18,984 research outputs found
Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation
The dynamics and the stationary states for the competition between pattern
reconstruction and asymmetric sequence processing are studied here in an
exactly solvable feed-forward layered neural network model of binary units and
patterns near saturation. Earlier work by Coolen and Sherrington on a parallel
dynamics far from saturation is extended here to account for finite stochastic
noise due to a Hebbian and a sequential learning rule. Phase diagrams are
obtained with stationary states and quasi-periodic non-stationary solutions.
The relevant dependence of these diagrams and of the quasi-periodic solutions
on the stochastic noise and on initial inputs for the overlaps is explicitly
discussed.Comment: 9 pages, 7 figure
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
Adaptive Matching for Expert Systems with Uncertain Task Types
A matching in a two-sided market often incurs an externality: a matched
resource may become unavailable to the other side of the market, at least for a
while. This is especially an issue in online platforms involving human experts
as the expert resources are often scarce. The efficient utilization of experts
in these platforms is made challenging by the fact that the information
available about the parties involved is usually limited.
To address this challenge, we develop a model of a task-expert matching
system where a task is matched to an expert using not only the prior
information about the task but also the feedback obtained from the past
matches. In our model the tasks arrive online while the experts are fixed and
constrained by a finite service capacity. For this model, we characterize the
maximum task resolution throughput a platform can achieve. We show that the
natural greedy approaches where each expert is assigned a task most suitable to
her skill is suboptimal, as it does not internalize the above externality. We
develop a throughput optimal backpressure algorithm which does so by accounting
for the `congestion' among different task types. Finally, we validate our model
and confirm our theoretical findings with data-driven simulations via logs of
Math.StackExchange, a StackOverflow forum dedicated to mathematics.Comment: A part of it presented at Allerton Conference 2017, 18 page
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
Retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks
The retrieval behavior and thermodynamic properties of symmetrically diluted
Q-Ising neural networks are derived and studied in replica-symmetric mean-field
theory generalizing earlier works on either the fully connected or the
symmetrical extremely diluted network. Capacity-gain parameter phase diagrams
are obtained for the Q=3, Q=4 and state networks with uniformly
distributed patterns of low activity in order to search for the effects of a
gradual dilution of the synapses. It is shown that enlarged regions of
continuous changeover into a region of optimal performance are obtained for
finite stochastic noise and small but finite connectivity. The de
Almeida-Thouless lines of stability are obtained for arbitrary connectivity,
and the resulting phase diagrams are used to draw conclusions on the behavior
of symmetrically diluted networks with other pattern distributions of either
high or low activity.Comment: 21 pages, revte
Statistical physics of neural systems with non-additive dendritic coupling
How neurons process their inputs crucially determines the dynamics of
biological and artificial neural networks. In such neural and neural-like
systems, synaptic input is typically considered to be merely transmitted
linearly or sublinearly by the dendritic compartments. Yet, single-neuron
experiments report pronounced supralinear dendritic summation of sufficiently
synchronous and spatially close-by inputs. Here, we provide a statistical
physics approach to study the impact of such non-additive dendritic processing
on single neuron responses and the performance of associative memory tasks in
artificial neural networks. First, we compute the effect of random input to a
neuron incorporating nonlinear dendrites. This approach is independent of the
details of the neuronal dynamics. Second, we use those results to study the
impact of dendritic nonlinearities on the network dynamics in a paradigmatic
model for associative memory, both numerically and analytically. We find that
dendritic nonlinearities maintain network convergence and increase the
robustness of memory performance against noise. Interestingly, an intermediate
number of dendritic branches is optimal for memory functionality
Period-two cycles in a feed-forward layered neural network model with symmetric sequence processing
The effects of dominant sequential interactions are investigated in an
exactly solvable feed-forward layered neural network model of binary units and
patterns near saturation in which the interaction consists of a Hebbian part
and a symmetric sequential term. Phase diagrams of stationary states are
obtained and a new phase of cyclic correlated states of period two is found for
a weak Hebbian term, independently of the number of condensed patterns .Comment: 8 pages and 5 figure
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