1,687 research outputs found
The VC-Dimension versus the Statistical Capacity of Multilayer Networks
A general relationship is developed between the VC-dimension and the statistical lower epsilon-capacity which shows that the VC-dimension can be lower bounded (in order) by the statistical lower epsilon-capacity of a
network trained with random samples. This relationship explains quantitatively how generalization takes place after memorization, and relates the concept of generalization (consistency) with the capacity of the optimal classifier over a class of classifiers with the same structure and the capacity of the Bayesian classifier. Furthermore, it provides a general methodology to evaluate a lower bound for the VC-dimension of feedforward multilayer
neural networks.
This general methodology is applied to two types of networks which are important for hardware implementations: two layer (N - 2L - 1) networks with binary weights, integer thresholds for the hidden units and
zero threshold for the output unit, and a single neuron ((N - 1) networks) with binary weigths and a zero threshold. Specifically, we obtain O(W/lnL)≤ d_2 ≤ O(W), and d_1 ~ O(N). Here W is the total number of weights of the (N - 2L - 1) networks. d_1 and d_2 represent the VC-dimensions
for the (N - 1) and (N - 2L - 1) networks respectively
Development of position tracking of BLDC motor using adaptive fuzzy logic controller
The brushless DC (BLDC) motor has many advantages including simple to
construct, high torque capability, small inertia, low noise and long life operation.
Unfortunately, it is a non-linear system whose internal parameter values will change
slightly with different input commands and environments. In this proposed
controller, Takagi-Sugeno-Kang method is developed. In this project, a FLC for
position tracking and BLDC motor are modeled and simulated in
MATLAB/SIMULINK. In order to verify the performance of the proposed
controller, various position tracking reference are tested. The simulation results show
that the proposed FLC has better performance compare the conventional PID
controller
Multilayer Networks
In most natural and engineered systems, a set of entities interact with each
other in complicated patterns that can encompass multiple types of
relationships, change in time, and include other types of complications. Such
systems include multiple subsystems and layers of connectivity, and it is
important to take such "multilayer" features into account to try to improve our
understanding of complex systems. Consequently, it is necessary to generalize
"traditional" network theory by developing (and validating) a framework and
associated tools to study multilayer systems in a comprehensive fashion. The
origins of such efforts date back several decades and arose in multiple
disciplines, and now the study of multilayer networks has become one of the
most important directions in network science. In this paper, we discuss the
history of multilayer networks (and related concepts) and review the exploding
body of work on such networks. To unify the disparate terminology in the large
body of recent work, we discuss a general framework for multilayer networks,
construct a dictionary of terminology to relate the numerous existing concepts
to each other, and provide a thorough discussion that compares, contrasts, and
translates between related notions such as multilayer networks, multiplex
networks, interdependent networks, networks of networks, and many others. We
also survey and discuss existing data sets that can be represented as
multilayer networks. We review attempts to generalize single-layer-network
diagnostics to multilayer networks. We also discuss the rapidly expanding
research on multilayer-network models and notions like community structure,
connected components, tensor decompositions, and various types of dynamical
processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure
Weight Space Structure and Internal Representations: a Direct Approach to Learning and Generalization in Multilayer Neural Network
We analytically derive the geometrical structure of the weight space in
multilayer neural networks (MLN), in terms of the volumes of couplings
associated to the internal representations of the training set. Focusing on the
parity and committee machines, we deduce their learning and generalization
capabilities both reinterpreting some known properties and finding new exact
results. The relationship between our approach and information theory as well
as the Mitchison--Durbin calculation is established. Our results are exact in
the limit of a large number of hidden units, showing that MLN are a class of
exactly solvable models with a simple interpretation of replica symmetry
breaking.Comment: 12 pages, 1 compressed ps figure (uufile), RevTeX fil
Neural Network Memory Architectures for Autonomous Robot Navigation
This paper highlights the significance of including memory structures in
neural networks when the latter are used to learn perception-action loops for
autonomous robot navigation. Traditional navigation approaches rely on global
maps of the environment to overcome cul-de-sacs and plan feasible motions. Yet,
maintaining an accurate global map may be challenging in real-world settings. A
possible way to mitigate this limitation is to use learning techniques that
forgo hand-engineered map representations and infer appropriate control
responses directly from sensed information. An important but unexplored aspect
of such approaches is the effect of memory on their performance. This work is a
first thorough study of memory structures for deep-neural-network-based robot
navigation, and offers novel tools to train such networks from supervision and
quantify their ability to generalize to unseen scenarios. We analyze the
separation and generalization abilities of feedforward, long short-term memory,
and differentiable neural computer networks. We introduce a new method to
evaluate the generalization ability by estimating the VC-dimension of networks
with a final linear readout layer. We validate that the VC estimates are good
predictors of actual test performance. The reported method can be applied to
deep learning problems beyond robotics
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