BSB training circuit

Figure. 51(a) summarizes the operational flow of the BSB training circuit. And the corre- sponding circuit diagram is illustrated in Figure.51(b). Our goal is to develop a method to train the memristor cross-point arrays as auto-associative memories for prototype patterns. The training scheme leverages the recall circuit to verify the training result and generate the control signals.

Step 1 : Initializing the crossbar arrays. At the beginning of a training procedure, all memristance values in M1 and M2 are initialized to an intermediate value. The initial-

ization does not have to be precisely accurate. Indeed, even when all of the memristors are all at either LRS or HRS, the crossbar arrays can still be successfully trained but it requires more time to reach convergence. For instance, training from HRS takes about 2,500 iter- ations under the setup of Experiment 1 in Section XXX, while initializing the memristors to intermediate states within their memristance range can reduce the iteration number to about 1,000.

Step 2 : Selecting a prototype pattern γ(k) _{∈ B}n_{(k = 1, . . . , m). Here, B}n _{is the}

n-dimension binary space (−1, 1). Assume a training set includes m prototype patterns and each pattern γ(k) _{has the same probability to be chosen every time. The counter ST is used}

to record in sequence the number of patterns that have been successfully trained. When ST¿0, those patterns that have been trained are excluded from the selection.

Step 3 : Sending γ(k) _{to the BSB recall circuit. We convert γ}(k) _{in binary space}

(−1, 1) to a set of input voltages within the boundary (−0.1V , 0.1V ). These input signals are supplied to the two memristor cross-point arrays simultaneously. The resulting signals VO can be obtained at the output of the BSB recall circuit.

Step 4 : Error detection. An error is defined as the difference between the prototype pattern and the recall result; that is, the difference between the input and output signals of the recall circuit. A piece of error detection circuitry for bit i is shown in Figure. 51(c), which generates only the direction of the weight change based on the simplified algorithm in Section 6.1.2. In total, N pieces of error detection blocks are needed for an N -by-N cross-point array.

VA+(t) VA-(t) M1 M2 SUM AMP SUM AMP SUM AMP vA+,i(t) vA-,i(t) vi(t) vi(t+1) V(t+1) COMP vi(t+1) COMP COMP vbn -vbn vconv -vbn vbn R4 R5 R6 R7 vi(t+1) R1 R2 R3 vA+,i(t) vi(t) vA-,i(t) V(0) ^ ^ ^ ^ ^ ^

Figure 51: Embedded BSB training circuit: (a) training flow; (b) conceptual circuit diagram; (c) error detection circuit.

Considering that the range of Vout(i) could be different from that of Vin(i), we apply

a scalar λ to the input vector and take λ · Vin(i) as the target output signal. Rather than

generating λ·Vin(i) in every training, we use the preset threshold voltages for error detection.

Since Vin(i) is either 0.1V or −0.1V , four thresholds are needed, including

V+th h = 0.1λ + θ, V+th l = 0.1λ − θ

V−th h = 0.1λ − θ, V−th l = 0.1λ + θ

. (6.11)

Here, θ represents the tolerable difference.

The error detection output Dif f (i) could be −1, 0, or 1. When |Vout(i)λ · Vin(i)| < θ,

Dif f (i) = 0, meaning the difference between the normalized Vin(i) and Vout(i) are so small

that we consider them logically identical. Otherwise, Dif f (i) = +1 or −1, indicating the normalized |Vout(i)| is greater or less than the normalized |Vin(i)|, respectively.

Step 5 : Training memristor crossbar arrays. If Diff is not a zero vector, which means some error has been detected, the crossbar arrays need to be further tuned. The training signal generation is based on the training rule in Eq. 6.8. In order to control the training step with a finer granularity, we modify only one memristor crossbar each time. For example, one could train M1 or M2 when the iteration number is odd or even, respectively.

The weight updating of a memristor crossbar array is conducted by columns, during which constant voltage pulse signals are applied to M1 or M2. Note that the real resistance change

of a memristor is also determined by its array location and device characteristics. In the de- sign, such difference can be compensated by properly controlling the amplitude/width/shape of training pulses and paying more training iterations.

The polarity of the training pulse for the jth column are determined by Dif f (j). The design supplies the training pulses on all the rows of a memristor crossbar. The jth column is connected to ground and all the others are supplied with half of the training voltage. For M1,

the training pattern is either the current selected prototype pattern γ(k) _{(if Dif f (j) = 1)}

or its element-wise negated version (if Dif f (j) = −1). The training signals to M1 and M2

have opposite polarities. That is, the training pattern of M2 uses the current prototype

Note that the mapping method uses M1 and M2 to represent the positive and negative

terms of the BSB connection matrix, respectively. However, the proposed training scheme operated in real design circumstance cannot and does not have to guarantee an identical mapping to software generated matrix. In fact, what matters most is the overall effect of M1 and M2, not exact memristance values in each individual crossbar array.

Step 6 : If training is completed? The counter ST increases by 1 if a prototype pattern goes through Steps 2 ∼ 5 and reports no error without further tuning M1 and M2.

Otherwise, ST is reset to 0 whenever an error is detected and all of the patterns in Bn are available in Step 2. ST= m means the entire training set has been successfully “learned” and hence the training stops.