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

Abstract

The human brain is a complex integrated spatiotemporal system, where space (which neuron fires) and time (when a neuron fires) both carry information to be processed by cognitive functions. To parallel the energy efficiency and computing functionality of the brain, methodologies operating over both the space and time domains are thus essential. Implementing spatiotemporal functions within nanoscale devices capable of synaptic plasticity would contribute a significant step toward constructing a large-scale neuromorphic system that emulates the computing and energy performances of the human brain. We present a neuromorphic approach to brain-like spatiotemporal computing using resistive switching synapses. To process the spatiotemporal spike pattern, time-coded spikes are reshaped into exponentially decaying signals that are fed to a McCulloch-Pitts neuron. Recognition of spike sequences is demonstrated after supervised training of a multiple-neuron network with resistive switching synapses. Finally, we show that, due to the sensitivity to precise spike timing, the spatiotemporal neural network is able to mimic the sound azimuth detection of the human brain.

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 I_C, where a large I_C 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 V_axon (middle), and POST internal potential V_int (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 V_axon and V_TE for relatively short (left) and long (right) delays Δt = t_PRE − t_POST 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 I_C driven by the exponential V_axon. (B) Relative change of synaptic weight G/G₀ as a function of Δt for potentiation (V_TE > 0) and depression (V_TE < 0). The weight change decreases for increasing Δt, thus evidencing STDP behavior of the 1T1R synapse. The peak value of V_axon was 2.5 V with time constant τ = 8 ms. The TE voltage was V_TE+ = 3 V for potentiation and V_TE− = −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 V_int 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 V_int for all possible test sequences of four spikes out of 16 channels after training. Sequences are ordered from the highest to the lowest V_int. The true pattern 1-4-9-16 induces the highest V_int, 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 V_int, while dissimilar patterns show low V_int. (B) Evolution of V_int 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, V_int 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 V_int 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 ΔV_int 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) V_int for the two POSTs with their corresponding difference. The difference ΔV_int 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 ΔV_int 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.