Multitasking Capability Versus Learning Efficiency in Neural Network Architectures
One of the most salient and well-recognized features of human goal-directed behavior is our limited ability to conduct multiple demanding tasks at once. Previous work has identified overlap between task processing pathways as a limiting factor for multitasking performance in neural architectures. This raises an important question: insofar as shared representation between tasks introduces the risk of cross-talk and thereby limitations in multitasking, why would the brain prefer shared task representations over separate representations across tasks? We seek to answer this question by introducing formal considerations and neural network simulations in which we contrast the multitasking limitations that shared task representations incur with their benefits for task learning. Our results suggest that neural network architectures face a fundamental tradeoff between learning efficiency and multitasking performance in environments with shared structure between tasks.
Multitasking Capability Versus Learning Efﬁciency
in Neural Network Architectures
Sebastian Musslick1,∗, Andrew M. Saxe2, Kayhan ¨
Biswadip Dey3, Greg Henselman4, and Jonathan D. Cohen1
1Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA.
2Center for Brain Science, Harvard University, Cambridge, MA 02138, USA.
3Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA.
4Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
∗Corresponding Author: firstname.lastname@example.org
One of the most salient and well-recognized features of human
goal-directed behavior is our limited ability to conduct mul-
tiple demanding tasks at once. Previous work has identiﬁed
overlap between task processing pathways as a limiting fac-
tor for multitasking performance in neural architectures. This
raises an important question: insofar as shared representation
between tasks introduces the risk of cross-talk and thereby lim-
itations in multitasking, why would the brain prefer shared task
representations over separate representations across tasks? We
seek to answer this question by introducing formal considera-
tions and neural network simulations in which we contrast the
multitasking limitations that shared task representations incur
with their beneﬁts for task learning. Our results suggest that
neural network architectures face a fundamental tradeoff be-
tween learning efﬁciency and multitasking performance in en-
vironments with shared structure between tasks.
Keywords: multitasking; cognitive control; capacity con-
straint; learning; neural networks
Our limited capability to execute multiple tasks at the same
time highlights one of the most fundamental puzzles con-
cerning human processing, which must be addressed by any
general theory of cognition (Shenhav, Botvinick, & Cohen,
2013; Kurzban, Duckworth, Kable, & Myers, 2013; Ander-
son, 2013): Why, for some tasks, is the human mind capa-
ble of a remarkable degree of parallelism (e.g., navigating a
crowded sidewalk while talking to a friend), while for others
its capacity for parallelism is radically limited (e.g., conduct
mental arithmetic while constructing a grocery list)?
Early theories of cognition, that have continued to be
highly inﬂuential, assert that the ability to multitask – that is,
to carry out a set of tasks concurrently1– can be understood
in terms of a fundamental distinction between automatic and
controlled processing, with the former relying on parallel pro-
cessing mechanisms (that can support multitasking) and the
latter assumed to rely on a serial processing mechanism with
limited capacity (Posner & Snyder, 1975; Shiffrin & Schnei-
der, 1977) that can only support processing of a single task at
1Multitasking can, in some situations, be achieved by rapid se-
quential processing (e.g., switching between asynchronous serial
processes, as is common in computers), rather than through true
synchronous processing. Here, our focus is on forms of multitask-
ing that reﬂect truly concurrent processing, sometimes referred to as
perfect timesharing or pure parallelism.
a time. In this view, the constraints on the number of control-
dependent tasks that can be executed at one time reﬂect an
intrinsic property of the control system itself. However, alter-
native (“multiple-resource“) accounts (Allport, 1980; Meyer
& Kieras, 1997; Navon & Gopher, 1979; Salvucci & Taat-
gen, 2008) have suggested that multitasking limitations arise
from local processing bottlenecks. That is, if two tasks share
the same local resources (i.e. representations required to per-
form the tasks), then executing them simultaneously can lead
to cross-talk and degraded performance. It has been argued
that the very purpose of cognitive control is to prevent such
cross-talk by limiting the number of active task processes
engaged (Cohen, Dunbar, & McClelland, 1990; Botvinick,
Braver, Barch, Carter, & Cohen, 2001). In this view, con-
straints in multitasking reﬂect the consequences of control
doing its job, rather than limitations intrinsic to the mecha-
nisms of control itself. This line of argument suggests that,
to better understand the conditions under which multitasking
is and is not possible, it is necessary to understand the extent
to which the task processes involved share representations,
and are thus subject to potential interference and the inter-
vention of control to limit processing. This, in turn, raises
the question of whether there are general principles of neural
architectures that determine the use of shared representation,
and how these interact with learning and processing.
One may argue that the constraints that shared represen-
tations impose on multitasking are negligibly small in a pro-
cessing system as large as the human brain. However, simula-
tion studies (Feng, Schwemmer, Gershman, & Cohen, 2014),
followed by analytic work (Musslick et al., 2016) have found
that the multitasking capability of a network can drop precip-
itously as a function of overlap between task processes (i.e.
number of shared representations), and that this effect is rel-
atively insensitive to the size of the network.
The ﬁndings above suggest that maximal parallel process-
ing performance is achieved through the segregation of task
pathways, by separating the representations on which they
rely. This raises an important question: insofar as shared rep-
resentation introduces the risk of cross-talk and thereby lim-
itations in parallel processing performance, why would the
brain prefer shared task representations over separate ones?
Insights gained from the study of learning and representation
in neural networks provide a direct answer to this question:
Shared representations across tasks can support inference and
generalization (Caruana, 1997). These beneﬁts are strongly
linked to the ability of neural networks to carry out “inter-
active parallelism“, that is, the ability to learn and to pro-
cess complex representations by simultaneously taking into
account a large number of interrelated and interacting con-
straints (McClelland, Rumelhart, & Hinton, 1986).
In this study, we examine the tension between interactive
parallelism that promotes learning efﬁciency through use of
shared representations, on the one hand, and “independent
parallelism“ (i.e. the ability to carry out multiple processes
independently), on the other hand. That is, we are interested
in studying biases that promote shared representations over
multitasking performance. We ﬁrst demonstrate that the well-
recognized (and valued) emergence of shared representations
(Hinton, 1986) in response to extrinsic biases (i.e. shared
structure in the task environment) leads to constraints in mul-
titasking performance. In the second part, we introduce a
formal characterization of a tradeoff between learning efﬁ-
ciency and multitasking performance and examine how in-
trinsic biases of the network toward the use of shared rep-
resentations can expose this tradeoff in neural network sim-
ulations. The source code for all simulations is available at
Neural Network Model
For the simulations described in the paper we focus on a net-
work architecture that has been used to simulate a wide array
of empirical ﬁndings concerning human performance (e.g.
Cohen et al., 1990; Botvinick et al., 2001), including recent
work on limitations in multitasking (Musslick et al., 2016).
In this section we lay out the architecture of this network, its
processing, as well as the task environments used to train it.
Network Architecture and Processing
The network consists of two input layers, one of which repre-
sents the stimulus presented to the network and another that
encodes the task that the network is instructed to perform on
the stimulus. Stimulus input features can take any real value
between 0 and 1 and can be grouped into stimulus dimen-
sions that are relevant for a particular task. The network is
instructed to perform a single task by clamping the corre-
sponding task unit in the task layer to 1 while all other task
units are set to 0. These stimulus and task input values are
multiplied by a matrix of connection weights from the re-
spective input layer to a shared associative layer, and then
passed through a logistic function to determine the pattern of
activity over the units in the associative layer. This pattern is
then used (together with a set of direct projections from the
task layer) to determine the pattern of activity over the output
layer. The latter provides a response pattern that is evaluated
by computing its mean squared error (MSE) with respect to
the correct (task-determined) output pattern. Similar to stim-
ulus features, output units can be grouped into response di-
mensions that are relevant for a particular task. Note that the
weight projections from each task unit can act as control sig-
nals that bias processing towards task-relevant stimulus infor-
mation represented at the associative and output layer.
In order to represent the task environment described below,
the stimulus layer is compromised of 45 input units (features)
and the task layer of nine task units. The output layer con-
sists of 15 units and is organized into three response dimen-
sions (with ﬁve units per response dimension.). The number
of units in the associative layer is set to 100.
Figure 1: Feedforward neural network used in simulations.
The input layer is composed of stimulus vector −→
xt. The activity of each element in the associative
yhis determined by all elements xsand xtand their
respective weights whs and wht to yh. Similarly, the activity
of each output unit yo∈−→
yois determined by all elements yh
and xtand their respective weights woh and wot to yo. A bias
of θ=−2 is added to the net input of all units yhand yo.
Blue shades in the input and output units (circles) correspond
to unit values of >0 and illustrate an example input pattern
with its respective output pattern: The second task requires
the network to map the vector of values in the ﬁrst ﬁve stim-
ulus input units to one out of ﬁve output units (yellow shade).
Each task is deﬁned as a mapping between a subspace of ﬁve
stimulus features (referred to as a task-relevant stimulus di-
mension) onto ﬁve output units of a task-speciﬁc response
dimension, so that only one of the ﬁve relevant output units is
permitted to be active (see Fig. 1). The value of each stimu-
lus feature is drawn from a uniform distribution U[0,1]. The
rule by which 5 relevant stimulus features of any task-relevant
stimulus dimension are mapped onto one of the 5 output units
of the task-relevant response dimension corresponds to a non-
linear function that was randomly generated2with a sepa-
rate “teacher“ network (cf. Seung, Sompolinsky, & Tishby,
1992), and is the same across tasks. However, tasks are con-
sidered to be independent in that they differ which stimulus
dimension is linked to which response dimension.
The task environment across all simulations encompasses
nine tasks. As illustrated in Fig. 2 groups of three tasks map
2Note that it is ensured that, for the uniform distribution U[0,1]
of stimulus unit activations in the task-relevant set of input units, ev-
ery relevant output unit is equally likely to be required for execution.
onto the same response dimension. However, similarity be-
tween tasks could be varied by manipulating the overlap be-
tween their relevant stimulus dimensions. At the extremes,
task environments can be generated such that tasks of differ-
ent response dimensions relate to separate stimulus features
(no feature overlap, Fig. 2a), or the same stimulus features
(full feature overlap, e.g. tasks 1-3 in Fig. 2b).
Relevan t Stimulus
Tas k St r uc tu re
Relevan t Stimulus
Respons e Units
Respons e Units
Figure 2: Task environments. For each task, the network was
trained to map a subset of 5 stimulus features onto a subset of
5 output units. At the extremes tasks that were mapped onto
different response dimensions (e.g. tasks 1-3) could either (a)
rely on separate stimulus features or (b) completely overlap
in terms of their relevant stimulus features.
Networks are initialized with a set of small random weights
and then trained on all tasks using the backpropagation algo-
rithm3(Rumelhart & Geoffrey E. Hinton, 1986) to produce
the task-speciﬁed response for each stimulus.
Multitasking Limitations Due to Shared
Structure in the Task Environment
A key feature of neural networks is their ability to discover
latent structure in the task environment, exploiting similarity
between stimulus features in the form of shared representa-
tions (Hinton, 1986; Saxe, McClelland, & Ganguli, 2013).
In this section we explore how the emergence of shared rep-
resentations as a function of structural similarities between
tasks can impact the multitasking performance of a network.
Simulation Experiment 1: Shared Task
Representations as a Function of Feature Overlap
In order to investigate the effect of structural similarities be-
tween tasks we generated task environments with varying
overlap between task-relevant stimulus features. We deﬁne
feature overlap as the number of relevant stimulus features
that are shared between any pair of tasks linked to different
response dimensions (see Fig. 3a). That is, two tasks in-
volving two different response dimensions could either share
3All reported results were obtained using gradient decent to min-
imize the MSE of each training pattern. However, we observed the
same qualitative effects using the cross-entropy loss function.
no relevant stimulus features (cf. Fig. 2a), all ﬁve stimu-
lus features (cf. Fig. 2b) or any whole number of features
in between, resulting in 6 different task environments. We
trained 100 networks in each of the environments. The net-
works were trained on all nine tasks with the same set of 50
stimulus samples until the network achieved an MSE of 0.01.
0.4 0.6 0.8 1
Learned Weight Correlation
Feature Overlap Between Tasks
0 0.5 1
Learned Task Correlation
Multitasking Accuracy (%)
Figure 3: Effects of task similarity. (a) Networks were trained
in task environments with varying degrees of feature overlap.
Yellow and red shades highlight task-relevant stimulus fea-
tures for two tasks involving different response dimensions.
(b) Final multitasking accuracy of the network as a function
of the learned similarity between tasks involving different
response dimensions. Colors indicate the degree of feature
overlap present in the task environment as illustrated in (a).
In order to assess the similarity of learned task representa-
tions we focus our analysis on the weights from the task units
to the associative layer, insofar as these reﬂect the compu-
tations carried out by the network required to perform each
task. For a given pair of tasks we compute the learned repre-
sentational similarity between them as the Pearson correlation
of their weight vectors to the associative layer.
We measured multitasking performance for pairs of tasks
(of different stimulus and response dimensions) by activating
two task units at the same time and evaluating the concurrent
processing performance in the response dimensions relevant
to the two tasks. The accuracy of a single task ASingl e can be
where aiis the activation of the ith output unit of the task-
relevant response dimension and acis the activation of the
correct output unit. The multitasking accuracy is simply the
mean accuracy of both engaged single tasks.
The simulation results conﬁrm well-known explorations in
neural networks (Hinton, 1986; McClelland & Rogers, 2003;
Saxe et al., 2013) that task similarities in the environment
can translate into similarities between learned task represen-
tations. Critically, this extrinsic bias toward the learning of
shared representations negatively affected multitasking per-
formance (Fig. 3b). To illustrate this, consider the simultane-
ous execution of tasks 1 and 5 in an environment as depicted
in Fig. 2b. If the network learns similar representations at the
associative layer for tasks 1 and 2 (note that both tasks rely on
the same stimulus features), then executing task 1 will implic-
itly engage the representation of task 2 which in turn causes
interference via its link to the response dimension of task 5.
Multitasking Limitations due to Intrinsic
In addition to environmental biases that shape the learning of
shared task representations there may be factors intrinsic to
the neural system that can regulate the degree to which such
representations are exploited in learning. In this section we
introduce a formal analysis of how such biases can affect the
tradeoff between learning efﬁciency and multitasking perfor-
mance. We then use weight initialization as a learning bias
in simulations to establish a causal relationship between the
use of shared representations on the one hand, and resulting
effects on learning and multitasking, on the other hand.
Formal Intuitions on the Tradeoff between Learning
Efﬁciency and Multitasking Capability
To gain formal intuition into the tradeoff between multitask-
ing ability and learning speed, we consider a stripped-down
version of the introduced network model that is amenable to
analysis. In the full model, nonlinear interactions between
the task units and the stimulus units occur in the associative
layer. Here we assume a gating model in which these non-
linear interactions are carried out through gating signals that
can zero out parts of the activity in the associative and output
layers, or pass it through unchanged. The choice of which
parts of each layer are gated through on each input is left to
the designer (not learned, as in the full model).
We study the scheme depicted in Fig. 4 consisting of M
input and response dimensions with full feature overlap (cf.
Fig. 2b). For the output layer, we assume that the gating
variables automatically zero all but the task-relevant response
dimensions. For the associative layer, we separate the hid-
den units into dimensions, one for each input dimension, and
make the gating variables zero all representations except the
one coming from the task-relevant input dimension (Fig. 4a).
Crucially, when the gating structure is known on a speciﬁc
example, the output of the network is a linear function of the
neurons that are on. Given this setting, the learning dynamics
can be solved exactly using methods developed by Saxe, Mc-
Clelland, and Ganguli (2014). The key advantage afforded by
the gating scheme is depicted in Fig. 4a: the input-to-hidden
weights for one input dimension can be shared by all tasks
that rely on that input dimension. This leads to a factor √M
speedup in learning relative to learning a single task by itself
(proof omitted due to space constraints).
However, with this gating system, multitasking is not pos-
sible: gating another task through to the output will lead to
interference. To counteract this, the gating scheme must be
changed: response dimensions can be divided into Qgroups,
each with a dedicated set of hidden units (Fig. 4b). This al-
lows tasks that use response dimensions in different output
groups to be performed simultaneously. Hence a maximum
of Qtasks can be performed simultaneously, but weight shar-
ing is reduced across tasks by a factor Q, slowing learning.
This analysis provides, at least in a simpliﬁed system, a
quantitative expression of the fundamental tradeoff between
Output gating signal
Figure 4: Gating model used for formal analysis. (a) Task
information directly switches on or off task-relevant dimen-
sions in the output and associative layers. This allows input-
to-hidden weights to be shared across the Mdifferent tasks
corresponding to different response dimensions, increasing
learning speed by a factor √M. However, two tasks that rely
on different input dimensions cannot be multitasked due to
crosstalk at the output (convergent red and green arrows). (b)
Multitasking ability can be improved by separating response
dimensions into Qgroups, each with a dedicated set of units
in the associative layer. Gating now permits one task from
each group to operate concurrently (red and green arrows no
longer converge). However, weight sharing is limited to the
group, yielding a learning speed of pM/Q.
learning speed and multitasking ability. Let tbe the number
of iterations required to learn all tasks, Qthe maximum num-
ber of concurrently executable tasks, and Mthe number of
input/response response dimensions. Then
where the proportionality constant is related to the statisti-
cal strength of the input-output association for one task, the
learning rate, and the error cut-off used to decide when learn-
ing is complete (Saxe, Musslick, & Cohen, 2017).
Due to the tradeoff in Eqn. (2), gating schemes that share
more structure will learn more quickly. Hence generic, ran-
domly initialized nonlinear networks will tend to favor shared
representations, as shown in Simulation Experiment 1.
Simulation Experiment 2: Effects of Learning
Biases for Shared Representations
In Simulation 2 we focus on a bias intrinsic to the neural sys-
tem, i.e. the initialization of the weights from the task layer.
We use this factor to systematically examine how the use of
shared representations facilitates the discovery of similarity
structure while diminishing multitasking performance. To do
so, we focus initially on a training environment in which tasks
are maximally similar, as this is the condition in which there
is most opportunity for exploiting shared representations. We
then examine environments with 80% and 0% feature overlap
between tasks, to test the generality of the observed effects.
To manipulate the bias towards shared task representations,
we initialized the weights from the task units to the associa-
tive layer, varying the similarity among the weight vectors
across tasks with the rationale that greater similarity should
produce a greater bias toward the use of shared representa-
tions in the associative layer. Weight vectors for tasks relying
on the same stimulus input dimensions were randomly ini-
tialized to yield a correlation coefﬁcient of value r. The cor-
relation value rwas varied from 0 to 0.975 in steps of 0.025
and was used to constrain initial weight similarities for 100
simulated networks per initial condition. The weight vectors
for tasks of non-overlapping stimulus dimensions were un-
correlated. Finally, all task weights to the associative layer
were scaled by a factor of 5 to enhance the effects of different
initial task similarities. The networks were trained using the
same parameters as reported for Simulation Experiment 1.
Simulation results indicate that networks with a higher
similarity bias tend to develop more similar representations
at the associative layer for those tasks (in terms of their ﬁ-
nal weight vector correlations), whereas a lower similarity
bias leads to more distinct task representations at this layer.
In environments with high feature overlap between tasks,
stronger initial biases toward shared representations lead to
increased learning speed (i.e. less iterations required to train
the network), as similarities between tasks can be exploited
(Fig. 5a). Critically, this comes at the cost of multitasking
performance. Learning beneﬁts gained from shared represen-
tations are less prevalent in environments with less feature
overlap between tasks. However, effects of weight similarity
biases on multitasking impairments remain (Fig. 5b).
Learning Speed &
100% Feature Overlap Effects Across Task Environments
70 75 80 85
Iterations Required To Train
Multitasking Accuracy (%)
Initial Task Correlation
60 70 80 90 100 110 120
Iterations Required To Train
Multitasking Accuracy (%)
Initial Task Similarity
0% Feature Overlap
Figure 5: Effects of weight similarity bias. Mean multitask-
ing accuracy (for two tasks simultaneously) plotted against
the mean number of iterations required to train the network.
Data points represent the mean measures across networks ini-
tialized with the same task similarity (constrained by task
weight vector correlation) for tasks relying on the same stim-
ulus dimensions. Effects are shown for (a) environments with
100% feature overlap between tasks, as well as (b) across
environments with different feature overlap. Different data
point clusters correspond to different training environments.
General Discussion and Conclusion
The limited ability to perform multiple control-dependent
tasks at the same time is one of the most salient character-
istics of human cognition, and is universally considered a
deﬁning feature of cognitive control. Despite these facts, the
sources of this capacity constraint associated with control re-
main largely unexplored. Here, we build upon the observation
that multitasking limitations can arise from shared representa-
tions between tasks (Feng et al., 2014; Musslick et al., 2016),
and use a combination of formal analysis and neural network
simulations to examine biases towards shared representations
that incur such costs in multitasking.
In the ﬁrst part of this study, we build upon early insights of
connectionism that shared representations emerge as a func-
tion of task similarities in the environment and demonstrate
the deleterious consequences for multitasking performance.
It has been shown that networks are capable of extracting sim-
ilarities from a hierarchically structured input space (Hinton,
1986). Recent analytic and empirical work in the domain of
semantic cognition paints a similar picture: neural systems
may gradually discover shared structure in the task environ-
ment with a bias towards the initial formation of shared, low-
dimensional representations (Saxe et al., 2013; McClelland &
Rogers, 2003). Our simulation results are in line with these
observations showing that shared task representations emerge
as a function of high stimulus feature overlap between tasks
and furthered the insight that such similarities in the task en-
vironment lead to multitasking limitations.
In the second part, we examined how intrinsic learning bi-
ases towards shared or separate representations (by means
of weight initialization) can be used to expose a tradeoff
between learning efﬁciency and multitasking performance.
Early work in machine learning suggests that learning bi-
ases towards a particular representation can be understood
as biases of the learner’s hypothesis space (Baxter, 1995),
that is, the set of all hypotheses a learner may use to ac-
quire new tasks. We formalized this hypothesis space in terms
of the amount of shared representations between tasks and
showed how this mediates an inverse relationship between
learning efﬁciency and interference-free multitasking. Our
neural network simulations conﬁrmed these analytical predic-
tions, showing that a weight initialization bias towards shared
representations enables faster learning if shared structure in
the environment can be exploited, but incurs a cost for multi-
tasking. A promising direction for future research may be to
explore another prediction: our formalism suggests a role for
such biases in regularizing the representational complexity of
the network, thereby promoting generalization performance.
Our analyses indicate that neural learning systems, whether
natural or artiﬁcial, are subject to a tension between “in-
teractive parallelism“ on the one hand, which exploits the
ﬁne grained structure of representations and similarity in the
service of learning, and “independent parallelism“ that sup-
ports concurrent processing of distinct tasks, on the other
hand. A similar tension can be found in the domain of learn-
ing and memory. The complementary learning systems hy-
pothesis proposes two separate learning systems, one system
that relies on shared representations to support inference, as
well as another system that uses separate representations to
support independent encoding and retrieval of information
(McClelland, McNaughton, & O’Reilly, 1995). The latter
system supports a form of independent parallelism for asso-
ciational processes that is similar to the form of independent
parallelism for executional processes described in this paper.
Altogether our results suggest that the brain may be con-
fronted with balancing multitasking capability against extrin-
sic and intrinsic biases towards shared representations. A ma-
jor goal for the development of artiﬁcial systems may be to
systematically conﬁgure the balance between interactive and
independent parallelism, as well as to exploit the relative ad-
vantages of each. Most efforts in complex neural architec-
tures have focused predominantly on the discovery of shared
representations for the purpose of inference and generaliza-
tion (Bengio, Courville, & Vincent, 2013). However, one of
the future challenges will be to explore the tension between
learning efﬁciency and multitasking in networks with higher
complexity (i.e. deep networks), as well as in more natu-
ralistic task environments. We hope that this work will help
inspire a proliferation of efforts to further explore this area.
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