242 research outputs found
Collective stability of networks of winner-take-all circuits
The neocortex has a remarkably uniform neuronal organization, suggesting that
common principles of processing are employed throughout its extent. In
particular, the patterns of connectivity observed in the superficial layers of
the visual cortex are consistent with the recurrent excitation and inhibitory
feedback required for cooperative-competitive circuits such as the soft
winner-take-all (WTA). WTA circuits offer interesting computational properties
such as selective amplification, signal restoration, and decision making. But,
these properties depend on the signal gain derived from positive feedback, and
so there is a critical trade-off between providing feedback strong enough to
support the sophisticated computations, while maintaining overall circuit
stability. We consider the question of how to reason about stability in very
large distributed networks of such circuits. We approach this problem by
approximating the regular cortical architecture as many interconnected
cooperative-competitive modules. We demonstrate that by properly understanding
the behavior of this small computational module, one can reason over the
stability and convergence of very large networks composed of these modules. We
obtain parameter ranges in which the WTA circuit operates in a high-gain
regime, is stable, and can be aggregated arbitrarily to form large stable
networks. We use nonlinear Contraction Theory to establish conditions for
stability in the fully nonlinear case, and verify these solutions using
numerical simulations. The derived bounds allow modes of operation in which the
WTA network is multi-stable and exhibits state-dependent persistent activities.
Our approach is sufficiently general to reason systematically about the
stability of any network, biological or technological, composed of networks of
small modules that express competition through shared inhibition.Comment: 7 Figure
Disappearance of Spurious States in Analog Associative Memories
We show that symmetric n-mixture states, when they exist, are almost never
stable in autoassociative networks with threshold-linear units. Only with a
binary coding scheme we could find a limited region of the parameter space in
which either 2-mixtures or 3-mixtures are stable attractors of the dynamics.Comment: 5 pages, 3 figures, accepted for publication in Phys Rev
NASA JSC neural network survey results
A survey of Artificial Neural Systems in support of NASA's (Johnson Space Center) Automatic Perception for Mission Planning and Flight Control Research Program was conducted. Several of the world's leading researchers contributed papers containing their most recent results on artificial neural systems. These papers were broken into categories and descriptive accounts of the results make up a large part of this report. Also included is material on sources of information on artificial neural systems such as books, technical reports, software tools, etc
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Shaping dynamics with multiple populations in low-rank recurrent networks
An emerging paradigm proposes that neural computations can be understood at
the level of dynamical systems that govern low-dimensional trajectories of
collective neural activity. How the connectivity structure of a network
determines the emergent dynamical system however remains to be clarified. Here
we consider a novel class of models, Gaussian-mixture low-rank recurrent
networks, in which the rank of the connectivity matrix and the number of
statistically-defined populations are independent hyper-parameters. We show
that the resulting collective dynamics form a dynamical system, where the rank
sets the dimensionality and the population structure shapes the dynamics. In
particular, the collective dynamics can be described in terms of a simplified
effective circuit of interacting latent variables. While having a single,
global population strongly restricts the possible dynamics, we demonstrate that
if the number of populations is large enough, a rank-R network can approximate
any R-dimensional dynamical system.Comment: 29 pages, 7 figure
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