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Why Bilateral Damage Is Worse than UnilateralDamage to the Brain

Anna C. Schapiro1,2, James L. McClelland1, Stephen R. Welbourne3,Timothy T. Rogers4, and Matthew A. Lambon Ralph3

Abstract

■ Human and animal lesion studies have shown that behav-ior can be catastrophically impaired after bilateral lesions butthat unilateral damage often produces little or no effect, evencontrolling for lesion extent. This pattern is found across manydifferent sensory, motor, and memory domains. Despite thesefindings, there has been no systematic, computational expla-nation. We found that the same striking difference betweenunilateral and bilateral damage emerged in a distributed, re-current attractor neural network. The difference persists insimple feedforward networks, where it can be understood in

explicit quantitative terms. In essence, damage both distortsand reduces the magnitude of relevant activity in each hemi-sphere. Unilateral damage reduces the relative magnitude ofthe contribution to performance of the damaged side, allowingthe intact side to dominate performance. In contrast, balancedbilateral damage distorts representations on both sides, whichcontribute equally, resulting in degraded performance. Themodelʼs ability to account for relevant patient data suggeststhat mechanisms similar to those in the model may operate inthe brain. ■

INTRODUCTION

There are indications from decades of research and clin-ical study that a unilateral lesion to a brain area canproduce a very subtle—sometimes clinically insignificant—neurocognitive impairment, whereas a bilateral lesionmay generate a profound deficit. Perhaps the best knowncase example arose in the 1950s, when Scoville produceda profound memory loss in patient HM by removing thehippocampus bilaterally. Scovilleʼs motivation for publish-ing these findings was not only to warn other neuro-surgeons of these clinically dramatic consequences butalso to note that they ran counter to the expectationsarising from patients after unilateral resections, in whomthe observed memory deficit is relatively mild (Scoville &Milner, 1953; Milner & Penfield, 1955).Why are there such different consequences of uni-

lateral and bilateral lesions? One possibility is that a bilat-eral neural system is simply redundant enough acrosshemispheres to accommodate the amount of damagecorresponding to complete unilateral removal. Althoughthis may be part of the story, we will review findingsstrongly suggesting that bilateral lesions are much moredetrimental than unilateral lesions even when unilaterallesions involve the same total amount of damage as bi-lateral lesions. This leads us to consider the possibilitythat there is something special about unilateral relative

to bilateral damage. The computational explorationreported here provides evidence for this possibility, de-monstrating that bilateral damage is much more detri-mental than unilateral damage in a range of distributedneural network models even when the amount of damageis equated.

To anchor the investigation with a concrete, nontrivialtest case, we applied the computational work to the domainof semantic memory. This choice was motivated by theavailability of a considerable body of relevant patient andneuroscience data. In addition, the new computationalinvestigation built on earlier modeling work in which dam-age to a single pool of hidden units was used to simulateeffects of bilateral anterior temporal lobe (ATL) atrophy insemantic dementia (SD; Rogers et al., 2004). The findingswe obtain generalize across tasks and to a range of differentnetwork architectures. Our results may help, therefore, toexplain the different effects of unilateral and bilateral dam-age that have been reported in many human and animalstudies across a range of task domains and brain areas.Such differences apply not only to effects of damage tothe human hippocampus (Scoville & Milner, 1957) andATL as examined in detail here but also to effects ofdamage in, for example, rat hippocampus (Li, Matsumoto,& Watanabe, 1999), primate anterior temporal cortex(Klüver & Bucy, 1939), primate frontal lobe (Warden,Barrera, & Galt, 1942), primate auditory cortex (Heffner &Heffner, 1986), human frontal lobe (DʼEsposito, Cooney,Gazzaley, Gibbs, & Postle, 2006), and human amygdala(Adolphs & Tranel, 2004).

1Stanford University, 2Princeton University, 3University of Man-chester, 4University of Wisconsin-Madison

© 2013 Massachusetts Institute of Technology Journal of Cognitive Neuroscience 25:12, pp. 2107–2123doi:10.1162/jocn_a_00441

We note, in advance, that our results will apply to effectsof unilateral versus bilateral damage to the extent thatthere is a balance of involvement of brain structures acrossthe hemispheres. In cases where a function is completelylateralized, damage to the hemisphere that specializes inthe function will naturally be more disruptive to perfor-mance than balanced bilateral damage. But, as we shallshow, a degree of asymmetry can still be consistent witha relatively milder deficit after unilateral damage, even tothe more dominant hemisphere. We will demonstrate thisby examining the effect of unilateral versus bilateraldamage on two semantic tasks. Performance in one ofthese tasks (word-to-picture matching) appears to be sub-served by the ATL approximately symmetrically, whereasperformance in the other (naming) is underpinned toa greater degree by the left ATL (Lambon Ralph, Ehsan,Baker, & Rogers, 2012; Lambon Ralph, McClelland,Patterson, Galton, & Hodges, 2001; Seidenberg et al.,1998). This is captured in the model before lesioningthrough a mild structural asymmetry.

The Role of Anterior Temporal Regions inSemantic Representation

As noted above, we chose the domain of semantic memoryas a test case for the simulations and, in particular, therole of left and right ATL regions in supporting semanticrepresentations. The degradation of semantic memory inSD and herpes simplex virus encephalitis is associated withbilateral damage to and hypometabolism of the ATLs(Mion et al., 2010; Rohrer et al., 2009; Noppeney et al.,2007; Nestor, Fryer, & Hodges, 2006). Behavioral datafrom these patients have suggested a model in which con-cepts are formed through the convergence of sensory,motor, and verbal experience in a transmodal representa-tional hub in the ATL (Rogers et al., 2004).

Although previously overlooked, there is now a grow-ing consensus that this transmodal ATL hub contributescritically to semantic cognition (Patterson, Nestor, & Rogers,2007). This emerging view reflects a convergence of theestablished clinical data on SD, herpes simplex virus en-cephalitis, etc., with contemporary neuroscience studies.Data from TMS and functional neuroimaging indicate

that both left and right ATL regions contribute to semanticmemory. For example, the multimodal, selective seman-tic impairment of SD can be mimicked in neurologicallyintact participants by applying rTMS to the left or rightlateral ATL (Pobric, Jefferies, & Lambon Ralph, 2007,2010; Lambon Ralph, Pobric, & Jefferies, 2009). Likewise,when using techniques that avoid (e.g., PET or MEG) orcorrect for the various methodological issues associatedwith successful imaging of the ATL (Visser, Jefferies, &Lambon Ralph, 2010; Devlin et al., 2000), studies find bilat-eral ATL activation for semantic processing across multipleverbal and nonverbal modalities (Visser & Lambon Ralph,2011; Binney, Embleton, Jefferies, Parker, & LambonRalph, 2010; Visser, Embleton, Jefferies, Parker, & LambonRalph, 2010; Sharp, Scott, & Wise, 2004; Marinkovic et al.,2003; Vandenberghe, Price, Wise, Josephs, & Frackowiak,1996).This domain is a highly pertinent one for the current in-

vestigation given that unilateral and bilateral ATL damagehave very different consequences on semantic perfor-mance (mirroring the pattern found in other cognitivedomains). This conundrum is summarized in Figure 1. Interms of clinical presentation, the bilateral atrophy of SD(Figure 1A) leads to a notable, selective semantic impair-ment (Patterson & Hodges, 1992; Snowden, Goulding,& Neary, 1989; Warrington, 1975). In contrast, patients withunilateral ATL damage (in this example, Figure 1B, afull en bloc ATL resection for intractable temporal lobeepilepsy [TLE]) do not report comprehension impairment(Hermann, Seidenberg, Haltiner, & Wyler, 1995; Hermannet al., 1994) but do complain of amnesia and anomia, espe-cially following left ATL resection (Glosser, Salvucci, &Chiaravalloti, 2003; Martin et al., 1998; Seidenberg et al.,1998). The two contrastive patients in Figure 1 are particu-larly pertinent given that the unilateral case represents acomplete removal of ATL tissue (Figure 1B) but had littleor no drop in accuracy on standard semantic tests (seebelow), whereas the bilateral case represents only par-tial tissue loss (Figure 1A) but exhibited considerablesemantic impairment. Although an exact comparison ofthe extent of relevant tissue loss is not possible, the nota-ble difference in the extent of deficit despite comparablelesion size suggests that size is only part of the story.

Figure 1. Example scans ofpatients with unilateral andbilateral ATL damage. (A) Anexample axial MRI for a patientwith semantic impairmentresulting from bilateral ATLatrophy (orange arrows).(B) A comparable axial slicefrom a patient following ATLunilateral resection for TLE (redarrow). The red region on thelateral view shows the resectedarea. Adapted from Figure 1 ofLambon Ralph et al. (2012).

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These clinical observations are striking but need to betreated with some caution given that clinical assessmentof TLE patients tends to focus on naming and episodicmemory and rarely on comprehension (Giovagnoli,Erbetta, Villani, & Avanzini, 2005). Two recent case seriesneuropsychological studies, therefore, assessed this clini-cally apparent contrast via in-depth explorations ofsemantic function. The results not only supported theclinical observations but also provided a bridge to theneuroimaging and rTMS data noted above. The first study(Lambon Ralph, Cipolotti, Manes, & Patterson, 2010) in-vestigated patientsʼ accuracy on a range of tasks takenfrom a multimodal semantic battery commonly used toassess patients with SD (Bozeat, Lambon Ralph, Patterson,Garrard, & Hodges, 2000). A case series of patients withunilateral left or right ATL damage (of mixed etiology)performed at or very close to normal levels of accuracyon the various comprehension tasks, whereas most SDpatients were impaired (Figure 2). In addition, like SDpatients with asymmetrically left-biased ATL atrophy(Lambon Ralph et al., 2001), the left unilaterally damagedpatients exhibited significantly greater anomia than theirright-sided counterparts. The second study focused spe-cifically on patients with left- or right-sided ATL resectionsfor the treatment of TLE (Lambon Ralph et al., 2012). Again,on standard accuracy-based measures of semantic func-tion, the vast majority of the resected TLE patients per-

formed within the normal range. However, mild semanticdysfunction was revealed when either the semantic de-mands of the tasks were increased (by probing specific-level concepts, low frequency, or abstract items) or bymeasuring RTs as well as accuracy (the patients were twoto three times slower than older controls even on thesimpler semantic tasks). Performance on these more de-manding semantic measures correlated significantly withthe volume of resected tissue and, again, the left-resectedpatients exhibited significantly greater anomia than theright-sided cases. Together, these results provided us witha series of target phenomena to be captured in the com-putational model:

i. regions within the left and right ATL jointly supportpan-modal semantic function in neurologically intactparticipants;

ii. unilateral resection or stimulation via rTMS generatesdetectable but mild semantic impairment;

iii. bilateral lesions generate significantly greater seman-tic impairment than unilateral damage, even whenoverall amount of damage is similar;

iv. left ATL damage generates greater naming impairmentthan equivalent levels of right ATL damage.

To fully account for the range of lesion scenarios, wealso explored the possibility that, in some patients,

Figure 2. Patient performance. The proportion of items correct (out of 64) on naming and word-to-picture matching tasks of patients withunilateral left, unilateral right, and bilateral ATL damage. Averages for each patient group are included on the far right of each graph, witherror bars indicating ±1 SEM. The full horizontal line denotes control–participant mean performance, and the dashed line shows 2 SD belowthe control mean. Adapted from Figure 2 of Lambon Ralph et al. (2010).

Schapiro et al. 2109

plasticity-related recovery after or during the course ofbrain damage may have affected postlesion performance(Keidel, Welbourne, & Lambon Ralph, 2010; Welbourne& Lambon Ralph, 2005; Wilkins & Moscovitch, 1978).Patients continue to engage in semantic processing afteran acute lesion or, in degenerative cases, as their diseaseprogresses, and this engagement may help to amelioratethe effects of damage (Welbourne & Lambon Ralph,2005). We considered the effects of plasticity-relatedrecovery in the model to demonstrate its applicabilityto these scenarios.

Overview of the Model

The model we used to account for the stark contrast be-tween the behavior of patients with unilateral and bilat-eral damage is an extension of a model used previously toexplain the deterioration of semantic task performance inSD (Rogers et al., 2004). It consisted of processing unitsthat were organized into layers and connected as shownin Figure 3. The connection weights between the unitswere established by training the network with patternsderived from descriptions and visual properties of familiarobjects. The input to the network came from the verbaldescriptor and visual feature layers, which are consideredanalogous to cortical areas that subserve high-level verbaland visual information, respectively. The verbal descriptorswere divided into sublayers that represent names, verbaldescriptions of perceptual features, functional descriptors,and encyclopedic information.

The model extended the previous simulation architec-ture (Rogers et al., 2004) by dividing what was previouslya single pool of hidden units into two: left demi-hub andright demi-hub. Units in these pools had no prespecifiedrepresentations—rather, the pools developed distributedrepresentations over the course of training that allowedthe network to map between the features of the objectsin the environment and to capture the similarity relations

of the objects to one another. The layers of the modelwere highly interconnected, with complete bidirectionalconnectivity (all the units in one layer connected bidirec-tionally to all the units in another layer) between verbaldescriptors and left demi-hub, visual features and leftdemi-hub, and visual features and right demi-hub. The pro-jection from the verbal descriptors to the right demi-hubwas complete, but the return projection had about 80% ofall the possible connections. The difference between den-sity of projection from the left demi-hub to verbal descrip-tors and that from the right demi-hub to verbal descriptorscaused the left demi-hub, over the course of training, toplay a somewhat more important role in tasks like namingfrom visual input that require a verbal response, aligningthis model with our previous one on laterality effects inSD (Lambon Ralph et al., 2001).An important feature of the model was the stipula-

tion that the density of the recurrent connections withineach hidden layer was 90% whereas the density of theprojection between the hidden layers was only 10%. Thisstipulation is consistent with the fact that there are moreintrahemispheric than interhemispheric connections incortex (Gee et al., 2011; Lewis, Theilmann, Sereno, &Townsend, 2009; Braitenberg & Schüz, 1998). As we shallsee, our model suggests that this difference may be animportant part of the reason why bilateral damage is moredisruptive than unilateral in neural populations with recur-rent connections.In what follows, we first demonstrate that our model

simulates an advantage of unilateral compared with bilat-eral damage when overall lesion severity is equated. Weproceed to consider this phenomenon in a range of net-work architecture variants, one of which is sufficiently sim-ple to allow us to express mathematically the fundamentalbasis for the advantage of unilateral lesions. Our analysisshows why the advantage occurs in a wide range of neuralnetwork architectures and, therefore, why it is natural toexpect that this advantage should occur in real biologicalneural networks such as those found in the brains ofhumans and other animals.

METHODS

The reported simulations were conducted using the LENSneural network simulation environment (www.stanford.edu/group/mbc/LENSManual/index.html). A network verysimilar to the one used by Rogers et al. (2004) was re-implemented within this environment. The followingdescribes the main simulation reported first in the Resultssection. Other simulations used similar methods; wheredetails differ from the main simulation, this is stated inthe Results section.

Network Initialization

In setting up the network, complete projections werecreated by simply connecting each unit in the projecting

Figure 3. Model architecture. The model consists of two input/outputlayers, verbal descriptors and visual features, and two hidden layers,left demi-hub and right demi-hub. Arrows indicate full connectivityfrom all the units in the projecting to the receiving layer, except wherethere are percentages written which specify a different degree ofconnectivity.


layer to each unit in the receiving layer. For sparser pro-jections, for example, the 10% connection between thetwo hidden layers, each unit in one hidden layer was con-nected to each unit in the other hidden layer with anindependent probability of 0.1. As a result, each instantia-tion of a network had a different pattern of connectivityand a somewhat variable proportion of connections.Weights were also assigned randomly before training,with values chosen uniformly between −1 and 1.

Activation Dynamics

Each unit in the verbal descriptors and visual featureslayers represented a unique verbal or visual property ofan object. To present an object to the network, the unitsrepresenting the features of the object took on the value 1,and otherwise had the value 0. The presentation of anitem to the network was divided into seven time intervals;in each interval, activation of each unit i was calculatedby first determining the net input, ni, to the unit:

ni ¼Xj

ajwij

where j indexes all units that project to unit i, aj is theactivation of unit j, and wij is the weight of the connec-tion from unit j to unit i. The activation of unit i was thencalculated based on the following logistic function, whichbounds activation between 0 and 1:

αi ¼ 11þ e−ni

:

All units were assigned a fixed, untrainable bias of−2, which deducts 2 from each unitʼs net input. Thisbias parameter, in the absence of other input, keeps unitactivations on the low end of their range (at approxi-mately 0.12).

Training

The network was trained and tested using 48 patternsorganized into six natural taxonomic categories (birds,mammals, vehicles, household objects, tools, fruits).Patterns were generated from the visual feature and ver-bal descriptor prototypes used by Rogers et al. (2004),which were designed to reflect the similarity relations oftypical objects in the six categories. The similarity of pat-terns within categories varies across categories as it doesfor real objects in the corresponding categories. Patternswere constructed exactly as in Rogers et al. (2004) withthe exception that object names were not given at differ-ent levels of specificity in the present work—each of the48 objects was assigned its own unique name.Training the network involved teaching it to “bring

to mind” the full information associated with an item,either from the name, the visual pattern, or from non-

name verbal descriptors of the item. Accordingly, in eachtraining trial, the units corresponding to one of these threeinputs (units in the name, other verbal descriptors, orvisual features layer) were set (hard-clamped) to the speci-fied input values for three intervals of processing. Theclamps were then removed, and the network cycled forfour more intervals, so that all unit activations were thendetermined by the propagation of activation through thenetworkʼs connections. During the last two intervals ofthe seven total, the target values for all visual and verbalpatterns (including name) were applied, and error de-rivatives for weights in the network were calculated. Train-ing was conducted using the standard back propagationgradient descent learning algorithm for recurrent networksin LENS, with 200,000 sweeps through each of the 48 train-ing patterns presented in a random order (each sweep iscalled an epoch). Weights were updated at the end ofeach epoch, except during recovery, when a finer grainof detail is necessary and weights were updated afterevery pattern. The model was trained with a learningrate of 0.005, weight decay of 0.0002 per epoch duringtraining (0.000001 per pattern during recovery), and nomomentum. Zero-mean 0.5 standard deviation Gaussiannoise was added to the net input of each unit at eachactivation update. Gaussian noise with the same stan-dard deviation was also included during testing unlessotherwise specified.

Testing

Testing for picture naming assessed the networkʼs abilityto activate the correct name unit from visual input. Thiswas implemented by clamping the visual feature units tothe values corresponding to a trained object, allowingactivation to propagate for three intervals, then removingthe input and allowing activation to continue to propagatefor four more intervals. The unit with the highest activa-tion was treated as the modelʼs name response to thepresented picture.

The test for word-to-picture matching compared thepattern across the hidden layers produced by an itemʼsname with the patterns produced by several alternativevisual input patterns. A trial was scored correct if the pat-tern produced by the name for an item was more similarto the pattern produced by the visual feature input patternfor the same item than it was to the pattern produced bythe visual input pattern for seven distractor items. To ac-complish this, the target name unit was clamped for thefirst three processing intervals; input was then removed,and activation continued to propagate for four intervals.The resulting pattern of activation across all units inboth hidden layers was recorded. This process was re-peated with visual feature input for the target conceptand each of the seven remaining items in the same seman-tic category (acting as the foils in the assessment). Theresulting patterns of hidden unit activation can be thoughtof as nine vectors (one resulting from presentation of the


name and eight from presentation of the visual features),where each unitʼs activation is an element of the vector.The cosine between the vector from the name input andthe vector from each of the visual feature inputs was usedas the measure of similarity.

The cosine indicates the degree of similarity betweentwo vectors, independent of their magnitudes, and isdefined as the dot product of the two vectors dividedby the product of their magnitudes:

cosðV1; V2Þ ¼ V1 � V2jjV1jjjjV2jj

where V1 � V2 ¼P

i V1iV2i and jjV jj ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiPi V

2i

p. The set of

visual features that resulted in the highest cosine with thename was interpreted as the modelʼs choice of picture.

Simulation of Behavioral Deficits under Damage

To investigate the effects of damage on task performance,the model was damaged at several levels of severity, bypermanently removing connections into and out of a layerwith a specified probability. Damage of, for example, 50%to a hidden layer consisted of removing connections intoand out of each unit in that layer with a probability of 0.5.For progressive damage simulations, where lesions wereapplied incrementally and the network was tested asdamage progressed, damage levels refer to the total cumu-lative proportion of connections removed up to that point.Bias weights were not lesioned, although results were thesame when lesions to bias weights were allowed.

In one of the simulations reported below, damage wassimulated by the removal of whole units rather than indi-vidual connections. In this case, damage to a layer con-sisted of unit removal with a specified probability. Aswith other forms of damage, removal was probabilistic,such that the actual number of units removed could vary.

Damage was applied to one or both of the hidden(demi-hub) layers. For a given severity level, a bilaterallesion was produced by applying this probability uniformlyacross the two hidden layers, whereas unilateral left andright lesions were produced by applying damage withtwice this probability to the connections into and out ofonly one of the two hidden layers. Following this pro-cedure, the largest possible unilateral lesion correspondedto a 50% bilateral lesion. However, we extended bilaterallesions beyond this severity level to 100% to simulate moresevere stages of SD and other bilateral diseases. In thecase of bilateral damage, the connections between thetwo hidden layers were removed at the associated uni-lateral damage level to ensure that the total number ofconnections was approximately equal in the unilateraland bilateral damage cases. For example, if 50% of theconnections between hidden layers were removed for aunilateral lesion, 50% of those connections were againremoved in the corresponding case of bilateral damage(as opposed to 25% removal twice—one for each hidden

layer—which would result in only 44% of these connectionsbeing lesioned).To examine how experience after damage or during the

course of degeneration might affect performance in themodel, we conducted simulations using varying amountsof recovery after performing a simulated lesion. Duringthis progressive damage, retraining occurred after eachround of lesioning, and the network was tested imme-diately before and after an episode of damage and theresults of the two tests were averaged. This was doneto approximate the more continuous mix of damage andexposure to the environment that patients with neuro-degenerative disease experience.Results reflect the performance of 10 trained networks

initialized with different random seeds. Each networkwas tested after each combination of lesion type (left,right, or bilateral), severity, and recovery amount (wherethese were varied), and the results were averaged overthe 10 separate networks.

RESULTS

Differential Effects of Unilateral versusBilateral Damage

Our first simulation demonstrates a striking differencebetween the effects of unilateral and bilateral lesions inthe recurrent network architecture shown in Figure 3.Figure 4 summarizes simulated picture naming and word-to-picture matching performance as a function of differ-ent levels of unilateral left, unilateral right, and bilateralconnection damage following training of the recurrentnetwork. Results are presented separately for differentamounts of recovery after each simulated lesion. Networkswith bilateral damage performed much worse than thosewith unilateral damage on both tasks, even with the sametotal amount of damage and recovery (see Table 1 forstatistics). Bilateral damage caused performance to fallrelatively quickly, whereas even a complete unilaterallesion, especially with some recovery, had a relativelysmall effect. The difference between the effect of unilateraland bilateral damage became more pronounced withincreasing lesion severity.One additional feature of these results is that in none of

these cases did performance drop off immediately as soonas there was any damage. The use of distributed representa-tions in the model, encouraged by the presence of noiseand weight decay in training and by retraining after dam-age, made the model quite robust. This graceful degrada-tion (Farah & McClelland, 1991; Hinton & Sejnowski,1983) is clear in patients as well—SD patients demonstratea drop in semantic performance over time and have someremaining semantic ability even after extensive atrophy.There was also a difference, especially in naming,

between left-sided and right-sided unilateral damage.Because of the somewhat greater role of the left demi-hubin mapping visual to verbal features, damage to the left


side of the network was more detrimental to naming thandamage to the right side. There was also a small differencebetween left-sided and right-sided unilateral damage inword-to-picture matching.The simulation results presented so far employed

cumulative damage with retraining after each stage oflesioning. Some of the unilateral patients, for example,those with long-standing epilepsy followed by resection,had damage that was only partially progressive and some,for example, those with stroke, had damage that wouldnot have been progressive at all. We ran additional simu-lations to test whether the model would perform differ-ently if damage were applied all at once, followed by aperiod of recovery (to mimic an acute neurological eventfollowed by spontaneous partial recovery) instead ofinterleaving damage and retraining. The results of thenonprogressive damage simulations were very similarto those for the progressive damage simulations (seeAppendix 1).

Effect of Lesions on Similarity Structure

Why does a unilateral lesion have less effect on perfor-mance than the same severity of lesion distributed bilater-ally? To understand these differential effects of unilateral

and bilateral damage in the model, we examined how thesimilarity structure of its internal representations changedwith damage. This is useful because distortions to the simi-larity structure were the source of errors in word-to-picturematching and contributed to errors in naming (for naming,weights from the hidden layers to the name layer alsocontribute). For this analysis, we used a network archi-tecture in which the differential connectivity from theleft and right demi-hubs to verbal output was eliminatedfor simplicity, and no recovery was allowed, althoughsimilar results were obtained with an architecture thatretained the differential connectivity and for networks withvarious levels of recovery.

We obtained the pattern of activation across both demi-hubs for presentations of each objectʼs name and eachobjectʼs visual input pattern, as in the word-to-picturematching task, then calculated the cosine similarity ofthe pattern produced by each name with the patternproduced by each visual input pattern, averaging theresults across 10 networks. This yielded a 48 × 48 matrix,with each item corresponding to a row of the matrix(visual feature input) and a column (name input), asshown in Figure 5. Objects in the same category aregrouped together. High cosine values along the diagonalof the matrix for the intact network (left-most panel of

Figure 4. Performance of the network on word-to-picture matching and naming with unilateral and bilateral damage. Proportion correct onthese tasks is shown for 20 levels of damage in each graph, labeled by the proportion of connections removed from units in both hidden layersor one hidden layer. Deterioration of performance is shown with no recovery throughout the course of damage, one epoch of recovery betweeneach episode of damage, and 10 epochs between each episode of damage.


figure) indicated that the network was able to associate anobjectʼs visual features correctly with its name. Althoughthe cosines are generally higher within than between cate-gory, the correct (diagonal) entry is strongest in each rowand each column before damage. As damage increased,the similarity structure of the unilaterally lesioned networkwas fairly well preserved, allowing it to distinguish anitem from the others in its category with fairly high accu-racy, even after a complete lesion to one side of the net-work. The bilaterally damaged network, in contrast, lostthe appropriate similarity structure rapidly; with a 50%lesion to each side of the network, the similarity struc-ture seen with the intact network was nearly completelyobliterated, accounting for its very poor performance.

Simpler Networks and Representation Analyses

The preceding analysis shows that bilateral damagedegrades the similarity structure of the networkʼs internalrepresentations, whereas unilateral damages leaves thislargely intact. What causes this phenomenon? Thebidirectional and recurrent connections in the currentmodel make it difficult to answer this question, so wenext considered a simpler network architecture in whichall connections were feedforward (i.e., projecting in onedirection, from input toward output).

Feedforward Network

In the feedforward network, each of the layers that waspreviously used as both input and output was duplicatedso that one copy could be used for the input and theother for the output (see Figure 6). In addition, there wereno recurrent connections within or between the twohidden layers, no recovery was allowed, and the connec-tions into and out of the two hidden layers were completeand symmetric. Although training affects both input andoutput connections to the hidden units in this model,only the input connections affect the internal represen-tations, allowing a focused analysis of the fundamentalbasis for the unilateral versus bilateral differences inword-to-picture matching in this version of the model. Wetrained 10 networks initialized with different random seedsas in the main simulation, then applied unilateral and bilat-eral damage to this feedforward architecture by removingconnections as in previous simulations. During trainingand testing, activations were calculated in a single feed-forward pass, and noise was included in processing asper the main simulation. Even in this simplified networkthere was still an advantage for unilateral compared withbilateral damage, both in word-to-picture matching andnaming (Appendix 2).

Representation Fidelity

We chose a measure which we call “fidelity” to quantifythe loss of similarity structure in this network. Because

Table 1. Analysis of Variance for Figure 4 Results

df F p

No Recovery

Word-to-picture matching

Damage 10, 90 301.2 <.0001

Bilateral vs. mean unilateral 1, 9 264.0 <.0001

Damage * unilateral vs. bilateral 10, 90 74.57 <.0001

Right vs. left unilateral 1, 9 4.53 .0622

Naming

Damage 10, 90 888.7 <.0001



Right vs. left unilateral 1, 9 62.52 <.0001

One Epoch Recovery


Damage 10, 90 405.9 <.0001




Naming

Damage 10, 90 372.1 <.0001




Ten Epochs Recovery


Damage 10, 90 81.85 <.0001




Naming

Damage 10, 90 172.3 <.0001




Two-factor repeated-measures ANOVAs treat network initializations as therandom effects factor, assessing overall effect of damage extent, effect ofunilateral (averaged across right and left damage) compared with bilateraldamage, the interaction between damage extent and the difference be-tween unilateral and bilateral damage, and the difference between rightand left unilateral damage. Damage levels include zero to full unilateraldamage over 11 increments (as in Figure 4 unilateral damage).


the relative values of the on- and off-diagonal cosinesin the matrices shown in Figure 5 govern the networkʼsability to perform semantic tasks like naming and word-to-picture matching, fidelity is defined as the differencebetween mean diagonal and off-diagonal cosine terms,including both within- and between-category off-diagonalentries (see Figure 7 caption for details). Although fidel-ity does not correspond directly to accuracy, greater fidel-ity is associated with more accurate performance. Thismeasure is useful because it can be applied to the leftand right demi-hubs separately to provide an assessmentof the extent to which each side carries the appropriatesimilarity information on its own. Figure 7A shows the fi-delity of an intact demi-hub on its own, a damaged demi-hub, the average of those two, and compares this to the

average of bilaterally damaged demi-hubs (each of whichproduces fidelity similar to this average). We found thatwithin a layer, fidelity was approximately equal to thefraction of connections remaining, with the result thatthe average fidelity was very similar in the unilateraland bilateral cases, equating for the total number of con-nections removed. (See Simplified Mathematical Analysisand Note 1 for an explanation of the divergence betweenaverage unilateral and bilateral fidelity at high levels ofdamage.)

If average fidelity across the left and right demi-hubs isas impaired after a unilateral lesion as it is after a bilaterallesion, why then is word-to-picture matching and namingmore accurate after the unilateral lesion? The reason isthat the fidelity calculated across both layers remainsmuch higher in the unilateral case. Figure 7B shows thefidelity measure calculated across both layers of the feed-forward network, either with unilateral damage orbilateral damage. As in word-to-picture matching andnaming performance, we found that the fidelity was alwayshigher in the unilateral than bilateral case (see Table 2).Interestingly, fidelity followed a U-shaped function,decreasing over low to moderate levels of damage, thenincreasing again as the extent of damage approached itsmaximal value. This occurs because variation from item toitem in the pattern of activation of the units in the damagedlayer diminishes as the fidelity decreases, and so these unitscontribute less and less to the overall fidelity of the repre-sentations. By the time their contributions become veryweak, the intact side of the network completely dominatesperformance. Thus, a layer with a large amount of unilateraldamage carries little information about the items but alsocontributes little to the overall performance of the networkbecause it does not provide a differential response acrossitems. This is the essence of the reason why unilateraldamage is so much more benign than bilateral damage:With more and more damage to just one side of the net-Figure 6. Feedforward model architecture.

Figure 5. Degradation ofsimilarity structure underunilateral and bilateral damage.The colors in the heatmapsrepresent the value of thecosines between hidden layeractivation vectors after eachset of visual features (indexedby rows) and each name(indexed by columns) werepresented to the intactnetwork and to the networkafter two levels of unilateraland bilateral damage. Namesand visual features are clusteredby category. Cosine values rangefrom 0 (blue) to 1 (red).


work, its own fidelity decreases, but the magnitude of itscontribution to differences among the representations ofdifferent items also decreases, reducing its impact on over-all fidelity, and therefore overall performance.

Simplified Mathematical Analysis

To see this effect in mathematical terms, we considered theeffect of lesions on the cosine of the vectors of net inputs(excluding bias) to units in the hidden layer in the simpli-fied feedforward architecture. Although activations, andnot net inputs, were used in the network testing and fidel-ity calculations reported thus far, the net input is the signalthat produces the meaningful differences among the hid-den unit patterns produced by different items. The activa-tion of each unit is a monotonic function of its net input,subject to perturbation by the Gaussian noise term addedto each unit's net input. As the net inputs tend toward 0, allhidden unit activation values tend toward uninformative,uniformly distributed random values based on the Gaus-

sian noise, causing the fidelity measure to fall to 0. Fidelitycalculated using net inputs instead of activations yielded re-sults similar to those in Figure 7A and 7B1. Based on theseconsiderations, the analysis of net inputs we present belowcaptures how the signal conveyed by the name or visualpattern for an item is affected by various levels of damageto connection weights.To begin our examination of the net input cosines, let

Vv be the net input across hidden layer units resultingfrom presentation of a particular objectʼs visual featuresand let Vn be the net input across hidden layer units re-sulting from presentation of that same objectʼs name.Each of these vectors can be broken up into the patternof activation for the left half of the hidden units, Vvl andVnl, and that for the right half, Vvr and Vnr. The cosinebetween the two complete vectors can be represented

cosðVv; VnÞ ¼P

i VvliVnli þP

i VvriVnriffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi V

2vli þ

Pi V

2vri

� � Pi V

2nli þ

Pi V

2nri

� �q :

Figure 7. Fidelity of semantic representations as a function of damage. Fidelity was defined as the difference between mean diagonal andmean off-diagonal cosine values. The value of this difference was normalized by the value for the intact network, which therefore had a fidelityvalue of 1. (A) Fidelity in the damaged layer alone (damaged unilateral), the remaining, undamaged layer (intact unilateral); the average of thesetwo (average unilateral); and the average of the fidelity across two bilaterally damaged demi-hubs matched for damage to the unilateralcases (average bilateral). (B) Fidelity measure applied directly over both hidden layers in the cases of unilateral and bilateral damage in thefeedforward network. (C) Same as B but in the recurrent architecture. (D) Same as C, but after unit instead of connection damage. This networkhad 400 instead of 64 hidden units, as discussed in the text.


Note that each of the two sums in the numerator cor-responds to the dot product of the corresponding vectors,and (from the definition of the cosine, in Methods) thedot product of two vectors is equal to the cosine betweenthe vectors times the product of the vectorsʼ magnitudes.Similarly, each summation in the denominator correspondsto the square of themagnitude of the corresponding vector.Thus, the above equation can be rewritten

cosðVv; VnÞ ¼ jjVvljjjjVnljjcosðVvl; VnlÞ þ jjVvrjjjjVnrjjcosðVvr; VnrÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijjVvljj2 þ jjVvrjj2� � jjVnljj2 þ jjVnrjj2

� �q :

We call this the “magnitude-weighted cosine equation.”We can now consider how unilateral versus bilateral dam-age affects this cosine by understanding how it affectsthe contributing magnitudes and cosines.First, we consider in general terms the effect of damage

to the weights coming into a common layer from twosources, corresponding to the name and the visual inputto a pool of hidden units, on the net input cosines andmagnitudes. The cosine reflects the degree to which thetwo net input vectors are similar. We consider the idealcase in which (before the lesion) the cosines on the leftand right are both equal to 1 (i.e., the visual and namenet inputs are identical). We also assume the left andright vectors have the same number of elements (samenumber of units on the left and on the right). We further

assume that a lesion affects incoming weights from thename and visual units with equal probability p, so thatthe expected fraction of remaining incoming name andvisual weights is R = 1 − p. These assumptions hold forthe lesions we have performed on our networks. We cannow examine how a lesion degrades this similarity rela-tionship. As shown in Figure 8A, the average value aftera lesion sparing proportion R of the weights (denotedby < >R) of the cosine between two vectors is simplyequal to R times the original value of the cosine:

< cosðVv; VnÞ >R¼ RcosðVv; VnÞ:

This “cosine shrinkage equation” applies to the effect of alesion to incoming weights on the cosine over either halfof the hidden units or to a uniform bilateral lesion overthe weights coming to all of the hidden units.2

To see how the cosine is affected by a unilateral or, moregenerally, an unequal lesion, we must consider the effectof damage to weights on the magnitudes of the contrib-uting net input vectors, as well as the effect on the con-tributing vectorsʼ cosines. The average effect of a lesionleaving R remaining weights on the magnitude of a net in-put vector is

ffiffiffiR

p jjV jj, where jjV jj represents the vectorʼsmagnitude before the lesion.3 For a lesion leaving thesame proportion R of the weights contributing to Vv andVn, we see that the average value of the product of thetwo vectorsʼ magnitudes after the lesion < jjVvjjjjVnjj >R

is equal to RjjVvjjjjVnjj, as shown in Figure 8B.Now, we can consider separately the effect of a unilateral

lesion versus a bilateral lesion. The remaining fraction ofweights on each side, Rr and Rl, determine the relativeweight of the right-side and left-side cosine in the value ofthe overall cosine (again, on each side, we treat the lesion asaffecting the incoming name and visual weights equally).We assume that, before the lesion, the name and visual vec-tors have the same magnitude, and that the magnitude ofthe left half of each vector is the same on average as themagnitude of the right half of each vector. Effectively thismeans that the magnitudes of the four vectors jjVvljj,jjVvrjj, jjVnljj, and jjVnrjj all have the same value M. Com-bining these assumptions with the finding above that< jjV jj >R¼

ffiffiffiR

p jjV jj, replacing R with Rl and R with Rr

for the proportions of connections remaining on theleft and right sides, respectively, substituting into themagnitude-weighted cosine equation and simplifying, wefind that

< cosðVv; VnÞ >Rl ;Rr¼Rl

Rl þ Rr< cosðVvl; VnlÞ >Rl

þ RrRl þ Rr

< cosðVvr; VnrÞ >Rr:

That is, after asymmetric damage, the relative weight ofthe left and right sides, wl and wr, are wl = Rl/(Rr + Rl)and wr = Rr/(Rr + Rl), respectively.

Table 2. Analysis of Variance for Figure 7 Results

df F p

Feedforward Architecture Fidelity over Both Hidden Layers

Damage 5, 45 1370.5 <.0001



Recurrent Architecture Fidelity over Both Hidden Layers

Damage 5, 45 861.61 <.0001



Recurrent Architecture Fidelity over Both Hidden Layers afterUnit Damage in Larger Network

Damage 5, 45 71.09 <.0001



Two-factor repeated-measures ANOVAs treat network initializations asthe random effects factor, assessing overall effect of damage extent,effect of unilateral compared with bilateral damage, and the interactionbetween damage extent and the difference between unilateral and bilat-eral damage. Damage levels include zero to full unilateral damage oversix increments (as in Figure 7).


In this equation, consider the effect of removal of someproportion of the connections coming into the right halfof the hidden units. This will reduce the magnitudes of thenet inputs to the right hidden units, and correspondinglyit will therefore reduce the relative weight of the right-side cosine—in the extreme case of a total right-sided le-sion, sparing all of the weights on the left (Rl = 1, Rr = 0),the right-side contribution goes to 0 and we are left onlywith the intact left side contribution, unaffected by thelesion. Crucially, in a bilaterally damaged network, whereafter the lesion Vvl and Vnl would have the same magnitudeas Vvr and Vnr, the magnitude normalization would notresult in domination by either side, and the distortion tothe overall cosine would be the same as the equivalentdistortion to each of the two cosines. These effects aredepicted in Figure 8C, where we plot the overall cosineresulting from a pure one-sided lesion and the overallcosine resulting from an equal bilateral lesion, under thefurther simplifying assumption that the right- and left-sided cosines are both equal to 1 before the lesion. Inthe latter case, the cosine falls linearly with damage; inthe former case, it actually follows a U-shaped pattern,decreasing then increasing again as damage weakens therelative contribution of units on the right hand side ofthe network. Once again the equation closely matchesthe result obtained by simulation.

The results of the analysis just described are closelyapproximated by the calculated values of the cosines aftersimulations of damage to the network, as shown by theagreement of the theoretical and simulation-based curvesshown in Figure 8. (For the simulation results, the originalvalues of the separate left, right, and overall cosines are

not exactly equal to 1, because the net inputs from thename and visual units are not exactly identical. The resultsshown are normalized by the prelesion value of the rele-vant cosine term—left, right, or overall.) It is importantto note that the expected (average) value of the cosine isnot an exact predictor of accuracy in word-to-picturematching performance; the differences between cosinesfor targets and foils and the variability in these differencesultimately determines whether the correct or incorrect al-ternative is chosen. Nevertheless, the analysis provides aclear demonstration of the reason why a unilateral lesionhas a relatively benign effect: Although the lesioned sidemay be grossly affected, its contribution to performanceis reduced as a consequence of the lesion.

Fidelity and the Unilateral versus BilateralAdvantage in the Recurrent Network

Returning now to the more realistic recurrent architecture(from Effect of Lesions on Similarity Structure section),we can apply the fidelity analysis as before. Figure 7Cshows the decreasing fidelity for unilateral and bilaterallydamaged networks at increasing levels of damage. Thesecurves resemble those for performance on word-to-picture matching and naming (Figure 4), indicating thatthese analyses provide a good account of the basis forthe difference between unilateral and bilateral perfor-mance in those tasks.It is interesting to consider why the fidelity falls more

rapidly overall with damage in the recurrent networkthan in the feedforward network. This can be understoodby noticing that, in the recurrent network, a lesion to

Figure 8. Effect of unilateral and bilateral connection weight removal on the cosine of the net input vectors at the hidden layer in the feedforwardnetwork. Analytic approximation (labeled “Equations”; solid lines) and actual values obtained in simulations (dashed lines). The cosine is calculatedbetween the net input vector produced by inputting the name of an item with the cosine of the vector produced by the visual input pattern forthe same item. (A) Effect of a lesion to weights coming into hidden units on one side on the cosine across the units on that side. (B) Effect of alesion to weights on one side on the product of the magnitudes of the two vectors on that side. (C) Effect of a unilateral or bilateral lesion onthe cosine of the net input vectors across both hidden layers. The curves labeled “equations” are based on the formulas given in the text. Thesimulation results were obtained by applying the following procedure to each of the 10 feedforward networks and averaging the results obtainedfor each network: At each lesion level, connections were removed from one or both hidden layers. Then all 48 names were presented, and theresulting hidden unit activation pattern was recorded for each. The same was done for all 48 visual patterns. There was no noise added to the netinputs in these simulations, and the bias term was not included in the net input value. The cosines (A and C) between each corresponding nameand visual pattern as well as the product of the magnitudes of the members of each corresponding pair (B) were calculated. For each network,the 48 resulting cosines and the 48 resulting magnitudes were averaged.


connections coming into hidden units on one side has acompounding effect. The first update to the activationsof the hidden units in both demi-hubs is affected only bythe damage to the connections from the pool that hasinputs clamped, just as in the feedforward network. Thedistortion to unit activations is propagated via these recur-rent connection weights, which themselves have beendamaged, thereby increasing the distortion. Note that thepropagated distortion affects both hubs to a degree, butbecause the extent of connectivity is greater within a hubthan between hubs, the damaged hub has fairly littleeffect on the hub that was not damaged, contributing tothe unilateral advantage.

Effect of Damage to Units in a Recurrent Network

Our simulations thus far have considered the effects ofconnection damage, but it might be argued that damageto whole units would be a more realistic model of damagein the brain, since degenerative illness, stroke, or resec-tion might affect whole neurons or groups of neurons.To extend our findings to address this possibility, we randamage simulations removing units instead of connec-tions, where removal of a unit effectively removed allthe connections into and out of that unit at once. Wetested 10 networks using the recurrent network architec-ture, using a larger total number of hidden units (400 in-stead of 64) and longer training time (400,000 epochs).For simplicity, this simulation employed full connectivitywithin the left and the right side demi-hubs, no connec-tions between the left and right sides, and no asymmetryin the output from hidden to verbal descriptors. We chosethe larger number of hidden units because information isoften not distributed very evenly across units in smallernetworks and, consequently, removal of a unit can causelarge network-specific changes that would not be expectedin networks—like the brain—with much larger numbersof units.4 The fidelity measure showed that unilateral da-mage was again less detrimental than bilateral damage andthat the difference between the unilateral and bilateral da-mage increased with increasing amounts of unit damage(Figure 7D). These effects on fidelity carry over, as in othercases, to word-to-picture matching and naming.The difference between unilateral and bilateral damage

here arises entirely from the difference in recurrent con-nections within a hub versus between hubs. Recall thatthe net input to a unit is equal to a sum of terms, eachof which is the activation of a sending unit multipliedby its connection weight to the receiving unit. Removalof units within a hub removes some of the terms fromthe net input to other units within the same hub, just asremoval of connection weights among the units within ahub would. Because there is greater connectivity amonghidden units within a hub than between hubs, the effectof unit removal is largely confined to units in the samehub. There can be indirect effects via recurrent influences

propagating throughout the network, but as before, inthe limit of removing all of the units on one side of thenetwork, neither signal nor noise are propagated by thisside of the network. In summary, a lesioned unit causesrelatively focal severing of connections to other unitsin the same hub. As with connection damage, when le-sioning is restricted to one side, that sideʼs contributionis both weakened and distorted, allowing the intact sideto dominate and thereby producing less of an overalldeficit than a comparable amount of damage spread evenlyacross both sides.

Within versus Between Hemisphere Redundancy

We now consider a related but distinct possible explana-tion for the different consequences of unilateral and bilat-eral damage in humans and other animals. According tothis explanation, the information contained in two homo-topic areas is more redundant between than within eachof the two areas, so if one is damaged, the informationlost may still be available on the other side, but if bothare damaged, some information lost from one side willalso be lost from the other. Although we cannot ruleout the possibility that such an account applies to lesionsin the brain, it does not seem to be the cause of the dif-ferential effect of unilateral versus bilateral damage in ournetworks.

In our networks, there does not appear to be a forcethat produces greater redundancy of representation be-tween versus within a hemisphere. Such a force certainlydoes not exist in our feedforward network (Figure 6). Be-cause there are no recurrent connections and all inputunits are connected to all hidden units and all hiddenunits are connected to all output units, the division ofthe hidden layer into two pools has no effect whatsoeverduring training—the architecture is indistinguishablefrom that of a network with a single hidden layer. Thus,two units that might represent a particular feature areequally likely to be located on the same side of the net-work as on two different sides of the network. A conse-quence of this is that removing x units from each side hasthe same average effect on the fidelity of the representa-tions in the network as removing 2x units from just oneside.

To demonstrate that this is indeed the case for thefeedforward network, we presented each itemʼs nameand visual input pattern, then computed the fidelity mea-sure after removing 2x units from one side or x unitsfrom both sides. We found no reliable difference across10 networks of unilateral versus bilateral removal acrossseveral values of the parameter x (x = 0.1, 0.3, and0.5; smallest p = .689). We also carried out a similaranalysis for two versions of the recurrent network: thenetwork from Effect of Lesions on Similarity Structuresection and the network with 400 hidden units. In bothcases, we examined the fidelity of combined patterns


across the two hidden layers after the network was testedwithout damage, simply excluding units either unilater-ally (2x units on one side) or bilaterally (x units on bothsides) in the analysis. As with the feedforward networks,for the same three values of x, we found no reliable effectof unilateral versus bilateral exclusion of units in eithercase (smaller network: smallest p = .512; larger network:smallest p = .558). These simulations are consistent withthe view that there is no difference in redundancy of unitrepresentation within versus between hemispheres inany of our networks.

Thus, although the greater redundancy between thanwithin hemispheres account may seem in some ways sim-ilar to the account offered by our models, the accountsare in fact different. In the models, the removal of con-nection weights on just one side distorts the overall inter-nal representation less than the removal of connectionweights on both sides because the lesion to both sidesdistorts the representation on both sides, whereas the le-sion on one side distorts the representation on only oneside. Although signal distortion is an important part ofthe story, by itself it is incomplete. If damage results insignal distortion and downstream brain areas collect in-formation from both hemispheres, the intact hemispherewould not necessarily override the noise arising from thedamaged hemisphere. The insight from the current mod-eling work is that unilateral damage distorts the signalon that side but also results in a reduction in signal mag-nitude on that side. This magnitude reduction is whatallows the intact side to dominate performance.

DISCUSSION

Across different species and multiple processing do-mains, unilateral damage can produce minimal effectswhereas profound impairment is only observed after bi-lateral damage. Despite the fact that evidence for this dif-ference in humans can be traced back for over half acentury (to the famous case of patient HM) and longerin nonhuman primates (Klüver & Bucy, 1939; Brown &Schafer, 1888), there has been no computational investi-gation of the factors that underlie this difference untilnow (although there has been computational work onhemispheric specialization; e.g., Weems & Reggia, 2004;Lambon Ralph et al., 2001). We implemented a neuralnetwork model that simulates this difference and appliedit to the domain of semantic memory, a domain in whichthere is a large body of relevant neuropsychological data.In line with the more general literature noted above, thepatient data indicated that unilateral damage to the ante-rior temporal region generates only mild semantic im-pairment, whereas substantial semantic deficits followbilateral ATL damage (as observed in SD and other bilat-eral diseases). Although matching for volume is difficult,the data suggest that unilateral damage is somehow in-herently less deleterious than bilateral.

Our computational model exhibited just such a unilat-eral advantage. For symmetrically represented functionssuch as receptive comprehension (as measured byword-to-picture matching), unilateral damage only pro-duced mild impairments, whereas the same quantity ofsimulated bilateral damage generated greater deficits atall levels of damage. For asymmetrically representedtasks such as picture naming, the simulations exhibitedthe expected laterality effect (lesions to the left demi-hub generated greater naming impairment than equiva-lent right demi-hub lesions; see also Lambon Ralphet al., 2001) while still showing an advantage, even for aunilateral lesion affecting the somewhat more dominanthemisphere, compared with equivalent damage spreadacross both hemispheres.Part of the reason why performance after bilateral dam-

age can be very poor is that it can affect all the unitsand connections whose function together determinesnetwork performance. As a result, as shown in Figure 4,the bilateral damage performance curves continue pastthe range possible for unilateral damage to yield verylow levels of performance. It is probable that some ofthe patients with bilateral damage (e.g., those with severeSD) have similarly high amounts of atrophy.Our work indicates that there are also other important

parts of the story. Within ranges where the model re-ceived equal amounts of damage unilaterally and bilater-ally, performance after bilateral damage was much worsethan after unilateral damage. The restriction of damage toone side of the model provides a considerable advantageover the same amount of damage distributed across bothsides. When damage is restricted to one side, the otherside can continue to perform much as it did when thenetwork was fully intact, with relatively little disruptionfrom the damaged side. Although it may be profoundlyimpaired, the damaged side contributes far less thanthe intact side because of the reduction in the variationin its activation from item to item, thereby allowing theintact side to dominate performance. When damage isapplied to both halves of the network, processing is dis-rupted throughout, leading therefore to significantlygreater behavioral impairment.A mathematical analysis of the effects of damage dem-

onstrated how distortion and signal magnitude interactin each hemisphere to produce different amounts ofoverall disruption in the unilateral and bilateral damagecases. This analysis combined with an understanding ofthe distributed representations and connectivity patternsof the network provides a clear picture of the causes un-derlying the differential effects of focal and diffusedamage.Our results apply very generally to information process-

ing in a highly interconnected system that is distributedbilaterally across the hemispheres of the brain. They mayalso be relevant to understanding effects of focal versusdiffuse damage within a hemisphere in cases where afunction is unilaterally represented over a brain region


of moderate extent. If in that case local connectivityamong participating neurons is greater than long-rangeconnectivity, then focal damage within the larger areawould be expected to behave similarly to unilateraldamage within our networks. More generally, although

our model simulated the effects of unilateral versus bilat-eral ATL damage on semantic memory, our observationsabout the differential consequences of focal and diffusedamage are likely to be relevant to similar effects ob-served in many other domains.

APPENDIX 1

Effects of unilateral and bilateral damage applied all at once (as opposed to progressively). Deterioration of performance is shown with no recovery(equivalent to the Figure 4 results), one epoch of recovery after the specified amount of damage, and 10 epochs of recovery after the specifiedamount of damage.

APPENDIX 2

Effects of unilateral andbilateral damage on namingand word-to-picture matchingin the feedforward architecture.Performance is shown for theintact network and at 10 levelsof damage, labeled by theproportion of connectionsremoved from units in bothhidden layers or one hiddenlayer. Deterioration ofperformance is shown withno recovery allowed.


Acknowledgments

We thank Ken Norman for helpful discussion and ideas about thesimulation analyses. This work was supported by the NationalScience Foundation Graduate Research Fellowship under GrantDGE-0646086 to A. C. S. and by Medical Research Councilprogram grants to M. A. L. R. (MR/J004146/1).

Reprint requests should be sent toAnnaC. Schapiro,Department ofPsychology, Green Hall, Princeton University, Princeton, NJ 08540,or via e-mail: [email protected]; Prof. Matthew A. LambonRalph, Neuroscience and Aphasia Research Unit, School of Psycho-logical Sciences, Zochonis Building, Brunswick Street, Manchester,M13 9PL, UK, or via e-mail: [email protected] James L. McClelland, 344 Jordan Hall, Bldg 420, 450 Serra Mall,Stanford, CA, 94305, or via e-mail: [email protected].

Notes

1. In fact, using net inputs, we found that fidelity calculatedfor each half of the network separately almost exactly followsthe fraction of connections remaining. For example, fidelityon either side after a 50% lesion is almost exactly .5. The aver-age of left and right sided fidelity measures is thus the samefor a bilateral lesion as it is for a unilateral lesion; there is nodivergence at high damage levels as seen in Figure 7A. Thisis because net-input-based cosines decrease linearly with in-creasing damage while fidelity based on differences betweenactivation-based cosines decrease non-linearly. The underlyingcosines themselves actually increase at high levels of damage dueto non-zero activation values.2. Note that the cosine shrinkage equation is an empirical char-acterization of the average effect of a lesion leaving a remainingfraction R of the existing connection weights. When the incomingweights to a given hidden unit from active input units are corre-lated, the effect of a lesion on the cosine will be more benign,whereas if there is just one active input unit, or if the weightscoming into each hidden unit from the ensemble of active inputunits are uncorrelated, the equation as given here should apply.It appears that the learning process results in connection weightvalues that are only weakly correlated in our simulations: First,as the figure shows, the equation closely matches the valuesobtained through simulations. Second, we estimated the corre-lation coefficient among the weights contributing to the net in-put to each hidden unit in each visual input pattern in each ofthe 10 feedforward networks (64 times 48 times 10 separateestimates) using the formula given in the Wikipedia article onVariance, section on Sum of correlated variables. Themeanvalueof these estimates was 0.0334. While the value is significantlydifferent from 0 (t(9) = 20.06, p < .001), it is clearly very small.3. As with the effect of a lesion on the cosine, this is anempirical observation. In this case, as the incoming weights toeach receiving unit from each active input unit became morecorrelated, the average effect of a lesion leaving R remainingweights on the length of a net input vector approaches RjjV jj,and not

ffiffiffiR

p jjV jj. The observed value (ffiffiffiR

p jjV jj) is once againwhat is expected if there is just one active input unit, or ifthe weights coming into each hidden unit from the ensembleof active input units are uncorrelated.4. Because there are far more connections than units, a lesionto connections tends to produce relatively more uniform effects,making smaller networks (which train far more quickly) sufficientfor the connection damage simulations.

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