A Superadditive-Impairment Theory 
of Optic Aphasia 
Michael C. Mozer 
Dept. of Computer Science 
University of Colorado 
Boulder, CO 80309-0430 
Mark Sitton 
Dept. of Computer Science 
University of Colorado 
Boulder, CO 80309-0430 
Martha Farah 
Dept. of Psychology 
University of Pennsylvania 
Phila., PA 19104 6196 
Abstract 
Accounts of neurological disorders often posit damage to a specific 
functional pathway of the brain. Farah (1990) has proposed an alterna- 
tive class of explanations involving partial damage to multiple path- 
ways. We explore this explanation for optic aphasia, a disorder in which 
severe performance deficits are observed when patients are asked to 
name visually presented objects, but surprisingly, performance is rela- 
tively normal on naming objects from auditory cues and on gesturing 
the appropriate use of visually presented objects. We model this highly 
specific deficit through partial damage to two pathways--one that maps 
visual input to semantics, and the other that maps semantics to naming 
responses. The effect of this damage is superadditive, meaning that 
tasks which require one pathway or the other show little or no perfor- 
mance deficit, but the damage is manifested when a task requires both 
pathways (i.e., naming visually presented objects). Our model explains 
other phenomena associated with optic aphasia, and makes testable 
experimental predictions. 
Neuropsychology is the study of disrupted cognition resulting from damage to functional 
systems in the brain. Generally, accounts of neuropsychological disorders posit damage to 
a particular functional system or a disconnection between systems. Farah (1990) sug- 
gested an alternative class of explanations for neuropsychological disorders: partial dam- 
age to multiple systems, which is manifested through interactions among the loci of 
damage. We explore this explanation for the neuropsychological disorder of optic aphasia. 
Optic aphasia, arising from unilateral left posterior lesions, including occipital cortex 
and the splenium of the corpus callosum (Schnider, Benson, & Scharre, 1994), is marked 
by a deficit in naming visually presented objects, hereafter referred to as visual naming 
(Farah, 1990). However, patients can demonstrate recognition of visually presented 
objects nonverbally, for example, by gesturing the appropriate use of an object or sorting 
visual items into their proper superordinate categories (hereafter, visual gesturing). 
Patients can also name objects by nonvisual cues such as a verbal definition or typical 
sounds made by the objects (hereafter, auditory naming). The highly specific nature of the 
deficit rules out an explanation in terms of damage to a single pathway in a standard model 
of visual naming (Figure 1), suggesting that a more complex model is required, involving 
A SuperadditiveImpairment Theory of Optic Aphasia 67 
FIGURE 1. A standard box-and-arrow 
model of visual naming. The boxes denote 
levels of representation, and the arrows 
denote pathways mapping from one level of 
representation to another. Although optic 
aphasia cannot be explained by damage to 
the vision-to-semantics pathway or the 
semantics-to-naming pathway, Farah 
(1990) proposed an explanation in terms of 
partial damage to both pathways (the X's). 
I semantic I 
multiple semantic systems or multiple pathways to visual naming. However, a more parsi- 
monious account is suggested by Farah (1990): Optic aphasia might arise from partial 
lesions to two pathways in the standard model--those connecting visual input to seman- 
tics, and semantics to naming--and the effect of damage to these pathways is superaddi- 
tive, meaning that tasks which require only one of these pathways (e.g., visual gesturing, 
or auditory naming) will be relatively unimpaired, whereas tasks requiring both pathways 
(e.g., visual naming) will show a significant deficit. 
1 A MODEL OF SUPERADDITIVE IMPAIRMENTS 
We present a computational model of the superadditive-impairment theory of optic apha- 
sia by elaborating the architecture of Figure 1. The architecture has four pathways: visual 
input to semantics (V->S), auditory input to semantics (A->S), semantics to naming 
(S-->N), and semantics to gesturing (S-->G). Each pathway acts as an associative memory. 
The critical property of a pathway that is required to explain optic aphasia is a speed-accu- 
racy trade off: The initial output of a pathway appears rapidly, but it may be inaccurate. 
This "quick and dirty" guess is refined over time, and the pathway output asymptotically 
converges on the best interpretation of the input. 
We implement a pathway using the architecture suggested by Mathis and Mozer 
(1996). In this architecture, inputs are mapped to their best interpretations by means of a 
two-stage process (Figure 2). First, a quick, one-shot mapping is performed by a multi- 
layer feedforward connectionist network to transform the input directly to its correspond- 
ing output. This is followed by a slower iterative clean-up process carried out by a 
recurrent attractor network. This architecture shows a speed-accuracy trade off by virtue 
of the .assumption that the feedforward mapping network does not have the capacity to 
produce exactly the right output to every input, especially when the inputs are corrupted 
by noise or are otherwise incomplete. Consequently, the clean up stage is required to pro- 
duce a sensible interpretation of the noisy output of the mapping network. 
Fully distributed attractor networks have been used for similar purposes (e.g., Plaut 
& Shallice, 1993). For simplicity, we adopt a localist-attractor network with a layer of 
state units and a layer of radial basis function (RBF) units, one RBF unit per attractor. 
Each RBF or attractor unit measures the distance of the current state to the attractor that it 
represents. The activity of attractor unit i, a i, is: 
FIGURE 2. Connectionist implementa- 
tion of a processing pathway. The path- 
way consists of feedforward mapping 
network followed by a recurrent clean- 
up or attractor network. Circles denote 
connectionist processing units and 
arrows denote connections between 
units or between layers of units. 
way output 
clean up network 
mapping network 
pathway input 
68 M. C. Mozer, M. Sitton and M. Farah 
i(t)-- exp(-lls(t)-,ll2/,) 
ai(t) 
ai(t ) - (2) 
where s(0 is the state unit activity vector at time t, gi is the vector denoting the location of 
attractor i, and 13 i is the strength of the attractor. The strength determines the region of the 
state space over which an attractor will exert its pull, and also the rate at which the state 
vill converge to the attractor. The state units receive input from the mapping network and 
from the attractor units and are updated as follows: 
si(t ) = di(t)ei(t ) + (1 -di(t))aj(t-1)gji (3) 
J 
where si(O is the activity of state unit i at time t, e i is the ith output of the mapping net, 
is the ith element of attractor j, and d/is given by 
di(t ) = hi1 bi(t- 1)] 
( J (4) 
where h[.] is a linear threshold function that bounds activity between -1 and +1, b i is a 
weighted time average of the ith output of the mapping net, 
i(t) = ctei(t) + (1 -ct)i(t-1) (5) 
In all simulations, ct = .02. 
The activity of the state units are governed by two forces--the external input from 
the feedforward net (first term in Equation 3) and the attractor unit activities (second 
term). The parameter di acts as a kind of attentional mechanism that modulates the relative 
influence of these two forces. The basic idea is that when the input coming from the map- 
ping net is changing, the system should be responsive to the input and should not yet be 
concerned with interpreting the input. In this case, the input is copied straight through to 
the state units and hence di should have a value close to 1. When the input begins to stabi- 
lize, however, the focus shifts to interpreting the input and following the dynamics of the 
attractor network. This shift corresponds to d i being lowered to zero. The weighted time 
average in the update rule for di is what allows for the smooth transition of the function to 
its new value. For certain constructions of the function d, Zemel and Mozer (in prepara- 
tion) have proven convergence of the algorithm to an attractor. 
Apart from speed-accuracy trade off, these dynamics have another important conse- 
quence for the present model, particularly with respect to cascading pathways. If pathway 
^ feeds into pathway 13, such as V-->S feeding into S-oN, then the state unit activities of 
act as the input to 13. Because these activities change over time as the state approaches a 
well-formed state, the dynamics of pathway 13 can be quite complex as it is forced to deal 
with an unstable input. This property is important in explaining several phenomena associ- 
ated with optic aphasia. 
1.1 PATTERN GENERATION 
Patterns were constructed for each of the five representational spaces: visual and auditory 
input, semantic, name and gesture responses. Each representational space was arbitrarily 
made to be 200 dimensional. We generated 200 binary-valued (-1,+1) patterns in each 
space, which were meant to correspond to known entities of that representational domain. 
For the visual, auditory, and semantic spaces, patterns were partitioned into 50 simi- 
larity clusters with 4'siblings per cluster. Patterns were chosen randomly subject to two 
constraints: patterns in different clusters had to be at least 80  apart, and siblings had to be 
between 25  and 50  apart. Because similarity of patterns in the name and gesture spaces 
was irrelevant to our modeling, we did not impose a similarity structure on these spaces. 
A Superadditive-Impairment Theory of Optic Aphasia 69 
Instead, we generated patterns in these spaces at random subject to the constraint that 
every pattern had to be at least 60  from every other. 
After generating patterns in each of the representational spaces, we established arbi- 
trary correspondences among the patterns such that visual pattern n, auditory pattern n, 
semantic pattern n, name pattern n, and gesture pattern n all represented the same concept. 
That is, the appropriate response in a visual-naming task to visual pattern n would be 
semantic pattern n and name pattern n. 
1.2 TRAINING PROCEDURE 
The feedforward networks in the four pathways (V->S, A->S, S-->N, and S-->G) were 
independently trained on all 200 associations using back propagation. Each of these net- 
works contained a single hidden layer of 150 units, and all units in the network used the 
symmetric activation function to give activities in the range [-1 ,+1]. The amount of train- 
ing was chosen such that performance on the training examples was not perfect; usually 
several elements in the output would be erroneous--i.e., have the wrong sign--and others 
would not be exactly correct i.e., -1 or +1. This was done to embody the architectural 
assumption that the feedforward net does not have the capacity to map every input to 
exactly the right output, and hence, the clean-up process is required. 
Training was not required for the clean-up network. Due to the 1ocalist representation 
of attractors in the clean-up network, it was trivial to hand wire each clean-up net with the 
200 attractors for its domain, along with one rest-state attractor. All attractor strengths 
were initialized to the same value, [=15, except the rest-state attractor, for which =5. The 
rest-state attractor required a lower strength so that even a weak external input would be 
sufficient to kick the attractor network out of the rest state. 
1.3 SIMULATION METHODOLOGY 
After each pathway had been trained, the model was damaged by "lesioning" or 
removing a fraction  of the connections in the V-->S and S-->N mapping networks. The 
lesioned connections were chosen at random and an equal fraction was removed from the 
two pathways. The clean-up nets were not damaged. The architecture was damaged a total 
of 30 different times, creating 30 simulated patients who were tested on each of the four 
tasks and on all 200 input patterns for a task. The results we report come from averaging 
across simulated patients and input patterns. Responses were determined after the system 
had been given sufficient time to relax into a name or gesture attractor, which was taken to 
be the response. Each response was classified as one of the following mutually exclusive 
response types: correct, perseveration (response is the same as that produced on any of the 
three immediately preceding trials), visual error (the visual pattern corresponding to the 
incorrect response is a sibling of the visual pattern corresponding to the correct response), 
semantic error, visual+semantic error, or other error. 
1.4 PRIMING MECHANISM 
Priming--the increased availability of recently experienced stimuli--has been found 
across a wide variety of tasks in normal subjects. We included priming in our model as a 
strengthening (increasing the i parameter) of recently visited attractors (see Mathis & 
Mozer 1996, for details, and Becker, Behrmann, & Moscovitch, 1993, for a related 
approach). In the damaged model, this mechanism often gave rise to perseverations. 
2 RESULTS 
We have examined the model's behavior as we varied the amount of damage, quantified by 
the parameter 'y. However, we report on the performance of simulated patients with y = .30. 
This intermediate amount of damage yielded no floor or ceiling effects, and also produced 
error rates for the visual-naming task in the range of 30-40%, roughly the median perfor- 
mance of patients in the literature. 
70 M. C. Mozer, M. Sitton and M. Farah 
TABLE 1. Error rate of the 
damaged model on various 
tasks. 
task error rate 
auditory gesturing 0.0% 
auditory naming 0.5% 
visual gesturing 8.7% 
visual naming 36.8% 
Table 1 presents the error rates of the model on four tasks. The pattern of errors 
shows a qualitative fit to human patient data. The model produced no errors on the audi- 
tory gesturing task because the two component pathways (A-->S and S-->G) were undam- 
aged. Relatively few errors were made on the auditory-naming and visual-gesturing tasks, 
each of which involved one damaged pathway, because the clean-up nets were able to 
compensate for the damage. However, the error rate for the visual-naming task was quite 
large, due to damage on both of its component pathways (V--->S and S-->N). The error rate 
for visual naming cannot be accounted for by summing the effects of the damage to the 
two component pathways because the sum of the error rates for auditory naming and 
visual gesturing, each of which involves one of the two partially damaged pathways, is 
nearly four times smaller. Rather, the effects of damage on these pathways interact, and 
their interaction leads to superadditive impairments. 
When a visual pattern is presented to the model, it is mapped by the damaged V-->S 
pathway into a corrupted semantic representation which is then cleaned up. While the cor- 
ruption is sufficiently minor that clean up will eventually succeed, the clean up process is 
slowed considerably by the corruption. During the period of time in which the semantic 
clean-up network is searching for the correct attractor, the corrupted semantic representa- 
tion is nonetheless fed into the damaged S-->N pathway. The combined effect of the (ini- 
tially) noisy semantic representation serving as input to a damaged pathway leads to 
corruption of the naming representation past the point where it can be cleaned-up properly. 
Interactions in the architecture are inevitable, and are not merely a consequence of 
some arbitrary assumption that is built into our model. To argue this point, we consider 
two modifications to the architecture that might eliminate the interaction in the damaged 
model. First, if we allowed the V--->S pathway to relax into a well-formed state before 
feeding its output into the S-->N pathway, there would be little interaction--the effects of 
the damage would be additive. However, cortical pathways do not operate sequentially, 
one stage finishing its computation and then turning on the next stage. Moreover, in the 
undamaged brain, such a processing strategy is unadaptive, as cascading partial results 
from one pathway to the next can speed processing without the introduction of errors 
(McClelland, 1979). Second, the interaction might be eliminated by making the S--->N 
pathway continually responsive to changes in the output of the V-->S pathway. Then, the 
rate of convergence of the V-->S pathway would be irrelevant to determining the eventual 
output of the S-->N pathway. However, because the output of the S-->N pathway depends 
not only on its input but its internal state (the state of the clean-up net), one cannot design 
a pathway that is continually responsive to changes in the input and is also able to clean up 
noisy responses. Thus, the two modifications one might consider to eliminate the interac- 
tions in the damaged model seriously weaken the computational power of the undamaged 
model. We therefore conclude that the framework of our model makes it difficult to avoid 
an interaction of damage in two pathways. 
A subtle yet significant aspect of the model's performance is that the error rate on the 
visual-gesturing task was reliably higher than the error rate on the auditory-naming task, 
despite the fact that each task made use of one damaged pathway, and the pathways were 
damaged to the same degree. The difference in performance is due to the fact that the dam- 
aged pathway for the visual-gesturing task is the first in a cascade of two, while the dam- 
aged pathway for the auditory-naming task is the second. The initially noisy response 
from a damaged pathway early in the system propagates to subsequent pathways, and 
A Superadditive-Impairment Theory of Optic Aphasia 71 
although the damaged pathway will eventually produce the correct response, this is not 
sufficient to ensure that subsequent pathways will do so as well. 
2.1 DISTRIBUTION OF ERRORS FOR VISUAL OBJECT NAMING 
Figure 2 presents the model's error distribution for the visual-naming task. Consis- 
tent with the patient data (Farah, 1990), the model produces many more semantic and per- 
severation errors than by chance. The chance error proportions were computed by 
assuming that if the correct response was not made, then all other responses had an equal 
probability of being chosen. 
To understand the predominance of semantic errors, consider the effect of damage to 
the V-->S pathway. For relatively small amounts of damage, the mapping produced will be 
close to the correct mapping. "Close" here means that the Euclidean distance in the 
semantic output space between the correct and perturbed mapping is small. Most of the 
time, minor perturbation of the mapping will be compensated for by the clean-up net. 
Occasionally, the perturbation will land the model in a different attractor basin, and a dif- 
ferent response will be made. However, when the wrong attractor is selected, it will be one 
"close" to the correct attractor, i.e., it will likely be a sibling in the same pattern cluster as 
the correct attractor. In the case of the V--->S pathway, the siblings of the correct attractor 
are by definition semantically related. A semantic error will be produced by the model 
when a sibling semantic attractor is chosen, and then this pattern is correctly mapped to a 
naming response in the S-->N pathway. 
In addition to semantic errors, the other frequent error type in visual naming is perse- 
verations. The priming mechanism is responsible for the significant number of persevera- 
tions, although in the unlesioned model, it facilitates processing of repeated stimuli 
without producing perseverations. 
Just as important as the presence of perseverative and semantic errors is the absence 
of visual errors, a feature of optic aphasia that contrasts sharply with visual agnosia 
(Farah, 1990). The same mechanisms explain why the rate of visual errors is close to its 
chance value and why visual+semantic errors are above chance. Visual-naming errors 
occur because there is an error either in the V-->S or S-->N mappings, or both. Since the 
erroneous outputs of these pathways show a strong tendency to be similar to the correct 
output, and because semantic and name similarity does not imply visual similarity (the 
patterns were paired randomly), visual errors should only occur by chance. When a visual 
error does occur, though, there is a high probability that the error is also semantic because 
of the strong bias that already exists toward producing semantic errors. This is the reason 
why more visual+semantic errors occur than by chance and why the proportion of these 
FIGURE 3. Distribution 
of error types made by 
model on the V-->N task 
(black bars) relative to 
chance (grey bars). 
0.8 
0.7 
0.6 
0.5 
0.3 
0.2 
0.1 
I actual 
I chance 
other 
semantic visual vis+sem perseverative 
Error type 
72 M. C. Mozer, M. Sitton and M. Farah 
errors is only slightly less than the proportion of visual errors. 
Plaut and Shallice (1993) have proposed a connectionist model to account for the 
distribution of errors made by optic aphasics. Although their model was not designed to 
account for any of the other phenomena associated with the disorder, it has much in com- 
mon with the model we are proposing. Unlike our model, however, theirs requires the 
assumption that visually similar objects also share semantic similarity. This assumption 
might be questioned, especially because our model does not require this assumption to 
produce the correct distribution of error responses. 
3 DISCUSSION 
In demonstrating superadditive effects of damage, we have offered an account of optic 
aphasia that explains the primary phenomenon: severe impairments in visual naming in 
conjunction with relatively spared performance on naming from verbal description or ges- 
turing the appropriate use of a visually presented object. The model also explains the dis- 
tribution of errors on visual naming. Although we did not have the space in this brief 
report to elaborate, the model accounts for several other distinct characteristics of optic 
aphasia, including the tendency of patients to "home in" on the correct name for a visually 
presented object when given sufficient time, and a positive correlation between the error 
rates on naming and gesturing responses to a visual object (Sitton, Mozer, & Farah, 1998). 
Further, the model makes several strong predictions which have yet to be tested experi- 
mentally. One such prediction, which was apparent in the results presented earlier, is that a 
higher error rate should be observed on visual gesturing than on auditory naming when the 
tasks are equated for difficulty, as our simulation does. 
More generally, we have strengthened the plausibility of Farah's (1990) hypothesis 
that partial damage to two processing pathways may result in close-to-normal perfor- 
mance on tasks involving one pathway or the other while yielding a severe performance 
deficit on tasks involving both damaged pathways. The superadditive-impairment theory 
thus may provide a more parsimonious account of various disorders that were previously 
believed to require more complex architectures or explanations. 
4 ACKNOWLEDGMENTS 
This research was supported by grant 97-18 from the McDonnell-Pew Program in Cogni- 
tive Neuroscience. 
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