PDF Ebook Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann
By downloading this soft file e-book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann in the on the internet web link download, you are in the 1st step right to do. This site really supplies you simplicity of ways to get the finest book, from best vendor to the brand-new launched e-book. You could discover a lot more e-books in this site by going to every link that we provide. Among the collections, Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann is one of the most effective collections to market. So, the very first you get it, the very first you will get all favorable regarding this publication Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann
PDF Ebook Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann
Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann. Allow's check out! We will frequently learn this sentence almost everywhere. When still being a childrens, mommy utilized to get us to consistently check out, so did the teacher. Some e-books Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann are fully reviewed in a week as well as we need the responsibility to support reading Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann What around now? Do you still enjoy reading? Is reading only for you which have responsibility? Not! We here offer you a brand-new book qualified Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann to check out.
As known, book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann is well known as the window to open the world, the life, and brand-new point. This is what the people now require a lot. Even there are many people that do not such as reading; it can be a selection as referral. When you actually need the ways to develop the following motivations, book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann will truly direct you to the method. Moreover this Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann, you will have no regret to get it.
To get this book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann, you could not be so confused. This is on the internet book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann that can be taken its soft file. It is different with the on the internet book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann where you can get a book and then the seller will certainly send the printed book for you. This is the location where you can get this Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann by online as well as after having manage getting, you can download and install Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann alone.
So, when you require quickly that book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann, it doesn't should wait for some days to receive the book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann You could straight obtain the book to save in your tool. Also you enjoy reading this Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann almost everywhere you have time, you can appreciate it to check out Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann It is definitely handy for you that wish to get the a lot more priceless time for reading. Why don't you spend 5 minutes as well as invest little money to obtain the book Neural Networks And Analog Computation: Beyond The Turing Limit (Progress In Theoretical Computer Science), By Hava T. Siegelmann right here? Never ever allow the new point goes away from you.
The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics. The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.
- Sales Rank: #2966141 in Books
- Brand: Brand: Birkhäuser
- Published on: 1998-12-01
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .50" w x 6.14" l, 1.00 pounds
- Binding: Hardcover
- 181 pages
- Used Book in Good Condition
Review
"All of the three primary questions are considered: What computational models can the net simulate (within polynomial bounds)? What are the computational complexity classes that are relevant to the net? How does the net (which, after all, is an analog device) relate to Church’s thesis? Moreover the power of the basic model is also analyzed when the domain of reals is replaced by the rationals and the integers."
―Mathematical Reviews
"Siegelmann's book focuses on the computational complexities of neural networks and making this research accessible...the book accomplishes the said task nicely."
---SIAM Review, Vol. 42, No 3.
From the Back Cover
The theoretical foundations of Neural Networks and Analog Computation conceptualize neural networks as a particular type of computer consisting of multiple assemblies of basic processors interconnected in an intricate structure. Examining these networks under various resource constraints reveals a continuum of computational devices, several of which coincide with well-known classical models. What emerges is a Church-Turing-like thesis, applied to the field of analog computation, which features the neural network model in place of the digital Turing machine. This new concept can serve as a point of departure for the development of alternative, supra-Turing, computational theories. On a mathematical level, the treatment of neural computations enriches the theory of computation but also explicated the computational complexity associated with biological networks, adaptive engineering tools, and related models from the fields of control theory and nonlinear dynamics.
The topics covered in this work will appeal to a wide readership from a variety of disciplines. Special care has been taken to explain the theory clearly and concisely. The first chapter review s the fundamental terms of modern computational theory from the point of view of neural networks and serves as a reference for the remainder of the book. Each of the subsequent chapters opens with introductory material and proceeds to explain the chapter’s connection to the development of the theory. Thereafter, the concept is defined in mathematical terms.
Although the notion of a neural network essentially arises from biology, many engineering applications have been found through highly idealized and simplified models of neuron behavior. Particular areas of application have been as diverse as explosives detection in airport security, signature verification, financial and medical times series prediction, vision, speech processing, robotics, nonlinear control, and signal processing. The focus in all of these models is entirely on the behavior of networks as computer.
The material in this book will be of interest to researchers in a variety of engineering and applied sciences disciplines. In addition, the work may provide the base of a graduate-level seminar in neural networks for computer science students.
Most helpful customer reviews
5 of 5 people found the following review helpful.
Elegant theoretical apparatus
By Erez Lieberman Aiden
This book provides a systematic overview of a beautiful theoretical apparatus that the author and collaborators have developed for describing the computational power of neural networks. It addresses neural networks from the standpoint of computational complexity theory, not machine learning.
A central issue that arises is what values the neural couplings can take on. The book outlines the consequences of various choices. Rational-valued neural networks turn out to be Turing machines, a contribution of general significance. The book shows (and perhaps unduly emphasizes) that irrational-valued couplings can yield Superturing computation, a result which has been controversial.
If irrational numbers can arise in a computational setting, then the work outlined here is clearly a major landmark that deserves the careful, systematic exposition the book provides. On the other hand, maybe irrational numbers are just not relevant to actual computational devices. (They certainly aren't yet.) If so, the book is still a worthwhile theoretical exercise leading to an elegant set of results. Even if one leans toward the latter option - and I would say that this is probably the vast majority - I don't think any of us really _know_ where the irrational numbers stand vis-a-vis our computational universe.
Even if you intuitively see that an infinitely rich source of information, which is what an irrational number provides, should yield Super-Turing computation, the book is still valuable. (If you don't have this intuition, think about it more!) There is a lot to be gleaned from the non-obvious (at least to me) details of how that intuition works itself out.
The book has more technical flaws. The author periodically states results without really explaining fully, or even at all. This leaves a good deal of work to the reader. I would expect to spend a few hours per page, here and there, though usually it will move quicker. A major issue is also the challenging notation, which is often more difficult than it needs to be. The book's introduction to advice turing machines is also insufficient; you'll need to do a bit of background reading if you don't know much about them.
8 of 9 people found the following review helpful.
Discussion of the consequences, not the original proof
By N. Hockings
Skeptics wanting to see the original proof, and how such "machines" can exist as natural phenomena within the constraints of physics, should refer to the author's peer reviewed articles
H.T. Siegelmann, "Computation Beyond the Turing Limit," Science, 238(28), April 1995: 632-637
and
H.T. Siegelmann, "Analog Computational Power" Science 19 January 1996 271: 373
This book discusses the consequences, and the limitations of analog computation using neural networks.
17 of 26 people found the following review helpful.
Hypercomputation in the limits of classical physical reality
By J. Felix Costa
A computer is an artifact. Through specific control mechanisms of electric currents it was possible to domesticate natural phenomena, and put them at men service, giving rise to the levels of automation that characterize the world in the turning of the millennium. But a computer is an analog artifact. Paul Cull, from Oregon State University, states this computational anecdote in the following terms: «That analog devices behave digitally is the basis for a large part of electronics engineering and allows for the construction of electronic computers. It is part of the engineering folklore that when the gain is high enough any circuit from a large class will eventually settle into one of two states, which can be used to represent booleans 0 and 1. As far as we can tell, this theorem and its proof has never been published, but it probably appears in a now unobtainable MIT technical report of the1950s.» Recently much work have been done to show that digital computers are a particular class of analog computers that exhibit greater computational power. In fact, digital computers are extreme (weak) analog computers. A book was needed to introduce these ideas to the graduate student on Theoretical Computer Science and to the general researcher on the new field of Non-standard Models of Computation. Hava Siegelmann's book partially fills this gap in the computational literature.
Over the last decade, researchers have speculated that although the Turing model is indeed able to simulate a large class of computations, it does not necessarily provide a complete picture of the computations possible in nature. As pointed out by Hava Siegelmann, the most famous proposals of new models were made by Richard Feynman and Roger Penrose. Feynman suggested making use of the non-locality of quantum physics. Penrose, who was motivated by the model of the human brain, argued that the Turing model of computing is not strong enough to model biological intelligence. In response, several novel models of computation have been put forth: among them the quantum Turing machine and the DNA computer. These models compute faster than Turing machines and thus are richer under time constraints. However they cannot compute non-recursive functions, and in this sense are not inherently more powerful than the classical model. The analog recurrent neural network model of Hava Siegemann computes more than the Turing machine, not only under time-constraints, but also in general. In this sense it can be referred to as a hypercomputation model.
The use of analog recurrent neural networks for computability analysis is due to Hava Siegelmann and Eduardo Sontag. In Hava Siegelmann's book, she used them to establish lower bounds on their computational power. These systems satisfy the classical constraints of computation theory, namely, (a) input is discrete (binary) and finite, (b) output is discrete (binary) and finite, and (c) the system is itself finite (control is finite). The infiniteness may originate from two different sources: the system is influenced by a real value, which can be a physical constant, directly affecting the computation, a probability of a biased binary random coin or any other process; the infiniteness may also come from the operations of an adaptive process interleaved with the computation process, like is the case in our brains. Neurons may hold values within [0,1] with unbounded precision. To work with such analog systems, binary input is encoded into a rational number between 0 and 1, and the rational output is decoded into an output binary sequence. The technique used in this book consists of an encoding of binary words into the Cantor Set of base 4. Within this (number-theoretic) model, finite binary words are encoded as rational numbers in [0,1]. We may then identify the set of computable functions by analog recurrent neural nets, provided that the type of the weights is given. This research program has been systematically pursued by Hava Siegelmann at the Technion and her collaborators.
The first level of nets is NET[integers]. These nets are historically related with the work of Warren McCulloch and Walter Pitts. As the weights are integer numbers, each processor can only compute a linear combination of integer coefficients applied to zeros and ones. The activation values are thus always zero or one. In this case the nets 'degenerate' into classical devices called finite automata. It was Kleene who first proved that McCulloch and Pitts nets are equivalent to finite automata and therefore they were able to recognize all regular languages. But they are not capable of recognizing well-formed parenthetic expressions or to recognize the nucleic acids for these structures are not regular...
The second relevant class Hava Siegelmann considers is NET[rationals]. Rationals are indeed computable numbers in finite time, and NET[rationals] turn to be equivalent to Turing machines. Twofold equivalent: rational nets compute the same functions as Turing machines and, under appropriate encoding of input and output, they are able to compute the same functions in exactly the same time. Even knowing that rationals are provided for free in nature, rationals of increasing complexity, this ressource do not even speed up computations with regard to Turing machines. The class NET[rationals] coincide with the class of (partial) recursive functions of Kurt Gödel and Kleene. About them it is said that they constitute the whole concrete, realizable, mathematical universe.
The third relevant (and maybe surprising to the reader) class is NET[reals]. Reals are indeed in general non computable. But theories of physics abound that consider real variables. If the reader look at these theories from a more epistemological point of view as approximative models, then we argue that while some alternative theories are not available, if the old models can encode hypercomputations, then they are not simulable in digital computers. The advantage of making a theory of computation on top of these systems is that nonuniform classes of computation, namely the classes that arise in complexity theory using Turing machines with advice, are uniformly described in NET[reals]. As shown in Hava Siegelmann's book all sets over finite alphabets can be represented as reals that encode the families of boolean circuits that recognize them. Under efficient time computation, these networks compute not only all efficient computations by Turing machines but also some non-recursive functions such as (a unary encoding of) the halting problem of Turing machines.
A novel connection between the complexity of the networks in terms of information theory and their computational complexity is developed, spanning a hierarchy of computation from the Turing to the fully analog model. This leads to the statement of the Siegelmann-Sontag thesis of 'hypercomputation by analog systems' analogously to the Church-Turing thesis of 'computation by digital systems'.
A beautiful non-standard theory of computation is presented in 'Neural Networks and Analog Computation'. I strongly recommend the careful reading of Hava Siegelmann's book, to enjoy the uniformity of nets description and to ponder where hypercomputation begins in the limits of classical physical reality.
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann PDF
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann EPub
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann Doc
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann iBooks
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann rtf
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann Mobipocket
Neural Networks and Analog Computation: Beyond the Turing Limit (Progress in Theoretical Computer Science), by Hava T. Siegelmann Kindle
Tidak ada komentar:
Posting Komentar