IEEE Circuits and Systems Magazine - Q3 2023 - 39

The SIMD architecture is flexible and can be programmed
to support diverse computation. In particular,
we illustrate how the VMM, MMM, and CONV operations
can be mapped onto a SIMD array for DNN processing.
VMM and MMM Operations: Fig. 4(b) shows the
MMM operation between an input matrix and a weight
matrix on a SIMD array. For an MMM operation, the vectors
of the input and weight matrices are loaded into the
SIMD array's memory to prepare for processing. During
processing, corresponding input data and weight data
pairs are accessed from the memory and dispatched to
the PEs for processing. The input and weight vectors in
the memory can be cached to exploit temporal locality
throughout the entire computation. Similarly, for the
VMM operation, the input vector is loaded and cached,
and is paired across all weight vectors for processing.
CONV Operation: Fig. 4(c) shows the CONV operation
between an HW C×× input activation (IA) and an
RS C×× convolution weight (W) on a SIMD array. Due
to the sliding window nature of the CONV operation, the
IA and W are first converted into 2D matrices: 1) IA is
converted to a XY CR S
()× ×× ×() matrix, where each
row matches the size of a RS C×× weight kernel; and
the IA values are partially replicated from one row to
the next row to correspond to the sliding window from
one step to the next step; and 2) W is converted to a
CR SK××
()× matrix, where each column corresponds
to a weight kernel. Note the process of converting IAs
and Ws in CONV into input and weight in MMMs, respectively,
is often referred as Im2Col operation. An MMM
operation can then be performed between the input and
the weight matrix to produce the output matrix of size
XY K×
()× .
The advantage of a SIMD architecture is its flexibility
and programmability to support diverse workloads.
In general, for computation with straightforward data
Figure 4. Illustration of the (a) SIMD array architecture, (b) matrix-matrix multiplication (MMM) operation, and (c) convolution
(CONV) layer operations on SIMD array.
THIRD QUARTER 2023
IEEE CIRCUITS AND SYSTEMS MAGAZINE
39

IEEE Circuits and Systems Magazine - Q3 2023

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