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-
- Neuron Digest Wednesday, 2 Dec 1992
- Volume 10 : Issue 22
-
- Today's Topics:
- Re: Beginning references
- Re: begining references on NN for Carl Vettore, Univ. of Verona
- Very Fast Simulated Reannealing version 6.20
- Position in cognitive psychology - U Mich
- Postdocs - computational neuroscience
- Vision postdoc position
- (1) HKP review in neuroprose and (2) NIPS time series workshop program
- NIPS workshop - REAL biological computation
-
-
- Send submissions, questions, address maintenance, and requests for old
- issues to "neuron-request@cattell.psych.upenn.edu". The ftp archives are
- available from cattell.psych.upenn.edu (130.91.68.31). Back issues
- requested by mail will eventually be sent, but may take a while.
-
- ----------------------------------------------------------------------
-
- Subject: Re: Beginning references
- From: arbib@cs.usc.edu (Michael Arbib)
- Date: Sat, 28 Nov 92 15:39:31 -0800
-
- Michael A. Arbib: Brains, Machines and Mathematics, Second Edition,
- Springer-Verlag, 1987. This places connectionism in a historical
- setting, introduces some of the main concepts (relatively brief), places
- it in the context of theoretical computer science, and includes chapters
- on self-reproducing automata and Godel's Incompleteness Theorem (both
- proofs and philosophical implications).
-
- It's not the best introduction to connectionism as a standalone subject,
- but is unrivalled for readers who want a "situated" view of the subject
- along the above lines.
-
- While advertising my books, I should also put in a word for "The
- Metaphorical Brain 2: Neural Networks and Beyond", Wiley-Interscience,
- 1989. The special strength of this relative to other books on
- connectionism is that it provides strong links to both Computational
- Neuroscience AND Artificial Intelligence. It also argues for Schema
- Theory: using schemas as a coarse-grain methodology for cooperative
- computation to complement the fine-grain methodology of neural networks.
- It closes with a view of Sixth Generation Computing based on this
- multi-level schema/NN methodology.
-
- Michael Arbib
- Center for Neural Engineering
- University of Southern California
- Los Angeles, CA 90089-2520, USA
- Tel: (213) 740-9220
- Fax: (213) 746-2863
- arbib@pollux.usc.edu
-
-
- ------------------------------
-
- Subject: Re: begining references on NN for Carl Vettore, Univ. of Verona
- From: kanal@cs.UMD.EDU (Laveen N. Kanal)
- Date: Sun, 29 Nov 92 10:55:43 -0500
-
-
- The two volumes by Maureen Caudill from M.I.T. Press should be a
- good place to start. The complete reference is cited in the following
- list of refernces for a course/seminar that I am offering next semester.
-
-
-
- .ce4
- CONNECTIONISTS MODELING OF INTELLIGENT SYSTEMS
- .br
- CMSC 727, SPRING 1993
- .br
- Instructor: Laveen Kanal
- .br
- Time: Tues & Thurs. 5:00 to 6:15 p.m.
- (If feasible, may be changed to meet once a week for
- a longer period at a time convenient to the attendees)
-
- This is a graduate course/seminar on Neural Networks and other connectionist
- dynamical systems and hybrid models currently being proposed for the
- modeling of intelligent systems for pattern recognition and problem-solving.
- The purpose is to introduce some of the theory and applications of such
- systems, discuss their role and potential in developing intelligent
- artificial systems, their relationships to other areas of A.I. and
- the question of local versus nonlocal representations.
- There will be lectures by the instructor, by invited
- persons working in these areas, and possibly by some students.
- Students registered for the course will
- be expected to do some projects using the suggested lab texts or other
- simulators. A mid semester report and a final project/paper will be required
- for a grade in the course.
-
- Text: Roberto Serra, Gianni Zanarini, COMPLEX SYSTEMS and COGNITIVE PROCESSES
- Springer-Verlag, 1990 ISBN 0-387-51393-0
-
- Lab. text: Maureen Caudill, Charles Butler, Understanding Neural Networks:
- Computer Explorations, vol.1 & vo2, The MIT Press
- (These volumes cover most of the major NN paradigms in an easy to
- follow manner and a PC or MAC software diskette is included).
- Vol 1 ISBN 0-262-53099-6 IBM compatible disk included
- ISBN 0-262-53102-x Macintosh compatible disk included
-
- Vol 2: ISBN 0-262-53100-3 IBM compatible disk included
- ISBN 0-262-53103-8 Macintosh Compatible disk included
-
- Optional lab. text:
- Adam Blum, Neural Networks in C++ , An Object Oriented Approach
- to building Connectionist Systems, John Wiley & Sons, Inc. 1992
- ISBN 0-471-55201-1(book/IBM disk set)
- ISBN 0-471-53847-7(papaerback book only)
-
- Useful
- Supplementary text:
-
- J.Hertz, A. Krogh, R.C. Palmer, An Introduction to the Theory of Neural
- Computation, Addison Wesley, 1991
- 2nd edition to appear shortly.
-
- Supplementary References:
-
- L.N. Kanal, On Pattern, Categories, and Multiple Reality, TR, UMD, 1993
-
- L.N. Kanal & S. Raghavan, Hybrid Systems-A Key to Intelligent Pattern
- Recognition, Proc. IJCNN, 1992.
-
- J. Hendler, Papers on Hybrid Systems
-
- J.A. Reggia, Papers on Competition-Based Local Processing for Spreading
- Activation Mechanisms in Neural Networks; also Chap.7 in
- Peng and Reggia, Abductive Inference Models for Diagnostic
- Problem-Solving, Springer-Verlag, 1990
-
- Todd C. Moody, PHILOSOPHY & ARTIFICIAL INTELLIGENCE, Prentice Hall, 1993
- ISBN 0-13-663816-3
-
- Satosi Watanabe, PATTERN RECOGNITION: HUMAN & MECHANICAL, John Wiley, 1985
- ISBN 0-471-80815-6
-
- Gerald M. Edelman, BRIGHT AIR,BRILLIANT FIRE...On the Matter of the Mind,
- Basic Books, 1992 . ISBN 0-465-05245-2
-
- George Lakoff, WOMEN, FIRE, and DANGEROUS THINGS--What Categories Reveal
- About the Mind, Univ. of Chicago Press, 1987
- ISBN 0-226-46803-8
-
- I.K. Sethi & A.K. Jain (Eds), ARTIFICIAL NEURAL NETWORKS AND STATISTICAL
- PATTERN RECOGNITION, North-Holland, 1991
- ISBN 0-444-88741-5 (paperback)
-
- K. Yasue, M. Jibu, and Karl Pribram, A Theory of Non Local Cortical
- Processing in the Brain, Appendices to K. Pribram, BRAIN & PERCEPTION,
- Lawrence Earlbaum Associates, 1991. ISBN 0-89859-995-4
-
- P.A. Flach, R.A. Meersman (Eds), FUTURE DIRECTIONS IN A.I., North-Holland,
- 1991. ISBN 0-444-89048-3
-
-
- Papers in IEEE Trans. on Neural Networks, the journal Neural Networks,
- Neural Computation, and Proceedings of Conferences on Neural Networks,
- Genetic Algorithms, Complex Systems, and Hybrid Systems.
-
-
- Hope this helps.
-
- L.K.
-
-
- ------------------------------
-
- Subject: Very Fast Simulated Reannealing version 6.20
- From: Lester Ingber <ingber@alumni.cco.caltech.edu>
- Date: Mon, 30 Nov 92 07:17:21 -0800
-
- VERY FAST SIMULATED REANNEALING (VFSR) (C)
-
- Lester Ingber ingber@alumni.caltech.edu
- and
- Bruce Rosen rosen@ringer.cs.utsa.edu
-
- The good news is that the people who have gotten our beta version of
- VFSR to work on their applications are very pleased. The bad news is
- that because of some blunders made in the process of making the code
- user-friendly, the code has to be modified to use as a standalone
- function call. This bug is corrected and some other fixes/changes
- are made in version v6.20.
-
- This version is now updated in netlib@research.att.com. It will
- eventually find its way into the other NETLIB archives.
-
- To access the new version:
-
- Interactive
- local% ftp research.att.com
- Name (research.att.com:your_login_name): netlib
- Password: [type in your_login_name or anything]
- ftp> cd opt
- ftp> binary
- ftp> get vfsr.Z
- ftp> quit
- local% uncompress vfsr.Z
- local% sh vfsr
-
- Electronic Mail Request
- local% mail netlib@research.att.com
- [mail netlib@ornl.gov]
- [mail netlib@ukc.ac.uk]
- [mail netlib@nac.no]
- [mail netlib@cs.uow.edu.au]
- send vfsr from opt
- ^D [or however you send mail]
-
- Lester
-
-
- || Prof. Lester Ingber ingber@alumni.caltech.edu ||
- || P.O. Box 857 ||
- || McLean, VA 22101 703-848-1859 = [10ATT]0-700-L-INGBER ||
-
-
- ------------------------------
-
- Subject: Position in cognitive psychology - U Mich
- From: zhang@psych.lsa.umich.edu
- Date: Fri, 27 Nov 92 10:12:04 -0500
-
- Position in Cognitive Psychology
- University of Michigan
-
- The University of Michigan Department of Psychology invites applications
- for a tenure-track position in the area of Cognition, beginning September
- 1, 1993. The appointment will most likely be made at the Assistant
- Professor level, but it is possible at any rank. We seek candidates with
- primary interests and technical skills in cognitive psychology. Our
- primary goal is to hire an outstanding cognitive psychologist, and thus
- we will look at candidates with any specific research interest. We have
- a preference for candidates interested in higher mental processes or for
- candidates with computational modeling skills (including connectionism).
- Responsibilities include graduate and undergraduate teaching, as well as
- research and research supervision. Send curriculum vitae, letters of
- reference, copies of recent publications, and a statement of research and
- teaching interests no later than January 8, 1993 to: Gary Olson, Chair,
- Cognitive Processes Search Committee, Department of Psychology,
- University of Michigan, 330 Packard Road, Ann Arbor, Michigan 48104. The
- University of Michigan is an Equal Opportunity/Affirmative Action
- employer.
-
-
-
- ------------------------------
-
- Subject: Postdocs - computational neuroscience
- From: Ken Miller <ken@cns.caltech.edu>
- Date: Sun, 29 Nov 92 06:29:29 -0800
-
-
- POSTDOCTORAL POSITIONS
- COMPUTATIONAL NEUROSCIENCE
- UNIVERSITY OF CALIFORNIA, SAN FRANCISCO
-
- I will soon be beginning a new lab at UCSF, and anticipate several positions
- for postdocs beginning in 1993 and 1994 (prospective graduate students are
- also encouraged to apply to the UCSF Neuroscience Program). The lab will
- focus on understanding both development and mature processing in the
- cerebral cortex. Theoretical, computational, and experimental approaches
- will be taken. Candidates should have skills relevant to one or more of
- those approaches. The most important criteria are demonstrated scientific
- ability and creativity, and a deep interest in grappling with the details of
- neurobiology and the brain.
-
- Past work has focused on modeling of development in visual cortex under
- Hebbian and similar ``correlation-based" rules of synaptic plasticity. The
- goal has been to understand these rules in a general way that allows
- experimental predictions to be made. Models have been formulated for the
- development of ocular dominance and orientation columns. A few references
- are listed below.
-
- Future work of the lab will extend the developmental modeling, and will also
- take various approaches to understanding mature cortical function. These
- will include detailed biophysical modeling of visual cortical networks,
- many-cell recording from visual cortex, and use of a number of theoretical
- methods to guide and interpret this recording. There will also be
- opportunities for theoretical forays in new directions, in particular in
- collaborations with the other Neuroscientists at UCSF. Facilities to
- develop new experimental directions that are relevant to the lab's program,
- for example slice studies and use of optical methods, will also exist.
-
- I will be part of the Keck Center for Systems Neuroscience at UCSF, which
- will be a very interactive environment for Systems Neurobiology. Other
- members will include:
- * Alan Basbaum (pain systems);
- * Allison Doupe (song learning in songbirds);
- * Steve Lisberger (oculomotor system);
- * Michael Merzenich (adult cortical plasticity);
- * Christof Schreiner (auditory system);
- * Michael Stryker (visual system, development and plasticity);
- Closely related faculty members include Roger Nicoll (hippocampus, LTP);
- Rob Malenka (hippocampus, LTP); Howard Fields (pain systems); and Henry
- Ralston (spinal cord and thalamus).
-
- Please send a letter describing your interests and a C.V., and arrange to
- have three letters of recommendation sent to
-
- Ken Miller
- Division of Biology 216-76
- Caltech
- Pasadena, CA 91125
- ken@cns.caltech.edu
-
- Some References:
-
- Miller, K.D. (1992). ``Models of Activity-Dependent Neural Development."
- Seminars in the Neurosciences, 4:61-73.
-
- Miller, K.D. (1992). ``Development of Orientation Columns Via Competition
- Between ON- and OFF-Center Inputs." NeuroReport 3:73-76.
-
- MacKay, D.J.C. and K.D. Miller (1990). ``Analysis of Linsker's simulations
- of Hebbian rules," Neural Computation 2:169-182.
-
- Miller, K.D. (1990). ``Correlation-based mechanisms of neural development,"
- in Neuroscience and Connectionist Theory, M.A. Gluck and D.E. Rumelhart,
- Eds. (Lawrence Erlbaum Associates, Hillsdale NJ), pp. 267-353.
-
- Miller, K.D., J.B. Keller and M.P. Stryker (1989). ``Ocular dominance
- column development: analysis and simulation," Science 245:605-615.
-
- Miller, K.D., B. Chapman and M.P. Stryker (1989). ``Responses of cells in
- cat visual cortex depend on NMDA receptors," Proc. Nat. Acad. Sci. USA
- 86:5183-5187.
-
-
- ------------------------------
-
- Subject: Vision postdoc position
- From: axon@cortex.rutgers.edu (Ralph Siegel)
- Date: Tue, 01 Dec 92 18:45:54 -0500
-
-
- PLEASE POST
-
- Postdoctoral position available in analysis of structure-from-motion.
- (visual psychophysics, electrophysiology, primate studies)
- in primates.
-
- Contact: Ralph Siegel
- Center for Molecular and Behavioral Neuroscience
- Rutgers, The State University
- 197 University Avenue
- Newark, NJ 07102
- phone: 201-648-1080 x3261
- fax: 201-648-1272
-
- email: axon@cortex.rutgers.edu
-
-
- Term: 24 months, beginning 2/1/93 or later
- Salary: NIH levels
-
- Please send statement of research interests, curriculum vitae, and
- names of three references.
-
-
- ------------------------------
-
- Subject: (1) HKP review in neuroprose and (2) NIPS time series workshop program
- From: Andreas Weigend <weigend@dendrite.cs.colorado.edu>
- Date: Sun, 29 Nov 92 04:30:55 -0700
-
- Two things: (1) a paper in neuroprose and (2) the program for a NIPS workshop.
-
-
- (1) Book review of Hertz-Krogh-Palmer in neuroprose:
-
- My 17-page book review (for Artificial Intelligence) is available via ftp,
- ftp archive.cis.ohio-state.edu (anonymous, neuron)
- cd pub/neuroprose
- binary
- get weigend.hkp-review.ps.Z
- (then uncompress and lpr)
-
-
- (2) The updated program for the time series NIPS workshop at Vail this Friday:
-
- "Time Series Analysis and Predic____"
-
- John Moody Mike Mozer Andreas Weigend
- moody@cse.ogi.edu mozer@cs.colorado.edu weigend@cs.colorado.edu
-
- --------------------------------------------------------------------------
- | Several new techniques are now being applied to the problem of |
- | predicting the future behavior of a temporal sequence and deducing |
- | properties of the system that produced the time series. Both |
- | connectionist and non-connectionist techniques will be discussed. |
- | Issues include: |
- | - algorithms and architectures, |
- | - model selection, |
- | - performance measures, |
- | - iterated single-step vs direct multi-step prediction, |
- | - short term vs long term prediction, |
- | - growth of error with prediction time, |
- | - presence or absence of deterministic chaos, |
- | - number of degrees of freedom of the system, |
- | - amount of noise in the data, |
- | - robust prediction and estimation, |
- | - detection and classification of signals in noise, etc. |
- --------------------------------------------------------------------------
-
- Intended audience: connectionists active in time series analysis.
-
- Half the available time has been reserved for discussion and
- informal presentations. Lively audience participation is encouraged.
-
-
- 7:30-9:30 General Overviews (20 minutes each) and Discussion.
-
- John MOODY: Time Series Modeling: Classical Methods and
- Nonlinear Generalizations
- Mike MOZER: Neural nets for temporal sequence processing
-
- Andreas WEIGEND: Ideas from the SFI competition for prediction
- and analysis
-
- 4:30-6:30 Special Topics. Talks (10-15 minutes each),
- Discussion and Ad-Hoc Presentations.
-
-
- The rest of this message contains the abstracts of the talks.
-
- John MOODY <moody@cse.ogi.edu>:
- I present an overview of classical linear timeseries modeling methods,
- including AR, MA, ARMA, ARIMA, and state-space representations, and discuss
- their strengths and weaknesses. I then describe how nonlinear
- generalizations of these models can be constructed.
-
- Mike MOZER <mozer@cs.colorado.edu>:
- I present a general taxonomy of neural net architectures for processing
- time-varying patterns. This taxonomy subsumes existing architectures in the
- literature, and points to several promising architectures that have yet to
- be examined. I also discuss some experiments on predicting future values
- of a financial time series (US dollar--Swiss franc exchange rates) from the
- Santa Fe competition, and make suggestions for future work on this series.
-
- Andreas WEIGEND <weigend@cs.colorado.edu>:
- For prediction, I first present `low-pass embedding', a generalization
- of the usual delay line that corresponds to filtered delay coordinates. I
- then focus on the estimation of prediction errors, including a generalization
- that predicts the evolution of the entire probability density function.
- For analysis, I first present `deterministic vs stochastic plots' (DVM)
- and then the information theoretic measure called `redundancy' that allows
- characterization of the underlying dynamic system without prediction.
-
- Volker TRESP <tresp@inf21.zfe.siemens.de>:
- Like many physiological processes, the blood glucose / insulin metabolism
- is highly nonlinear and involves multiple time scales and multi-dimensional
- interactions. We present a model of the blood glucose / insulin metabolism of
- a diabetic patient. The model is a hybrid "compartment" / neural network
- model and was trained with data from a diabetic patient using the dynamic
- backpropagation algorithm. We demonstrate how our model can be used both for
- prediction of blood glucose levels and control of the patient's therapy.
- (Joint work with J. Moody and W.R. Delong)
-
- William FINNOFF:
- In financial and economic applications, data sets are typically small
- and noisy. The standard "black box" approach to network learning tends to
- overfit the training data and thus generalizes poorly. In this talk, we
- will discuss the microeconomic foundations of neural network model
- structures used to perform economic forecasting. Further, we will describe
- a variety of extended regularization techniques used to prevent overfitting.
-
- Eric WAN <wan@isl.stanford.edu>:
- A neural network for time series prediction which uses Finite Impulse
- Response (FIR) linear filters to provide dynamic interconnectivity is
- presented. The FIR network and associated training algorithm are reviewed.
- Examples from the Santa Fe competition in prediction and dynamic modeling
- of laboratory data and simulated chaotic time series are used to
- demonstrate the potentials of the approach.
-
- Fernando PINEDA <fernando@aplcomm.jhuapl.edu>:
- A fast and elegant numerical algorithm for estimating generalized
- dimensions and coarse grained mutual information will be be presented.
- The relationship to other more well known algorithms will be discussed.
- Examples from the Santa Fe time series analysis competition will be used
- to demonstrate how to use the algorithm for choosing delay times for
- delay coordinate embeddings.
-
- Fu-Sheng TSUNG: <tsung@cs.ucsd.edu>:
- When modeling a system that generates a time series, what is known about
- the system constrains the architecture of the model. As an example, I will
- present a recurrent network model of a lobster neural circuit, discuss what
- we learned from the model, where the model failed, and possible improvements
- from using a pair of sigmoids as a "near-oscillator" primitive for a neuron.
-
-
- ------------------------------
-
- Subject: NIPS workshop - REAL biological computation
- From: Jim Schwaber <schwaber@eplrx7.es.duPont.com>
- Date: Wed, 25 Nov 92 10:11:01 -0500
-
-
- - -----------NIPS 92 WORKSHOP----------------------
-
- Real Applications of Real Biological Circuits
-
- or
-
- "If back-prop is not enough how will we get more?"
-
- or
-
- "Is anybody really getting anywhere with biology?"
-
- - ---------------------------------------------------
-
- When: Friday, Dec. 4th
- ====
-
- Intended Audience: Those interested in detailed biological modeling.
- ================== Those interested in nonlinear control.
- Those interested in neuronal signal processing.
- Those interested in connecting the above.
-
-
- Organizers:
- ===========
- Richard Granger Jim Schwaber
- granger@ics.uci.edu schwaber@eplrx7.es.dupont.com
-
- Agenda:
- =======
-
- Morning Session, 7:30 - 9:30, Brain Control Systems and Chemical
- - --------------- Process Control
-
- Jim Schwaber Brainstem reflexes as adaptive controllers
- Dupont
-
- Babatunde Ogunnaike Reverse engineering brain control systems
- DuPont
-
- Frank Doyle Neurons as nonlinear systems for control
- Purdue
-
- John Hopfield Discussant
- Caltech
-
- Afternoon Session, 4:30 - 6:30, Real biological modeling, nonlinear
- - ----------------- systems and signal processing
-
- Richard Granger Signal processing in real neural systems: is
- UC Irvine it applicable?
-
- Gary Green The single neuron as a nonlinear system - its
- Newcastle Volterra kernels as described by neural networks.
-
-
- Program:
- ========
-
- We anticipate that the topic will generate several points of view.
- Thus, presenters will restrict themselves to a very, very few slides
- intended to make a point for discussion. Given that there now are
- concrete examples of taking biological principles to application, we
- expect the discussion will center more on how, and at what level,
- rather than whether "reverse engineering the brain" is useful.
-
- Granger (UC Irvine):
- - -------
- The architectures, performance rules and learning rules of most artificial
- neural networks are at odds with the anatomy and physiology of real
- biological neural circuitry. For example, mammalian telencephelon
- (forebrain) is characterized by extremely sparse connectivity (~1-5%),
- almost entirely lacks dense recurrent connections, and has extensive lateral
- local circuit connections; inhibition is delayed-onset and relatively
- long-lasting (100s of milliseconds) compared to rapid-onset brief excitation
- (10s of milliseconds), and they are not interchangeable. Excitatory
- connections learn, but there is very little evidence for plasticity in
- inhibitory connections. Real synaptic plasticity rules are sensitive to
- temporal information, are not Hebbian, and do not contain "supervision"
- signals in any form related to those common in ANNs.
-
- These discrepancies between natural and artificial NNs raise the question of
- whether such biological details are largely extraneous to the behavioral and
- computational utility of neural circuitry, or whether such properties may
- yield novel rules that confer useful computational abilities to networks
- that use them. In this workshop we will explicitly analyze the power and
- utility of a range of novel algorithms derived from detailed biology, and
- illustrate specific industrial applicatons of these algorithms in the fields
- of process control and signal processing.
-
- Ogunnaike (DuPont):
- - -----------
- REVERSE ENGINEERING BRAIN CONTROL SYSTEMS:
- EXPLORING THE POTENTIAL FOR APPLICATIONS IN CHEMICAL PROCESS CONTROL.
- =====================================================================
-
- The main motivation for our efforts lies in the simple fact that there
- are remarkable analogies between the human body and the chemical
- process plant. Furthermore, it is known that while the brain has been
- quite successful in performing its task as the central supervisor of
- intricate control systems operating under conditions which leave very
- little margin for error, the control computer in the chemical process
- plant has not been so successful.
-
-
- We have been concerned with seeking answers to the following question:
-
- ``Is it possible to ``reverse engineer'' a biological control system
- and use the understanding to develop novel approaches to chemical
- process control systems design and analysis?''
-
- Our discussion will provide an overview of the tentative answers we
- have to date. We will first provide a brief summary of the salient
- features and main problems of chemical process control; we will then
- introduce the biological control system under study (the baroreceptor
- vagal reflex); finally we will present an actual industrial process
- whose main features indicate that it may benefit from the knowledge
- garnered from the neurobiological studies.
-
- Doyle (Purdue):
- - ------
- We are focusing our research on two levels:
- 1) Neuron level: investigating novel building blocks for process
- modeling applications which are motivated by realistic biological
- neurons.
- 2) Network Level: looking for novel approaches to nonlinear dynamic
- scheduling algorithms for process control and modeling (again,
- motivated by biological signal processing in the baroreceptor reflex).
-
- Green (Newcastle):
- - -------
- I would love to tell the NIPS people about Volterra series,
- especially as we have now made a connection between neural
- networks, Volterra series and the differential geometric
- representation of networks. This allows us to say why one, two or
- more layers are necessary for a particular analytic problem. We can
- also say how to invert nets which are homeomorphic in their
- mappings. More importantly for us biologists we can turn the state
- equations of membrane currents, using neural networks into
- approximate Volterra kernels which I think (!) helps understand the
- dynamics. This gives a solution to the differential equations,
- albeit an approximate one in practical terms. The equations are
- invertible and therefore allow a formal link between current clamp
- and voltage clamp at the equation level. The method we have used to
- do this is of interest to chem. eng. people because we can use the
- same concepts in non-linear control. It appears at first glance
- that we can link the everyday use of neural networks to well
- established theory through a study of tangent spaces of networks.
- We construct a state space model of a plant, calculate the
- differential of the rate of change of output with respect to the
- input. Calculate the same for a neural network. Compare
- coefficients. The solution to the set of simultaneous equations for
- the coefficents produces a network which is formally equivalent to
- the solution of the original differential equation which defined
- the state equations.
-
-
- We will be making the claim that analytic solutions of non-linear
- differential equations is possible using neural networks for
- some problems. For all other problems an approximate solution is
- possible but the architecture that must be used can be defined.
- Last I'll show how this is related to the old techniques using
- Volterra series and why the kernels and inverse transforms can be
- directly extracted from networks. I think it is a new method of
- solving what is a very old problem. All in 20 minutes !
-
-
- ------------------------------
-
- End of Neuron Digest [Volume 10 Issue 22]
- *****************************************
-
-