Table 2.

The energy scaling for all the operations is given.

Operation	Analog energy scaling	Digital energy scaling	Repetitions per batch
MATRIX OPERATIONS
Multiplication: A(t)T × yk	O(N × M)	O(N3∕2 ×M3∕2)	p
Multiplication: A(t) × xk	O(N × M)	O(N3∕2 ×M3∕2)	p
Multiplication/Training: $\left(y_k-A(t)x_k\right)\times \text{sgn}{(x_k)}^T$	O(N × M)	O(N3∕2 × M3∕2)	p
VECTOR OPERATIONS
Threshold: thresholdC $\left(A{(t)}^T{y}_k\right)$	O(N × 2b)	O(N × b)	p
Subtraction: yk − A(t)xk	O(M × 2b)	O(M × b)	p
Sign function: sgn(xk)	O(N × 2b)	O(N × b)	P
COMMUNICATION
Vector: (yk − A(t)xk)	O(N × M)	O(N1∕2 × M3∕2)	P
Vector: sgn(xk)T	O(M × N)	O(N3∕2 × M1∕2)	P
Matrix: g(t)	O(N2 × M)	O(N3∕2 × M3∕2)	1
SERIAL OPERATIONS
Read: g(t)	O(N2 × M)	O(N3∕2 × M3∕2)	1
Write: $A(t+1)=A(t)-\frac{\eta }{p}g(t)$(t)	O(N2 × M)	O(N3∕2 × M3∕2)	1

We consider the finite precision case such that 2^b < M.