memristive tunnel junctions for neuromorphic circuits · neuromorphic computing aims to use...
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Fakultät für Physik
ESA, ACT ESTEC April 29, 2015
Memristive Tunnel Junctions for
Neuromorphic CircuitsAndy Thomas
Acknowledgments
O. SimonN. Shepheard
O. Schebaum
I.-M. Imort
J. Münchenberger
M. SchäfersS. Fabretti
Z. Kugler
L. Schnatmann M. Schirmer
S. Niehörster
J. Sterz
2
G. Reiss A. Hütten
Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen
Center for Spinelectronic Materials and Devices
Collaborations
Spin electronic C. Felser, MPI Dresden J. Moodera, M.I.T. T. Kampfrath, FHI Berlin K. Nielsch, U Hamburg
Spin caloritronics M. Münzenberg, U Greifswald
S. Goennenwein, WMI Garching C. Heiliger, U Gießen M. Kläui, U Mainz
Memristive systems C. Kaltschmidt, U Bielefeld E. Chicca, U. Rückert, CITEC Bielefeld mem
ristor
−∞ −∞
3
Why neuromorphic circuits?
Bio-inspired neural networks
Andy Thomas and Christian Kaltschmidt
1 Introduction
Memristors have attracted great interest for a variety of applications in recent years.An obvious use would be as a memory device [17, 52, 50] or, more ambitiously,a reconfigurable logic device [88, 10, 89, 11, 64]. However, the most interestingimplementation of memristive devices is neuromorphic computing.
Neuromorphic computing aims to use biological mechanisms operating withinthe brain as a blueprint to construct novel computer architectures. Carver Meadbuilt the foundation of this field and proposed large-scale adaptive analogue systemsbecause of their robustness as well as good power efficiency [61]. The efficiency ofthese systems is particularly promising, as shown in Table 1.
Table 1 Comparison of the power consumption of three different technologies [74]. A biologicalneuron draws less power and consumes less area than a digital computer or silicon neuron.
Digital computer Silicon neuron Biological neuron
Energy consumption (J/spike) 10�5 10�8 10�11
Size (µm2) 108 3⇥103 10
Despite its power efficiency and robustness, some tasks are very challenging forthe human brain, e.g., solving coupled differential equations. However, it is veryeasy to find a solution for this problem with the help of a von-Neumann/Zuse com-puter [92, 67]. However, some tasks are also difficult for a state-of-the-art computer
Andy ThomasPhysics department, Bielefeld University, Germany, e-mail: [email protected], andPhysics department, Osnabruck University, Germany
Christian KaltschmidtBiology department, Bielefeld University, Germany, e-mail: [email protected]
1
[74] C.S. Poon, Frontiers in neuroscience 5 (2011) 1
Arithmetische Einheit
Kontrolleinheit
Speicher
Lochkartenleser
MCA
CC
R
Efficiency
Avoid von Neumann bottleneck
Scientific curiosity Maximum reduction?
presynaptic cell
postsynaptic cell
synapse
impulses
dendrite
axon
synapse
Biological neural networks
Biological neural networks
6
presynaptic cell
postsynaptic cell
synapse
impulses
dendrite
axon
synapse
presynaptic cell postsynaptic cell
synapse
impulses
need neurons and synapses neurons are connected via the synapses.
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Neurons integrate signals and fire when exceeding threshold
leaky integrate and fire
oversampled ΣΔ modulators= 1-Bit AD converter
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Thomas, J. Phys D: Appl. Phys. 46 (2013) 093001, Thomas, Kaltschmidt, Memristor Networks, Ed. Adamatzky, Chua (2014) 151-172
Biological synapse
7
Axon
Pre-synpase
synaptic cleft
Post-synapse
vesicles containing neurotransmitters
vesicle fusion Glu
Glu
Glu
Glu
GluGlu
Ca2+
gene expression via CREB, NF-kappaB
Simplify the mechanisms via a simple model: One effective connection strength.
Mayford, Siegelbaum, Kandel, Cold Spring Harbor Perspectives in Biology 4(6), a005,751 (2012)
Electronic symbols
8
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
presynaptic cell postsynaptic cell
synapse
impulses
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
Symbols
presynaptic cell postsynaptic cell
Biological synapses
9
100
50
0
-50
pote
ntia
tion
(%)
43210time (h)
input
output
3
2
1
γ
β
α
(a)
(b)100
50
0
-50-60 -40 -20 0 20 40 60
spike timing (ms)
change (%)
1.0
0.5
0.0
syna
ptic
stre
ngth
3020100-10time (min)
Exhibit LTP, LTD, STDP
T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103, S. Cassenaer et al, Nature 448 (2007) 709
Long-term potentiation (LTP)
Long-term depression (LTD)
Spike-time dependent plasticity (STDP)
Observations in a biological neural network
The synapses exhibit LTP (cooperative, associative, and input-specific), LTD, and STDP. CONTENTS 7
Bliss and Collingridge also reported that ltp is characterized by three basic
properties: cooperativity, associativity and input-specificity [43]. We will discuss these
three characteristics in the following paragraphs.
Figure 7. A low- (a) and high-intensity stimulus (b) was applied to a fibre. The low-intensity stimulus produced a reaction, but it was short lasting. The high-intensitystimulation lasted for a longer time. Reprinted from Brain Res. [46], with permissionfrom Elsevier.
Cooperativity means that there is an intensity threshold to induce ltp, and this
threshold is above the stimulus threshold that leads to a minimal synaptic response [46].
This process is illustrated in figure 7. A small-intensity stimulus was used in figure 7a.
While there is a reaction, the potentiation disappeared approximately 5 minutes after
application of the stimulus. This behaviour changes if a stimulus of higher intensity is
used (figure 7b.). The potentiation lasts a longer time, although the initial potentiation
is of comparable size. The stimulation in a biological system is usually a tetanus,
i.e., rapidly repeated impulses. Therefore, the threshold for inducing ltp is a complex
[complicated] function of the intensity and pattern of the tetanic stimulation (Bliss and
Collingridge [43]). This concept is discussed in more detail by [47].
Associativity indicates that many weak tetani in separate but convergent inputs
still trigger ltp [49]. Figure 8 depicts the potentiation resulting from the application
of two stimuli at the same time. First, the weak stimulus W is used, and no long-term
potentiation can be observed. The same is true if another strong, solitary stimulus S
is applied. However, a combined W plus S tetanus results in a long-term potentiation,
which is visible in figure 8.
Finally, input-specificity means that only the plasticity of the active connection is
potentiated [51, 50]. This was investigated using a tetanized pathway and a control path
in 17 matched-pair experiments by Lynch et al. [50]. The result is shown in table 1. The
CONTENTS 8
Figure 8. The application of the weak stimulus W or a strong stimulus S does notlead to a potentiation. If W and S are applied at the same time, long-term potentiationcan be observed. Reprinted from Proc. Nat. Acad. Sci. [48], Copyright (1983).
post tetanus (min) Pre 5 10 15
Tetanised pathway (%) 100 390 380 332
Control pathway (%) 100 74 67 73
Table 1. Population spike amplitude of tetanised and control pathways before andafter stimulation (N=17). Adapted by permission from Macmillan Publishers Ltd:Nature [50], copyright (1977).
tetanized path changed its amplitude by more than a factor of three, while the control
pathway remained approximately constant.
2.2. Long term depression ( ltd) and retention
We have to distinguish two di↵erent types of processes to investigate the term long-
term depression (ltd) and compare it with ltp. The first process is the antagonist of
ltp, which is consequently labelled ltd. The similarity of ltd to ltp is apparent in
figure 9, where the current traces were recorded before and after the stimulus. Although
the synaptic strength initially remains constant, the stimulus weakens the connection.
Afterward, the synaptic strength recovers over the course of several minutes, but it
remains less than its initial value. This result is indeed the analogue of ltp with an
opposite sign of the change in connection strength.
The second process is more involved and could possibly be described by the
depotentiation (reversal) of the ltp at the single-neuron level. However, beginning with
a top-bottom approach may be instructive. Therefore, it appears natural to connect
the potentiation of the various synaptic inputs with learning and, consequently, the
depotentiation with forgetting. This process occurs on a more extended timescale and
is of great interest to psychological researchers. In their review, Rubin and Wenzel
collected one hundred years data regarding forgetting. They provided a quantitative
Cooperative Associative
Input-specific: required by general causalityB.L. McNaughton, Brain. Res. 157 (1978) 277
G. Barrioneuvo, Natl. Acad. Sci. 80 (1983) 7347
Spike timing dependent plasticity (STDP)
11
input
output
3
2
1
γ
β
α
(a)
(b)100
50
0
-50-60 -40 -20 0 20 40 60
spike timing (ms)
change (%)
S. Cassenaer et al, Nature 448 (2007) 709
Spike-time dependent plasticity (STDP)
potentiate α
output
1
output
1
2
depress α
coincidence detector
2
α
Memristor
Thin film samples @ Bielefeld
Materials ‘development’: Ferromagnets, e.g. Heusler (HMF) SC: e.g. Heusler, MgB2 Oxides: e.g. Ta-O, HfO2, MgO
Spintronic devices: sensors memory logic
Spin caloritronics: TMS vs TMR thermal spin transfer torque spin pumping
Memristors: artificial neural networks integration with CMOS hybrid samples with biological neurons
Metal
Insulator
Lithography: optical e-beam ion beam etching
Thin film devices
13
Sample preparation
Thin film (co-)deposition on Si-wafer, MgO, STO, ..., substrates
Optional in- and ex-situ anneal, ex-situ optional field cool
Lithography (e-beam, optical), subsequent ion-beam etching
Transport measurements (0.3-500K, up to 4T)
Insulator
Ferromagnet
Superconductor
Meservey-Tedrow- Tunnel Junction
Metal
Metal
Insulator
Memristor
Ferromagnet
Ferromagnet
Insulator
Magnetic Tunnel Junction
Examples of the prepared thin film devices14
Memristive tunnel junctions
15
0
curre
nt
0voltage
v=v0 sin(ωt)
•
••••
152
151
150
149
resi
stan
ce (Ω
)
806040200flux (Vs)
•
••
••
•
•
••
•
•
••
•
••
•
•
• current flows one direction => turn knob one direction
+I: resistance up
current flows other direction => turn knob other direction
-I: resistance down
!"#$%&'()$!"$*+()$
,-$*+()$
Abbildung 1: Stack
-10-505
10
Curr
ent [
mA]
-0.4 0.0 0.4Voltage [V]
Abbildung 2: Loop mit Switching Effekt von 120% (MgO 12%)
Die oberen 3 Kurven wurden aus der gleichen Probe generiert. Die Barrierewurde hergestellt indem 2nm Ta mit Sauerstoffplasma oxidiert wurden. DieBeschleunigugnsspannung betrug -80V und die Oxidationszeit betrug 200s.
1
Ta/TaO/Pd
Metal
Metal
Insulator
Electrically controlled, two terminal, bipolar, analog devices
Thomas, J. Phys D: Appl. Phys. 46 (2013) 093001, Krzysteczko,..., AT, Appl. Phys. Lett. 95 (2009) 112508 Semicond. Sci. Technol. 29 (2014), guest Editor: A. Thomas
Memristor based synapses
Long term potentiation and depression
17
-0.5
0.0
0.5
1050time (min)
2
1
0
cond
ucta
nce
chan
ge (%
) LTP
LTD
excitatory
inhibitatoryneuronsynapse
I
excitatory
inhibitatoryneuronsynapse
I
220
219
218
217
R(Ω)
121086420
Time (min)
-15
0Flux(Vs)
-0.5
0.0v
(V)
Figure 49: Memristive mtj
activated by a standard spiketrain of negative polarity. Theposition of the applied trainis shown by the bottom trace.The resulting flux is givenby the middle trace, the to-tal flux-contend of the train is�15 Vs. The resistance of thememristive synapse is mod-ulated by the train and re-mains stable when the activ-ity is terminated.
in figure 48 are applied. They are characterized by only two pa-rameters: the amplitude of the sine profile vmax and the numberof spikes per train Nsp.
A typical measurement is shown in figure 49. The graph con-sists of three traces. The bottom trace plots the applied voltage.The middle trace displays the corresponding flux. The top traceshows that due to the voltage treatment, the resistance is drivenfrom a lower stable level to a higher stable level. This is ex-actly how an artificial synapse should respond. The activity atthe synaptic connection leads a stable modification thereof—theactivity is remembered.
223
222
221
220
219
218
217
R(Ω)
50403020100
Time (min)
0
1
23
4Figure 50: The effect ofsubsequent train application.The resistive states are num-bered. The state zero is theresult of the refreshing pro-cedure shown in fig. 51. Theother states are induced bystandard spike trains.
Figure 50 shows the effect of repeated treatment (4 times) witha 30-spike train and vmax = �500 mV. To control the barrier qual-ity, every 12 minutes (dashed lines) the constant magnetic field isreleased to measure the magnetic minor loop. If the minor loopshows a tmr ratio close to 100 % the data measured so far is con-
59
Successive pulses cause successive potentiation/ depression
100
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Biological System
T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103
Pulse shaping for spike timing dependent plasticity
18
�t > 0 �t < 0
�
vpre
vpost vpost
vpre
vMR vMR
t
t
t
t
t
t-vth
+vth
�
Figure 61: Flux-dependentplasticity induced by thevoltage at the memristorv
mr
= vpost � vpre. The fluxcalculated from v
mr
>vth canbe defined as positive forDt > 0 and negative for Dt <0. This asymmetry is thebasis of stdp of memristivemtjs. Reproduced from B.Linares-Barranco et al., Na-ture Precedings (2009)
in the first chapter and use the well-defined dependence of theresistance on the flux as discussed on page 62.
We follow the scheme proposed by Linares-Barranco et al.85
85 B. Linares-Barranco andT. Serrano-Gotarredona,Nature Precedings (2009)
The action potential (spike) is assumed to have the form presentedin figure 61. It consists of an on-set side and an off-set side. Bothmight be described by exponential functions and characterizedby parameters like amplitude and curvature. The exact shape ofthe spike is irrelevant at this point. The important features are(i) a not vanishing temporal extent of the pulse and (ii) an am-plitude higher than the threshold voltage for memristor activa-tion vth. The meaning of vth is visualized in figure 62 where thehysteresis of the R(f)-curve opens only within a critical windowdefined by the fth values.
The temporal extend of the pulses is important because wewant to use the temporal overlap of both pulses. If vpre is appliedto one terminal of the memristor and vpost to the other terminalthen the net voltage at the synaptic mtj will be v
mr
= vpost� vpre.If furthermore, the spike timing Dt is small enough—this is theHebbian rule for synaptic plasticity—the two overlapping spikeswill create a signal as shown on the bottom of figure 61. The pre-eminent role of vth is visualized by the reddish area. This areaenclosed by vth and v
mr
can be identified with the over-thresholdflux fth.
th
188.0
183
177.6
R (!)
0 42 84
Flux (Vs)
�
th�
Figure 62: (cf. fig. 14)Typical resistance hysteresis.The hysteresis is open withina critical flux-window as in-dicated by the reddish lines.
The timing sensibility is introduced by the reversed sign of theover-threshold part of vMR for reversed temporal order of presy-naptic and postsynaptic spike. This is visualized on the right side
65
Take real properties into account
190.9188
184
180
176.0
R(Ω)
-0.55 0.0 0.55Voltage (V)
RH,P
RL,P
R H
R L
input
output
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1
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β
α
(a)
(b)100
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spike timing (ms)
change (%)
Spike timing dependent plasticity
19
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wileyonlinelibrary.com © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Mater. 2012, 24, 762–766
We next turned our attention from synapses to neurons and from the barrier properties to the magnetic electrodes of the MTJs. With a new perspective on a phenomenon known as back-hopping,[8–11] we were able to demonstrate that memris-tive MTJs can emulate the behavior of neurons. Figure 4 shows an STT measurement, where the free magnetic electrode was switched by a spin-polarized current. At t 0.2 min, the mag-netic configuration was switched from the parallel state to an intermediate state with R 360 . For this first switching, a voltage of 420 mV was applied, which drove a current density of j 1.8 106 A cm 2. The occurrence of an intermediate state can be explained by the presence of magnetic domains within the free magnetic layer.[32–34] The intermediate state, however, was unstable. The magnetization of the free layer switched repeatedly between the intermediate state and the antiparallel state, indicating that back-hopping had been activated. When the positive bias was released (note the color scale), the sample remained in the antiparallel magnetic state of approximately 440 . Under negative bias, no switching or back-hopping was
A striking qualitative similarity between bio-logical synapses and memristive MTJs can be observed from the resistance traces presented in Figure 1 and 2 (compare, e.g., references [29,30]). The electrical activity at the memris-tive MTJ (synapse) led to a nonvolatile modu-lation of resistivity (synaptic strength). This is analogous to LTP and LTD, depending on the polarity of the bias. The next logical step was to verify a learning rule similar to the STDP observed for biological synapses (Figure 3A). To accomplish this step, we employed the voltage pulses described by v t. Given that u1(t) is the potential at the bottom electrode (presynaptic spike) and u2(t) is the poten-tial at the top electrode (postsynaptic spike), the bias at the memristive MTJ (synapse) is defined as the time delay-dependent func-tion v t(t). Provided that the amplitudes of the sawtooth functions are well chosen, a timing-dependent resistance modulation is observed. For high t, the bias does not exceed vth at any time, and resistance remains unchanged. For low t, however, negative or positive bias in excess of vth is applied, depending on the sign of t. The resulting STDP of memris-tive MTJs is presented in Figure 3B. Using sawtooth spikes with an amplitude of 0.3 V, we found a critical time delay of t 100 s for the resistance to be modified. The resist-ance change reached 4.59% for positive t and 3.48% for negative t. Note that because of the well-defined dependence of R on the flux, one is not restricted to sawtooth-shaped spikes. The actual shape of the stimulus is not decisive, since the resistance change R is determined by the flux, i.e., by the area enclosed by v t.
Figure 2. Resistance increase induced by a stimulus resulting from two sawtooth spikes with a positive delay of 40 s. The sawtooth spikes are presented on the top trace. The resulting difference signal is shown on the right axis. The resistance trace is colored according to the applied bias; the color scale is given by the inset. The activation threshold vth is indicated by dotted lines. See the Supporting Information for details on the estimation of the activation threshold.
173176179182
R (
)
121086420
Time (min)
-0.30.00.3
u (V
)
-0.5
0.0
0.5
v (V
)
t u1
u2
0.5-0.5v (V)
Figure 3. The STDP of biological and artificial synapses. A) The STDP observed for cultures of dissociated embryonic rat hippocampal neurons, data from reference [14]. B) The STDP of memristive MTJs. An initial state of 173.77 0.73 was modulated by R depending on the value of the positive delay t. For negative delays, the initial state was set to 180.26 0.21 . Selected voltage traces are presented in the insets; dotted lines indicate vth. See the Supporting Information for details on the initial state setting and all voltage and resistance traces.
80
40
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-40Cha
nge
in E
PS
Cam
plitu
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%)
-100 -50 0 50 100
Spike timing (ms)
A
B
-8
-4
0
4
8R
()
t (s)
-200 200100-100 0
764
www.advmat.dewww.MaterialsViews.com
COM
MUN
ICATI
ON
wileyonlinelibrary.com © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Mater. 2012, 24, 762–766
We next turned our attention from synapses to neurons and from the barrier properties to the magnetic electrodes of the MTJs. With a new perspective on a phenomenon known as back-hopping,[8–11] we were able to demonstrate that memris-tive MTJs can emulate the behavior of neurons. Figure 4 shows an STT measurement, where the free magnetic electrode was switched by a spin-polarized current. At t 0.2 min, the mag-netic configuration was switched from the parallel state to an intermediate state with R 360 . For this first switching, a voltage of 420 mV was applied, which drove a current density of j 1.8 106 A cm 2. The occurrence of an intermediate state can be explained by the presence of magnetic domains within the free magnetic layer.[32–34] The intermediate state, however, was unstable. The magnetization of the free layer switched repeatedly between the intermediate state and the antiparallel state, indicating that back-hopping had been activated. When the positive bias was released (note the color scale), the sample remained in the antiparallel magnetic state of approximately 440 . Under negative bias, no switching or back-hopping was
A striking qualitative similarity between bio-logical synapses and memristive MTJs can be observed from the resistance traces presented in Figure 1 and 2 (compare, e.g., references [29,30]). The electrical activity at the memris-tive MTJ (synapse) led to a nonvolatile modu-lation of resistivity (synaptic strength). This is analogous to LTP and LTD, depending on the polarity of the bias. The next logical step was to verify a learning rule similar to the STDP observed for biological synapses (Figure 3A). To accomplish this step, we employed the voltage pulses described by v t. Given that u1(t) is the potential at the bottom electrode (presynaptic spike) and u2(t) is the poten-tial at the top electrode (postsynaptic spike), the bias at the memristive MTJ (synapse) is defined as the time delay-dependent func-tion v t(t). Provided that the amplitudes of the sawtooth functions are well chosen, a timing-dependent resistance modulation is observed. For high t, the bias does not exceed vth at any time, and resistance remains unchanged. For low t, however, negative or positive bias in excess of vth is applied, depending on the sign of t. The resulting STDP of memris-tive MTJs is presented in Figure 3B. Using sawtooth spikes with an amplitude of 0.3 V, we found a critical time delay of t 100 s for the resistance to be modified. The resist-ance change reached 4.59% for positive t and 3.48% for negative t. Note that because of the well-defined dependence of R on the flux, one is not restricted to sawtooth-shaped spikes. The actual shape of the stimulus is not decisive, since the resistance change R is determined by the flux, i.e., by the area enclosed by v t.
Figure 2. Resistance increase induced by a stimulus resulting from two sawtooth spikes with a positive delay of 40 s. The sawtooth spikes are presented on the top trace. The resulting difference signal is shown on the right axis. The resistance trace is colored according to the applied bias; the color scale is given by the inset. The activation threshold vth is indicated by dotted lines. See the Supporting Information for details on the estimation of the activation threshold.
173176179182
R (
)
121086420
Time (min)
-0.30.00.3
u (V
)
-0.5
0.0
0.5
v (V
)
t u1
u2
0.5-0.5v (V)
Figure 3. The STDP of biological and artificial synapses. A) The STDP observed for cultures of dissociated embryonic rat hippocampal neurons, data from reference [14]. B) The STDP of memristive MTJs. An initial state of 173.77 0.73 was modulated by R depending on the value of the positive delay t. For negative delays, the initial state was set to 180.26 0.21 . Selected voltage traces are presented in the insets; dotted lines indicate vth. See the Supporting Information for details on the initial state setting and all voltage and resistance traces.
80
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Cam
plitu
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%)
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B
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R (
)
t (s)
-200 200100-100 0
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Biological system Memristor system
S. Cassenaer et al, Nature 448 (2007) 709
Memristors as artificial synapses
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inhibitatoryneuronsynapse
I
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Biological System
T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103S. Cassenaer et al, Nature 448 (2007) 709
Memristive System
-8
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Δ R
(Ω)
-200 -100 0 100 200spike timing (s)
450
400
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stan
ce (Ω
)
40200time (s)
back-hopping
20ms
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input
output
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(a)
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)
STDP
Neuromorphic circuits
Memristor plus CMOS
22
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
J. Phys. D: Appl. Phys. 46 (2013) 093001 Topical Review
I(t)
CR
pulse triggersswitch
voltage thresholdtriggers pulse
Figure 12. Integrate-and-fire circuits: the perfect integrate-and-firemodel consists of a capacitor, threshold detector and switch (withoutresistor). Once the voltage reaches a threshold, the spike is fired andthe switch is closed to shunt the capacitor. In the leaky version, aresistor is added that slowly drains the capacitor with time. Thiscorresponds to leakage current through a membrane in a living cell.
integrate-and-fire [68–71]. The rather simple model capturestwo of the most important aspects of neuronal excitability;specifically, the neuron integrates the incoming signals andgenerates the spikes once a certain threshold is exceeded(figure 12).
This behaviour is often explained using two simple electriccircuits [72]. The perfect integrate-and-fire circuit consistsof a capacitor, threshold detector and switch. Once a spikeis fired, the switch closes and shunts the capacitor. Anadditional resistor is included in the leaky integrate-and-fire circuit. The resistor slowly drains the capacitor andcorresponds to leakage currents in the membrane. However,the integrate-and-fire functionality of a neural network isconsiderably simpler to implement than the synaptic efficacy.For example, oversampled Delta-Sigma modulators, which are1-bit analogue- digital converters, can mimic the integrate-and-fire behaviour [73, 74]. Therefore, the following paragraphsprimarily describe the use of memristive systems as synapsesbecause the integrate-and-fire functionality can be achievedusing conventional CMOS-technology.
2.5. Minimal requirements
We can summarize the primary requirements for a bio-inspiredneural network as follows.
(i) Devices that act as neurons and devices that behave likesynapses are needed, and the neurons are interconnectedvia the synapses.
(ii) The neurons integrate inhibitory and excitatory incomingsignals and fire once a threshold is exceeded.
(iii) The synapses exhibit LTP (cooperative, associative, andinput-specific), LTD, and STDP.
3. Implementations using memristive systems
The question may be asked as to why we want to constructneuromorphic systems that emulate the presented biologicalmechanisms. Carver Mead pioneered a considerable amount
excitatory
inhibitatoryneuronsynapse
Figure 13. Schematic symbols for synapses and neurons as used inthe following paragraphs.
of the research on this topic and explained the reasoning in thefollowing way [75]: For many problems, particularly those inwhich the input data are ill-conditioned and the computationcan be specified in a relative manner, biological solutions aremany orders of magnitude more effective than those we havebeen able to implement using digital methods. [...] Large-scale adaptive analog systems are more robust to componentdegradation and failure than are more conventional systems,and they use far less power. The need for less power isparticularly obvious if we compare the performance of thebrain of even an invertebrate with a computer CPU and contrastthe power consumption. However, there are some tasks thatare difficult for a human and easy for a computer, such asmultiplying two long numbers, and other problems that ahuman can easily solve but computers fail to solve.
In 2008, the use of memristors to mimic biologicalmechanisms, such as STDP, was already hypothesized[76]. Snider implemented the spike time dependence usingmemristive nanodevices as synapses and conventional CMOStechnology as neurons. He also suggested two electronicsymbols for neurons and synapses [76] that have been adaptedby some groups as well as in this paper; the symbols aredepicted in figure 13. Furthermore, Snider indicated thatwe should note that STDP alone might not be sufficient toimplement stable learning; more complex synaptic dynamicsand additional state variables may be required and refers towork by Carpenter et al [77] as well as Fusi and Abbott [78].
Although Snider suggested a new paradigm that useslarge-scale adaptive analogue systems, the approach still uses aglobal clock signal. In 2010, Pershin and Di Ventra described asmall system composed of three neurons and two synapses thatis fully asynchronous [79, 80]. The memristive behaviour wasemulated by a microcontroller combined with other commonelectronic components. They demonstrated how Ivan Pavlov’sfamous experiment [81] can be imitated with the basic circuitdepicted in figure 14 [79].
Initially, the output signal (salivation) is recorded independence on the sight of food or a bell sound. Only thesight of food (input signal 1) leads to salivation (neuron 3output); the bell (input signal 2) is not associated with food.There is a subsequent learning period where the input 1and input 2 signals are applied simultaneously. Afterwards,both individual input signals induce salivation. The elegantexperiment demonstrates how an important function of thebrain, namely associative memory [79], can be constructedwith a circuit, as shown in figure 14.
A similar simulation was conducted by Cantley et al usingSPICE (UC Berkeley, CA, USA) and MATLAB (Natick, MA,USA), and they noted Also, it should be pointed out that theassociation as presented (in figure 4) can be unlearned. This
6
Use existing CMOS Use memristors
mem
ristor
−∞−∞
Implementation of memristors
23
Neuromorphic nanoscale memristor synapses 13
VddVddVdd
VddVdd
Ith
I�
Isyn
Vin3
Vin2
Vw
IwN
Vin1
Vin4
VinNVw
Vw
Vw
VwIw
(a) (b)
Figure 6: Neuromorphic memristive synapse. (a) Schematic circuit implementing an
array of memristive synapses, with independent inputs and synaptic weights, but with
shared temporal dynamics. (b) SPICE simulations of the circuit in Fig. 6a showing the
output Isyn EPSC in response to a pre-synaptic input spike, for 4 di↵erent memristor
conductance values.
produce. Larger memristor conductances, which represent a larger number of open
proteic channels in real synapses, correspond to larger synaptic weights.
Figure 6b shows the results of SPICE simulations of the circuit in Fig. 6a, for a
180 nm CMOS process. The Ithr and I⌧ current sources were implemented with p-type
MOSFETs, biased to produce 2 pA and 10 pA respectively, and the Vw voltage bias was
set to 700mV. The data was obtained by simulating the response of one input memristive
branch to a single input spike, while sweeping the memristor impedance from 1K⌦ to
7K⌦. In these simulations we set the memristor in its LRS, and assumed we could
modulate the value of the resistance to obtain four distinct analog states analogous to
the ones measured experimentally in Fig. 2b. Of course the circuit supports also the
operation of the memristor as a binary device, working in either the HRS state or the
LRS one. This bi-stable mode of using the memristor would encode only an “on” or
“o↵” synaptic state, but it would be more reliable and it is compatible with biologically
plausible learning mechanisms, such as those proposed in [71], and implemented in [69].
The circuit of Fig. 6a shows only the circuit elements required for a “read” operation,
i.e., an operation that stimulates the synapse to generate an EPSC with an amplitude set
by the conductance of the memristor. Additional circuit elements would be required to
change the value of the memristor’s conductance, e.g., via learning protocols. However
the complex circuitry controlling the learning mechanisms would be implemented at the
Input/Output (I/O) periphery of the synaptic array, for example with pulse-shaping
circuits and architectures analogous to the ones described in Section 3, or with circuits
that check the state of the neuron and of it’s recent spiking history, such as those
G. Indiveri et al., Nanotech. 24 (2013) 384010
existing neuromorphic chip design + memristor pads + additional electronics
= neuronal circuit with synaptic weights
Existing neuromorphic chips often lack synaptic weights (>1000 Neurons)
Neuromorphic chip design (AG E. Chicca, Citec Bielefeld),
Memristor preparation and lithography (AG A. Thomas, U Bielefeld)
Take home message
25
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1050time (min)
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) LTP
LTD
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inhibitatoryneuronsynapse
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3020100-10time (min)
Biological System
T. Bliss at al, Nature 361 (1993) 31, Y. Goda et al, Neuron 16 (1996) 103S. Cassenaer et al, Nature 448 (2007) 709
Memristive System
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