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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 !