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Learning of spatiotemporal patterns in a spiking neural network with resistive switching synapses

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Science Advances  12 Sep 2018:
Vol. 4, no. 9, eaat4752
DOI: 10.1126/sciadv.aat4752
  • Fig. 1 Illustrative scheme of biological and hardware neural networks.

    (A) Illustration of a biological neural subsystem with PREs connected with a POST via plastic synapses. PREs spike by generating an action potential along its axon and through the synapse. PREs spiking at various times form a spatiotemporal spiking pattern. (B) The biological synapse can be represented by a RRAM device, where the conductivity changes by voltage-induced ion migration and corresponding formation/dissolution of a conductive filament. (C) Typical current-voltage (I-V) curves of the RRAM device, where a positive voltage applied to the TE causes set transition (resistance change from HRS to LRS) and a negative voltage causes reset transition (resistance change from LRS to HRS). The transition to LRS is controlled by the compliance current IC, where a large IC results in a high conductance of the LRS, thus enabling time-dependent potentiation of the RRAM synapse. (D) Schematic diagram of a 1T1R synapse, connecting a PRE axon to the POST, the latter providing a feedback spike for potentiation and depression.

  • Fig. 2 Recognition of spatiotemporal patterns.

    (A) Schematic SNN with three PREs and one POST. Increasing weights w1 = 10 μs, w2 = 20 μs, and w3 = 50 μs were assumed in the simulation. (B) Conceptual scheme of a spatiotemporal network where the synaptic weight increases from synapse #1 to synapse #3, and PRE spikes have different timing. (C) Calculated PRE spikes (top), axon potential Vaxon (middle), and POST internal potential Vint (bottom), and spike sequence 1-2-3 with spike times T1 = {t1 = 2 ms, t2 = 4 ms, t3 = 6 ms}. (D) Same as (C), but for the opposite spike sequence, namely, 3-2-1 with spike times T2 = {t1 = 6 ms, t2 = 4 ms, t3 = 2 ms}. The POST internal potential overcomes the threshold in (C) due to the positive correlation between synaptic weights and spike timing, thus enabling spatiotemporal recognition.

  • Fig. 3 Time-dependent potentiation and depression.

    (A) Measured Vaxon and VTE for relatively short (left) and long (right) delays Δt = tPREtPOST between PRE and POST spikes (top) and corresponding change of the synaptic weight (bottom). Short and long delays lead to a strong and weak potentiation, respectively, due to the variation of IC driven by the exponential Vaxon. (B) Relative change of synaptic weight G/G0 as a function of Δt for potentiation (VTE > 0) and depression (VTE < 0). The weight change decreases for increasing Δt, thus evidencing STDP behavior of the 1T1R synapse. The peak value of Vaxon was 2.5 V with time constant τ = 8 ms. The TE voltage was VTE+ = 3 V for potentiation and VTE− = −1.6 V for depression. Calculation results (lines) obtained by a physical-based analytical RRAM model accurately describe the experimental behavior.

  • Fig. 4 Experimental learning of spatiotemporal patterns.

    (A) Schematic illustration of the input spike patterns submitted to a 16 × 1 spatiotemporal neuromorphic network supervised by a teacher signal. The network consists of 16 PREs, 1 POST, and 16 RRAM synapses. PRE spikes are grouped in spatiotemporal patterns of four spikes, which form a training cycle. For the true sequence 1-4-9-16 (cycle i), the teacher spike is submitted to the POST to guide potentiation/depression. (B) Teacher signal and measured Vint during the training experiment, and (C) true fire, false fire, and false silence events occurring during training. (D) Color plot of the evolution of the synaptic weights. False silence events lead to synaptic potentiation of the synapses #1, #4, #9, and #16, while false fire events cause synaptic depression. After training, the synapses #1, #4, #9, and #16 are found in LRS with increasing weight, as a result of time-dependent potentiation, while other synapses are found in HRS.

  • Fig. 5 Experimental recognition of spatiotemporal patterns.

    (A) Measured Vint for all possible test sequences of four spikes out of 16 channels after training. Sequences are ordered from the highest to the lowest Vint. The true pattern 1-4-9-16 induces the highest Vint, confirming the high learning efficiency of the WH supervised learning scheme. Patterns with high similarity with the true sequence (for example, permutations of the true pattern) also show relatively high Vint, while dissimilar patterns show low Vint. (B) Evolution of Vint in response to the application of the true pattern 1-4-9-16, and (C) of a false pattern 16-7-4-1. For the true pattern, Vint shows accumulation of spikes eventually exceeding the threshold for POST fire, whereas weaker accumulation and no fire are seen for the false sequence. The evolutionary accumulation of Vint resembles the EPSP observed in a biological neural system.

  • Fig. 6 Sound location via spatiotemporal processing.

    (A) Schematic illustration of binaural effect, where the ITD provides an estimate of the direction of the sound propagation with respect to the listener. (B) Schematic structure of a 2 × 2 SNN to detect the sound direction from the ITD. The difference ΔVint between internal potentials in the two POSTs serves as the output of the network, providing information about sound direction. The inset shows the map of synaptic weights in the 2 × 2 synapse array, which enables discrimination between different directions. (C) Experimental sound waveforms of left and right ears, (D) corresponding axon potential of the two PREs, and (E) Vint for the two POSTs with their corresponding difference. The difference ΔVint in correspondence to the second PRE spike reveals the direction of the sound from the right of the listener in (C). (F) Measured and calculated ΔVint as a function of sound azimuth revealing analog information about the sound propagation direction. To correct for the different axon potential decay constant (τ = 8 ms in the hardware circuit, compared to a biological time τ = 0.5 ms), the experimental time scale in (F) was reduced by a factor of 16.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaat4752/DC1

    Note S1. STDP characteristics of single RRAM synapse.

    Note S2. Inference of the network.

    Note S3. Learning algorithm.

    Note S4. Hardware implementation of POSTs and weight updates.

    Fig. S1. Coding methods in SNN.

    Fig. S2. Neuron and axon circuits.

    Fig. S3. STDP experiments.

    Fig. S4. Hardware implementation of the SNN.

    Fig. S5. Simulation of supervised learning of spatiotemporal patterns.

    Fig. S6. Experimental demonstration of spatiotemporal learning.

    Fig. S7. Convergence of the network training for various initial conditions.

    Fig. S8. Synaptic weight for various initial conditions.

    Fig. S9. Comparison between POST potential and DL distance.

  • Supplementary Materials

    This PDF file includes:

    • Note S1. STDP characteristics of single RRAM synapse.
    • Note S2. Inference of the network.
    • Note S3. Learning algorithm.
    • Note S4. Hardware implementation of POSTs and weight updates.
    • Fig. S1. Coding methods in SNN.
    • Fig. S2. Neuron and axon circuits.
    • Fig. S3. STDP experiments.
    • Fig. S4. Hardware implementation of the SNN.
    • Fig. S5. Simulation of supervised learning of spatiotemporal patterns.
    • Fig. S6. Experimental demonstration of spatiotemporal learning.
    • Fig. S7. Convergence of the network training for various initial conditions.
    • Fig. S8. Synaptic weight for various initial conditions.
    • Fig. S9. Comparison between POST potential and DL distance.

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