WO2000029970A1 - Ordinateur neuromimetique oscillatoire a connectivite dynamique - Google Patents

Ordinateur neuromimetique oscillatoire a connectivite dynamique Download PDF

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Publication number
WO2000029970A1
WO2000029970A1 PCT/US1999/026698 US9926698W WO0029970A1 WO 2000029970 A1 WO2000029970 A1 WO 2000029970A1 US 9926698 W US9926698 W US 9926698W WO 0029970 A1 WO0029970 A1 WO 0029970A1
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Prior art keywords
neurocomputer
oscillating
frequency
elements
input
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PCT/US1999/026698
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English (en)
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WO2000029970A9 (fr
Inventor
Frank C. Hoppensteadt
Eugene Izhikevich
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Arizona Board Of Regents, A Body Corporate Acting On Behalf Of Arizona State University
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Priority to US09/831,812 priority Critical patent/US6957204B1/en
Publication of WO2000029970A1 publication Critical patent/WO2000029970A1/fr
Publication of WO2000029970A9 publication Critical patent/WO2000029970A9/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/049—Temporal neural networks, e.g. delay elements, oscillating neurons or pulsed inputs

Definitions

  • the present invention relates generally to computational devices and more particularly to a neural network computer requiring a minimal number of connective devices between processing elements.
  • Artificial neural networks are biologically inspired; that is, they are composed of elements that perform in a manner analogous to the most elementary functions of the biological neuron.
  • a neurocomputer is composed of a number (n) of processing elements that may be switches or nonlinear amplifiers. These elements are then organized in a way that may be related to the anatomy of the brain. The configuration of connections, and thus communication routes, between these elements represents the manner in which the neurocomputer will function, analogous to that of a program performed by digital computers.
  • artificial neural networks exhibit a surprising number of the brain's characteristics. For example, they learn from experience, generalize from previous examples to new ones, and abstract essential characteristics from inputs containing irrelevant data.
  • the neurocomputer does not execute a list of commands (a program). Rather, the neurocomputer performs pattern recognition and associative recall via self-organization of connections between elements.
  • Artificial neural networks can modify their behavior in response to their environment. Shown a set of inputs (perhaps with desired outputs), they self-adjust to produce consistent responses. A network is trained so that application of a set of inputs produces the desired (or at least consistent) set of outputs. Each such input (or output) set is referred to as a vector. Training is accomplished by sequentially applying input vectors, while adjusting network weights according to a predetermined procedure. During training, the network weights gradually converge to values such that each input vector produces the desired output vector.
  • oscillatory neurocomputers are among the more promising types of neurocomputers.
  • the elements of an oscillatory neurocomputer consist of oscillators rather than amplifiers or switches.
  • Oscillators are mechanical, chemical or electronic devices that are described by an oscillatory signal (periodic, quasi-periodic, almost periodic function, etc.).
  • the output is a scalar function of the form
  • N is a fixed wave form (sinusoid, saw-tooth or square wave), ⁇ is the
  • ⁇ is the phase deviation (lag or lead).
  • Recurrent neural networks have feedback paths from their outputs back to their inputs. As such, the response of such networks is dynamic in that after applying a new input, the output is calculated and fed back to modify the input. The output is then recalculated, and the process is repeated again and again. Ideally, successive iterations produce smaller and smaller output changes until eventually the outputs become constant.
  • neural networks such as is required by Hop field's network, must have a fully connected synaptic matrix. That is, to function optimally, recurrent network processing elements must communicate data to each other.
  • Hop field's network To properly exhibit associative and recognition properties, neural networks, such as is required by Hop field's network, must have a fully connected synaptic matrix. That is, to function optimally, recurrent network processing elements must communicate data to each other.
  • a neurocomputer that exhibits pattern recognition and associative recall capabilities while requiring only n connective junctions for every n processing elements employed thereby.
  • the neurocomputer comprises n oscillating processing elements that can communicate through a common medium so that there are required only n connective junctions.
  • a rhythmic external forcing input modulates the oscillatory frequency of the medium which, in turn, is imparted to the n oscillators.
  • Any two oscillators oscillating at different frequencies may communicate provided that the input's power spectrum includes the frequency equal to the difference between the frequencies of the two oscillators in question.
  • selective communication, or dynamic connectivity, between different neurocomputer oscillators occurs due to frequency modulation of the medium by external forcing.
  • FIG. 1 is a schematic diagram of a prior art recurrent neural network employing five neural processing elements.
  • FIG. 2 is a schematic diagram of a neural network according to principles of the present invention and employing five neural processing elements.
  • FIG. 3 is a diagrammatic illustration of results obtained through simulation of the neurocomputer according to principles of the present invention using a phase deviation
  • n 60, t e [0, 10].
  • FIG. 4 is a schematic block diagram of a phase-locked loop.
  • FIG. 5 is a diagrammatic illustration of the relationship between demodulated output voltage and input frequency and phase of a phase-locked loop as depicted in FIG. 4.
  • FIG. 6 is a schematic block diagram of a neural network according to principles of the present invention employing two phase-locked loops as depicted in FIG. 4.
  • FIG. 7 is a diagrammatic illustration of one frequency multiplication performed in the neural network depicted in FIG. 6.
  • FIG. 8 is a schematic diagram showing the circuit components of the neural network of FIG. 6 according to principles of the present invention.
  • FIG. 9 is a schematic block diagram of a five-oscillator neural network with associated function generator and oscilloscopes connected for testing.
  • FIGS. 10A-10E are oscilloscope traces of the oscillator responses of the network of FIG. 9 with a signal sin t impressed on the input.
  • FIGS. 11 A-l IE are oscilloscope traces of the oscillator responses of the network of FIG. 9 with a signal sin 2t impressed on the input.
  • FIGS. 12A-12E are oscilloscope traces of the oscillator responses of the network of FIG. 9 with a signal sin 3t impressed on the input.
  • FIGS. 13A-13E are oscilloscope traces of the oscillator responses of the network of FIG. 9 with a signal sin lOt impressed on the input.
  • Elements 20 may comprise switches, amplifiers, oscillators or any other suitable neurocomputer element type known in the art. In order for each of elements 20 to communicate with the others
  • n in this case, 25
  • connective junctions 30 to which conductors 40 are attached.
  • FIG. 2 schematically illustrates a neurocomputer 50 according to principles of the present invention.
  • Neurocomputer 50 comprises a finite number n (in this case, n-5) oscillatory neural processing elements 60A, 60B, 60C, 60D and 60E.
  • Elements 60A, 60B, 60C, 60D and 60E can comprise voltage-controlled oscillators, optical oscillators, lasers, microelectromechanical systems, Josephson junctions, macromolecules, or any other suitable oscillator known in the art.
  • Each element 60 A, 60B, 60C, 60D and 60E oscillates at a particular frequency that may or may not be the same frequency as that of the others of elements 60 A, 60B, 60C, 60D and 60E.
  • the neurocomputer 50 further comprises a medium 70 connected to each of elements 60 A, 60B, 60C, 60D and 60E by means of connective junctions 80A, 80B, 80C, 80D and 80E, respectively.
  • Medium 70 may comprise a unitary body or multiple connected bodies.
  • Neurocomputer 50 further comprises a rhythmic forcing signal source 90 able to apply a modulated oscillatory frequency to medium 70 by means of a connection 100.
  • the medium 70 can be a conductive medium electrically connected to the oscillators 60A, 60B, 60C, 60D and 60E by conductive connection junctions 80A, 80B, 80C, 80D and 80E.
  • the rhythmic forcing signal source 90 can be an electrical signal generator such as a frequency modulated transmitter connected by a conductive connection 100 to the medium 70.
  • any two elements such as 60B and 60E, can be said to communicate to each other if changing the phase deviation of one influences the phase deviation of the other. Such is the case if the two elements oscillate at the same frequency. Accordingly, if elements 60B and 60E oscillate at the same frequency, they will communicate in such manner.
  • any two oscillators such as 60B and 60E, can be made to communicate by filling the frequency gap between them. That is, the uniform oscillatory signal must include a frequency equal to the difference between the respective frequencies of elements 60B and 60E. Accordingly, if elements 60B and 60E are
  • a neurocomputer may be comprised mainly of phase-locked loops, amplifiers, and band-pass filters.
  • a schematic of such a neurocomputer is shown in FIG. 8.
  • the major components include a phase detector 120, low-pass filter 130, unity amplifier 140, and a voltage controlled oscillator (“NCO”) 150.
  • Phase locked loops use a feedback loop to produce a replica of an input signal's frequency.
  • op-amps operational amplifiers
  • a PLL amplifies the frequency difference of the inputs and sets them equal to each other, so that the internally generated signal in the VCO 150 is an exact replica of the input signal (pin 4 of the PLL).
  • the PLL 110 is said to be in the "locked on” state.
  • any change in the input's frequency is detected by the phase detector 120 as an error signal.
  • This error signal is applied to the internal signal, which is a replica of the input, so that it will match the input signal's frequency.
  • the error signal is essentially the phase difference in the signal, which is the information waveform.
  • the encoded information is extracted from pin 7 of the PLL 110.
  • PLLs may be set up to perform frequency multiplication. This is accomplished by placing an open circuit between pins 3 and 4 in FIG. 4 and inputting a second source at pin 3. Since the phase detector 120 of PLL 110 is classified as type 1, it has a highly linear XOR gate and a built-in four-quadrant multiplier. The four-quadrant multiplier allows PLL 110 to perform frequency multiplication very accurately. A PLL connected in this manner produces an output that is the frequency multiplication of the two inputs.
  • the free running frequency (f 0 ) is ideally the center frequency level of the signal that is to be demodulated.
  • the value for the free running frequency is obtained from
  • the capture-range (f c ) is the frequency range over which the PLL will try to lock on to an input's frequency. The following formula may be used to determine the capture-range.
  • C2 is the capacitance of the similarly designated capacitor in FIG. 5 and fj is the lock-range.
  • the lock-range (f ⁇ is the range over which the PLL will remain in the locked on state. This range is generally larger than the capture-range and can be increased by increasing Ncc of the PLL as shown in the following equation.
  • Communication can occur when a signal is outside the capture range if it is conditioned by another signal. This can be demonstrated by implementing the multiple PLL circuit 170 as shown in FIG. 6.
  • the key to designing the circuit depicted in FIG. 6 is the ability to obtain the sum and difference of two input frequencies, which can be accomplished through multiplication.
  • FIG. 7 shows what occurs when multiplying 8kHz and 42kHz, as at the multiplier
  • these 8kHz and 42kHz components are present in the output 172 of the multiplier 171. Also present are 50kHz and 34 kHz, the sum and difference of 8 kHz and 42 kHz, respectively. Interfering harmonics are also present. Here, 8 kHz and 42 kHz were chosen to obtain an adequate separation between the harmonics and the desired frequency components.
  • band pass filters were placed in the circuit.
  • the filter was comprised of an inductor and capacitor. To isolate the single frequency desired, the following formula was used:
  • the PLL 181 By modulating the 8 kHz carrier frequency of the function generator 178 with a 100 Hz sine wave modulation and multiplying the modulated signal with a 42 kHz carrier frequency, the PLL 181 was able to demodulate the input signal and output the 100 Hz information signal. Similarly, the PLL 182 was able to demodulate the 100 Hz information signal. Testing of the circuit depicted in FIG. 6 demonstrates that communication can still occur even if a signal is outside the capture range of a PLL if the information signal is combined with another carrier signal.
  • the multipliers 172 and 173 are LM 565 phase locked loops from National Semiconductor.
  • National Semiconductor op amps LM 324 are used in the band pass filter and amplification stages 175 and 176 along with the inductor and capacitor filtering circuit elements of the values shown.
  • the phase locked loops 181 and 182 connected as oscillators employ the LM 565 phase locked loops from National Semiconductor.
  • VCCi from the PLL oscillator 181 at the upper right, is fed back to the multiplier 173 at the lower left and VCC 2 is fed back from the PLL oscillator 182 at the lower right to the multiplier 172 at the upper left.
  • VCCi from the PLL oscillator 181 at the upper right
  • a five-element neural network 190 is shown.
  • These oscillators are forced by a common function generator 198.
  • the function generator is connected to the oscillators via the conductors 200 and 202 serving as the conductive medium and connectors, respectively, of the neural network 190 previously discussed.
  • Oscilloscopes 211, 212, 213, 214, and 215 are connected to the oscillators as illustrated to demonstrate the output signals of the oscillators responsive to various inputs from the function generator 198.
  • a summing circuit 217 is connected into a feedback loop 218 common to each of the oscillators.
  • FIGS. 10-13 illustrate the responses of the oscillators 191-195, respectively, to four input signals generated by the function generator 198.
  • FIG. 10 shows the traces of the oscilloscopes 211-215 corresponding to the oscillating signals of oscillators 191-195, respectively, when the forcing voltage from the function generator 198 is sin t. None of the oscillators 191-195 are in communication and the oscillator signals are unrelated, as shown by the traces 10A- 10E.
  • the oscillators respond with signals as shown by the traces of FIGS. 11A to 1 IE.
  • the oscillators 191, 193 and 195 communicate, producing the oscilloscope traces of FIGS. 11 A, 11C and 1 IE, and the oscillators 192 and 194 communicate producing the traces of FIGS. 1 IB and 1 ID.
  • the oscillators 191-195 produce in the oscilloscopes 211-215 the traces shown at FIGS. 12A- 12E, respectively.
  • Oscillators 191 and 194 communicate, producing the traces of FIGS. 12A and 12D.
  • Oscillators 192 and 195 communicate producing the traces shown at FIGS. 12B and 12E.
  • the oscillator 193 is not in communication with any other of the oscillators and it produces the trace shown at FIG. 12C.
  • FIGS. 13A-13E shown are traces illustrating the response of the oscillators 191-195 when a signal sin lOt is impressed by the function generator 198. None of the oscillators here are communicating.
  • a further, more generalized example of implementation of the present invention will now be described using a network of n voltage controlled oscillators (known as Kuramoto's phase model) and represented by:
  • the external input a(t) can be chaotic or noisy. It can dynamically connect the rth and they ' th oscillators if its Fourier transform has a non-zero entry corresponding to
  • connection matrix S (s tJ ) is symmetric
  • phase model (5) is a gradient system. Indeed, it can be written in the form
  • System (5) has multiple attractors and Hopfield-Grossberg-like associative properties as also shown in FIG. 3. Therefore, system (1) with external forcing has oscillatory associative memory.

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Abstract

Cet ordinateur neuromimétique (50) comprend n éléments de traitement oscillants (60A, 60B, 60C, 60D et 60E) qui communiquent par l'intermédiaire d'un support commun (70) de sorte que seulement n jonctions de connexion (80A, 80B, 80C, 80D et 80E) sont nécessaires. L'entrée d'une contrainte, extérieure, rythmique (90) module la fréquence oscillatoire du support (70), laquelle est à son tour appliquée aux n oscillateurs (60A, 60B, 60C, 60D et 60E). Deux oscillateurs quelconques, oscillant à des fréquences différentes, peuvent communiquer pourvu que le spectre de la puissance d'entrée comprenne la fréquence égale à la différence entre les fréquences des deux oscillateurs en question. Ainsi, il se produit une communication sélective, ou une connectivité dynamique, entre différents oscillateurs de l'ordinateur neuromimétique, par suite de la modulation de fréquence du support (70) au moyen d'une contrainte extérieure.
PCT/US1999/026698 1998-11-13 1999-11-12 Ordinateur neuromimetique oscillatoire a connectivite dynamique WO2000029970A1 (fr)

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Cited By (5)

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WO2005006250A1 (fr) * 2003-06-25 2005-01-20 Variance Dynamical, Inc. Appareil et procedes de detection et d'analyse de composantes spectrales
WO2005088535A2 (fr) * 2004-03-17 2005-09-22 Canon Kabushiki Kaisha Appareil de traitement parallele de signaux a impulsions, appareil de reconnaissance de formes et appareil de saisie d'images
EP3045872A1 (fr) * 2015-01-14 2016-07-20 Insitu, Inc. Systèmes et procédés de quantification de signal
RU2663546C1 (ru) * 2017-05-31 2018-08-07 Федеральное государственное бюджетное образовательное учреждение высшего образования "Петрозаводский государственный университет" Способ взаимодействия в системе связанных осцилляторов на базе оксидных структур с эффектом электрического переключения
RU2697947C1 (ru) * 2018-06-29 2019-08-21 Федеральное государственное бюджетное образовательное учреждение высшего образования "Петрозаводский государственный университет" Способ распознавания образов в системе связанных осцилляторов

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Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2005006250A1 (fr) * 2003-06-25 2005-01-20 Variance Dynamical, Inc. Appareil et procedes de detection et d'analyse de composantes spectrales
US7474973B2 (en) * 2003-06-25 2009-01-06 Variance Dynamicaz, Inc. Apparatus and method for detecting and analyzing spectral components in predetermined frequency bands within a signal, frequency filter, and related computer-readable media
WO2005088535A2 (fr) * 2004-03-17 2005-09-22 Canon Kabushiki Kaisha Appareil de traitement parallele de signaux a impulsions, appareil de reconnaissance de formes et appareil de saisie d'images
WO2005088535A3 (fr) * 2004-03-17 2007-02-15 Canon Kk Appareil de traitement parallele de signaux a impulsions, appareil de reconnaissance de formes et appareil de saisie d'images
US7707128B2 (en) 2004-03-17 2010-04-27 Canon Kabushiki Kaisha Parallel pulse signal processing apparatus with pulse signal pulse counting gate, pattern recognition apparatus, and image input apparatus
EP3045872A1 (fr) * 2015-01-14 2016-07-20 Insitu, Inc. Systèmes et procédés de quantification de signal
US9753068B2 (en) 2015-01-14 2017-09-05 Insitu Inc. Systems and methods for signal quantization
RU2663546C1 (ru) * 2017-05-31 2018-08-07 Федеральное государственное бюджетное образовательное учреждение высшего образования "Петрозаводский государственный университет" Способ взаимодействия в системе связанных осцилляторов на базе оксидных структур с эффектом электрического переключения
RU2697947C1 (ru) * 2018-06-29 2019-08-21 Федеральное государственное бюджетное образовательное учреждение высшего образования "Петрозаводский государственный университет" Способ распознавания образов в системе связанных осцилляторов

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