Emulation of Astrocyte Induced Neural Phase Synchrony in Spin-Orbit Torque Oscillator Neurons
EEmulation of Astrocyte Induced Neural Phase Synchrony in Spin-Orbit TorqueOscillator Neurons
Umang Garg, ∗ Kezhou Yang, and Abhronil Sengupta † School of Electrical Engineering & Computer Science,Department of Materials Science and Engineering,The Pennsylvania State University, University Park, PA 16802, USA
Astrocytes play a central role in inducing concerted phase synchronized neural-wave patternsinside the brain. In this article, we demonstrate that injected radio-frequency signal in underlyingheavy metal layer of spin-orbit torque oscillator neurons mimic the neuron phase synchronizationeffect realized by glial cells. Potential application of such phase coupling effects is illustrated in thecontext of a temporal “binding problem”.
I. INTRODUCTION
Neuromorphic engineering is emerging to be a disrup-tive computing paradigm in recent times driven by theunparalleled efficiency of the brain at solving cognitivetasks. Brain-inspired computing attempts to emulatevarious aspects of the brain’s processing capability rang-ing from synaptic plasticity mechanisms, neural spikingbehavior to in-situ memory storage in the underlyinghardware substrate and architecture. This work is guidedby the observation that current neuromorphic computingarchitectures have mainly focused on emulation of bio-plausible computational models for neuron and synapsebut have not focused on other computational units of thebiological brain that might contribute to cognition.Over the past few years, there has been increasing ev-idence that glial cells, and in particular, astrocytes playa putative role in multitude of brain functions [1]. Itis estimated that glia form approximately 50% of thehuman brain cells [2, 3] and participate by modulatingthe neuronal firing behaviour, though unable to dischargeelectrical impulses of their own. Indeed, these glial-cellswork in coordination with neural assemblies, to enableinformation processing in the human brain and perform-ing incisive operations. Astrocytes hold the recipe topotentiate or suppress neurotransmitter activity withinnetworks and are responsible for phenomenon like syn-chronous network firing [4, 5] and self-repair mechanisms[6, 7]. It is therefore increasingly important to capturethe dynamics of such ensembles, a step towards realiz-ing better sophisticated neuromimetic machines and ul-timately enabling cognitive electronics.Recently, there has been extensive literature report-ing astrocyte computational models and their impact onsynaptic learning [8, 9]. Continuing these fundamen-tal investigations to decode neuro-glia interaction, therehave been recent neuromorphic implementations of astro-cyte functionality in analog and digital ComplementaryMetal Oxide Semiconductor (CMOS) hardware [3, 10–14]. While there has been extensive work on exploringpost-CMOS technologies for mimicking bio-realistic com-putations due to the prospects of low-power and compact hardware design, they have been only studied from stan-dalone neuron/synapse perspective. Emulation of theneuron-astrocyte crosstalk using bio-mimetic devices hasvastly been neglected, and no such literature exists hith-erto, to the best of our knowledge. This work is thereforean effort to bridge this gap and, specifically, elucidatesthe emulation of transient synchronous activity result-ing from neural-glial interactions by utilizing spin-orbittorque induced phase synchronization of spintronic oscil-lator neurons. It is worth mentioning here that we ab-stract the neuron functionality as a non-linear oscillator,in agreement with prior neuroscience and computationalmodels [15, 16]. This work present an important addi-tion to the wide variety of next-generation computationalparadigms like associative computing, vowel-recognition,physical reservoir computing among others [17–22], beingimplemented using spin-torque oscillator devices.
II. NEUROSCIENCE BACKGROUND
The human brain houses multiple-independent localneuronal groups which perform dedicated computationsin relevance to their assigned tasks. Besides this generalun-correlated activity of neurons, multiple neural spikingdata recordings reveal that the independent signals fromthese neural assemblies frequently coalesce in time to gen-erate a synchronous output [4, 23]. Multiple reports onthe cause of such patterns now provide compelling evi-dence that astrocytes are the agents of this underlinedphenomenon [5, 24]. Astrocytes modulate the concentra-tion of neurotransmitters like glutamate inside the synap-tic clefts in response to its internal Calcium ( Ca ) os-cillations [25, 26]. A single astrocyte spans more thantens of thousands of synapses, where units called mi-crodomains monitor the activity for a group of neuronsand perform subsequent chemical actions [27, 28]. Theastrocyte-derived glutamate binds to extrasynaptic NM-DAR (N-methyl-D-aspartate) receptor channels, and in-duce Slow-inward Currents (SIC) in the post-synapticmembrane. SICs are attributed to triggering a simul-taneous response in different synapses with high timing a r X i v : . [ c s . ET ] J u l precision, and its large amplitude and slow-decay rateprovide an increased timescale for the correlated activity[5, 24]. Fig. 1(a) captures the biological perspective ofsuch a system which controls the neural synchronizationamong neurons present in these different sub-networks.Sub-network A and B each consist of three different neu-rons, which in-turn generate oscillatory outputs. Thetemporal profiles, shown in Fig. 1(b), depict the neuronoutputs before and after synchronization is initiated byAstrocyte 1 in the network A. III. ASTROCYTIC SYNCHRONIZATIONEMULATION
In this work, we utilize Magnetic Tunnel Junctions(MTJs) [29] as the core hardware primitive to mimic neu-ral oscillations. Other variants of oscillatory behavior canbe achieved by modified spin device structures [30]. TheMTJ consists of two ferromagnetic layers (pinned layerand free layer) with a spacer oxide layer in between. Thedirection of magnetization of the pinned layer (PL) isfixed, while that of the free layer (FL) can be manipu-lated by external stimuli (spin current/magnetic field).The MTJ stack exhibits a varying resistance dependingon the relative magnetic orientations of the PL and theFL. The extreme resistive states are referred to as theparallel (P) and anti-parallel (AP) states depend on therelative FL magnetization. The magnetization dynamics A s t r o c y t e N e t w o r k Synchronization control signals
Astrocyte 2Astrocyte 1 Network A N a N a N a Network B N b N b N b (a) time (ns scale) M a g n e t o r e s i s t a n c e M a g n e t o r e s i s t a n c e time (ns scale) (b) FIG. 1. (a) Top-level network depicting the synchronizationcontrol by astrocytic injection. Astrocytes share informationamong their glial network. (b) The curves show the synchro-nized and un-synchronized outputs of Neurons 1-3 in NetworkA depending on the astrocyte input. of the FL can be modeled by Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation with stochastic thermalnoise [31]: d ˆ mdt = − γ ( ˆ m × H eff )+ α ( ˆ m × d ˆ mdt )+ 1 qN s ( ˆ m × I s × ˆ m ) (1)In Eq. (1), ˆ m is the unit vector representing the mag-netization direction of FL, H eff is the effective magneticfield including thermal noise [32], demagnetization fieldand external magnetic field, γ is the gyromagnetic ratio, α is Gilbert’s damping ratio, I s is the spin current, and N s = M s Vµ B is the number of spins in free layer of vol-ume V ( M s is saturation magnetization and µ B is Bohrmagneton). If the magnitude of spin current and exter-nal magnetic field are chosen appropriately such that thedamping due to the effective magnetic field is compen-sated, a steady procession of the FL magnetization canbe obtained.In order to achieve decoupled output oscillator read-out and astrocyte injection induced phase coupling, weutilize a three terminal device structure, as shown inFig. 2(a), in which a nanomagnet with in-plane mag-netic anisotropy lies on top of a heavy metal (HM) layerwith high spin-orbit coupling. Due to spin-Hall effect[33], a transverse spin current is injected into the MTJFL by charge current, I c , flowing through the HM be-tween terminals T2 and T3. The relation between spincurrent I s and charge current I c is, I s = θ SH A F M A HM (cid:18) − sech (cid:18) tλ sf (cid:19)(cid:19) I c (2)where, A F M and A HM are the FM and HM cross-sectional areas respectively and θ SH is the spin-Hall angle[33]. Note that an in-plane magnetic field, H , is also ap-plied to achieve sustained oscillation. The MTJ state isread using the current sensed through terminal T1. Thedevice simulation parameters are tabulated in Fig. 2(b)and are based on typical experimental measurements re-ported in literature [18]. However, the conclusions pre-sented in this study are not specific to these param-eters. Experimental demonstration of injection lockedspin-torque oscillators have been achieved [34–37]. PLFL HM
Write current c1 T T I s I Read current Magnetic fi eldH (a) as the core hardware primitive to mimic neuraloscillations. Other variants of oscillatory behavior can beachieved by modified spin device structures . The MTJconsists of two ferromagnetic layers (pinned layer andfree layer) with a spacer oxide layer in between. The di-rection of magnetization of the pinned layer (PL) is fixed,while that of the free layer (FL) can be manipulated byexternal stimuli (spin current/magnetic field). The MTJstack exhibits a varying resistance depending on the rel-ative magnetic orientations of the PL and the FL. Theextreme resistive states are referred to as the parallel (P)and anti-parallel (AP) states depend on the relative FLmagnetization. The magnetization dynamics of the FLcan be modeled by Landau-Lifshitz-Gilbert-Slonczewski(LLGS) equation with stochastic thermal noise : d ˆ mdt = − γ ( ˆ m × H eff )+ α ( ˆ m × d ˆ mdt )+ 1 qN s ( ˆ m × I s × ˆ m ) (1)In Eq. (1), ˆ m is the unit vector representing the mag-netization direction of FL, H eff is the effective magneticfield including thermal noise , demagnetization field andexternal magnetic field, γ is the gyromagnetic ratio, α is Gilbert’s damping ratio, I s is the spin current, and N s = M s Vµ B is the number of spins in free layer of vol-ume V ( M s is saturation magnetization and µ B is Bohr (a) time (ns scale) M a g n e t o r e s i s t a n c e M a g n e t o r e s i s t a n c e time (ns scale) (b) FIG. 1. (a) Top-level network depicting the synchronization controlby astrocytic injection. Astrocytes share information among their glialnetwork. (b) The curves show the synchronized and un-synchronizedoutputs of Neurons 1-3 in Network A depending on the astrocyte input. magneton). If the magnitude of spin current and exter-nal magnetic field are chosen appropriately such that thedamping due to the effective magnetic field is compen-sated, a steady procession of the FL magnetization canbe obtained.In order to achieve decoupled output oscillator readoutand astrocyte injection induced phase coupling, we utilizea three terminal device structure, as shown in Fig. 2, inwhich a nanomagnet with in-plane magnetic anisotropylies on top of a heavy metal (HM) layer with high spin-orbit coupling. Due to spin-Hall effect , a transversespin current is injected into the MTJ FL by charge cur-rent, I c , flowing through the HM between terminals T2and T3. The relation between spin current I s and chargecurrent I c is, I s = θ SH A FM A HM (cid:18) − sech (cid:18) tλ sf (cid:19)(cid:19) I c (2)where, A FM and A HM are the cross-sectional area ofFM and HM layers respectively and θ SH is the spin-Hallangle . Note that an in-plane magnetic field, H , is alsoapplied to achieve sustained oscillation. The MTJ statecan be read using the current sensed through terminalT1. MTJ Device Simulation Parameters
Parameters Value
Ferromagnet Area, A FM nm × nm HM thickness, t nm Energy barrier E b M s π A/mSpin-Hall Angle, θ SH α H
750 OeTMR ratio,
TMR T
300 K
PLFL HM
Write current c1 T T I s I Read current Magnetic fi eldH FIG. 2.
Spin-orbit torque device undergoes oscillation due to appliedexternal magnetic field, H , and charge current, I c . Device simulationparameters are tabulated. (b) FIG. 2. (a) Spin-orbit torque device undergoes oscillation dueto applied external magnetic field, H , and charge current, I c .(b) Device simulation parameters are tabulated. V DD ReferenceMTJ
PLPLFLFL HM dc I AstrocyteMTJ V DD Coupling HM Layer dc I N N N MTJ Neurons
FIG. 3. Electrical emulation of astrocyte induced neuralsynchrony is shown where an astrocyte device drives an alter-nating current through a common HM substrate to phase-lockthe MTJ oscillator neurons.
The electrical analogue of Fig. 1(a) is shown in Fig. 3,where the MTJs represent the oscillatory neurons presentin a particular network. The neurons share a HM layerwhich acts as the common substrate for the driving as-trocyte signal. The current flowing through the HM hastwo components - a DC current input which determinesthe free-running frequency of the oscillator and a radio-frequency signal which represents the astrocyte input.Fig. 4(a) highlights the oscillation characteristics of theMTJ. The DC current controls the precession frequencyin absence of other inputs. This DC input is analogous tothe external stimulus determining the frequency of neu-ron oscillation in a particular network. In the absenceof the RF signal, all the neurons oscillate at the samefrequency (dependent on stimulus magnitude or DC cur-rent) but out-of-phase due to thermal noise. Upon theapplication of the external RF astrocyte signal, the de-vice oscillation locks in phase and frequency to this input.Higher peak-to-peak amplitude of the astrocyte lockingsignal increases the locking range of the device. It isworth mentioning here that the locking frequency of neu-rons in a particular network is dependent on the stimulusand astrocytes only induce phase locking. Therefore the
350 400 450 500
DC current ( A) M ag n e t o re s i s t a n ce o s c ill a t i o n f re qu e n c y ( GH z ) AC injection frequency A A A A (a) Frequency (Hz) C r o ss - s p ec t r u m P h a s e (5GHz,7.22 ° ) (b) FIG. 4. (a) Oscillator frequency plotted against the DC cur-rent input to the device. Higher AC amplitudes lead to in-creased DC locking range to the injected RF signal of 6 . GHz frequency. (b) Cross-spectrum phase for 100 independentstochastic LLGS simulations of two noisy MTJ neurons, underRF injection of 5
GHz . Average CPSD phase indicates tightphase-coupling at the required frequency with un-correlatedactivity at other frequencies. alternating astrocyte signal flowing through the HM layercan be generated from a separate astrocyte device thatis driven by the corresponding DC input of the network,thereby ensuring independent phase and frequency con-trol. The astrocyte device is interfaced with a ReferenceMTJ and a PMOS transistor to drive the alternating cur-rent signal through the common HM layer.In order to evaluate the degree of phase synchroniza-tion in presence of thermal noise, we consider two MTJdevices lying on top of a common HM layer at room tem-perature. Cross-correlation metric is evaluated for thetwo MTJ output signals to measure the similarity amongthem as a function of displacement of one relative to theother. Considering two time-domain functions x ( t ) and y ( t ), whose power spectrum density (PSD) is given by S xx ( ω ) and S yy ( ω ) respectively, their cross-correlation isdefined by: R xy ( t ) = ( x (cid:63) y )( τ ) = (cid:90) ∞−∞ x ( t − τ ) y ( t ) dt (3)where, x ( t ) represents the complex conjugate of x ( t ) and τ denotes the lag parameter. Further, cross-power spec-tral density (CPSD) is defined as the Fourier transforma-tion of cross-spectrum in (3) and is given by: S xy ( ω ) = (cid:90) ∞−∞ R xy ( t ) e − jωt dt (4) S xy comprises of both magnitude and phase ( ∠ ) informa-tion at different frequencies present in (cid:2) ω (cid:3) vector. Whentwo signals are phase synchronized, the cross-spectrumphase vector becomes zero, indicating high correlation.Such a property is highlighted in Fig. 4(b) where 100independent stochastic-LLGS simulations are performedfor two neuronal devices placed on a common HM layerwith a 5 GHz injected RF current. Cross-spectrum phaseat the injection frequency, i.e. 5
GHz converges close tozero. Average cross-spectrum phase is also shown in theplot depicting tight phase-coupling between the neuronsat the injection frequency. Notably, a sharp reduction ofaverage phase offset to just 7 . ◦ at 5 GHz is observedcompared to 90 ◦ for other frequencies, thereby establish-ing the robustness of the synchronization scheme. IV. BINDING PROBLEM
Next, we discuss a renowned problem which is en-visioned to be solved by neural synchronous activ-ity. Amongst the most intriguing themes of neuro-psychological studies is the “binding problem” [39, 40]. Itconcerns with how different attributes of sensory informa-tion are encoded, processed and perceived for decision-making by the human brain circuits. With a now widelyaccepted viewpoint of distributive computing and segre-gated processing for different features (especially visual)
HMHM (a) (b)
PLFL PLFLPLFL PLFL PLFL PLFL I dc,1 I dc,2 I dc, a I dc, b N N N N N a N b f f f f Complex feature processing To Astrocyte M Astrocyte M f f Glial Network
Bistable image
B1 2 higher layers
FIG. 5. (a) The optical illusion induces confusion in the viewer concerning association among different apparent limbswith the body and the background (Courtesy of Roger Shepard’s ”L’egsistential paradox”) [38]. (b) MTJ system architecturedepicting hierarchical organization of neurons. The illustrated binding problem is mapped to this hardware with one possibleinterpretation shown. Devices N , N and N b operate at 6 . GHz , 6 . GHz and 7 . GHz free-running frequencies respectively. -
123 7.5 7.55 7.6 7.65 7.7 time (sec) - M T J R e s i s t a n ce ( K ) FIG. 6. Temporal evolution profile for the three devices,namely 1 (blue curve), 2 (yellow curve) and B (red curve)in Fig. 5(b) is depicted. (Top panel) Astrocyte network ac-tivates the synchronous regime at 50 ns leading to coherentneural patterns for all devices within 2 ns . (Bottom panel) De-synchronization regime starts at 75 ns causing the devices tounlock, therefore reverting to independent oscillations states. and later integration into a unified percept via re-entrantconnections [41, 42], we have progressed further towardsunderstanding cognition. Primate brains have evolved tocontinuously assimilate the voluminous perceptive infor-mation available in their social setting and find a bestfit for the agent’s goals in the quickest manner. Hierar-chical organization of neural assemblies is now believedto be the fabric for such a unified experience and re-lated actions [43]. This training and growth, althoughvery crucial in most situations – sometimes also leads to“misbinding” [44]. In particular, optical illusions, suchas shown in Fig. 5, are attempted towards exploiting thefeature patterns ingrained in the human visual percept,causing misbinding. The figure is a bistable portrait ofan elephant, or an overlap of two (seemingly) possibleinterpretations, obtained by associating different bodyparts to other features of the image. For instance, thelabels 1 and 2 can be viewed associated with the body(A), while 3 and 4 to the background (B) to paint onesuch possible interpretation. The other interpretationcan be visualized if the roles A and B are reversed. For an in-depth discussion, interested readers are directed toRef. [45, 46]. Clearly, attention plays the role of spatio-temporal integration among multiple attributes capturedby a visual scene. Meanwhile, synchronous activity inthe neurons is considered as the underlying mechanism inbrain to create a coherent episode of perception, and per-haps cognition. Indeed, it is now becoming more evidentthat cognitive processes like attention and behavioral ef-ficiency elicit targeted synchronous activity in differentbrain regions tuned to responding to spatial and featuralattributes of the attended sensory input [47, 48].In order to correlate our spin-orbit torque oscillatorphase synchronization due to astrocyte injection lockingin the context of “temporal binding”, we consider a net-work as shown in Fig. 5(b). Adhering to the currentlyprominent view of hierarchical organization in the neu-ral assemblies, spin-torque neurons N , N , N , N hereare dedicated to processing simple attributes, while N a and N b together perform complex feature processing cor-responding to the assigned task. In reference to poten-tial processing applications like cognitive feature bind-ing, each spin-torque neuron in the network representsthe corresponding feature in the elephant’s bistable im-age, previously shown in Fig. 5(a). N , N and N , N together operate at f and f free-running frequenciesrespectively due to I dc,1 and I dc,2 DC drives. Similarly,I dc,a and I dc,b
DC currents operate N a and N b devicesat f and f frequencies respectively. For a lucid illus-tration, the connections between only N , N and N b areshown in Fig. 5(b), where I dc,1 and I dc,b are 400 µA and450 µA respectively. The astrocyte can sense the infor-mation either independently or through long-range glialnetwork signalling, and thus is responsible to initiate orrevoke the synchronous regime. The premise for trigger-ing the synchronous activity via astrocyte is accreditedto the sensory attention as discussed before, and can bemapped in our proposed system to the amplitude of RFinjection signal. Similar to better binding observed withincreased attention, larger amplitudes lead to improvedneural coupling. Fig. 6 plots the magnetoresistance-timeevolution for N , N and N b devices. Initially N and N operate at f = 6 . GHz frequency with un-correlatedphases due to device’s inherent thermal noise, while thedevice N b operates at a higher frequency f = 7 . GHz .Astrocyte M there forth activates the RF injection at50 ns to initiate the synchronization process as shown inFig. 6 (top panel). It is to observed that within 2 ns ofactivation (i.e. 52 ns ), the devices N and N achieve acoherent phase, while the device N b gets frequency-lockedto the injection signal. Bio-physically equivalent, this canbe interpreted as a tight correlation among the attributes1 , B , corresponding to one of the interpretation ofthe bistable image. Similarly, Fig. 6 (bottom panel) high-lights the increasing phase-mismatch in neuronal outputsof both devices N and N , when the synchronization isrevoked by the astrocytes at 75 ns . The device N b revertsto its original free running frequency f = 7 . GHz . Thiscan be attributed to a diverted attention towards the sen-sory modal-input features leading to the impairment incorrelated activity.
V. DISCUSSION
Even though this work proves to be a good preliminaryframework for emulating such brain-like functions, moreinvestigation is required for decoding the neural code insuch processes along with integrating these insights inArtificial Intelligence (AI) systems. For instance, se-lectivity bias towards some features among the myriadavailable sensory information, and, reductionism (down-streaming) of such higher-level modal inputs to local neu-ronal groups in the hierarchical structure, is poorly un-derstood. There have been some efforts to study suchprocesses using a reverse approach, where robots likeDarwin VIII, inspired by the re-entrant neuroanatomyand synaptic plasticity, are developed and trained onvisual mode data [49]. In agreement with our work,they show synchronous activity binds different represen-tative features of the detected object. Incorporating suchconnections in our system can be explored to furtherbridge the gap between real cortical networks and therespective inspired models. Supported by both neuro-science research and AI hardware developments, coupledastrocyte-neuron network architectures can potentiallypave the way for a new generation of artificial cognitive-intelligence.
ACKNOWLEDGMENTS
The work was supported in part by the National Sci-ence Foundation. ∗ Also at Dept. of Electronics & Instrumentation Engineer-ing, Birla Institute of Technology and Science (BITS),Pilani † [email protected][1] S. L. Allam, V. S. Ghaderi, J.-M. C. Bouteiller, A. Legen-dre, A. Nicolas, R. Greget, S. Bischoff, M. Baudry, andT. W. Berger, Frontiers in computational neuroscience ,70 (2012).[2] C. S. von Bartheld, J. Bahney, and S. Herculano-Houzel,Journal of Comparative Neurology , 3865 (2016).[3] C. Mller, J. Lcke, J. Zhu, P. M. Faustmann, andC. [von der Malsburg], Cognitive Systems Research ,28 (2007).[4] J. Fell and N. Axmacher, Nature Reviews Neuroscience , 105 (2011).[5] J. J. Wade, L. J. McDaid, J. Harkin, V. Crunelli, andJ. A. S. Kelso, PLOS ONE , 1 (2011).[6] J. Wade, L. McDaid, J. Harkin, V. Crunelli, andS. Kelso, Frontiers in Computational Neuroscience , 76(2012).[7] M. Navarrete and A. Araque, Neuron , 113 (2010).[8] T. Manninen, R. Havela, and M.-L. Linne, Frontiers inComputational Neuroscience , 14 (2018).[9] M. De Pitt`a, V. Volman, H. Berry, V. Parpura,A. Volterra, and E. Ben-Jacob, Frontiers in computa-tional neuroscience , 98 (2012).[10] M. Naeem, L. J. McDaid, J. Harkin, J. J. Wade, andJ. Marsland, IEEE Transactions on Neural Networks andLearning Systems , 2370 (2015).[11] Y. Irizarry-Valle and A. C. Parker, IEEE Transactionson Biomedical Circuits and Systems , 175 (2015).[12] G. Karimi, M. Ranjbar, M. Amirian, and A. Shahim-aeen, Neurocomputing , 197 (2018).[13] M. Ranjbar and M. Amiri, Neural Computing and Ap-plications , 1109 (2017).[14] F. Faramarzi, F. Azad, M. Amiri, and B. Linares-Barranco, Frontiers in Neuroscience , 998 (2019).[15] H. Jaeger and H. Haas, Science , 78 (2004).[16] W. Maass, T. Natschlger, and H. Markram, Neural Com-putation , 2531 (2002).[17] M. Romera, P. Talatchian, S. Tsunegi, F. Abreu Araujo,V. Cros, P. Bortolotti, J. Trastoy, K. Yakushiji,A. Fukushima, H. Kubota, S. Yuasa, M. Ernoult, D. Vo-denicarevic, T. Hirtzlin, N. Locatelli, D. Querlioz, andJ. Grollier, Nature , 230 (2018).[18] D. Fan, S. Maji, K. Yogendra, M. Sharad, and K. Roy,IEEE Transactions on Nanotechnology , 1083 (2015).[19] S. Tsunegi, T. Taniguchi, K. Nakajima, S. Miwa,K. Yakushiji, A. Fukushima, S. Yuasa, and H. Kubota,Applied Physics Letters , 164101 (2019).[20] M. Romera, P. Talatchian, S. Tsunegi, K. Yakushiji,A. Fukushima, H. Kubota, S. Yuasa, V. Cros, P. Bor-tolotti, M. Ernoult, D. Querlioz, and J. Grollier, “Bind-ing events through the mutual synchronization of spin-tronic nano-neurons,” (2020).[21] M. Riou, J. Torrejon, B. Garitaine, F. A. Araujo, P. Bor-tolotti, V. Cros, S. Tsunegi, K. Yakushiji, A. Fukushima,H. Kubota, et al. , Physical review applied , 024049(2019).[22] J. Torrejon, M. Riou, F. A. Araujo, S. Tsunegi,G. Khalsa, D. Querlioz, P. Bortolotti, V. Cros, K. Yakushiji, A. Fukushima, H. Kubota, S. Yuasa,M. D. S. Stiles, and J. Grollier, Nature , 428 (2017).[23] P. Fries, Trends in Cognitive Sciences , 474 (2005).[24] T. Fellin, O. Pascual, S. Gobbo, T. Pozzan, P. G. Hay-don, and G. Carmignoto, Neuron , 729 (2004).[25] E. A. Newman, Trends in Neurosciences , 536 (2003).[26] A. D. Garbo], M. Barbi, S. Chillemi, S. Alloisio, andM. Nobile, Biosystems , 74 (2007), selected Paperspresented at the 6th International Workshop on NeuralCoding.[27] P. G. Haydon and G. Carmignoto, Physiological Reviews , 1009 (2006).[28] A. Volterra and J. Meldolesi, Nature Reviews Neuro-science , 626 (2005).[29] M. Julliere, Physics Letters A , 225 (1975).[30] R. Matsumoto, S. Lequeux, H. Imamura, and J. Grollier,Phys. Rev. Applied , 044093 (2019).[31] A. Sengupta and K. Roy, Applied Physics Reviews ,041105 (2017).[32] W. Scholz, T. Schrefl, and J. Fidler, Journal of Mag-netism and Magnetic Materials , 296 (2001).[33] J. Hirsch, Physical Review Letters , 1834 (1999).[34] W. Rippard, M. Pufall, and A. Kos, Applied PhysicsLetters , 182403 (2013).[35] W. H. Rippard, M. R. Pufall, S. Kaka, T. J. Silva, S. E.Russek, and J. A. Katine, Physical review letters ,067203 (2005).[36] B. Georges, J. Grollier, M. Darques, V. Cros, C. Deran-lot, B. Marcilhac, G. Faini, and A. Fert, Physical reviewletters , 017201 (2008). [37] V. Demidov, H. Ulrichs, S. Gurevich, S. Demokritov,V. Tiberkevich, A. Slavin, A. Zholud, and S. Urazhdin,Nature communications , 1 (2014).[38] R. N. Shepard, Mind sights: Original visual illusions,ambiguities, and other anomalies, with a commentaryon the play of mind in perception and art. (W H Free-man/Times Books/ Henry Holt & Co, New York, NY,US, 1990) pp. x, 228–x, 228.[39] R. D. Fields, A. Araque, H. Johansen-Berg, S.-S. Lim,G. Lynch, K.-A. Nave, M. Nedergaard, R. Perez, T. Se-jnowski, and H. Wake, The Neuroscientist , 426(2014), pMID: 24122821.[40] J. Feldman, Cognitive Neurodynamics , 1 (2013).[41] P. M. Milner, Psychological Review , 521 (1974).[42] A. Bartels and S. Zeki, Vision Research , 2280 (2006).[43] J. Duncan and G. W. Humphreys, Psychological Review , 433 (1989).[44] D. Whitney, Current Biology , R251 (2009).[45] B. Hasz and P. Miller, “Storing autoassociative memoriesthrough gamma-frequency binding between cell assem-blies of neural oscillators,” thesis, Brandeis University(2013).[46] M. Ignatov, M. Ziegler, M. Hansen, and H. Kohlstedt,Science Advances (2017), 10.1126/sciadv.1700849.[47] L. M. Ward, Trends in Cognitive Sciences , 553 (2003).[48] T. Womelsdorf and P. Fries, Current Opinion in Neuro-biology , 154 (2007), cognitive neuroscience.[49] A. K. Seth, J. L. McKinstry, G. M. Edelman, and J. L.Krichmar, Cerebral Cortex14