Fig. 4: RNS-based AIMC architectures.
From: Achieving high precision in analog in-memory computing systems
a Concept scheme of RNS-based representation of integers {0, …, 29} using the moduli set {5,6}. Each integer is uniquely identified by a set of remainders with respect to the moduli set, with e.g., 8 corresponding to {2,3}. b Number of required moduli and (c) corresponding moduli bit-width as a function of the bit-width of partial multiplications aij × bj and matrix size. d Concept scheme of in-memory RNS. Remainders of the problem matrix A and input vector b against a set of coprime moduli {m1, m2, m3} are first computed and forwarded to separate AIMC macros. Partial analog results are converted to the digital domain under the corresponding modulo. In the final reconstruction stage, the CRT identifies the unique number associated with the computed remainders. e The moduli set can be augmented with additional coprime moduli to create redundant moduli sets. Multiple candidate results are reconstructed by randomly grouping the available moduli and forwarded to a decision logic, typically implemented by majority voting, to mitigate the impact of burst-type errors. f Alternatively, non-coprime moduli sharing a common divisor k can be selected, allowing to tolerate small, distributed inaccuracies on the output of each modulo computation. g Median relative error for an RNS-based 128 × 128 MVM with 16-bit operands as a function of the perturbation magnitude σ, for increasing values of redundancy factor k from k = 1 (6-bit moduli) up to k = 16 (10-bit moduli), highlighting a nonlinear dependence on σ.
