Abstract: Over-parameterized neural networks have attracted a
great deal of attention in recent deep learning theory research,
as they challenge the classic perspective of over-fitting when
the model has excessive parameters and have gained empirical
success in various settings. While a number of theoretical works
have been presented to demystify properties of such models, the
convergence properties of such models are still far from being
thoroughly understood. In this work, we study the convergence
properties of training two-hidden-layer partially over-parameterized
fully connected networks with the Rectified Linear Unit activation via
gradient descent. To our knowledge, this is the first theoretical work
to understand convergence properties of deep over-parameterized
networks without the equally-wide-hidden-layer assumption and
other unrealistic assumptions. We provide a probabilistic lower bound
of the widths of hidden layers and proved linear convergence rate of
gradient descent. We also conducted experiments on synthetic and
real-world datasets to validate our theory.
Abstract: In this paper, ways of modeling dynamic measurement
systems are discussed. Specially, for linear system with single-input
single-output, it could be modeled with shallow neural network.
Then, gradient based optimization algorithms are used for searching
the proper coefficients. Besides, method with normal equation and
second order gradient descent are proposed to accelerate the modeling
process, and ways of better gradient estimation are discussed. It
shows that the mathematical essence of the learning objective is
maximum likelihood with noises under Gaussian distribution. For
conventional gradient descent, the mini-batch learning and gradient
with momentum contribute to faster convergence and enhance model
ability. Lastly, experimental results proved the effectiveness of second
order gradient descent algorithm, and indicated that optimization with
normal equation was the most suitable for linear dynamic models.
Abstract: The approach proposed here is oriented in the direction of fuzzy system for the analysis and the synthesis of intelligent climate controllers, the simulation of the internal climate of the greenhouse is achieved by a linear model whose coefficients are obtained by identification. The use of fuzzy logic controllers for the regulation of climate variables represents a powerful way to minimize the energy cost. Strategies of reduction and optimization are adopted to facilitate the tuning and to reduce the complexity of the controller.