Submittted to the Cognitive Science Conference, 2018

Three levels of neural reuse through the dynamical lens: structural network,
autonomous dynamics and transient dynamics.
Madhavun Candadai (madcanda@indiana.edu)
Cognitive Science Program, Indiana University
Bloomington, IN 47406 USA

Eduardo Izquierdo (edizquie@indiana.edu)

arXiv:1802.03891v1 [] 12 Feb 2018

Cognitive Science Program and School of Informatics, Computing, and Engineering, Indiana University
Bloomington, IN 47406 USA
Abstract
The brain in conjunction with the body is able to adapt to new
environments and perform multiple behaviors through reuse
of neural resources and transfer of existing behavioral traits.
Although mechanisms that underlie this ability are not well
known, they are largely attributed to neuromodulation. In this
work, we demonstrate that an agent can be multifunctional using the same sensory and motor systems across behaviors, in
the absence of modulatory mechanisms. Further, we lay out the
different levels at which neural reuse can occur through a dynamical filtering of the brain-body-environment system’s operation - structural network, autonomous dynamics, and transient dynamics. Notably, transient dynamics reuse can only be
explained by studying the brain-body-environment system as
a whole and not just the brain. The multifunctional agent we
present here demonstrates neural reuse at all three levels.
Keywords: multifunctionality; neural reuse; neural networks;
dynamical systems theory; brain-body-environment systems

Introduction
A crucial aspect to adaptation in cognitive beings is their
ability to exploit regularities in the environment and reuse
existing resources/skills across multiple behaviors. Extensive empirical evidence shows that neural resources developed during the course of learning one behavior is reused
for others (Anderson, 2010). This multi-functional ability
of neural circuits has been demonstrated in the seemingly
small and simple nervous systems of the nematode worm
Caenorhabditis elegans(302 neurons) (Hobert, 2003) as well
as in the macro scale of the human brain (100 billion neurons) (Lizier, Heinzle, Horstmann, Haynes, & Prokopenko,
2011). The mechanisms that facilitate this phenomenon have
largely been attributed to neuromodulation and synaptic plasticity (Briggman & Jr., 2008; Getting, 1989; Morton &
H.J.Chiel, 1994).
The goal of this work is to show a concrete example of
how interaction between brain, body and environment enables
neural networks to perform multiple behaviors and elucidate
the dynamical aspects that lead to it. Reuse in embodied recurrent neural networks unfold over three levels - structural
network, autonomous dynamics of the neural network, and
transient dynamics of the neural network (Fig. 1). Structure
is defined by the neural circuit itself, the intrinsic parameters
of the neurons, and the synaptic strength of connectivity between them. While it is possible that an agent possesses specialized circuits for performing different behaviors (Fig. 1A),

Figure 1: Three levels of neural reuse in multifunctional
agents - structure (blue circles), autonomous dynamics (green
squares) and transient dynamics (orange triangles). [A] Specialized structural circuits are used for each behavior (nonoverlapping circles). Autonomous and transient dynamics associated with independent structures are used to be multifunctional denoting no reuse at any level. [B] Structure is reused
through employing overlapping neural circuits for the two behaviors (overlapping circles). Autonomous and transient dynamics are unique to each behavior. [C] From structurally
reused circuits, the sets of attractors associated with each behavior are also shared (overlapping circles and squares), but
the transient dynamics around those attractors are unique to
each behavior. [D] While utilizing overlapping neural circuits, behaviors also use overlapping sets of attractors and
reuse transient dynamics between them (overlapping circles,
squares and triangles).

reuse at this level involves utilizing overlapping circuits to
produce multiple behaviors (Fig. 1B,C,D). The next level,
when structure is reused, is that of the neural network’s autonomous dynamics isolated from the body. Each behavior
is associated with a set of phase-portraits corresponding to
the inputs the agent experiences while performing them. The
sets of phase-portraits (and the attractors therein) could be
overlapping (Fig. 1C,D) or could be unique to each behavior
(Fig. 1B). The set of all attractors from all phase-portraits corresponding to a behavior are also referred to as attractor set

of the behavior in this paper. The third level of reuse is that
of ongoing transient dynamics as the agent is in continuous
closed-loop interaction with the environment. When there is
attractor reuse from the previous level, it is possible that multiple behaviors navigate different transients around those attractors (Fig. 1C) or, they might be reused too (Fig. 1D). We
show for the first time to our knowledge that reuse of transients, namely indistinguishable neural dynamics, can produce starkly distinguishable behaviors in embodied dynamical neural networks. This can only be observed when the
brain is studied in conjunction with the closed-loop interaction between the body and the environment.
We believe that this three level approach, where the earlier
levels subsume the later ones, provides a systematic framework to study neural reuse in biological systems. Each level
could further be expanded into sub-levels. For instance, structural reuse can further check if specific types of neurons are
reused, or if network properties such as communities or rich
clubs are reused and so on. In this paper, we have explored
autonomous and transient dynamics reuse in greater detail.

Methods
This section outlines the agent design and its neural controller, the categorization and pole-balancing task set up and
the evolutionary optimization algorithm. The agent and environment are continuous time systems, that were simulated by
Euler stepping them with a step size of 0.1.

Agent design
The agent design is identical to (Beer, 1996) being circular
with a diameter of 30 units and is equipped with 7 sensory
rays radiating from its center, equally distributed over an angle of π/6. The rays constitute the “eye” of the agent and
they have a range of 265 units. Each sensory ray feeds into a
sensory neuron, and the magnitude of input is inversely proportional to the distance at which that ray is intersected by
an object (Fig. 2). The sensory neurons are stateful units that
are governed by the following dynamics τs ṡi = −si + Ii where
i ∈ [1, 7]. τs refers to the time-constant which is fixed to be
the same across all 7 neurons, si refers to the state of the
neuron, and Ii to the sensory input received from the corresponding ray. Neuron output is oi = σ(−gs (si + θs )) where
σ(x) = 1/(1 + exp(−x)) is the sigmoid function of the state
with a gain, gs , and bias θs , that are also fixed to be the
same across all sensory neurons. The sensory neurons are
fully connected to an interneuron layer, made up of a fully
recurrently connected continuous-time recurrent neural network (CTRNN). The interneurons are governed by
N

7

τi ṡi = −si + ∑ w ji σ(g j (s j + θ j )) + ∑ wki ok
j=1

(1)

k=1

where the last term refers to the input to interneuron i defined
as the weighted sum of the outputs of the sensory neurons,
ok , with the weight from the kth sensory neuron being wki .
Being a fully connected recurrent network, the interneuron

Figure 2: Agent design and task setup. [A] 7 rays of vision
feed into sensory neurons (black). These neurons are fully
connected to the recurrent interneuron layer (red), that in turn
feed the left and right motor neurons (grey). [B] Categorization task with circle and line trial. The falling object needs to
be caught if it is a circle and avoided if it is a line. [C] Polebalancing task. The pole attached to the agent’s center is expected it to keep balanced within the rays.
dynamics also incorporate the activity of other interneurons
weighted by w ji (from j to i). The state of the interneurons are
denoted by si , their gains by gi (=1) and their bias by θi . The
interneuron network size is denoted by N. They project to two
motor neurons that take on dynamics similar to the interneurons but they are not connected to each other. Unlike in (Beer,
1996), the motor neurons control the effective acceleration
of the agent, a, as follows a = gm (σ(sr + θm ) − σ(sl + θm ))
where gm refers to the gain, sr and sl are the internal state
variables for the right and left motor neurons respectively, σ
is the standard sigmoidal activation function and θm is the
common bias term for both motor neurons.

Categorization task design
The categorization task involves differentiating between the
falling objects (circles and lines) by moving towards one (circles) and away from the other (lines) (Beer, 1996). The circles’ diameter and the line’s length were both set at 30 units.
To encourage generalization, each evaluation of the agent’s
performance was conducted over 8 different trials for each
type of object, with the objects’ starting horizontal offset from
the agent uniformly distributed in the range [−50, 50]. The
objects fall with a constant velocity of 0.3 units per second.
Performance in this task was quantified by averaging over
1 − |di | for the circle trials and |di | for the line trials; where
di is the normalized distance between the center of the agent
and the center of the object when the vertical offset between
the agent and the object reaches 0 (offset of over 45 units was
clipped at 45).

Pole-balancing task design
The second task, pole-balancing, was inspired by the first implementation in (Barto, Sutton, & Anderson., 1984). It was
re-designed such that the agent has the pole attached to its
center and can sense it through the same rays used for sensing the falling objects (Candadai & Izquierdo., 2017). The
sensory input, as the pole sw.pdf across a ray at angle φ◦ ,
increases linearly from 0 at (φ − 1)◦ reaching the maximum
value at φ◦ and falling back to 0 at (φ + 1)◦ and vice verse.

Note that the agent senses the pole only when it intersects
with a ray but it “disappears” from view while passing between rays. The pole Was considered dropped if it fell beyond the rays, or if the agent moved over 45 units on either
side from its starting position. Performance was calculated
by averaging cos(θ ∗ 6) at each time step, where θ is the pole
angle with the vertical, over the 500s of evaluation duration.
Just like the categorization task, to promote generalization of
the behavior, performance was averaged over 16 trials with
the pole starting from 4 different angles on either side of the
agent in [−9◦ , 9◦ ] with angular velocity -0.1 or 0.1.

Evolutionary optimization
An evolutionary search algorithm was used to optimize
the parameters of the agent - time-constant, gain and bias
for sensory neurons (3), weights from sensory layer to Ninterneurons (N ∗ 7), recurrent weights between interneurons (N 2 ), bias and time-constant for each interneuron (2N),
weights from interneurons to motor neurons (2N) and gain,
bias and time-constant for motor neurons (3): totaling D =
3 + 7N + N 2 + 2N + 2N + 3 parameters. The search starts
with a random population of 100 solutions encoded as Ddimensional genotype vectors with each element in [-1,1].
These elements were scaled and mapped on to the different
parameters to build the agents. Gains are scaled to be in
[1,20], time constants in [1,2], biases in [-4,4] and all weights
are scaled to be in [-5,5]. These agents were then evaluated
for their performance (fitness). Based on fitness, an elitist
fraction of the top 4% solutions were retained while their
copies were subject to a Gaussian mutation noise with mean
0 and variance 0.3 to produce a new population of 100 solutions, and this process was repeated for a fixed number of
generations.
Since optimization is stochastic, 100 independent runs
were carried out for the single and multi-task scenarios. For
the individual tasks, optimization was carried out over 1000
generations in each run. In the multi-task setting, fitness was
computed as the product of fitness in each task. These experiments were conducted in three different task presentation paradigms: (1) evolve for both categorization and polebalancing over 2000 generations, (2) evolve only for polebalancing for the first 500 generations, and then evolve for
both tasks for 1500 generations and (3) evolve for categorization for the first 1000 generations, and then for both tasks
for another 1000. The 500 generation limit for paradigm 2
and 1000 for 3 was based on number of generations taken to
acquire good performance in each task when optimized individually. The product of the individual task fitness was used
as opposed to sum or average because it guarantees good performance in both tasks, while still keeping the fitness in [0, 1].

Results
Minimal neural resource requirement for each task
In order to evaluate the level of reuse in the multifunctional
network, we first systematically explored the minimal re-

sources required to solve each task individually. We used an
evolutionary optimization technique to train networks of different sizes for both tasks: pole-balancing and categorization.
100 independent evolutionary runs were performed for networks of different sizes for each task. The smallest network
that could perform pole-balancing had two interneurons. The
best of these agents achieved a 98.44% fitness and was able
to move the pole to its upright position from a broad range of
initial positions and keep it balanced for an extended duration
of time (Fig. 3A). The smallest network that could perform
the categorization task also had two interneurons. The best of
these agents had a fitness of 98.5% and was able to successfully catch all circles and avoid all lines falling from the full
range of starting positions (Fig. 3D).
Effectively addressing multifunctionality using these two
asks is only possible if the two tasks involve sufficiently different behaviors: solving one task, at most, only helps partially solve the second, and vice verse. In order to test this,
all agents that have been optimized to perform one task were
evaluated on the other. Agents that were trained to balance
the pole were as good as random agents at the categorization
task (Fig. 3B,E), while agents that were trained to categorize
could balance the pole only slightly better than random controllers (Fig. 3C,E). This suggests each task requires its own
unique set of sensory-motor skills and that ultimately solving
one task does not guarantee good performance in the other
task.

Structural network reuse: Fully overlapping circuits
were used to perform both behaviors.
The highest level of reuse is that of structure - an agent performing more than one behavior could acquire specialized circuitry to perform each behavior or could share neural circuits
between them. In order to test this, using the same evolutionary optimization approach described previously we evolved
networks of different sizes to perform both behaviors.
Interestingly, agents with networks no larger than the ones
that could solve the individual tasks could also solve both
tasks. The best 2-neuron multifunctional agent could perform
categorization with a fitness of 95.8% and pole-balancing
with a fitness of 95.4%. This agent used the same circuit to
successfully catch circles while avoiding lines and also balance a pole (Fig. 4). It is to be noted that the agent had no external signal indicating which task to solve. Furthermore, the
agent also had no synaptic plasticity or neuromodulatory signal that could be responsible for re-configuring the circuit for
the different tasks. Since performing each behavior individually required at least 2 neurons, it follows that the 2-neuron
multifunctional agent shared the same structural resources.

Autonomous dynamics reuse: Overlapping sets of
attractors were used to perform both behaviors.
Given that the circuit is the same across the two behaviors
of categorization and pole-balancing, going one level deeper
into its autonomous dynamics, we evaluated reuse at three
levels of increasing specificity - attractor composition, basins

Figure 4: Behavior of the best multifunctional agent from 100
runs. [A] The agent was able to bring to center and balance
the pole starting from different pole angles. [B] The same
agent, using the same neural network was also able to catch
the circles (red) while avoiding lines (orange).

Figure 3: Behavior and performance on individual tasks.
[A] Best agent from 100 runs of optimizing for polebalancing alone. The agent was able to bring the pole to the
center and keep it balanced from different initial pole angles.
[B] Best pole-balancer shown in A is unable to categorize
circles (red) from lines(orange) and avoids both. [C] Best
agent from 100 runs evolved for categorization alone is unable to balance the pole. [D] Best categorization agent shown
in C, demonstrating its ability to catch circles (red) while
avoiding lines (orange). [E] Optimizing for one task results in performance similar to a random agent on the other
task. Fitness distribution from 100 runs of agents evolved for
pole-balancing (black) in pole-balancing and categorization,
and similarly that of the agents evolved for categorization
only (gray) in pole-balancing and categorization, and random
agents (white) on both tasks.
of attraction and location of attractors in the sets of phaseportraits associated with the different behaviors. A phaseportrait is the dynamical landscape of the neural network
upon subjecting it to a fixed input under different initial conditions. A phase-portrait for a particular input, could have
one or more attractors. The set of phase-portraits associated
with a behavior (say circle catching) can be obtained by fixing
the inputs to what the agent experiences during that behavior
(circle at fixed positions relative to the agent), and allowing
the network to settle into its attractors from different initial
states. The three sets of phase-portraits corresponding to circle catching, line avoiding and pole-balancing were compared
on the above mentioned levels to evaluate reuse.
All phase-portraits associated with all three behaviors in

the best multifunctional agent were composed of one fixedpoint attractor, thus showing reuse in the highest level of
autonomous dynamics, namely attractor composition. This
denotes that the set of phase-portraits of one behavior do
not have to undergo bifurcation to lead to the set of phaseportraits of the other. Even though the phase-portraits are
qualitatively matching across behaviors, they could have different basins of attractions, which could lead to different behaviors operating in its own region of the phase-space (dynamical modularity). In this case, since only one fixed-point
attractor exists in each phase-portrait, there exists only one
basin of attraction in each of them and hence is the same
across all behaviors.
Even with shared phase-portraits and basins of attractions,
the locations of the attractors from phase-portraits of different behaviors do not have to be the same. Differentiated by
their location, each behavior could have a unique set of attractors or they could overlap to different extents. Upon analyzing their locations we discovered that, even quantitatively,
the multifunctional agent reused its attractors between these
behaviors (Fig. 5). This reuse was only partial since each behavior also had its own set of unique attractors that were not
shared. This reuse means that different inputs from different
behaviors were mapped to the same phase-portrait suggesting
an inherent degeneracy between the sensory inputs and the
requisite behavioral pattern for the three behaviors. In fact,
agents may evolve to take advantage of such a degeneracy,
where two distinct perceptual scenarios might require similar
interpretations by the interneurons or indeed a similar action,
and hence are mapped to the same phase-portrait.

Transient dynamics reuse: Phases of the behaviors
reused the same transient dynamics.
Our analysis started at the level of structural reuse and went
on to discover reuse at the level of autonomous dynamics in
the best multifunctional agent. The next level is that of ongoing dynamics as the nervous system coupled with its body
and environment performs the behaviors. Note that in the previous level, attractors were identified by fixing the relative

Figure 5: Attractor reuse. Locations of attractors from the
three sets of phase-portraits corresponding to circle-catching,
line-avoiding and pole-balancing tasks are overlapped. This
shows that each behavior has its own set of unique attractors
as well as shares them with other behaviors.

position of the agent with the object and then allowing the
network to settle. However, during behavior, both the agent
and the object are in constant movement. Therefore, at any
given time, for a particular relative positioning of the agent
and the object, the sensory input might change before the network settles into the attractor associated with that fixed input.
As a result, dynamics of the network are in constant transient movement across the phase-portraits (and the attractors
therein) associated with that behavior. Therefore, at this level,
the relevant question that explores reuse is whether multiple
behaviors have their own unique transient trajectory or if they
could possibly share them.
Transient dynamics were shared partially between the
circle-catching and pole-balancing tasks in the best multifunctional agent. In order to explore this, we looked at the entire sensorimotor loop as this agent performed both behaviors.
While in each case there were times when their transients
were different, for a particular phase during these behaviors,
the dynamics almost exactly matched (Fig. 6A). Interestingly,
inputs to the interneurons, their outputs, and motor neuron
outputs were all identical suggesting that the agent’s nervous
system does not differentiate between these phases of the two
behaviors. This leads to two interesting questions (1) Are the
two behaviors indistinguishable during this phase? (2) If not,
where does the difference come from?
Although the dynamics in the inter-neurons are identical,
the behaviors were different in the circle-catching and polebalancing tasks. In the former, the agent was receiving oscillatory inputs only along ray 1, meaning that the agent oriented
itself so as to track the circle along that ray before catching
it (Fig. 6B). In contrast, the sensory inputs during the same
transient dynamics in the pole-balancer shows that during this
phase of the behavior, the agent mostly maintains the pole oscillating around ray 3 while bring it around across rays 4,5
and 6. This is an interesting outcome since it demonstrates
that neural activity that is completely indistinguishable to
the level of transient dynamics could still produce behaviors

Figure 6: Transient/Driven dynamics reuse. [A] Activity of
inter-neurons for the circle-catching (red) and pole-balancing
(blue) tasks, time-shifted to show identical neural activity.
[B] Sensory inputs to the 7 rays showing that although neural
activity is indistinguishable, the agent tracks the circle along
ray 1(red) but the pole is along rays 3 and 4 (blue).
starkly different from each other. The difference arises from
the parts of the behavior leading up to this shared transient
phase, where the agent has its own unique dynamics for each
behavior through its interaction with the environment. Note
that the weights to the interneurons from sensory rays 1 and
3 are not the same. This transient reuse emerges purely from
the recurrent and dynamical properties of the inter-neurons.

Related work
The work presented here builds on (Izquierdo & Bhrmann,
2008), (Williams & Beer., 2013) and (Agmon & Beer.,
2014) by developing a computational model of a brain-bodyenvironment system that performs multiple behaviors using the same sensory and motor capacities. In the work
by Izquierdo et. al., the same neural network without any
changes in parameters or mechanisms of modulation was
shown to perform two qualitatively different behaviors while
placed in two different bodies. Williams et. al. showed that
when different motor systems are used for different tasks, the
qualitative difference in environmental feedback drives the
same network differently to produce different behaviors. Agmon et. al. presented a model where different sensory apparatus in the agent, sensitive to different stimuli in the environment, performed different associated behaviors using the
same motor control systems. In these models, although the
neural network remained the same, the body was changing.

The model presented in this paper, used the same sensory and
motor control mechanisms for the two tasks - object categorization and pole-balancing. We also show through dynamical
analysis that reuse to the level of transient dynamics can be
observed when the brain, body, environment and their interaction are taken into account.

Discussion
To summarize, we first evolved embodied recurrent neural
networks to perform object categorization, pole-balancing
and then both. We then systematically explored the different levels of reuse discovering reuse of neural circuits at the
structural level, followed by reuse of autonomous dynamics
with qualitative sharing of phase-portraits, overlapping basins
of attraction and reuse of attractors identical in the location of
their fixed-points. Furthermore, we discovered reuse of transient dynamics in the best multifunctional agent. The two
main contributions of our work are (1) the same neural circuit
can perform multiple behaviors using the same sensory and
motor systems in the absence of explicit task identifying signals or processes such as neuromodulation (2) indistinguishable neural activity, displaying reuse to the level of transients,
can still produce completely different behaviors.
The rationale behind transient reuse in this multifunctional
agent and can be explained by observing the environmentbody relationship and transient dynamics. The similarity in
dynamics arises out of the agent generalizing between the two
behaviors by learning to align an object along a single ray pole along center ray and circle along corner ray (Fig. 4 and
6). Generalization requires learning to use only one ray because the pole only intersects one ray at a time. The circle
had to be balanced along the corner ray because otherwise it
would intersect multiple rays and the pole needs to be balanced along the center ray to maximize fitness.
The disparity in behavior, however, arises out of the unique
transient dynamics prior to shared transient phase of the behaviors. The unique dynamics in circle-catching orients the
falling object along the corner ray even if the circle starts from
the center, whereas in pole-balancing it brings the pole to the
center, thereby setting up the system to perform the generalized oscillatory “object tracking along a single ray” for both
behaviors (Fig. 4B). This is possible because of the structure
provided by the environment and the body. Objects intersect
only one ray or multiple rays, yet the agent is required to align
with the object in both cases. Thus, multifunctionality in this
agent is enabled by the closed-loop interaction between the
body, environment and a nervous system that affords reuse at
all levels of dynamics.
The three-level framework presented here is rooted in dynamical systems theory and has the potential to explain reuse
in any model or biological system. While an information theoretic approach would also be able to explain reuse in analogous levels, the key point to be noted is that there are levels of
reuse that can be explained only by looking at the brain-bodyenvironment system as a whole, and not just the brain (the

neural network). The model presented in this paper, while
using only a small neural network for two seemingly simple tasks of categorization and adaptive control, raises several cognitively interesting questions. The analogous nature
of these two tasks in catching and balancing led to reuse here.
Are specific environmental structures associated with reuse at
different levels? Since the interneurons was limited to two,
reuse was forced in this case. Does reuse always happen
whenever possible? Can the same set of behaviors be performed with different levels of reuse? Transient reuse shown
in our model hints at embodied neural network modeling approaches to higher level cognitive phenomena such as analogy making and empathy.

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