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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2133–2147
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Ultrafast all-optical implementation of a leaky integrate-and-fire neuron

Konstantin Kravtsov, Mable P. Fok, David Rosenbluth, and Paul R. Prucnal  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2133-2147 (2011)
http://dx.doi.org/10.1364/OE.19.002133


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Abstract

In this paper, we demonstrate for the first time an ultrafast fully functional photonic spiking neuron. Our experimental setup constitutes a complete all-optical implementation of a leaky integrate-and-fire neuron, a computational primitive that provides a basis for general purpose analog optical computation. Unlike purely analog computational models, spiking operation eliminates noise accumulation and results in robust and efficient processing. Operating at gigahertz speed, which corresponds to at least 108 speed-up compared with biological neurons, the demonstrated neuron provides all functionality required by the spiking neuron model. The two demonstrated prototypes and a demonstrated feedback operation mode prove the feasibility and stability of our approach and show the obtained performance characteristics.

© 2011 Optical Society of America

1. Introduction

Neural processing has provided an alternative to the digital model of computation that has proven to be useful both with respect to the design of algorithms (e.g. robust adaptive pattern recognition), and the hardware implementation of sensor processing (e.g, silicon cochlea, retina,etc.) Considerable effort was aimed at optical realization of neurons. That can take advantage of the huge optical bandwidth that allows ultra-fast modulation, and providing superior computational power compared to electronic approaches. Since the early 90s, several types of optical neurons or neuron-like devices have been reported [1

1. C.-H. Wang and B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990). [PubMed]

, 2

2. A. V. Grigor’yants and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994). [Sov. J. Quantum Electron. 24, 469–470 (1994)].

, 3

3. S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

, 4

4. E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

, 5

5. G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).

, 6

6. M. T. Hill, E. E. E. Frietman, H. de Waardt, G.-d. Khoe, and H. J. S. Dorren, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

, 7

7. G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).

]. A major focus of current research in theoretical neuroscience, is on the considerable computational capabilities of spiking models of neurons that exploit precise timing of spikes both for encoding and processing information. An optical realization of the prototypical computational primitive of these third generation neural models, the integrate-and-fire, “spiking neuron,” requires new optical hardware to be implemented.

The photonic processing devices presented in this paper enable terahertz processing rates with the high level of parallelism typical for neural networks. Being approximately 108 times faster than biological neurons, they also significantly outperform VLSI circuit-based neurons [8

8. R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007). [PubMed]

] and can be used in relatively simple neural networks where high information throughput is a critical factor.

2. Spiking neuron model

The integrate-and-fire neuron is one of the most widely used models of biological neurons in modern theoretical neuroscience [15

15. C. Koch, Biophysics of Computation (Oxford University Press, 1999).

]. Despite its abstraction of biological neurons into a small set of essential operations (delay, weighting, summation, temporal integration, and thresholding), the behavior of networks of these elements retains much of the richness found in biological neuron ensembles. Interest has been growing outside the theoretical neuroscience community in spiking neurons as efficient computational devices [16

16. W. Maass and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).

].

Spike processing is a natural hybrid of analog and digital processing in the sense that the output of a neuron is binary in amplitude, while processing in the neuron itself is analog: it does analog weighting and summation/subtraction of the input signals. This type of processing has evolved in biological systems (nervous systems) in order to overcome the problem of noise accumulation inherent in purely analog computation [17

17. R. Sarpeshkar, “Analog versus digital: Extrapolating from electronics to neurobiology,” Neural Comput. 10, 1601–1638 (1998). [PubMed]

]. Thus all information passed down to the following neuron in the network is contained only in presence or absence of spikes, but not in their shape or amplitude. Only the timing of the spikes provides the means for encoding information with spike processing. Spike processing algorithms are well-understood in a number of important biological sensory processing systems and are finding growing use in signal processing applications [16

16. W. Maass and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).

]. From the standpoint of computability and complexity theory, integrate-and-fire neurons are powerful computational primitives that are capable of simulating both Turing machines and traditional neural networks [16

16. W. Maass and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).

]. Another important advantage of the spiking neuron computational model is its ability to naturally incorporate learning and adaptation through spike time dependent plasticity (STDP) mechanisms.

The standard Leaky Integrate-and-Fire (LIF) model of a neuron has the following properties [16

16. W. Maass and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).

]:
  1. A neuron has N inputs σi(t) that represent induced conductance in input synapses; it has an internal activation state Vm(t); and it has a single output state O(t). At rest, the internal state is actively maintained at Vrest.
  2. Inputs σi(t) are continuous time series consisting of either spikes or continuous analog values.
  3. Inputs are weighted by wi and delayed by δi to give wiσi(tδi). Since wi can be negative and positive, both excitation and inhibition may be implemented.
  4. Delayed and weighted input time series are combined through pointwise summation, i=1Nwiσi(tδi).
  5. The activation state Vm(t) is an exponentially weighted temporal integration of the induced input currents divided by the neuron capacitance, Vm(T)=Vrest1CmTI(t)eTtτmdt, where τm is the integration time constant, I(t)=Vm(t)i=1Nwiσi(t+δi) is the electrical current induced by the aggregated input, and Cm is the neuron capacitance.
  6. The moment the magnitude of the temporally integrated signal drops below the threshold, then the neuron outputs a spike, O(t) = 1 if |Vm(t)| < |Vthresh|.
  7. After issuing a spike there is a short period of time, the refractory period, during which no other spikes can be issued, if O(t) = 1 then O(t – Δt) = 0, ΔtTrefract.
  8. The output of the neuron consists of a continuous time series of spikes
The parameters determining the behavior of the device are: wi, δi, Vthresh, Vrest, Trefract, and the integration time constant τm.

This model is derived from studies of morphology and physiology of biological neurons. A typical simplified neuron is schematically depicted in Fig. 1. It consists of a dendritic tree, which is a set of inputs, collecting, weighting, and delaying signals from other neurons; a soma, where all input signals are combined together and temporally integrated; and an axon, where output spikes, or action potentials, are formed provided the aggregated input exceeds the threshold. Since fiber optic implementation of dendrites is quite straightforward (using fiber couplers, attenuators/modulators, and delay lines), and optical pulse thresholders have been previously demonstrated (see [18

18. K. Kravtsov, P. R. Prucnal, and M. M. Bubnov, “Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA,” Opt. Express 15, 13114–13122 (2007). [PubMed]

] and refs there), the only part missing was a mechanism for leaky integration, which was demonstrated for the first time in [14

14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

].

Fig. 1 Schematic drawing of a biological neuron.

In order to unveil the connection between biological neurons and our photonic approach, we first describe the leaky temporal integrator we employ. In [14

14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

] we have found a direct correspondence between the equations governing temporal integration in the standard LIF neuron and the equations governing the carrier density in a semiconductor optical amplifier (SOA). According to the standard LIF neuron model, neurons are treated as electrical devices, which have their membrane potential, i.e., the voltage between the neuron’s body and the outside, Vm, as the primary internal state variable. The electrical properties of the soma surrounded by the membrane can be modeled as an RC circuit, with R referring to the resistance of the membrane and C — to the capacitance associated with the membrane. That is, the soma is effectively a first-order low-pass filter, or a leaky integrator, with the time constant τm = RmCm. The leakage current through Rm drives the membrane voltage Vm to 0, but an active membrane pumping current counteracts it and maintains a resting membrane voltage at a value of Vm = Vrest. Consequently, there are three influences on Vm: passive leakage of current, an active pumping current, and external inputs generating time-varying membrane conductance changes σ(t), which help to “discharge” the neuron. These three influences are the three terms contributing to the differential equation describing Vm in equation 1 below.

ActivationActive pumpingLeakageExternal input
dVm(t)dt=VrestτmVm(t)τm1CmVm(t)σ(t)
(1)
dN(t)dt=NrestτeN(t)τeΓaEpN(t)I(t)
(2)

Similarly, the gain dynamics of a short SOA is governed by equation 2 [19

19. M. Premaratne, D. Nešić, and G. P. Agrawal, “Pulse amplification and gain recovery in semiconductor optical amplifiers: A systematic analytical approach,” J. Lightwave Technol. 26, 1653–1660 (2008).

]. Its primary internal state variable is the carrier density above transparency N′(t) = N(t) – N0 where N(t) is the actual carrier density and N0 is the carrier density at transparency. Again, there are three contributors to changing N′(t): a passive leakage due to spontaneous light emission leading to the carrier decay; an active pumping provided by the driving current of the SOA; and stimulated light emission due to the neuron inputs, which also ”discharges” the neuron reducing its state variable N′(t). It is remarkable that the electrical model of membrane voltage is essentially identical to the optical model of SOA carrier density. The integration constant of the photonic neuron, τe, is equal to the carrier lifetime, while the stimulated emission term in the Eq. 2 depends on the total input light intensity I(t), mode confinement factor Γ, differential gain coefficient a, and photon energy Ep.

3. Experimental demonstration of a LIF neuron

Following the neuron design proposed in [14

14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

], we built a complete setup shown in Fig. 2 that consists of five processing blocks: passive weighting, delay, and summation of inputs; temporal integration; first thresholding stage; inverting, and the second thresholding stage. While the first three have been implemented in [14

14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

], the inversion and the second thresholding stage deserve some additional attention. All-optical inversion, required for this neuron design, typically cannot be performed ideally, but with some error, leading to worsening the contrast between zeroes and ones. This signal degradation is not tolerable at the neuron output since it can lead to computational errors further down the neural network. Therefore, a second thresholding stage is required to improve the signal quality at the output.

Fig. 2 Block diagram of the photonic neuron. G — variable attenuator, T — variable delay line, SOA — semiconductor optical amplifier, HD fiber — heavily GeO2-doped fiber, TOAD — terahertz optical asymmetric demultiplexer.

The full optical implementation of the complete neuron is shown in Fig. 3. The first three blocks are built replicating the setup in [14

14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

]. The entire setup is based on fiber optic components operating in the 1550 nm telecommunication band. For the master pulse source we use a 1.25 GHz mode-locked fiber ring laser. To provide pulse trains at multiple wavelengths, a super-continuum generator is utilized that provides more than 10 nm of available wavelength range, which is then sliced with 200 GHz bandpass filters. Wavelengths of 1551.6 and 1553.2 nm were used as the neuron inputs, and wavelengths of λ1 = 1549.2 nm and λ2 = 1544.8 nm were used to realize gain sampling and inversion, respectively. The width of optical pulses after spectral slicing is about 3 ps FWHM. Two Mach-Zehnder optical modulators and a pattern generator were used for creating the different pulse patterns required to perform measurements. A typical probe pulse energy for SOA gain sampling was from 0.02 to 0.1 of the energy of the input signals, or about 5-20 fJ in absolute units.

Fig. 3 Experimental setup. G — variable attenuator, T — variable delay line, PC — polarization controller, TI — tunable isolator [18], EDFA — erbium-doped fiber amplifier, C — circulator, HD NL fiber — heavily GeO2-doped nonlinear fiber.

The setup contains two all-optical thresholders having design similar to that reported in [18

18. K. Kravtsov, P. R. Prucnal, and M. M. Bubnov, “Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA,” Opt. Express 15, 13114–13122 (2007). [PubMed]

]. This thresholder design provides an efficient cubic transfer function operating at a relatively low power level. The heavily GeO2-doped (HD) fiber used in both thresholders provides a high nonlinear coefficient, and at the same time is easily spliceable with a standard single-mode fiber. The parameters of the HD fiber, measured at λ = 1550 nm, are: nonlinear coefficient 35 W−1 km−1, optical loss 36 dB/km, chromatic dispersion −70 ps/nm km, refractive index difference Δn = 0.11 ([20

20. E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23, 3500–3508 (2005).

], preform 311). The lengths of nonlinear fiber are slightly different in the two thresholders, but their performance is very similar. We believed that both lengths are close to the optimal and small variations of length only slightly affect the threshold power level.

The inverter is based on a conventional TOAD [21

21. J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

]. Pulses from the thresholder are used as the control signal for the TOAD; they create switching windows of 40 ps duration. Sampling pulses at the wavelength λ2 are used as the signal input of the TOAD, and the reflection port of the TOAD is used as the inverter output. Both pulse streams must be synchronized to ensure that the sampling pulses fall into the switching window created by the control pulse stream. In our demonstration, both pulse streams were derived from the same mode-locked laser, and therefore were perfectly synchronized. Spectral filtering is performed with a 200 GHz bandwidth thin film filter, to remove the TOAD control signal at its output. The second wavelength conversion and signal regeneration at the inverter helps to restore the optical signals to their original form, and also makes the output wavelength completely independent of the input wavelengths, allowing for direct feedback of the output signal.

Fig. 4 Signal propagating through the neuron. (A) — input signal, (B) — signal after the integrator, (C) — result of the first thresholding, (D) — inverted sequence, (E) — neuron output.

Although the output signal resembles the input, it is only a reconstruction of the imprint that the incoming signal makes on the SOA. In fact, the original signal is substituted with a new pulse stream two times while propagating through the neuron. Besides the integrator, which is the heart of the neuron, the remainder of the setup is required for sampling the SOA gain, inverting the sampling result, and thresholding, thus reconstructing the original signal.

Another, more complicated, example shows excitation of the neuron by multiple pulses per SOA recovery time. Figure 5 briefly shows neuron operation under this condition. The specially prepared input signal consists of six pulse streams (entering the six neuron inputs) at three wavelengths 1550.0, 1551.6, and 1553.2 nm, schematically shown in Fig. 5a by different colors. The repetition rate for all of the inputs is 622 MHz. All six neuron inputs are divided into two groups such that each wavelength appears in each group. While the pulses in the first group are aligned in time within a few ps, the pulses in the other group have delays of 83 and 67 ps between them. The groups are modulated with a bit sequence “0011” with a one bit delay between them, so that there are four different types of bit periods: with no pulses (the first column in the figure), with pulses only from the second group (the 2nd column), with pulses from the first group only (3rd column), and with pulses from both groups together (4th column). Sampling of the SOA gain is also performed faster than the SOA recovery time. Three sampling pulses spaced by 64 and 72 ps in each bit period are used. The sampling signal is shown in Fig. 5f using the same time scale. Since the bit period is long enough for a complete SOA gain recovery (1600 ps vs. 180 ps recovery time), each bit period can be treated independently, that is, there is no bit-to-bit memory in the SOA.

Fig. 5 Neuron excitation with multiple pulses per integration time. All the graphs show a part of a particular bit period in a sequence with 622 MHz repetition rate. Rows a and b show the model of the input signal and its measured time dependence respectively. c corresponds to the output of the neuron’s integration stage, sampled with three pulses per bit period shown in f. The last row (d) shows a measured thresholder output, equivalent to detection of the smallest pulses in the sequence i.e. detection of the aligned pulse triplets. Part e is a measured eye diagram of the input signal.

The aggregated input signal measured with a 30 GHz bandwidth sampling oscilloscope is shown in Fig. 5b. It is easy to see a direct correspondence between the measured data and the model described above. Figure 5e shows an eye diagram of the input signal. As follows from the diagram, the distance between the aligned pulses of the first group and the first pulse from the second group is about 16 ps. The sampling pulses are aligned such that the first pulse arrives within these 16 ps.

The measured result of the first thresholding is shown in Fig. 5d, where discrimination between the smallest pulses and all others is achieved. This way the neuron is set up to detect the presence of the first (aligned) group of pulses. If it is present, the neuron fires, if not — it does not. Since further inversion and the second thresholding is straightforward, it is not shown in the figure.

As follows from the demonstration, the neuron properly responses to multiple input spikes, which are integrated, sampled and thresholded to produce meaningful output signal pattern.

4. Symmetric neuron with excitatory and inhibitory inputs

The ability to incorporate inhibition into neural circuits is of significant importance from the computational standpoint, from the engineering standpoint of designing stable circuits, and from the empirical neuroscience standpoint where the important role of inhibition in nervous system is well established. A realization of a spiking neuron without ability to incorporate inhibition would be substantially limited in its range of possible applications. In addition to lacking inhibition, the previously reported architecture is somewhat inefficient, because two thresholders are required. This was unavoidable because the second thresholder was needed to counteract the imperfections of the inverter. However, it makes the setup overly complicated and expensive.

A solution of both problems is given in this section. As the SOA is operated in cross gain modulation regime, its output is always inverted with respect to its input. Implementing two successive inversions can restore the original signal, keeping all the other properties the same. Figure 6 schematically shows such a symmetric neuron with both excitatory and inhibitory inputs.

Fig. 6 Schematic of the symmetric photonic neuron with excitatory and inhibitory inputs. The setup consists of two identical SOA integration stages with corresponding passive input circuits, and the thresholder. G — variable gain/attenuation; T — variable time delay. The inset shows an example of signal propagation through the neuron. Each waveform is measured at the certain point in the setup: a and b are excitatory and inhibitory inputs respectively, c is the output of the second integration stage, and d is the neuron output, i.e. the thresholded version of c.

This design is called symmetric because it contains two identical SOAs, which treat the excitatory (first SOA) and inhibitory (second SOA) inputs exactly the same way, providing the same temporal integration and firing properties for both of them. The only difference, which makes one of them excitatory and the other inhibitory, is that the second SOA not only accepts the inhibitory signal, but also inverts the first SOA output, which becomes positive, i.e., working as an excitatory signal. Thus this design has the complete functionality of a neuron and at the same time is simpler than the one discussed above. The thresholder is again required in the output stage to provide discrimination and standardization of the output pulses.

We performed a few simple experiments to demonstrate operation of this symmetric neuron. The inset in Fig. 6 shows the measured waveforms at different points in the setup. In this experiment, the spacings between the pulses (≈1.6 ns) are much larger than the SOA recovery time (≈0.1 ns), so each bit interval can be treated completely independently. Each excitatory pulse (a) increases the potential of the neuron to fire, which results in an increase of the amplitude of the corresponding pulse in the point (c). On the contrary, each inhibitory pulse (b) suppresses the pulses in (c) making them smaller. Thus, the largest pulse in (c) (4th pulse) corresponds to a pulse in (a) and no pulse in (b). Similarly, the smallest pulse in (c) (2nd pulse) comes from no pulse in (a) and a pulse in (b). If both excitatory and inhibitory pulses or neither of them are present (1st and 3rd bit intervals respectively) the resulting pulses in (c) have intermediate sizes. The thresholder is adjusted such that only the tallest pulses in (c) produce output spikes (d). This example shows a situation in which inhibitory pulses can suppress excitatory ones. So the neuron fires only if the excitatory pulse was present and the inhibitory was not. The mode of operation can be changed by modifying the input weights or the threshold level.

A more detailed insight in the neuron behavior is illustrated in Fig. 7. To represent the binary (pulse/no pulse) input sequences we use digits (1 and 0 respectively). The first row shows the excitatory channel input and the second — the inhibitory. The third and the fourth rows display measured waveforms at the output of the first and the second SOAs respectively.

Fig. 7 Measured waveforms at the outputs of the two SOA stages of the neuron shown together with the input data. Column a — only excitatory pulses are sent to the neuron; b — inhibitory pulses only; c — both excitatory and inhibitory pulse streams are provided.

The situation shown in the column a, where no inhibitory pulses are sent to the neuron, allows to see double inversion in the SOAs. The 1st SOA output is an inverted version of the excitatory input, but the second SOA performs another inversion, so its output is positive and matches the provided excitation pattern. Similarly, column b illustrates the action of inhibitory pulses only. As the first SOA output does not depend on the inhibitory input (see the diagram in Fig. 6), it has “all ones” — the inversion of no excitatory pulses. The second SOA takes both the output of the first SOA and the inhibitory channel and provides their inverted version at the output. Consequently, the bottom diagram in the column b is inverted with respect to the inhibitory input. Column c represents both the excitatory and the inhibitory actions together, which is similar to the already discussed case in the inset of Fig. 6.

5. Feedback operation mode

As with inhibition, the ability to incorporate feedback loops into processing architectures using spiking computation primitives is of significant importance from the standpoint of computational power, from the standpoint of engineering cost and efficiency, and from the standpoint of empirical neuroscience since the role and importance of feedback loops in nervous systems is well established. Feedback loops coupled with the ability to reconfigure processing elements provides a natural means for reusing expensive hardware through temporal multiplexing and implementing long and complex processing chains. In the following we show how a chain of optical neurons can be emulated using just one neuron with its output connected to one of its inputs such that the signal passes through the same device many times. The parameters of the neuron can be potentially changed from pass to pass to allow for imitation of different neurons in the chain. Such a trade-off between the number of required neurons and the speed of operation may help in designing more complicated optical neural networks with only several physical neurons available. In this work the simplest case of a feedback mode operation is demonstrated, where neuron parameters stay the same. One of the examples of such operation realized in our study is optical signal buffering in the loop.

The operation of our neuron-based signal buffer is very similar to the previously demonstrated optical loop memory [22

22. T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

, 23

23. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

, 24

24. C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994). [PubMed]

, 25

25. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

] with the only difference that our demonstration involves the photonic neuron. Although the principle of the loop memory is trivial (pulses circulate around the loop and the signal losses are compensated with an amplifier), its practical implementation requires active electronics to help counteract signal distortion and noise amplification. There are several techniques used for this purpose, which serve the two goals: keeping the pulses within allocated time slots and keeping their amplitude at a either “zero” or “one” level. While the latter can be implemented in the optical domain by using optical nonlinearity (e.g. soliton propagation [23

23. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

] or nonlinear polarization rotation [24

24. C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994). [PubMed]

, 25

25. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

]), the first goal typically requires the use of electronics. However, the simplest and the most straightforward technique, which was used in [22

22. T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

], is optical-to-electrical conversion and electronic-based signal detection and retransmission, that we use in this work for the feedback loop.

The principle of operation of the neuron-based storage loop is shown in Fig. 8. In order to store a repeating pulse pattern, it has to be first sent to the neuron through one of its inputs keeping the feedback off (a). Next, the in-loop delay has to be adjusted such that the fed back pattern coincides with the external one (b). This is achieved if the total in-loop delay (including the delay inside the neuron) is a multiple of the pattern length. Then the feedback should be enabled and the input signal may be turned off (c). As the fed back signal now substitutes the external signal, the pattern propagates in the loop without changes.

Fig. 8 Principle of storing data in a neuron-based loop with positive feedback. Three stages of the process are shown.

The block diagram of the experimental setup is shown in Fig. 9. In the setup we use optical-to-electrical conversion with a photodetector and a clock and data recovery (CDR) unit. The rest of the setup is built to realize the functionality shown in the block diagram in Fig. 8. The first input of the neuron takes the MLL pulse train modulated with the data from a pattern generator, and the second takes the pulses modulated using the signal from the output of the neuron. Although the neuron always works with fresh optical pulses from the laser, the data that modulate the pulses in the second input are extracted from the neuron output, providing the feedback. The length of the stored pattern is defined by the total round-trip time in the loop, which is equal to 0.39 microsecond. At the repetition rate used of 1.25 Gbit/s, this makes 485 bit intervals. Therefore, a bit pattern of 485 bit long should be able to stably propagate in the loop without changes, provided the neuron threshold is set to low enough value to allow firing caused by the feedback channel. Even if the external input with the data from the pattern generator is disconnected, the pattern continues its propagation in the loop. This way a bit pattern is stored in the neuron feedback loop.

Fig. 9 Block diagram of the feedback-mode operation of the neuron. Mod — Mach-Zehnder intensity modulator.

In the experiments we are able to “write” a bit pattern into the neuron, sending the modulated pulse train into the first input, and then observing the propagation of the pattern in the loop after the first input is disconnected. Together with the pattern length of 485 bits, it is also possible to store shorter patterns whose length is a factor of 485. A full factorization of 485 is 5 × 97 so the pattern lengths of 5 and 97 bits can also be used. In the Fig. 10 we show examples of the stored bit patterns in the neuron with the feedback. The stability of the feedback mode operation is such that the same pattern can propagate in the loop for hours without changing, which indicates the high reliability of such a configuration involving the neuron, even in a feed forward configuration.

Fig. 10 Examples of the stored bit patterns in the neural feedback loop. The total round-trip time is equal to 485 bit intervals, so patterns of a length of 5, 97, and 485 bits can be stored in this configuration. The diagram shows one example of a 97 bit-long pattern, two examples of different 5-bit patterns, and, in the last column, a 485-bit pattern. The last one, due to its large length, has also a zoomed-in version of its part.

6. Discussion

The two demonstrated photonic neuron configurations and the neural feedback loop show the feasibility of the SOA-based approach in realizing photonic neural networks. However, there are several open questions that require special attention. As biological neurons are very flexible and highly tunable elements, the tunability ranges of artificial neurons are of a great importance. Our approach allows for wide variation of many parameters.

The input circuit that controls delays and weights of incoming signals can be modified in very wide ranges. As for the weights, they can be adjusted very quickly with lithium niobate amplitude modulators, which may have a bandwidth of 40 GHz and more. Their tuning range is at least 20 dB, which can be extended using slower intensity attenuators. The delays are much harder to control on a similar time scale. A fast approach may be in switching the inputs through fiber paths of different lengths, but that requires several electro-optical switches that cause signal attenuation. Low-loss mechanical or MEMS switches are much slower, but can be used for changing the delay in large steps. Relatively slow precise continuous variable delay lines are also acceptable, but they usually have limited range, which is defined by their physical sizes.

The integration time and the threshold level adjustments are also possible in the proposed neuron design. The first is directly connected with the type of SOA used and its driving current. The higher the driving current the faster the gain recovery, i.e., the shorter the integration time. The two types of commercially available SOAs that we use cover a range of recovery times from less than 100 ps to approximately 500 ps. Going towards shorter integration constants is also possible because there are much faster SOAs commercially available, whose recovery time is as short as 25 ps. The second parameter, the threshold level, is also tunable. Although the threshold level of the thresholder itself is defined by the nonlinear element and is therefore fixed, the effective threshold level is adjustable via changing the gain in the erbium-doped fiber amplifier preceding the thresholder.

Another problem is connected with signal representation in our neuron model. First of all, as an optical signal is used instead of voltage, there is an additional degree of freedom in choosing a wavelength of operation. To prevent signal interference and coherent effects between neuron’s inputs they all should use different wavelengths. At the same time, SOA gain sampling requires a sampling wavelength, which is different from all the input wavelengths. Though this poses limitations on the network design, its impact is minimized because the output wavelength of each neuron can be chosen independently of the input wavelengths, thanks to the “double wavelength conversion” in the proposed setup. Besides wavelength issues, the pulsed nature of optical signals is somewhat different from the original spiking neuron model. Since pulses are not produced by our neuron itself, but rather are modulated by it, they retain the synchronous pattern of the pulse source used. Proper operation of the neuron thus requires that pulse spacings are smaller than the SOA recovery time, so every gain drop is guaranteed to be sampled. It is believed that by increasing the sampling rate we can eliminate this imperfection.

Another network level problem that we did not address so far in our study is learning mechanisms. This important feature would require an external electronic circuit that controls weights, delays and other neuron parameters. On the way towards fully all-optical neural network realization, learning is another open avenue for research.

7. Conclusions

We present an optical approach to realization of spiking neurons. Two types of integrate-and-fire photonic neurons are demonstrated experimentally. Because the governing equations for a standard integrate-and-fire neuron model and the SOA, the processing core of its photonic realization, are identical, a proper integration behavior is observed experimentally. The analog properties of the demonstrated neuron make it well suited for efficient signal processing applications, while its digital properties make it possible to implement complex computations without excessive noise accumulation. The demonstrated neural feedback loop imitates neuron behavior in an optical neural network.

While the fastest timescale on which biological neurons operate is in the order of milliseconds, the experimentally demonstrated optical integrate-and-fire device operates on picosecond width pulses, and has an integration time constant in the order of 100 ps, which is at least 108 faster. Reconfiguration of device parameters enables it to perform a wide variety of signal processing and decision operations.

Acknowledgments

This work was supported by the Lockheed Martin Advanced Technology Laboratory and by the Defense Advanced Research Projects Agency (DARPA) under contract MDA972-03-1-0006.

References and links

1.

C.-H. Wang and B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990). [PubMed]

2.

A. V. Grigor’yants and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994). [Sov. J. Quantum Electron. 24, 469–470 (1994)].

3.

S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).

4.

E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).

5.

G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).

6.

M. T. Hill, E. E. E. Frietman, H. de Waardt, G.-d. Khoe, and H. J. S. Dorren, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).

7.

G. Moagar-Poladian and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).

8.

R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007). [PubMed]

9.

G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006). [PubMed]

10.

R. Pashaie and N. H. Farhat, “Optical realization of bioinspired spiking neurons in the electron trapping material thin film,” Appl. Opt. 46, 8411–8418 (2007). [PubMed]

11.

A. R. S. Romariz and K. H. Wagner, “Tunable vertical-cavity surface-emitting laser with feedback to implement a pulsed neural model. 1. Principles and experimental demonstration,” Appl. Opt. 46, 4736–4745 (2007). [PubMed]

12.

A. R. S. Romariz and K. H. Wagner, “Tunable vertical-cavity surface-emitting laser with feedback to implement a pulsed neural model. 2. High-frequency effects and optical coupling,” Appl. Opt. 46, 4746–4753 (2007). [PubMed]

13.

S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).

14.

D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).

15.

C. Koch, Biophysics of Computation (Oxford University Press, 1999).

16.

W. Maass and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).

17.

R. Sarpeshkar, “Analog versus digital: Extrapolating from electronics to neurobiology,” Neural Comput. 10, 1601–1638 (1998). [PubMed]

18.

K. Kravtsov, P. R. Prucnal, and M. M. Bubnov, “Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA,” Opt. Express 15, 13114–13122 (2007). [PubMed]

19.

M. Premaratne, D. Nešić, and G. P. Agrawal, “Pulse amplification and gain recovery in semiconductor optical amplifiers: A systematic analytical approach,” J. Lightwave Technol. 26, 1653–1660 (2008).

20.

E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23, 3500–3508 (2005).

21.

J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).

22.

T. Aida and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett 27, 1544–1546 (1991).

23.

M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett 29, 729–730 (1993).

24.

C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994). [PubMed]

25.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

OCIS Codes
(190.4360) Nonlinear optics : Nonlinear optics, devices
(200.4260) Optics in computing : Neural networks
(200.4700) Optics in computing : Optical neural systems

ToC Category:
Optics in Computing

History
Original Manuscript: November 3, 2010
Manuscript Accepted: January 10, 2011
Published: January 20, 2011

Citation
Konstantin S. Kravtsov, Mable P. Fok, Paul R. Prucnal, and David Rosenbluth, "Ultrafast All-Optical Implementation of a Leaky Integrate-and-Fire Neuron," Opt. Express 19, 2133-2147 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2133


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References

  1. C.-H. Wang, and B. K. Jenkins, “Subtracting incoherent optical neuron model: analysis, experiment, and applications,” Appl. Opt. 29, 2171–2186 (1990). [PubMed]
  2. A. V. Grigor’yants, and I. N. Dyuzhikov, “Formation of a neuron-like pulsed response in a semiconductor resonator cavity with competing optical nonlinearities,” Kvant. Elektron. 21, 511–512 (1994) (Sov. J. Quantum Electron. 24, 469–470 (1994)).
  3. S. Tariq, M. K. Habib, and H. A. Helmy, “Opto-electronic neuron-type operation via stimulated Raman scattering in optical fiber,” J. Lightwave Technol. 15, 938–947 (1997).
  4. E. C. Mos, J. J. L. Hoppenbrouwers, M. T. Hill, M. W. Blum, J. J. H. B. Schleipen, and H. de Waardt, “Optical neuron by use of a laser diode with injection seeding and external optical feedback,” IEEE Trans. Neural Netw. 11, 988–996 (2000).
  5. G. Moagar-Poladian, “Reconfigurable optical neuron based on photoelectret materials,” Appl. Opt. 39, 782–787 (2000).
  6. M. T. Hill, E. E. E. Frietman, H. de Waardt, G.-d. Khoe, and H. J. S. Dorren, “All fiber-optic neural network using coupled SOA based ring lasers,” IEEE Trans. Neural Netw. 13, 1504–1513 (2002).
  7. G. Moagar-Poladian, and M. Bulinski, “Optical reconfigurable neuron by using the transverse Pockels effect,” J. Optoelectron. Adv. Mater. 4, 929–936 (2002).
  8. R. J. Vogelstein, U. Mallik, J. T. Vogelstein, and G. Cauwenberghs, “Dynamically reconfigurable silicon array of spiking neurons with conductance-based synapses,” IEEE Trans. Neural Netw. 18, 253–265 (2007). [PubMed]
  9. G. Indiveri, E. Chicca, and R. Douglas, “A VLSI array of low-power spiking neurons and bistable synapses with spike-timing dependent plasticity,” IEEE Trans. Neural Netw. 17, 211–221 (2006). [PubMed]
  10. R. Pashaie, and N. H. Farhat, “Optical realization of bioinspired spiking neurons in the electron trapping material thin film,” Appl. Opt. 46, 8411–8418 (2007). [PubMed]
  11. A. R. S. Romariz, and K. H. Wagner, “Tunable vertical-cavity surface-emitting laser with feedback to implement a pulsed neural model. 1. Principles and experimental demonstration,” Appl. Opt. 46, 4736–4745 (2007). [PubMed]
  12. A. R. S. Romariz, and K. H. Wagner, “Tunable vertical-cavity surface-emitting laser with feedback to implement a pulsed neural model. 2. High-frequency effects and optical coupling,” Appl. Opt. 46, 4746–4753 (2007). [PubMed]
  13. S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Excitability in optical systems close to Z2-symmetry,” Phys. Lett. A 374, 739–743 (2010).
  14. D. Rosenbluth, K. Kravtsov, M. P. Fok, and P. R. Prucnal, “A high performance photonic pulse processing device,” Opt. Express 17, 22767–22772 (2009).
  15. C. Koch, Biophysics of Computation (Oxford University Press, 1999).
  16. W. Maass, and C. M. Bishop, eds., Pulsed Neural Networks (The MIT Press, 1999).
  17. R. Sarpeshkar, “Analog versus digital: Extrapolating from electronics to neurobiology,” Neural Comput. 10, 1601–1638 (1998). [PubMed]
  18. K. Kravtsov, P. R. Prucnal, and M. M. Bubnov, “Simple nonlinear interferometer-based all-optical thresholder and its applications for optical CDMA,” Opt. Express 15, 13114–13122 (2007). [PubMed]
  19. M. Premaratne, D. Neˇsi’c, and G. P. Agrawal, “Pulse amplification and gain recovery in semiconductor optical amplifiers: A systematic analytical approach,” J. Lightwave Technol. 26, 1653–1660 (2008).
  20. E. M. Dianov, and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23, 3500–3508 (2005).
  21. J. P. Sokoloff, P. R. Prucnal, I. Glesk, and M. Kane, “A terahertz optical asymmetric demultiplexer (TOAD),” IEEE Photon. Technol. Lett. 5, 787–790 (1993).
  22. T. Aida, and P. Davis, “Storage of optical pulse data sequences in loop memory using multistable oscillations,” Electron. Lett. 27, 1544–1546 (1991).
  23. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya, “Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains,” Electron. Lett. 29, 729–730 (1993).
  24. C. R. Doerr, W. S. Wong, H. A. Haus, and E. P. Ippen, “Additive-pulse mode-locking/limiting storage ring,” Opt. Lett. 19, 1747–1749 (1994). [PubMed]
  25. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).

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