30 research outputs found
The evolutionary origins of hierarchy
Hierarchical organization -- the recursive composition of sub-modules -- is
ubiquitous in biological networks, including neural, metabolic, ecological, and
genetic regulatory networks, and in human-made systems, such as large
organizations and the Internet. To date, most research on hierarchy in networks
has been limited to quantifying this property. However, an open, important
question in evolutionary biology is why hierarchical organization evolves in
the first place. It has recently been shown that modularity evolves because of
the presence of a cost for network connections. Here we investigate whether
such connection costs also tend to cause a hierarchical organization of such
modules. In computational simulations, we find that networks without a
connection cost do not evolve to be hierarchical, even when the task has a
hierarchical structure. However, with a connection cost, networks evolve to be
both modular and hierarchical, and these networks exhibit higher overall
performance and evolvability (i.e. faster adaptation to new environments).
Additional analyses confirm that hierarchy independently improves adaptability
after controlling for modularity. Overall, our results suggest that the same
force--the cost of connections--promotes the evolution of both hierarchy and
modularity, and that these properties are important drivers of network
performance and adaptability. In addition to shedding light on the emergence of
hierarchy across the many domains in which it appears, these findings will also
accelerate future research into evolving more complex, intelligent
computational brains in the fields of artificial intelligence and robotics.Comment: 32 page
Phase transitions in Pareto optimal complex networks
The organization of interactions in complex systems can be described by
networks connecting different units. These graphs are useful representations of
the local and global complexity of the underlying systems. The origin of their
topological structure can be diverse, resulting from different mechanisms
including multiplicative processes and optimization. In spatial networks or in
graphs where cost constraints are at work, as it occurs in a plethora of
situations from power grids to the wiring of neurons in the brain, optimization
plays an important part in shaping their organization. In this paper we study
network designs resulting from a Pareto optimization process, where different
simultaneous constraints are the targets of selection. We analyze three
variations on a problem finding phase transitions of different kinds. Distinct
phases are associated to different arrangements of the connections; but the
need of drastic topological changes does not determine the presence, nor the
nature of the phase transitions encountered. Instead, the functions under
optimization do play a determinant role. This reinforces the view that phase
transitions do not arise from intrinsic properties of a system alone, but from
the interplay of that system with its external constraints.Comment: 14 pages, 7 figure
Diffusion-based neuromodulation can eliminate catastrophic forgetting in simple neural networks
A long-term goal of AI is to produce agents that can learn a diversity of
skills throughout their lifetimes and continuously improve those skills via
experience. A longstanding obstacle towards that goal is catastrophic
forgetting, which is when learning new information erases previously learned
information. Catastrophic forgetting occurs in artificial neural networks
(ANNs), which have fueled most recent advances in AI. A recent paper proposed
that catastrophic forgetting in ANNs can be reduced by promoting modularity,
which can limit forgetting by isolating task information to specific clusters
of nodes and connections (functional modules). While the prior work did show
that modular ANNs suffered less from catastrophic forgetting, it was not able
to produce ANNs that possessed task-specific functional modules, thereby
leaving the main theory regarding modularity and forgetting untested. We
introduce diffusion-based neuromodulation, which simulates the release of
diffusing, neuromodulatory chemicals within an ANN that can modulate (i.e. up
or down regulate) learning in a spatial region. On the simple diagnostic
problem from the prior work, diffusion-based neuromodulation 1) induces
task-specific learning in groups of nodes and connections (task-specific
localized learning), which 2) produces functional modules for each subtask, and
3) yields higher performance by eliminating catastrophic forgetting. Overall,
our results suggest that diffusion-based neuromodulation promotes task-specific
localized learning and functional modularity, which can help solve the
challenging, but important problem of catastrophic forgetting
Network constraints on learnability of probabilistic motor sequences
Human learners are adept at grasping the complex relationships underlying
incoming sequential input. In the present work, we formalize complex
relationships as graph structures derived from temporal associations in motor
sequences. Next, we explore the extent to which learners are sensitive to key
variations in the topological properties inherent to those graph structures.
Participants performed a probabilistic motor sequence task in which the order
of button presses was determined by the traversal of graphs with modular,
lattice-like, or random organization. Graph nodes each represented a unique
button press and edges represented a transition between button presses. Results
indicate that learning, indexed here by participants' response times, was
strongly mediated by the graph's meso-scale organization, with modular graphs
being associated with shorter response times than random and lattice graphs.
Moreover, variations in a node's number of connections (degree) and a node's
role in mediating long-distance communication (betweenness centrality) impacted
graph learning, even after accounting for level of practice on that node. These
results demonstrate that the graph architecture underlying temporal sequences
of stimuli fundamentally constrains learning, and moreover that tools from
network science provide a valuable framework for assessing how learners encode
complex, temporally structured information.Comment: 29 pages, 4 figure
Spatial Gibbs random graphs
Many real-world networks of interest are embedded in physical space. We
present a new random graph model aiming to reflect the interplay between the
geometries of the graph and of the underlying space. The model favors
configurations with small average graph distance between vertices, but adding
an edge comes at a cost measured according to the geometry of the ambient
physical space. In most cases, we identify the order of magnitude of the
average graph distance as a function of the parameters of the model. As the
proofs reveal, hierarchical structures naturally emerge from our simple
modeling assumptions. Moreover, a critical regime exhibits an infinite number
of discontinuous phase transitions.Comment: 29 pages, 5 figures. Revised from previous versio
Development of Multiple Behaviors in Evolving Robots
We investigate whether standard evolutionary robotics methods can be extended to support the evolution of multiple behaviors by forcing the retention of variations that are adaptive with respect to all required behaviors. This is realized by selecting the individuals located in the first Pareto fronts of the multidimensional fitness space in the case of a standard evolutionary algorithms and by computing and using multiple gradients of the expected fitness in the case of a modern evolutionary strategies that move the population in the direction of the gradient of the fitness. The results collected on two extended versions of state-of-the-art benchmarking problems indicate that the latter method permits to evolve robots capable of producing the required multiple behaviors in the majority of the replications and produces significantly better results than all the other methods considered