IEEE Circuits and Systems Magazine - Q3 2023 - 46

to recover the indices of the W data in the uncompressed
format. The recovered indices are used to select
the corresponding IA data to form IA-W pairs for
computation.
E. Full Sparsity-Channel-Last Processing
There are generally two ways to handle full sparsity,
i.e., sparsity in both W and IA: channel-last processing
or channel-first processing. In this subsection, we will
cover channel-last processing, an
example of which is SCNN [34].
The channel-last dataflow is
illustrated in Fig. 14. In the channel-last
processing, the nonzero
W and IA data are ordered in the
RS HW,/ ,
() () dimension first and
C dimension last for compressed
storage and processing. Subsequently,
as compressed W and IA
data are fetched for processing,
their channel indices are easily
aligned. As long as a nonzero W's
and a nonzero IA's channel indices
are matched, they can be paired
for multiplication.
Shown in Fig. 14(a) and (b), the
Figure 14. Illustration of channel-last dataflow for sparse DNN processing. (a) IA and
W data in dense format, (b) front-end dataflow, and (c) back-end dataflow of channellast
processing. Adopted from [31] ©2021 IEEE.
compressed W and IA data of the
same channel index can be cross
paired and multiplied together
using a 2D multiplier array. The
advantage of the channel-last processing
is the simple frontend, but
the drawback is the complicated
writeback because the OA addresses
of the psums depend on
the RS HW,/ ,() () indices of the
IA/W data, which are irregular for
sparse data. There is little opportunity
to reduce the psums before
writeback, resulting in writeback
traffic jam. It requires complex
hardware or wiring, e.g., a crossbar
switch, to resolve the contention,
and it may cause pipeline
stalls.
This backend challenge is illusFigure
15. Architecture of SCNN, adopted from [34] ©2017 ACM.
46
IEEE CIRCUITS AND SYSTEMS MAGAZINE
trated in Fig. 14(c). The psums need
to be distributed by a switch to the
corresponding buffer bank. The
red lines indicate the psum writebacks
that lead to buffer contentions.
To avoid contentions, conflicting
psums need to be held. In
the example, one output requires
the accumulation of three psums,
resulting in a three-cycle writeback
and stalling the multiplier array
for two cycles.
THIRD QUARTER 2023

IEEE Circuits and Systems Magazine - Q3 2023

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