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Keynote speechProf. Massimiliano Di Ventra, Dept. of Physics,University of California, San Diego
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Smart Memory Y. V. Pershin F. L. Traversa M. Di Ventra
Memcomputing:computing with and in memoryM. Di Ventra
M. Di Ventra and Y.V. Pershin, Nature Physics 9, 200 (2013)F.L. Traversa, F. Bonani, Y.V. Pershin, M. Di Ventra, Nanotechnology (in press) F.L. Traversa and M. Di Ventra, arxiv (2014)
Yuriy PershinFabio TraversaOutline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
Outline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
Universal Turing Machine
formal definition
UTM = object operating on a tape
Turing machine implementation:von Neumann architectureMain feature: Memory and CPU are physically separatedProblem: Limited data transfer rate between CPU and memoryMEMORYCPUCONTROLUNITARITHMETIC/LOGIC UNITINPUTOUTPUTVON NEUMANN ARCHITECTURE and
Energy costs of computing
Amazon
What do we do?Learn from Nature !
The most incredible computing machine
Energy costs:
~ 25 Watts to perform 1016 operations/seconda supercomputer would require 108 Watts to do same number of operations Outline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
The physical properties of the brain Computing and storing on the same platformSelf-healing properties when damaged
analog massive parallelisminformation overheadfunctional polymorphism
Neurons
Hodgkin-Huxley model
1212Hodgkin-Huxley model
Hodkin and Huxley, J. Physiology (1952)?1313
Neurons
Ionic memcapacitorsM. Krems, Y.V. Pershin, and M. Di Ventra, Nano Lett. (2010)
Ionic memcapacitorsM. Krems, Y.V. Pershin, and M. Di Ventra, Nano Lett. (2010)
TheoryExperimentD. Wang, et al., JACS (2011)1V/s
Solid-state memcapacitors
J. Martinez-Rincon, YM. Di Ventraa, Y.V. Pershin, Phys. Rev. B. (2010)1717Solid-state memcapacitors
J. Martinez-Rincon, YM. Di Ventraa, Y.V. Pershin, Phys. Rev. B. (2010)1818
Circuit elements with memory:memristors, memcapacitors, meminductorsM. Di Ventra, Y.V. Pershin and L.O . Chua, Proc. IEEE (2009) L.O. Chua IEEE Trans. Circuit Theory (1971)
x = a set of state variables
very low frequencies: nonlinear elementvery high frequencies: linear element
A new computing paradigm?
analog massive parallelisminformation overheadfunctional polymorphismmemoryOutline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
Universal Memcomputing Machines
Universal Memcomputing Machines
UMM = object computing with and in memoryformal definition
F.L. Traversa and M. Di Ventra, arxiv (2014)memprocessors
Properties of UMMs
Theorem:UMMs can simulate any Turing MachineF.L. Traversa and M. Di Ventra, arxiv (2014)Open question:Can a Turing Machine simulate a UMM?UMMs are not Turing MachinesproofWe do not knowIntrinsic Parallelismacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalg1(a,b,c,d)g2(a,b,c,d)g3(a,b,c,d)g4(a,b,c,d)Signal Signal Functional PolymorphismabcdefghiInformation OverheadCONTROLUNITCONTROLUNIT
Intrinsic parallelismF.L. Traversa and M. Di Ventra, arxiv (2014)MEMORYCPUMEMORYCPUMEMORYCPUMEMORYCPUStandard Parallelismm1m2m3m4mnCONTROLUNITIntrinsic ParallelismIntrinsic Parallelismacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalg1(a,b,c,d)g2(a,b,c,d)g3(a,b,c,d)g4(a,b,c,d)Signal Signal Functional PolymorphismabcdefghiInformation OverheadCONTROLUNITCONTROLUNIT
Functional polymorphismF.L. Traversa and M. Di Ventra, arxiv (2014)Intrinsic Parallelismacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalacdbf1(a,b,c,d)f2(a,b,c,d)f3(a,b,c,d)f4(a,b,c,d)Applied Signalg1(a,b,c,d)g2(a,b,c,d)g3(a,b,c,d)g4(a,b,c,d)Signal Signal Functional PolymorphismabcdefghiInformation OverheadCONTROLUNITCONTROLUNIT
Properties of UMMsF.L. Traversa and M. Di Ventra, arxiv (2014)abcdefghiInformation Overhead
Information overheadF.L. Traversa and M. Di Ventra, arxiv (2014)a1a2a3a4akMeasurement Unita2 + a3 + a4
Solution Treex(j1)x(j2)x(j1)x(j2)x(j3)x(j4)x(j1)x(j2)x(j3)x(j4)x(j5)x(j6)x(j7)x(j8)x(j1)UMM(No Information Overhead)a1b1b2c1c2c3c4d1d2d3d4d5d6d7d8Formal proof see: F.L. Traversa and M. Di Ventra, arxiv (2014)
UMMs solve NP-complete problems in polynomial timeFormal proof: F.L. Traversa and M. Di Ventra, arxiv (2014)
UMMs solve NP-complete problems in polynomial time and polynomial resourcesSolution TreeUMM(With Information Overhead)a1b1b2c1c2c3c4d1d2d3d4d5d6d7d8x(j1)a1(x)x(j1)x(j2)b1(x)x(j1)x(j2)x(j3)x(j1)x(j2)x(j3)x(j4)b2(x)c2(x)c1(x)c4(x)c3(x)d2(x)d1(x)d6(x)d5(x)d4(x)d3(x)d8(x)d7(x)
UMMs solve NP-complete problems in polynomial timeF.L. Traversa and M. Di Ventra, arxiv (2014)This does not mean
NP = P !Outline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
Solution of the subset-sum problem:numerical implementation
NP-complete
F.L. Traversa and M. Di Ventra, arxiv (2014)Our method vs.dynamic programming
Solution of the subset-sum problem:hardware implementation
F.L. Traversa and M. Di Ventra, arxiv (2014)
Solution of the subset-sum problem:hardware implementation
F.L. Traversa and M. Di Ventra, arxiv (2014)
CVM1
CVMn
Band-pass filterSignal analyzerInterconnected CVMsFFTTwo-spectra combiner frequencyfrequencyHardware solution in only 1 step!DCRAMDynamic Computing Random Access Memory
DCRAMPolymorphic Computing
Outline Motivation
Emulating the brains computational abilitiesUniversal Memcomputing MachinesPractical examples
Whats next
Learning from UMMs how the brain works
The critical brain
Ising modelBrainD.R. Chialvo, Nature Physics (2010).
Scale-free properties as an epiphenomenon of memoryCaravelli, Hamma, Di Ventra (2013).
Scale-free properties as an epiphenomenon of memoryCaravelli, Hamma, Di Ventra (2013)
Time
No memory With memory
Scale-free properties as an epiphenomenon of memoryCaravelli, Hamma, Di Ventra (2013)
Optimal memory rangeCaravelli, Hamma, Di Ventra (2013)
There is an optimal memory for scale-free properties
The physical properties of the brainSelf-healing properties when damaged
Self-organization and healing innetworks with memory
4545Self-healing properties of networks with memory
Self-organized solution!4646Conclusions
Universal memcomputing machines
Can teach us a lot about how the brain works
Huge market potential
Acknowledgments
Group members
Dr. Sebastiano Peotta (UCSD)Dr. Fabio Traversa (Italy)Prof. Yuriy Pershin (USC)Dr. Guy Cohen (UCSD)Dr. Alex Stotland (Israel)Dr. Tom Driscoll (exp., Duke U.)Dr. Matt Krems (UCSD)S. La Fontaine (UW)
CollaboratorsProf. Dimitri Basov (exp., UCSD)Dr. Alioscia Hamma (Perimeter Institute)Dr. Francesco Caravelli (Oxford Univ.)
Yuriy PershinFabio TraversaThank you !
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