987 research outputs found
Digital Filters
The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature
Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network
Because of their effectiveness in broad practical applications, LSTM networks
have received a wealth of coverage in scientific journals, technical blogs, and
implementation guides. However, in most articles, the inference formulas for
the LSTM network and its parent, RNN, are stated axiomatically, while the
training formulas are omitted altogether. In addition, the technique of
"unrolling" an RNN is routinely presented without justification throughout the
literature. The goal of this paper is to explain the essential RNN and LSTM
fundamentals in a single document. Drawing from concepts in signal processing,
we formally derive the canonical RNN formulation from differential equations.
We then propose and prove a precise statement, which yields the RNN unrolling
technique. We also review the difficulties with training the standard RNN and
address them by transforming the RNN into the "Vanilla LSTM" network through a
series of logical arguments. We provide all equations pertaining to the LSTM
system together with detailed descriptions of its constituent entities. Albeit
unconventional, our choice of notation and the method for presenting the LSTM
system emphasizes ease of understanding. As part of the analysis, we identify
new opportunities to enrich the LSTM system and incorporate these extensions
into the Vanilla LSTM network, producing the most general LSTM variant to date.
The target reader has already been exposed to RNNs and LSTM networks through
numerous available resources and is open to an alternative pedagogical
approach. A Machine Learning practitioner seeking guidance for implementing our
new augmented LSTM model in software for experimentation and research will find
the insights and derivations in this tutorial valuable as well.Comment: 43 pages, 10 figures, 78 reference
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