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Fig. 5. Results with frequency of 0.5 GHz, simulation time: 100 ns, amplitude power: 5mW, delay: 6.25 ps, fixed input-output weights, SOA input current: 80 mA, 25 nodes: (left) — photonic reservoirs with and without feedback, (right) — classical reservoirs versus photonic reservoirs with feedback

Figure 5 Results with frequency of 0.5 GHz, simulation time: 100 ns, amplitude power: 5mW, delay: 6.25 ps, fixed input-output weights, SOA input current: 80 mA, 25 nodes: (left) — photonic reservoirs with and without feedback, (right) — classical reservoirs versus photonic reservoirs with feedback

Related Figures (5)

The reservoir cou the signal into a spa any recurrent neura the network should d be seen as an integration of the temporal correlations in tial correlation in the reservoir state. This is not to say that network will do. Rather, it appears that the dynamics of be in the dynamic region which corresponds to the edge of stability [IJ]. The dynamics depend on the amount of gain and losses in the network and they should be balanced. If the network is over-damped there is no memory inside t chaotically. he reservoir, if it is under-damped the network will react
The reservoir cou the signal into a spa any recurrent neura the network should d be seen as an integration of the temporal correlations in tial correlation in the reservoir state. This is not to say that network will do. Rather, it appears that the dynamics of be in the dynamic region which corresponds to the edge of stability [IJ]. The dynamics depend on the amount of gain and losses in the network and they should be balanced. If the network is over-damped there is no memory inside t chaotically. he reservoir, if it is under-damped the network will react
Fig. 2. (left) tanh for analog ANN — (right) SOA: steady state Because the specifications for the reservoir do not seem to be very rigid, the choice of possible nanophotonic components was vast. We opted for coupled Semiconductor Optical Amplifiers (SOA), based on two observations. First of all, the steady-state curve of an SOA resembles the S-curve used in analog neural networks (figure [2}) — at least for the upper branch, but since optical power is non-negative this is a restriction we have to cope with. This resemblance made SOAs more likely to be able to bridge the reservoir and the photonic world. The dynamic behavior of an SOA is however more complex in comparison to the classical analog implementations. The carrier dynamics come into play at high data rates and because of this a reservoir of SOAs is a middle ground between simple nodes with a complex network (the classical tanh reservoirs) and one very complex node. Second, SOAs are broadband which makes the communication between different nodes less critical as would be the case with resonating structures.
Fig. 2. (left) tanh for analog ANN — (right) SOA: steady state Because the specifications for the reservoir do not seem to be very rigid, the choice of possible nanophotonic components was vast. We opted for coupled Semiconductor Optical Amplifiers (SOA), based on two observations. First of all, the steady-state curve of an SOA resembles the S-curve used in analog neural networks (figure [2}) — at least for the upper branch, but since optical power is non-negative this is a restriction we have to cope with. This resemblance made SOAs more likely to be able to bridge the reservoir and the photonic world. The dynamic behavior of an SOA is however more complex in comparison to the classical analog implementations. The carrier dynamics come into play at high data rates and because of this a reservoir of SOAs is a middle ground between simple nodes with a complex network (the classical tanh reservoirs) and one very complex node. Second, SOAs are broadband which makes the communication between different nodes less critical as would be the case with resonating structures.
Fig. 3. Two topologies: (left) a feed-forward network — (right) a waterfall network with feedback connections (long dash) at the edges The classical reservoir implementations with neural networks have random inter- connection topologies. Since the standard optical chip is still 2D we investigated structures that can be realized without intersections. Two of those structures are depicted in figure [3] The left structure is a waterfall system which acts as a nonlinear delay-line. Although this feed-forward topology is relatively simple, it has already been successfully used to model nonlinear systems [15]. The other network has feedback connections on the sides in order to avoid crossings. Since the SOAs are modeled as unidirectional, the connections are too.
Fig. 3. Two topologies: (left) a feed-forward network — (right) a waterfall network with feedback connections (long dash) at the edges The classical reservoir implementations with neural networks have random inter- connection topologies. Since the standard optical chip is still 2D we investigated structures that can be realized without intersections. Two of those structures are depicted in figure [3] The left structure is a waterfall system which acts as a nonlinear delay-line. Although this feed-forward topology is relatively simple, it has already been successfully used to model nonlinear systems [15]. The other network has feedback connections on the sides in order to avoid crossings. Since the SOAs are modeled as unidirectional, the connections are too.
Fig. 4. Pattern recognition task: a) Input signal with different transitions between the rectangular and triangular waveform b) desired output c) state (i.e. optical power level) of some of the reservoir nodes d) The approximation (blue) of the desired output (black) by the readout function, e) final output of the system (red)
Fig. 4. Pattern recognition task: a) Input signal with different transitions between the rectangular and triangular waveform b) desired output c) state (i.e. optical power level) of some of the reservoir nodes d) The approximation (blue) of the desired output (black) by the readout function, e) final output of the system (red)
Fig. 6. This figure shows the influence of the reservoir size on the performance of the classical and photonic reservoirs (with feedback)
Fig. 6. This figure shows the influence of the reservoir size on the performance of the classical and photonic reservoirs (with feedback)
Related topics:
Machine LearningReservoir ComputingSEMICONDUCTOR OPTICAL AMPLIFIEROptical Signal Processing
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