input lines; similarly, inputs a,t ... differ in d 
lines, but that inputs from the sets X and Y differ from each other in Dx,  d lines, 
such that the Xs and the Ys form distinct natural categories. Then the performance of 
the network should give rise to output (layer H cell) firing patterns that are very similar 
among members of either category, but different for members of different categories; 
i.e., there should be a single spatial pattern of response for members of X, with little 
variation in response across members, and there should be a distinct spatial pattern of 
response for members of Y. 
Considering a matrix constructed by uniform selection of neurons, each with a hy- 
pergeometric distribution for its synapses, as an approiraation of the bidimensional 
hypergeometric matrix described above, the following results can be derived. The ex- 
pected value of , the Hamming distance between responses for two input cues differing 
by 2d LOT lines (input Hamming distance of d) is: 
where No is the number of postsynaptic cells, each $i is the probability that a cell will 
have precisely i active contacts from one of the two cues, and I(i, j) is the probability 
that the number of contacts on the cell will increase (or decrease) from i to j with 
the change in d LOT lines; i.e., changing from the first cue to the second. Hence, the 
first term denotes the probability of a cell decreasing its number of active contacts from 
above to below some threshold, , such that that cell fired in response to one cue but not 
the other (and therefore is one of the cells that will contribute to the difference between 
responses to the two cues). Reciprocally, the second term is the probability that the 
cell increases its number of active synapses such that it is now over the threshold; this 
cell also will contribute to the difference in response. We restrict our analysis for now 
to rostral pitiform, in which there are assumed to be few if any collateral axons. We 
will return to this issue in the next subsection. 
324 
The value for each $8, the probability of a active contacts on a cell, is a hypergeo- 
metric function, since there are a fixed number of contacts anatomically between LOT 
and (rostral) phiform cells: 
$, = p(a active ynape) = 
where N is the number of LOT lines, A is the number of active (firing) LOT lines, n is 
the number of synapses per dendrite formed by the LOT, and a is the number of active 
such synapses. The formula can be read by noting that the first binomial indicates 
the number of ways of choosing a active synapses on the dendrite from the A active 
incoming LOT lines; for each of these, the next expression calculates the number of 
ways in which the remaining n - a (inactive) synapses on the dendrite are chosen from 
the N - A inactive incoming LOT lines; the probability of active synapses on a dendrite 
depends on the sparseness of the matrix (i.e., the probability of connection between any 
given LOT line and dendrite); the solution must be normalized by the number of ways 
in which n synapses on a dendrite can be chosen from N incoming LOT lines. 
The probability of a cell changing its number of contacts from a to h is: 
[(a, &) =  I. d - l g , g 
where N, n, A, and a are as above, I is the "loss" or reduction in the number of active 
synapses, and g is the gain or increase. Hence the left expression is the probability of 
losing l active synapses by changing d LOT lines, and the right-hand expression is the 
probability of gaining g active synapses. The product of the expressions are suxnmed 
over all the ways of choosing I and g such that the net change g - I is the desired 
difference a - &. 
If training on each cue induces only fractional LTP, then over trials, synapses con- 
tacted by any overlapping parts of the input cues should become stronger than those 
contacted only by unique parts of the cue. Comparing two cues from within a category, 
rs. two cues from between categories, there may be the same number of active synapses 
lost across the two cues in either case, but the expected strength of the synapses lost in 
the former case (within category) should be significantly lower than in the latter case 
(across categories). Hence, for a given threshold, the difference J between output firing 
patterns will be smaller for two within-category cues than for cues from two different 
categories. 
It is important to note that clustering is an operation that is quite distinct from 
stimulus generalization. Observing that an object is a car does not occur because of a 
comparison with a specific, previously learned car. Instead the category "car" emerges 
from the learning of many different cars and may be based on a "prototype" that has 
no necessary correspondence with a specific, real object. The same could be said of 
the network. It did not produce a categorical response when one cue had been learned 
325 
and second similar stimulus was presented. Category or cluster responses, as noted, 
required the learning of several exemplars of a similarity-based cluster. It is the process 
of extracting commonalities from the environment that defines clustering, not the simple 
noting of similarities between two cues. 
An essential question in clustering concerns the location of the boundaries of a given 
group; i.e., what degree of similarity must a set of cues possess to be grouped together? 
This issue has been discussed from any number of theoretical positions (e.g., information 
theory); all these analyses incorporate the point that the breadth of a category must 
reflect the overall homogeneity or heterogeneity of the environment. In a world where 
things are quite similar, useful categories will necessarily be composed of objects with 
much in common. Suppose, for instance, that subjects were presented with a set of 
four distinct coffee cups of different colors, and asked later to recall the objects. The 
subjects might respond by listing the cups as a blue, red, yellow and green coffee cup, 
reflecting a relatively specific level of description in the hierarchy of objects that are 
coffee cups. In contrast, if presented with four different objects, a blue coffee cup, a 
drinking glass, a silver fork and a plastic spoon, the cup would be much more likely 
to be recalled as simply a cup, or a coffee cup, and rarely as a blue coffee cup; the 
specificity of encoding chosen depends on the overall heterogeneity of the environment. 
The categories lornted by the simulation were quite appropriate when judged by an 
information theoretic measure, but how well it does across a wide range of possible 
worlds has not been addressed. 
ANALYSIS OF PROBLEMS ARISING FROM CAUDAL AXON FLOW 
The anatomical feature of directed flow of collateral axons gives rise to an immediate 
problem in principle. In essence, the more rostral cells that fire in response to an input, 
the more active inputs there are from these cells to the caudal cells, via collateral axons, 
such that the probability of caudal cell firing increases precipitously with probability of 
rostral cell firing. Conversely, reducing the number of rostral cells from firing, either 
by reducing the number of active input LOT axons or by raising the layer II cell firing 
threshold, prevents sufficient input to the caudal cells to enable their probability of 
firing to be much above zero. 
This problem can be stated formally, by making assumptions about the detailed 
nature of the connectivity of LOT and collateral axons in layer I as these axons proceed 
from rostral to caudal pitiform. The probability of contact between LOT axons and 
layer-H-cell dendrites decreases caudally, as the number of collateral axons is increasing, 
given their rostral to caudal flow tendency. This situation is depicted in Figure 4. 
Assuming that probability of LOT contact tends to go to zero, we may adopt a labelling 
scheme for axons and synaptic contacts, as in the diagram, in which some combination 
of LOT axons (z) and collateral axons (h,) contact any particular layer II cell dendrite 
(h,), each of which is itself the source of an additional collateral axon flowing to cells 
more caudal than itself. Then the cell firing function for layer H cell h, is: 
where the za denote LOT axon activity of those axons still with nonzero probability 
of contact for layer H cell h,, the hm denote activity of layer H cells rostral of h,, t is 
326 
the cell firing threshold, w,., is the synaptic strength between axon m and dendrite n, 
and H is the Heaviside step function, equal to 1 or 0 according to whether its argument 
is positive or negative. If we assume instead that probability of cell firing is a graded 
function rather than a step function, we may eliminate the H step function and calculate 
the firing of the cell (hn) from its inputs (hn,.t) via the logistic: 
m<n 
1 
hn: 
1 + + 
Then we may expand the expression for firing of cell h,. as follows: 
hn = [l + e-([]],,,<n h,,,wn,,, + []]l,_>n zl, wnl, + )] -1 
By assuming a fixed firing threshold, and varying the number of active input LOT 
hnes, the probabihty of cell firing can be examined. Numerical simulation of the above 
expressions across a range of LOT spatial activation patterns demonstrates that proba- 
bility of cell firing remains near zero until a critical number of LOT hnes are active, at 
which point the probabihty flips to close to 100% (Figure 5). This means that, for any 
given firing threshold, given fewer than a certain amount of LOT input, practically no 
pitiform cells will fire, whereas a shght increase in the number of active LOT hnes will 
mean that practically all pitiform cells should fire. 
This excruciating dependence of cell firing on amount of LOT input indicates that 
normalization of the size of the LOT input alone will be insttfficient to stabihze the 
size of the layer II response; even shght variation of LOT activity in either direction has 
extreme consequences. A number of solutions are possible; in particular, the known local 
anatomy and physiology of layer II inhibitory interneurons provides a mechanism for 
controlling the amount of layer II response. As discussed, inhibitory interneurons give 
rise to both feedforward (activated by LOT input) and feedback (activated by collateral 
axons) activity; the influence of any particuar interneuron is hmited anatomically to 
a relatively small radius around itself within layer II, and the influence of multiple 
interneurons probably overlap to some extent. Nonetheless, the 'sphere of influence' of 
a particular inhibitory interneuron can be viewed as a local patch in layer II, within 
which the number of active excitatory cells is in large measure controlled by the activity 
of the inhibitory cell in that patch. If a number of excitatory cells are firing with varying 
alepolarization levels within a patch in layer II, activation of the inhibitory cells by the 
excitatory cells will tend to weaken those excitatory cells that are less depolarized than 
the most strongly-firing cell within the patch, leading to a competition in which only 
those cells firing most strongly within a patch will burst, and these cells will, via the 
interneuron, suppress multiple firing of other cells within the patch. Thus the patch 
takes on some of the characteristics of a 'winner-take-all' network (Feldman, 1982): only 
the most strongly firing cells will be able to overcome inhibition sufficiently to burst, 
some additional cells will pulse once and then be overwhelmed by inhibition, and the 
rest of the cells in the patch will be silent, even though that patch may be receiving a 
large amount of excitatory input via LOT and collateral axon activity in layer I. 
327 
EMERGENT CATEGORIZATION BEHAVIOR IN THE MODEL 
The probabilistic quantal transmitter-release properties of pitiform synapses de- 
scribed above give rise to probabilistic levels of postsynaptic alepolarization. This in- 
herent randomness of cell firing, in combination with activity of local inhibitory patches 
in layer II, selects different sets of bursting and pulsing cells on different trials if no 
synaptic enhancement has taken place. The time-locked firing to the theta rhythm 
enables distinct spatial patterns of firing to be read out against a relatively quiescent 
background firing rate. Synaptic LTP enhances the conductances and alters the prob- 
abilistic nature of communication between a given axon and dendrite, which tends to 
overcome the randomness of the cell firing patterns in untrained cells, yielding a stable 
spatial pattern that will reliably appear in response to the same input in the future, 
and in fact will appear even in response to degraded or noisy versions of the input pat- 
tern. urthermore, subsequent input patterns that differ in only minor respects from a 
learned LOT input pattern will contact many of the already-potentiated synapses from 
the original pattern, thereby tending to give rise to a very similar (and stable) output 
firing pattern. Thus as multiple cues sharing many overlapping LOT lines are learned, 
the layer II cell responses to each of these cues will strongly resemble the responses 
to the others. Hence, the response(s) behave as though simply labelling a category 
of very-similar cues; sufficiently different cues will give rise to quite-different category 
responses. 
EMERGENT DIFFERENTIATION BEHAVIOR IN THE MODEL 
Potentiated synapses cause stronger depolarization and firing of those cells partic- 
ipating in a 'category' response to a learned cue. This increased depolarization causes 
strong, cell-specific afterhyperpolarization (AHP), effectively putting those cells into a 
relatively long-lasting ( lsec) refractory period that prevents them from firing in re- 
sponse to the next few sampling sniffs of the cue. Then the inhibitory 'winner-take-all' 
behavior within patches effectively selects alternate cells to fire, once these strongly- 
firing (learned) cells have undergone AHP. These alternates will be selected with some 
randomness, given the probabilistic release characteristics discussed above, since these 
cells will tend not to have potentiated synapses. These alternate cells then activate 
their caudally-fiowing recurrent collaterals, activating distinct populations of synapses 
in caudal layer Ib. Potentiation of these synapses in combination with those of still- 
active LOT axons tends to 'recruit' stable subpopulations of caudal cells that are distinct 
for each simulated odor. They are distinct for each odor because first rostral cells are 
selected from the population of unpotentiated or weakly-potentiated cells (after the 
strongly potentiated cells have been removed via AHP); hence they will at first tend to 
be selected randomly. Then, of the caudal cells that receive some activation from the 
weakening caudal LOT lines, those that also receive collateral innervation from these 
semi-randomly selected rostrals will be those that will tend to fire most strongly, and 
hence to be potentiated. 
The probability of a cell participating in the rostral semi-randomly selected groups 
for more than one odor (e.g., for two similar odors) is lower than the probability of 
cells being recruited by these two odors initially, since the population are those that 
receive not enough input from the LOT to have been recruited as a category cell and 
potentiated, yet receive enough input to fire as an alternate cell. The probability of any 
caudal cell then being recruited for more than one odor by these rostral cell collaterals 
328 
in combination with weakening caudal LOT lines is similarly low. The product of these 
two probabilities is of course lower still. Hence, the probability that any particular 
caudal cell potentiated as part of this process will participate in response to more than 
one odor is very low. 
This means that, when sampling (sniffing), the first pattern of cell firing will indicate 
similarity among learned odors, causing AHP of those patterns; thus later sniffs will 
generate patterns of firing that tend to be quite different for different odors, even when 
those odors are very similar. Empirical tests of the simulation have shown that odors 
consisting of 90%-overlapping LOT firing patterns will give rise to overlaps of between 
85% and 95% in their initial layer II spatial firing patterns, whereas these same cues 
give rise to layer II patterns that overlap by less than 20% on 2nd and 3rd sniffs. 
The spatio-temporal pattern of layer II firing over multiple samples thus can be taken 
as a strong differentiating mechanism for even very-similar cues, while the initial sniff- 
response for those cues will nonetheless give rise to a spatial firing pattern that indicates 
the similarity of sets of learned cues, and therefore their 'category membership' in the 
clustering sense. 
CLUSTERING 
Incremental clustering of cues into similarity-based categories is a more subtle pro- 
cess than might be thought and while it is clear that the pitiform simulation performs 
this function, we do not lnow how optimal its performance is in an information-theoretic 
sense, relative to some measure of the value or cost of information in the encoding. 
Building a categorical scheme is a non-monotonic, combinatorial problem: that is, each 
new item to be learned can have disproportionate effects on the existing scheme, and 
the number of potential categories (clusters) climbs factorially with the number of items 
to be categorized. Algorithmic solutions to problems of this type are computationally 
very expensive. Calculation of an ideal categorization scheme (with respect to particu- 
lar cost measures in a performance task), using a hill-climbing algorithm derived from 
an information-theoretic measure of category value, applied to a problem involving 22 
simulated odors, required more than 4 hours on a 68020-based processor. The simu- 
lation network reached the same answer as the game-theoretic program, but did so in 
seconds. It is worth mentioning again that the simulation did so while simultaneously 
learning unique encodings for the cues, as described above, which is itself a nontrivial 
task. 
Humans, on at least some tasks, may carry out clustering by building initial clusters 
and then merging or splitting them as more cues are presented. Thus far, the networks 
do not pass through successive categorization schema. However, experiments on hu- 
w_a categorization have almost exclusively involved situations in which all cues were 
presented in rapid succession and category membership is taught explicitly, rather than 
developed independently by the subject. Hence, it is not clear from the experimental 
literature whether or not stable clusters develop in this way from stimuli presented at 
widely spaced intervals with no category membership information iven, which is the 
problem corresponding to that given the network (and that is likely common in na- 
ture). It will be of interest to test cateorizin skills of rats learning successive olfactory 
discriminations over several days. Using appropriately selected stimuli, it should be pos- 
sible to determine if stable clusters are constructed and whether merging and splitting 
occurs over trials. 
329 
Any useful clustering device must utilize information about the heterogenity of the 
stimulus world in setting the heterogeneity of individual categories. Heterogeneity of 
categories refers to the degree of similarity that is used to determine if cues are to be 
grouped together or not. Several network parameters will influence category size and we 
are exploring how these influence the individuation function; one particularly interesting 
possibility involves a shifting threshold function, an idea used with great success by 
Cooper in his work on visual cortex. The problems presented to the simulation thus far 
involve a totally naive system, one that has had no "developmental" history. We are 
currently exploring a model in which early experiences are not learned by the network 
but instead set parameters for later ("adult") learning episodes. The idea is that early 
experience determines the heterogenity of the stimulus world and imprints this on the 
network, not by specific changes in synaptic strengths, but in a more general fashion. 
CONCLUSIONS 
Neurons have a nearly bewildering array of biophysical, chemical, electrophysiologi- 
cal and anatomical properties that control their behavior; an open question in neural net- 
work research is which of these properties need be incorporated into networks in order to 
simulate brain circuit function. The simulation described here incorporates an extreme 
amount of biological data, and in fact has given rise to novel physiological questions, 
which we have tested experimentally with results that are counterintuitive and previ- 
ously unsuspected in the existing physiological literature (see, e.g., Lynch and Granger, 
1988; Lynch et al., 1988). Incorporation of this mass of physiological parameters into 
the simulation gives rise to a coherent architecture and learning and performance rules, 
when interpreted in terms of computational function of the network, which generates a 
robust capability to encode multiple levels of information about learned stimuli. The 
coherence of the data in the model is useful in two ways: to provide a framework for 
understanding the purposes and interactions of many apparently-disparate biological 
properties of neurons, and to aid in the design of novel artificial network architectures 
inspired by biology, which may have useful computational functions. 
It is instructive to note that neurons are capable of many possible biophysical func- 
tions, yet early results fror chronic recording of cells from olfactory cortex in animals 
activell engaged in learning mahdi novel odors in an olfactory discrimination task clearly 
shows a particular operating mode of this cortical structure when it is actively in use 
by the animal (Larson et al., unpublished data). The rats in this task are very familiar 
with the testing paradigm and exhibit very raid learning, with no difficulty in acquiring 
large numbers of discriminations. Sampling, detection and responding occur in fractions 
of a second, indicating that the utilization of recognition memories in the olfactory sys- 
tem can be a rapid operation; it is not surprising, then, that the odor-coded units so 
far encountered in our physiological experiments have rapid and stereotyped responses. 
Given the dense innerration of the olfactory bulb by the brain, it is possible that the 
type of spatial encoding that appears to be responsible for the preliminary results of 
these chronic experiments would not appear in animals that were not engaged in ac- 
tive sampling or were confronted with unfamiliar problems. That is, the operation of 
the olfactory cortex might be as dependent upon the behavioral 'state' and behavioral 
history of the rat as upon the actual odors presented to it. It will be of interest to 
compare the results from well-trained freely-moving animals with those obtained using 
more restrictive testing conditions. 
330 
The temporal properties of synaptic currents and afterpotentials, results from sim- 
ulations and chronic recording studies, taken together, suggest two useful caveats for 
biological models: 
Cell firing in cortical structures (e.g., pitiform, hlppocampus and possibly neocor- 
tex) is linked to particular rhythms (theta in the case of pitiform and hippocam- 
pus) during real learning behavior, and thus it is likely that the 'coding language' 
of these structures involves spatial cell firing patterns within a brief time window. 
This stands in contrast to other methods such as frequency coding that appears 
in other structures (such as peripheral sensory structures, e.g., retina and cochlea; 
see, e.g., Sivilotti et al., 1987). 
Temporal sequences of spatial patterns may encode different types of information, 
such as hierarchical encodings of perceptions, in contrast with views in which 
either asynchronous 'cycling' activity occurs or a system yields a single puncrate 
output and then halts. 
In particular, simulation of piriform gives rise to temporal sequences of spatial patterns 
of synchronized cell firing in layer II, and the patterus change over time: the physiology 
and anatomy of the structure cause successive 'sniffs' of the same olfactory stimulus 
to give rise to a sequence of spatial patterns, each of which encodes successively more 
specific information about the stimulus, beginning with its similarity to other previously- 
learned stimuli, and ending with a unique encoding of its characteristics. It is possible 
that both the early similarity-based 'cluster' information and the late unique encodings 
are used, for different purposes, by brain structures that receive these signals as output 
from pitiform. 
ACKNOWLEDGEMENTS 
Much of the theoretical underpinning of this work depends critically on data gener- 
ated by John Larson; we are grateful for his insightful advice and help. This work has 
benefited from discussions with Michel Baudry, Mark Gluck, and Ursula Staubli. 
Ambros-Ingerson is supported by a fellowship from Hewlett-Packard, Mxico, adminis- 
tered by UC MEXUS. 
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200 ms 
S2 [] 
) 8ec 
I I I I I i I I I i I I I 
i t I I 
10 
140t 
190 
I i I I i I I I I 
30 40 SO 60 yo 
TIME (MIMUTES) 
c 
BEFORE AFTER SUPER I MPOSED 
Figure 1. LTP induction by short high-frequency bursts involves sequential "prim- 
ing" zd consolidation"events. 
A) S1 and S2 represent separate groups of Shaffer/commissural fibers converging on a 
single CA1 pyramidal neuron. The stimulation pattern employed consisted of pairs of 
bursts (each 4 pulses at 100Hz) given to S1 and S2 respectively, with a 200ms delay 
between them. The pairs were repeated 10 times at 2 sec intervals. 
B) Only the synapses activated by the delayed burst (S2) showed LTP. The top panel 
shows measurements of amplitudes of intracellular EPSPs evoked by single pulses to 
S1 before and after patterned stimulation (given at 20 mln into the experiment). The 
middle panel shows the amplitude of EPSPs evoked by S2. Bottom panel shows EPSP 
amplitudes for both pathways expressed as a percentage of their respective sizes before 
burst stimulation. 
C) Shown are records of EPSPs evoked by S1 and S2 five min. before and 40 min. after 
patterned burst stimulation. Calibration bar: 5mV, 5msec. (From Larson and Lynch, 
1986). 
334 
[I 
EPSP *-20msec Na 
IPSP -,.100msec 1 
..,,]P-] LHP ~.5 sec K 
 AHP .--1 sec K 
Figure 2. Onset and duration of events comprising stimulation of a layer II cell 
in piriforw cortex. Axonal stimulation via the lateral olfactory tract (LOT) activates 
feedforward EPSPs with rapid onset and short duration (20msec) and two types of 
feedforward inhibition: short feedforward IPSPs with slower onset and somewhat longer 
duration (100m-ec) than the EPSPs, and longer hyperpolarizing potentials (LHP) 
lasting 500m.ec. These two types of inhibition are not specific to firing cells; an 
additional, very long-lasting (lsec) inhibitory afterhyperpolarizing current (AHP) is 
induced in a cell-specific fashion in those cells with intense firing activity. Finally, 
feedback EPSPs and IPSPs are induced by activation via recurrent collateral axons 
from layer II cells. 
335 
S1 
FIRST SECOND TENTH 
Figure 3. When short, high-frequency bursts are input to cells 200ms after an 
initial 'priming' event, the broadened EPSPs (see Figure 1) will allow the contributions 
of the second and subsequent pulses comprising the burst to sum with the depolarization 
of the first pulse, yielding higher postsynaptic depolarization sufficient to cause the cell 
to spike. (Prom Lynch, Larson, Staubli and Baudry, 1987). 
336 
probability of LOT contact per axon decreases- ""is constant 
probability o assoc. contact per axon is constant- nn" ncraasas 
alaciva 
to spiking 
call 
anterior ferior 
Figure 4. Organization of extrinsic and feedback inputs to layer-II cells ofpiriform 
cortex. The axons comprising the lateral olfactory tract (LOT), originating from the 
bulb, innervate distal dendrites, whereas the feedback collateral or associational fibers 
contact proximal dendrites. Layer II cells in anterior (rostral) pitiform are depicted as 
being dominated by extrinsic (LOT) input, whereas feedback inputs are more prominent 
on cells in posterior (caudal) pitiform. 
337 
lOO 
8o 
6o 
4o 
2o 
Tapered Feedforward Firing Probabilities 
-a,., Stimulus A 
 -e.- Stimulus B 
-m.. Stimulus C 
 .o- Stimulus D 
i ,.'- CumHypergrnt 
o 
0 I 2 3 4 5 6 7 8 9 lO 11 12 13 14 15 
Number Firing (of 40 Connections) 
Figure 5. Probability oflayer-II-cell fring as a function ofn,,mher of LOT axons ac- 
tive, in the absence of local inhibitory patches. The hypergeometric function ('C,mHy- 
pergrot') spec/fies the probability of layer H cell firing in the absence of caudaUy-directed 
feedback collaterals, i.e., assuming that all collaterals are equally probable to travel ei- 
ther rostraUy or caudaUy. In this case, there is a smooth S-shaped function for probabil- 
ity of cell firing with increasing LOT activity, so that adjustment of global firing thresh- 
old (e.g., via nonspec/fic cholinergic inputs affecting all pirfform inhibitory interneurons) 
can effectively normalize pitflorin layer H cell firing. However, when feedback axons are 
caudally directed, then probability steepens markedly, becoming a near step function, 
in which the probability of cell firing is exquisitely sensitive to the number of active 
inputs, across a range of empirically-tested LOT stimulation patterns (A - D in the 
figure). In this case, global adjustment of inhibition will fail to adequately normalize 
layer H cell firing: the probability of cell firing will always be either near zero or near 
1.0; i.e., either nearly all cells will fire or almost none will fire. Local inhibitory control 
of 'patches' of layer H solve this problem (refer to text). 
