7,059 research outputs found
Dynamics of Neural Networks with Continuous Attractors
We investigate the dynamics of continuous attractor neural networks (CANNs).
Due to the translational invariance of their neuronal interactions, CANNs can
hold a continuous family of stationary states. We systematically explore how
their neutral stability facilitates the tracking performance of a CANN, which
is believed to have wide applications in brain functions. We develop a
perturbative approach that utilizes the dominant movement of the network
stationary states in the state space. We quantify the distortions of the bump
shape during tracking, and study their effects on the tracking performance.
Results are obtained on the maximum speed for a moving stimulus to be
trackable, and the reaction time to catch up an abrupt change in stimulus.Comment: 6 pages, 7 figures with 4 caption
Analysis of Oscillator Neural Networks for Sparsely Coded Phase Patterns
We study a simple extended model of oscillator neural networks capable of
storing sparsely coded phase patterns, in which information is encoded both in
the mean firing rate and in the timing of spikes. Applying the methods of
statistical neurodynamics to our model, we theoretically investigate the
model's associative memory capability by evaluating its maximum storage
capacities and deriving its basins of attraction. It is shown that, as in the
Hopfield model, the storage capacity diverges as the activity level decreases.
We consider various practically and theoretically important cases. For example,
it is revealed that a dynamically adjusted threshold mechanism enhances the
retrieval ability of the associative memory. It is also found that, under
suitable conditions, the network can recall patterns even in the case that
patterns with different activity levels are stored at the same time. In
addition, we examine the robustness with respect to damage of the synaptic
connections. The validity of these theoretical results is confirmed by
reasonable agreement with numerical simulations.Comment: 23 pages, 11 figure
Characterizing Self-Developing Biological Neural Networks: A First Step Towards their Application To Computing Systems
Carbon nanotubes are often seen as the only alternative technology to silicon
transistors. While they are the most likely short-term one, other longer-term
alternatives should be studied as well. While contemplating biological neurons
as an alternative component may seem preposterous at first sight, significant
recent progress in CMOS-neuron interface suggests this direction may not be
unrealistic; moreover, biological neurons are known to self-assemble into very
large networks capable of complex information processing tasks, something that
has yet to be achieved with other emerging technologies. The first step to
designing computing systems on top of biological neurons is to build an
abstract model of self-assembled biological neural networks, much like computer
architects manipulate abstract models of transistors and circuits. In this
article, we propose a first model of the structure of biological neural
networks. We provide empirical evidence that this model matches the biological
neural networks found in living organisms, and exhibits the small-world graph
structure properties commonly found in many large and self-organized systems,
including biological neural networks. More importantly, we extract the simple
local rules and characteristics governing the growth of such networks, enabling
the development of potentially large but realistic biological neural networks,
as would be needed for complex information processing/computing tasks. Based on
this model, future work will be targeted to understanding the evolution and
learning properties of such networks, and how they can be used to build
computing systems
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