A Heteroassociative Learning Model Robust to Interference

Randa Kassab and Fr

eric Alexandre

Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, 33405, Talence, France

LaBRI, Universit

e de Bordeaux, Bordeaux INP, CNRS, UMR 5800, Talence, France

Institut des Maladies Neurod

eratives, Universit

e de Bordeaux, CNRS, UMR 5293, Bordeaux, France

Keywords:

Associative Memory, Interference, Hippocampus.

Abstract:

Neuronal models of associative memories are recurrent networks able to learn quickly patterns as stable states

of the network. Their main acknowledged weakness is related to catastrophic interference when too many or

too close examples are stored. Based on biological data we have recently proposed a model resistant to some

kinds of interferences related to heteroassociative learning. In this paper we report numerical experiments

that highlight this robustness and demonstrate very good performances of memorization. We also discuss

convergence of interests for such an adaptive mechanism for biological modeling and information processing

in the domain of machine learning.

1 INTRODUCTION

Generalization is often reported as a desirable prop-

erty of artiﬁcial neural networks. This phenomenon

occurs if, when a network is presented with an ex-

ample it has never seen before, it is able to interpo-

late a satisfactory response from the combination of

close previously learned examples. Such a response

can be judged satisfactory not only because from a

limited learning phase the network behaves well in

a wider domain but also because in some sense learn-

ing went beyond speciﬁc cases and was able to extract

some general structures or regularities in the example

space. In some cases, however, this property might be

considered a ﬂaw. This is the case for example when

there is no useful topography in the example space or

when the goal is to learn some arbitrary association.

Consider for example learning to associate a phone

number with a name: there is nothing to learn from

the euclidean distance between two such numbers and

you can in no way discover an association if it was not

instructed to you before. This contrasts the cases of

learning a general rule from a set of examples, as it is

for example studied with layered architectures like the

multilayer perceptron, versus learning by heart spe-

ciﬁc cases like in associative memories.

Neural models of associative memories have been

proposed with recurrent networks like the Hopﬁeld

model (Hopﬁeld, 1982) and the Willshaw model

(Willshaw et al., 1969). Based on classical connec-

tionist characteristics (like units with non linear acti-

vation functions and hebbian learning), the recurrent

architecture of these networks indicates that learning

is mainly focused on the inner characteristics of an ex-

ample to be memorized and not on the elaboration of

abstract representations in intermediate layers. Nev-

ertheless, some problems can appear if too close ex-

amples are learned. In such a case, the network might

elaborate an answer from the combination of several

learned examples; what would be called generaliza-

tion in other circumstances is called here interference.

As a consequence, models of associative memo-

ries are generally used as content addressable memo-

ries, where few prototypes are stored as stable states

of the network and noisy or incomplete patterns are

presented as inputs and reconstructed to the closest

stored example. Beyond this use as an autoassocia-

tive memory (where initial input and ﬁnal result have

the same dimension), the adaptation to heteroassocia-

tive memory is straightforward: just virtually split the

recurrent network in two sets of neurons A and B. The

recurrent connectivity includes connections within A

and within B (seen as two autoassociative memories)

and between A and B (heteroassociative memory be-

tween the two sets of different dimension A and B).

As conﬁgurations of A+B are learned as prototypes,

proposing an incomplete pattern A (B neurons be-

ing set to 0) will result in the reconstruction of A+B,

yielding the answer B. The main acknowledged weak-

ness of these models is about their limited capacity of

Kassab, R. and Alexandre, F..

A Heteroassociative Learning Model Robust to Interference.

In Proceedings of the 7th International Joint Conference on Computational Intelligence (IJCCI 2015) - Volume 3: NCTA, pages 49-57

ISBN: 978-989-758-157-1

storage and the associated risk of catastrophic inter-

ference when this capacity is exceeded or when too

close prototypes are stored (Graham and Willshaw,

1997; Knoblauch et al., 2010). The best solution to

this problem is to require a sparse coding, which in-

trinsically also limits the maximum number of stored

prototypes. An associated strategy is to orthogonal-

ize the inputs and project their encoding in higher di-

mensions, which results in larger weight matrices to

manipulate (McNaughton and Nadel, 1990).

Models of associative memory have also been

studied for their complementarity with classical neu-

ral models of pattern matching like the multilayer per-

ceptron and for the deep cognitive anchoring of this

complementarity. Indeed, it was proposed 20 years

ago (McClelland et al., 1995) that the brain exploits

complementary learning systems, with a slow and

procedural learning in the cortex, able to extract struc-

tures and regularities in the data and to generalize,

compared with a quick learning of novel information

in the hippocampus.

In a recent work, we have proposed a reﬁnement

of hippocampal model (Kassab and Alexandre, 2015),

inspired from recent biological data (Samura et al.,

2008). These data report heterogeneities in the hip-

pocampal structure that might support the coexis-

tence of autoassociative and heteroassociative mem-

ories in this region. Speciﬁcally, the hippocam-

pus is a neuronal structure known to be involved in

episodic memory (Tulving, 1972), corresponding to

the storage of speciﬁc episodes including their con-

text and their emotional or motivational signiﬁcance.

For example, the hippocampus in involved in contex-

tual learning of pavlovian conditioning (Carrere and

Alexandre, 2015), linking neutral stimuli and their

context to biologically signiﬁcant events (reward and

punishment). Though primarily oriented toward bio-

logical modeling, we have also explained in (Kassab

and Alexandre, 2015) the interest of such a segre-

gation from an information processing point of view

(cf. the concluding section for a summary). In ad-

dition, we have also postulated an additional mecha-

nism for the association of autoassociative memories,

that might result in a more robust system, particularly

more resistant to interference. The goal of this paper

is to evaluate more precisely the performances of this

mechanism from an information processing point of

view.

In the next section, we will present this model

together with its formalism based on the associative

memory initially proposed by Willshaw (Willshaw

et al., 1969). Then we will report the experiments

that were conducted to evaluate its resistance to inter-

ference and the associated results. We will conclude

by explaining the interest of such a mechanism both in

neuroscience and in information processing domains.

2 MULTIPLE

ASSOCIATIVE-MEMORY

MODEL OF THE

HIPPOCAMPUS

Our hippocampal model is made up of two autoas-

sociative networks that are heteroassociatively linked

through a layer of intermediate cells (Figure 1). The

goal of this model is to store and recall speciﬁc

episodes including a perceptual part (coming from the

perception of the outer world: exteroception) and an

emotional part (coming from the perception of inter-

nal cues of different valences related to pain and plea-

sure: interoception).

The two autoassociative networks considered in

the model receive and store independently these two

types of input patterns, a

(e)

and a

(i)

. The layer of in-

termediate cells is organized into a small number of

ordered groups of valence cells that receive valence-

related information from the same interoceptive path-

ways as the interoceptive autoassociative network.

The cells in the ﬁrst group can be directly activated

by interoceptive inputs to the model and can therefore

be thought of as the primary valence cells. Interocep-

tive inputs on the cells in the other groups, which are

termed associated cells, are conditional, that is, they

can not evoke postsynaptic activity within associated

cells unless a concomitant signal, m

, related to the

activity pattern of a precedent group is applied.

The valence cells belonging to the same group

of intermediate cells are not interconnected but in-

hibitory connections, I

i j

, exist between cells belong-

ing to different groups. The inhibitory connections

are not plastic. They are prewired such that an in-

hibitory connection from cell i to cell j exists (I

i j

1) if the two cells belong respectively to different

groups, k and l, and l precedes k (l < k). Thus, each

group of associated cells, once activated, silences ex-

citable cells in its preceding groups including the pri-

mary group of valence cells. This means that at most

valence cells in one group can be active at a time.

The formation of extero-interoceptive associa-

tions is done at the level of heteroassociative links,

(e−v)

i j

, between the exteroceptive autoassociative net-

work and the groups of intermediate valence cells.

These latter provide direct excitatory input to the inte-

roceptive autoassociative network through non-plastic

connections, w

(v−i)

i j

. These connections are prewired

only between valence cells that are sensitive to the

NCTA 2015 - 7th International Conference on Neural Computation Theory and Applications

Figure 1: The architecture of the hippocampal model. Black lines denote the basic circuit of the model while blue lines denote

changes in circuitry mediated by one group of associated cells (blue) following the detection of valence-overload interference

(red arrow). Autoassociative and heteroassociative connectivities between hippocampal cells are denoted respectively by

bidirectional dashed lines and simple dashed lines without arrows. Inhibitory connections between valence cells are denoted

by lines ended with circles. Stable non-plastic connections, both excitatory and inhibitory, are denoted by solid lines.

same kind of valence.

The classical binary version of the Willshaw net-

work (Willshaw et al., 1969) is chosen as the ba-

sis for the implementation of both auto- and het-

eroassociative memory functions in the model. The

neurons are simple McCulloch-Pitts binary threshold

units and learning begins with all the synaptic weights

set to zero. Synaptic plasticity is achieved accord-

ing to a clipped version of Hebbian learning: a single

coincidence of presynaptic and postsynaptic activity

changes the synaptic weight w

i j

from 0 to 1, while

further co-activations do not induce further changes.

The recall process is done by presenting a cue pat-

tern ˜x and counting the dendritic sum for each cell j

∑

i=1

i j

˜x

) in one-time step. The output cells

that have a dendritic sum equal to or higher than the

number of active inputs are activated. The quality of a

recalled pattern can be assessed according to its Ham-

ming distance (HD) from the originally stored pattern

(i.e. the number of elements that differ between the

two patterns. For example, if x=(0 1 1 1 0) and y=(1

1 0 1 0) then HD(x,y)=2).

Similarly to cholinergic models of the hippocam-

pus (Hasselmo et al., 1996; Meeter et al., 2004), our

model operates in transition between two modes, stor-

age and recall, depending on a hyperparameter ACh.

This mechanism is inspired from biological data de-

scribing mode switching under the dynamic regu-

lation of the levels of acetylcholine (ACh) released

from septal cholinergic projections to the hippocam-

pus. During recall, a retrieval cue, a

(e)

, is applied to

the exteroceptive autoassociative network. The pat-

tern of activity obtained at the output, ˆa

(e)

, drives re-

trieval in the heteroassociative network. An interme-

diate valence cell, l, can ﬁre only if the dendritic sum

of its excitatory inputs exceeds the threshold value

and if it does not receive inhibitory inputs from other

valence cells that have already ﬁred. The activity of

the intermediate valence cells, ˜a

(i)

, triggers recall in

the interoceptive autoassociative network yielding the

valence prediction by the model, ˆa

(i)

Just after delivery of the interoceptive informa-

tion, two novelty-detection processes take place to

compare the retrieved patterns to the actual patterns

from extero- and interoception. The novelty condi-

tion occurs when the Hamming distance between two

patterns exceeds pre-speciﬁed thresholds (HD

(e)

> e

or HD

(i)

> v). Novelty induces ACh dynamics that

favor learning of new inputs, otherwise the model set-

tles in recall mode.

During learning, excitatory intrinsic synaptic

transmission along the recurrent connections is re-

moved and activity in the model is purely driven by

afferent extero- and interoceptive inputs, a

(e)

and a

(i)

In the model, two kinds of interference can occur due

to a saturation, or overload of learning. The ﬁrst

kind of interference occurs within the autoassocia-

tive memories when too many or too close inputs are

stored. It is called pattern overload and will not be

considered here for simplicity (we will present sparse

patterns during experiments to avoid this kind of in-

terference). The second kind of interference is called

valence overload and occurs when stimuli are simul-

taneously associated to different valences. Consider

for example learning AB+, AC- and BD-, where A,

B, C and D are exteroceptive stimuli and + and - are

interoceptive valences. Since A and B are simulta-

neously associated to + and - valences, the recall of

AB would probably generate an interference (both re-

sponses produced). The model deals with valence-

A Heteroassociative Learning Model Robust to Interference

Figure 2: Inﬂuence of the number of stored patterns on the accuracy of valence prediction. (A) Percentage of prediction errors

of the model without associated cells (w/o) and with associated cells after one block (W (P1)) and two blocks (W (P2)) of

training trials. (B,C) Details of the simulation results when the block size is set to 100. B: Rates of interference detection

during the ﬁrst (T1) and second (T2) training trials. C: Number of groups of associated cells needed to resolve interference

detected during training trials T1 and T2.

Figure 3: Performance of the proposed model after training on 100 input patterns. The model is tested using partial cues in

which 1, 2, or 3 out of 6 active elements in the original inputs are turned off. (A) Pattern completion performance, deﬁned

as the percentage of retrieved patterns that differ at least by one element from the originally stored patterns. (B) Pattern

completion performance, deﬁned in terms of Hamming distance between the stored and retrieved patterns. (C, D) Valence

prediction performance of the proposed model with (w) and without (w/o) associated cells after one and two blocks of

training trials. (E) Maximal number of groups of associated cells needed to resolve interference detected under all simulation

conditions (one and two blocks of training trials P1 and P2, and for 1/6, 2/6 and 3/6 partial-cue conditions).

overload interference by monitoring activity of in-

termediate valence cells, y

(v)

. If any activity is ob-

served among intermediate valence cells (

∑

(v)

> 0)

in response to exteroceptive inputs a matching pro-

cess takes place to determine whether this activity

matches interoceptive valence-speciﬁc inputs. A mis-

match (HD

(v)

> v) signals a potential interference to

a successive group of associated valence cells that be-

NCTA 2015 - 7th International Conference on Neural Computation Theory and Applications

Figure 4: Discrimination reversal learning. (A) Percentage of prediction errors of the model with (w) and without (w/o)

associated cells. (B) Rates of interference detection over each block of trials. (C) Number of groups of associated cells

needed to resolve interference across the different blocks of trials.

come able to respond to valence-related inputs and

rapidly silence valence cells that were active in pre-

ceding groups.

3 EXPERIMENTS

The validity of the proposed model is examined

through a series of numerical experiments (cf.

(Kassab and Alexandre, 2015) for the description of

other numerical experiments with this model). The

simulated model is conﬁgured with 150 cells in the

exteroceptive autoassociative network and 3 cells in

the interoceptive autoassociative network. The inter-

mediate valence cells are organized into 5 groups of 3

cells each.

Inputs are provided to the model as two indepen-

dent patterns of activity. The exteroceptive inputs

are generated as random 150-element binary patterns

with 6 elements being active (set to 1). The interocep-

tive inputs are modeled by 3 binary cells to differenti-

ate positive, negative and neutral valence states. One

of these cells switches to its active state according to

whether a pleasant (100), unpleasant (010), or neutral

(001) stimulus is present.

The performance is evaluated by comparing the

output patterns recalled by the model against the orig-

inal representation of the input patterns that were

A Heteroassociative Learning Model Robust to Interference

given as new information to be stored in the model.

Speciﬁcally, two kinds of recall errors are considered

when evaluating simulation results. Pattern comple-

tion errors which reﬂect the Hamming distance be-

tween the learned and retrieved activation for extero-

ceptive patterns, and valence prediction errors which

reﬂect the Hamming distance between the correct and

predicted valence. In both cases, errors are scored

when Hamming distance is greater than zero.

Two types of simulations are set out to test the

model for its ability to rapidly link exteroceptive pat-

terns and their emotional valences while avoiding va-

lence overload interference. The ﬁrst set of simu-

lations examines the effect of the number of stored

patterns on the accuracy of valence prediction. The

model is tested under full-cue and partial-cue re-

call conditions. In both cases the performance of

the proposed model is compared with that of a re-

duced model with the groups of associated cells re-

moved. The second set of simulations focuses on how

to quantify the ability of associated valence units to

orthogonalize conﬂicting associations arising from a

change in previously learned valence values. In all

simulations, we assume that the representations of in-

put patterns are sufﬁciently pulled apart so that no

interference can occur at the level of autoassociative

memories (no pattern overload). This is important to

ensure that the effects observed in the model stem di-

rectly from valence overload interference at the level

of heteroassociative links between exteroceptive and

interoceptive patterns. All results are averaged over

5 simulation runs and are displayed throughout the

ﬁgures as mean ± standard error of the mean. The

novelty-detection thresholds, e and v, are set to zero

for all the simulations.

4 RESULTS

4.1 Overloading

The ﬁrst set of simulations is run by varying the num-

ber of training patterns and observing how valence

prediction is affected with and without the groups

of associated cells included in the model (Figure 2).

Training patterns are presented randomly into blocks

of N trials. Following the ﬁrst presentation of training

patterns, the prediction of the full and reduced mod-

els is perfect up to N=20, after which point prediction

errors begin to occur more frequently with increasing

size of the blocks of training trials. At N=100, the

percentage of prediction errors is a little more than

30% for the reduced model but falls to about 17% for

the full model. This reduction results from the identi-

ﬁcation of about 8% of the stored associations as in-

terfering associations (Figure 2B). Interference effect

is accordingly reduced through the recruitment of one

group of associated cells (Figure 2C). During the sec-

ond presentation of training patterns, the full model

detects all the interfering associations that remain and

orthogonalizes them using the same group of asso-

ciated cells (Figure 2C). Therefore, the performance

of valence prediction differs signiﬁcantly between the

two models after the second presentation of training

patterns: the reduced model continues to commit the

same prediction errors while the proposed model per-

forms with no errors at all.

Next, the model is trained in the same manner as

in the previous simulations except that recall is trig-

gered by partial versions of the original trained pat-

terns. Speciﬁcally, the block size is set to 100 training

patterns and the model is cued with partial versions

with either 1, 2 or 3 of the 6 active inputs turned

off. Figures 3C and D show that the accuracy of

valence prediction with the 1/6 partial-cue condition

is the same as that obtained with the full-cue condi-

tion. This is because exteroceptive patterns are al-

most perfectly reconstructed as shown in Figures 3A

and B. The removal of two or three of the six active

cues causes a proportional decrease in the accuracy

of pattern completion of exteroceptive patterns. Con-

sequently, the improvement in valence prediction by

the proposed model is less pronounced but still highly

signiﬁcant as compared to the reduced model. For

all percentages of removal tested, the model makes

use of one group of associated cells to tackle valence-

overload interference (Figure 3E).

4.2 Discrimination and Reversal

Here we investigate the functional signiﬁcance of the

groups of associated cells using numerical simula-

tions with reversal learning tasks. The task in the

ﬁrst set of simulations involves two phases. In the

ﬁrst phase the model is presented repeatedly with 50

training patterns [e.g. A+, B-, C (neutral), etc.] over

4 blocks of trials and the percentage of prediction er-

rors made at the beginning of each trial is measured

and displayed in Figure 4A. This is a simple discrim-

ination learning problem similar to those tested in

the previous simulations. Thus as was observed be-

fore, valence-overload interference occurs at the early

stages of learning and exhibits the recruitment of one

group of associated cells to tackle it. When the groups

of associated cells are removed the reduced model

shows impaired performance that persists over the re-

peated trials. In the second phase, emotional valences

of the training patterns are randomly changed to other

NCTA 2015 - 7th International Conference on Neural Computation Theory and Applications

Table 1: The experimental design of the task of (Levy-Gigi et al., 2011). Note. A–H refer to eight cue shapes, 1–8, eight

contexts, + and – indicate respectively positive and negative valences.

Training patterns Task

Group 1 Group 2 Group 3 Phase 1 Phase 2

(original) (cue reversal) (context reversal) (acquisition) (retention & reversal)

A1+ E1– A5– Group1 Group1

B2+ F2– B6– Group2

C3– G3+ C7+ Group3

D4– H4+ D8+

value with a probability of 50% [e.g. A-, B (neutral),

C (neutral), etc.]. As shown in Figure 4A the pro-

posed model quickly learns to reverse its behavior as

all the emotionally changed patterns are detected and

learned on the ﬁrst training trials after reversal. On

the other hand, the reduced model fails to acquire the

new associations since the old ones have not been un-

learned.

The second set of simulations involves a cue-

context reversal learning task similar to that estab-

lished by (Levy-Gigi et al., 2011) to investigate rever-

sal learning in patients with mild amnesic cognitive

impairment. To simulate this task, three groups of 4

exteroceptive patterns each are formed such that one

of the 6 active elements is used to encode the presence

of a sensory cue and the others to encode contextual

cues. No overlap is allowed between cells encoding

for different cues or contexts (cf. Table 1).

In the ﬁrst phase of acquisition, the model is re-

peatedly presented with the training patterns in the

ﬁrst group and valence prediction is evaluated over

four blocks of training trials. Figure 5 shows that both

full and reduced models make correct valence predic-

tion after a single exposure to the training patterns.

Then, the reversal phase is immediately followed by

exposing the models to new training patterns from the

second and third groups, in addition to the old ones.

The training patterns are also presented repeatedly

four times in random order. The results show that,

in the ﬁrst block of trials, valence prediction errors

are made for both new and old patterns. This reﬂects

the fact that heteroassociative connections are irrele-

vantly strengthened between the original patterns and

valences of new patterns. When interference is de-

tected, one group of valence-associated cells is re-

cruited and prediction errors fall to zero rapidly on

the third block of trials after reversal. In contrast, the

number of prediction errors the reduced model makes

is still the same as the blocks progress for the same

reason stated above.

5 DISCUSSION

This paper sets emphasis on a class of connectionist

models, associative memories, with powerful proper-

ties for learning by heart speciﬁc patterns and recall-

ing them from partial information. Such models can

be simply used for pattern retrieval but also in het-

eroassociation between two classes of inputs. In our

biologically informed model (Kassab and Alexandre,

2015), we propose such a heteroassociation between

exteroception and interoception. From an informa-

tion processing point of view, we explain in that pa-

per that a heteroassociation between two data spaces

of different size leads to more robust retrieval than a

simple autoassociation with a ﬂat vector concatenat-

ing both kinds of information because the evaluation

of the Hamming distance between stored and actual

patterns would consider in this latter case that one er-

ror in any dimension yields the same penalty, which is

obviously not the case. Beyond the case for pavlovian

conditioning with intero- and exteroceptive cues, we

believe that it is not rare in the information processing

domain to cope with such associations between data

of different dimensions, as it is the case for example

with labeled data (high-dimensional data associated

with a symbolic label). In this case, we claim that

combining auto- and heteroassociation as proposed

here results in more robustness in the retrieval phase.

Results reported in the present paper were cen-

tered on another powerful property of our model,

for managing interferences. When an association is

learned between a high dimensional data space and

a smaller space representing labels (valences in the

present case), one central problem is about the as-

sociation of close patterns with different labels or of

different combinations of patterns with different la-

bels. This classical problem has been termed conﬁg-

ural learning (Buhusi and Schmajuk, 1996). Based

on biological data and also beneﬁting from the sepa-

ration between exteroceptive and interoceptive data,

we have proposed in the present model a mecha-

A Heteroassociative Learning Model Robust to Interference

Figure 5: Cue-context reversal learning. (A) Percentage of prediction errors of the model with (w) and without (w/o) associ-

ated cells. (B) Rates of interference detection over each block of trials. (C) Number of groups of associated cells needed to

resolve interference across the different blocks of trials.

nism able to automatically detect such interference at

the heteroassociative level and to trigger new learn-

ing accordingly. The experiments reported here show

that our model is very efﬁcient at performing such

a learning. In addition, this learning process is very

quick, which preserves another important speciﬁcity

of episodic learning.

These results have been described here in the

framework of information processing, but one of the

experiments has also been designed to reproduce be-

havioral and cognitive data in the medical domain for

amnesic impairments (Levy-Gigi et al., 2011). Re-

lated medical data strongly suggest the central role of

the hippocampus in this memory process, giving ad-

ditional interest to the complementary learning sys-

tem hypothesis (O’Reilly et al., 2011). This cognitive

framework also postulates how procedural learning in

the cortex, slowly learning and able of generalization,

might be instructed by speciﬁc cases learned quickly

in the hippocampus avoiding interferences. Coming

back to the information processing domain, we be-

lieve that better understanding these processes and

modeling them more faithfully is of high interest for

designing machine learning systems combining dif-

ferent memory processes for higher performances.

NCTA 2015 - 7th International Conference on Neural Computation Theory and Applications

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A Heteroassociative Learning Model Robust to Interference