Anticipative Tracking with the Short-Term Synaptic Plasticity of Spintronic Devices

Real-time tracking of high-speed objects in cognitive tasks is challenging in the present artificial intelligence techniques because the data processing and computation are time consuming, resulting in impeditive time delays. A brain-inspired continuous attractor neural network (CANN) can be used to track fast moving targets, where the time delays are intrinsically compensated if the dynamical synapses in the network have short-term plasticity. Here, we show that synapses with short-term depression can be realized by a magnetic tunnel junction, which perfectly reproduces the dynamics of the synaptic weight in a widely applied mathematical model. Then, these dynamical synapses are incorporated into one-dimensional and two-dimensional CANNs, which are demonstrated to have the ability to predict a moving object via micromagnetic simulations. This portable spintronics-based hardware for neuromorphic computing needs no training and is therefore very promising for the tracking technology of moving targets.

Figure 1

(a) Schematic of the 1D CANN. The black circles represent the neurons located at position ${\mathbf{x}}_i=(\cos {\theta }_i,\sin {\theta }_i)$. When external stimuli $I^{\mathrm{ext}}(t)$ move along the chain of neurons, the firing rate $r(t)$ of neurons is determined by the external input and the signal received from other neurons. The light-green line is the unidirectional connection, which allows the output of the $i\mathrm{th}$ neuron to be transmitted to the $j\mathrm{th}$ neuron, as indicated by Eq. (2). (b) The hardware implementation of a synapse consisting of a constant component and a dynamical component with STD. The constant weight $J_{ij}$ is modeled by an electric resistor, and the dynamical synapse $p_i$ is simulated by a MTJ. GND represents the ground in the circuit.

Figure 2

(a) Schematic illustration of a MTJ consisting of a fixed $\mathrm{Co}\mathrm{Fe}\mathrm{B}$ layer, insulating $\mathrm{Mg}\mathrm{O}$ layer, and free $\mathrm{Co}\mathrm{Fe}\mathrm{B}$ layer from bottom to top. The upward magnetization of the fixed layer is pinned by exchange bias from an antiferromagnetic substrate, and the free layer has an in-plane magnetic anisotropy, which precesses under an injected electric current. (b) Calculated electrical resistance of the MTJ as a function of time. The injected current density is $8\times {10}^7{\mathrm{A/m}}^2$ from $t=20$ to $30$ ns and $4\times {10}^7{\mathrm{A/m}}^2$ otherwise. The red line represents the average resistance $\overline{R}$ as a function of time. (c) Average resistance $\overline{R}$ as a function of the current density for stable oscillation. The yellow shaded region is the current density range used in this work.

Figure 3

(a) Current density injected into the MTJ as a function of time to drive the magnetization precession of the free layer. (b) Calculated average resistance $\overline{R}$ of the MTJ due to the precessional motion of the free-layer magnetization. At $t\le 20$ ns, the MTJ is at the steady oscillatory state with $j=4\times {10}^7{\mathrm{A/m}}^2$, and $\overline{R}$ is a constant. Average resistance $\overline{R}$ increases and decreases gradually with increasing or decreasing $j$, indicating the short-term memory effect. (c) Synaptic efficacy $p$ obtained from the calculated $\overline{R}$ using Eq. (8) as a function of time (red solid line). The open black circles are the efficacy of a dynamic synapse, which is the solution of phenomenological Eq. (9). The firing rate is denoted by the blue dashed line. The parameters $\tau =25$ ns and $\tilde{\eta }=0.79$ are used in Eq. (9).

Figure 4

(a)–(e) Anticipative tracking in the 1D CANN. The external signal (red solid line) with a Gaussian-type distribution moves from left to right. The firing rate of neurons is plotted as the blue solid line, which is ahead of the external signal at $t>100$ ns. The green dashed line represents the firing rate of the neurons without MTJs as the dynamic synapses for comparison. The green bump shows delayed tracking since it always follows the external signal with a finite delay in position. (f) The central positions of the external signal (red line) and the firing rate bump (blue line) as a function of time. Inset: the magnified plot at small $t$.

Figure 5

The phase diagram of the 1D CANN. The external signal moves with a constant angular velocity ${\omega }_{\mathrm{ext}}=0.005$ rad/ns (a) and ${\omega }_{\mathrm{ext}}=0.01$ rad/ns (b). The graph shows the tracking performance of the network achieved by varying the STD strength $\eta$ and the inhibition strength $k$. It is examined by comparing the central positions of the firing rate bump and the external signal at $t=80$ ns.

Figure 6

(a)–(c) Schematic illustration of the computational process of the 2D CANN. The $544\times 960$-pixel frames of the recorded video are first converted into an external input matrix by integrating every group of $32\times 32$ pixels into one matrix element. Every element containing the orange rolling ball is set as 0.8, while the others are set as 0. The dimensions of the 2D CANN are $N_{\mathrm{NW}}\times N_{\mathrm{NH}}=27\times 40$, including additional elements on each side of the boundary to avoid a technical problem due to the broken translational symmetry. After the computation using the 2D CANN, the location of the maximum firing-rate value is determined using cubic spline interpolation. This location represents the predicted moving direction of the rolling ball. (d)–(g) Illustration of the prediction. The red circles are the real-time predictions at given frames, which closely follow the real trajectory of the rolling ball indicated by the white dashed line.