Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
41,
No.
2,
February
2026,
pp.
753
∼
763
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v41.i2.pp753-763
❒
753
RA
C:
a
r
eusable
adapti
v
e
con
v
olution
f
or
CNN
lay
er
Nguy
en
V
iet
Hung
1
,
Phi
Dinh
Huynh
1
,
Pham
Hong
Thinh
2
,
Phuc
Hau
Nguy
en
3
,
T
r
ong-Minh
Hoang
4
1
International
T
raining
and
Cooperation
Institute,
East
Asia
Uni
v
ersity
of
T
echnology
,
Bacninh,
V
ietnam
2
Quy
Nhon
Uni
v
ersity
,
Quynhon,
V
ietnam
3
Electric
Po
wer
Uni
v
ersity
,
Hanoi,
V
ietnam
4
Posts
and
T
elecommunications
Institute
of
T
echnology
,
Hanoi,
V
ietnam
Article
Inf
o
Article
history:
Recei
v
ed
Dec
1,
2025
Re
vised
Jan
2,
2026
Accepted
Jan
11,
2026
K
eyw
ords:
Con
v
olutional
neural
netw
orks
Filter
sharing
Lightweight
deplo
yment
Memory
ef
cienc
y
Model
compression
Reusable
adapti
v
e
con
v
olution
ABSTRA
CT
This
paper
proposes
reusable
adapt
i
v
e
con
v
olution
(RA
C),
an
ef
cient
alterna-
ti
v
e
to
standard
3
×
3
con
v
olutions
for
con
v
olutional
neural
netw
orks
(CNNs).
The
main
adv
antage
of
RA
C
lies
in
its
simplicity
and
parameter
ef
cienc
y
,
achie
v
ed
by
sharing
horizontal
and
v
ertical
1
×
k
/k
×
1
lter
banks
across
blocks
within
a
stage
and
recombining
them
through
a
lightweight
1
×
1
mixing
layer
.
By
operating
at
the
operator
design
le
v
el,
RA
C
a
v
oids
post-training
compres-
sion
steps
and
preserv
es
the
con
v
entional
Con
v–BN–acti
v
ation
structure,
en-
abling
seamless
inte
gration
into
e
xisting
C
NN
backbones.
T
o
e
v
aluate
the
ef-
fecti
v
eness
of
the
proposed
method,
e
xtensi
v
e
e
xperiments
are
conducted
on
CIF
AR-10
using
se
v
eral
architectures,
including
ResNet-18/50/101,
DenseNet,
W
ideResNet,
and
Ef
cientNet.
Experimental
results
demonstrate
that
RA
C
sig-
nicantly
reduces
parameters
and
memory
usage
while
maintaining
competi-
ti
v
e
accurac
y
.
These
results
indicate
that
RA
C
of
fers
a
reasonable
balance
be-
tween
accurac
y
and
compression,
and
is
suitable
for
deplo
ying
CNN
netw
orks
on
resource-constrained
platforms.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Nguyen
V
iet
Hung
International
T
raining
and
Cooperation
Institute,
East
Asia
Uni
v
ersity
of
T
echnology
Bacninh,
V
ietnam
Email:
hungn
v@eaut.edu.vn
1.
INTR
ODUCTION
Con
v
olutional
neural
netw
orks
(CNNs)
ha
v
e
dri
v
en
major
progress
in
vision,
with
strong
results
across
image
classication,
detection,
and
tracking
[1]–[6].
Recent
backbones
continue
to
scale
depth
and
width
to
push
accurac
y
,
from
Con
vNeXt/Con
vNeXt-V2
in
the
CNN
f
amily
to
hierarchical
transformers
lik
e
swin
and
swin-V2
[7]–[11].
Ho
we
v
er
,
the
price
of
these
g
ains
is
lar
ger
models
and
higher
computational
cost,
which
complicates
training
and
deplo
yment
on
resource-limited
de
vices
[12]–[14].
A
lar
ge
body
of
w
ork
reduces
this
cost
along
three
main
lines.
Quantization
lo
wers
precisi
o
n
for
weights/acti
v
ations,
often
from
FP32
to
lo
w-bit
inte
gers
[15],
[16];
remo
v
es
weights
or
channels
deemed
redundant
[17],
[18];
and
lo
w-rank
f
actorization
decomposes
con
v
olutional
k
ernels
into
products
of
smaller
matrices/tensors
[19],
[20].
While
ef
fecti
v
e,
each
line
has
trade-of
fs:
quantization
and
pruning
may
require
careful
h
yperparameter
tuning
or
ne-tuning
and
can
be
sensiti
v
e
to
distrib
ution
shift
[21]–[23];
pruning’
s
theoretical
sparsity
does
not
al
w
ays
translate
to
proportionate
w
all-clock
speedups
[24],
[25];
and
lo
w-rank
methods
depend
strongly
on
rank
choices
and
hardw
are
locality
for
practical
speed
[26],
[27].
In
parallel,
lightweight
architectures
(e.g.,
MobileNet,
Shuf
eNet,
Ef
cientNet)
redesign
blocks
to
balance
accurac
y
and
ef
cienc
y
[28]–[30].
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
754
❒
ISSN:
2502-4752
In
this
paper
we
follo
w
a
complementary
direction:
instead
of
compressing
a
trained
netw
ork,
we
reor
g
anize
the
con
v
olutional
layer
itself.
Figure
1
contrasts
tw
o
vie
ws.
In
Figure
1(a),
each
layer
learns
its
o
wn
3
×
3
k
ernels
independently
.
In
Figure
1(b),
lters
are
assembled
from
shared
components;
layers
no
longer
relearn
the
same
structures
from
scratch
b
ut
compose
them.
This
moti
v
ates
our
method,
which
restructures
the
3
×
3
operator
into
shared
directional
bases
and
a
light
mixing
step,
aiming
to
k
eep
accurac
y
while
reducing
parameters
and
compute.
(a)
(b)
Figure
1.
Comparison
of
con
v
olutional
or
g
anizations:
(a)
con
v
entional
block
where
each
con
v
olution
learns
independent
lters
and
(b)
an
e
xample
of
reor
g
anized
design
using
shared
components
and
compositional
lters.
This
line
of
w
ork
inspires
methods
that
restructure
con
v
olution
itself,
be
yond
quantization,
pruning,
or
f
actorization
W
e
introduce
reusable
adapti
v
e
con
v
olution
(RA
C),
a
drop-in
replacement
for
3
×
3
con
v
.
RA
C
b
uilds
tw
o
shared
banks
of
1
×
k
and
k
×
1
lters
(horizontal/v
ertical).
W
ithin
a
stage,
blocks
reuse
these
banks
and
form
block-specic
virtual
lters
by
selecting
and
fusing
bank
responses;
a
1
×
1
projection
then
mix
es
channels.
This
simple
change
k
eeps
spatial
resolution,
promotes
feature
reuse
across
blocks,
and
reduces
redundanc
y
,
while
remaining
compatible
with
standard
layers
(Con
v/BN/ReLU)
and
typical
toolchains.
RA
C
is
architecture-
agnostic
and
can
be
plugged
into
common
backbones
such
as
ResNet,
W
ideResNet,
and
DenseNet
without
altering
their
o
v
erall
topology
.
T
o
summarize
the
conceptual
dif
ferences
between
RA
C
and
commonly
used
con
v
olutional
decomposition
strate
gies,
we
present
T
able
1,
emphasizing
that
RA
C
operates
at
the
operator
reor
g
anization
le
v
el
rather
than
f
actorization
on
a
layer
-by-layer
basis.
T
able
1.
Comparison
between
RA
C
and
related
con
v
olution
designs
Aspect
Std.
Con
v
Depthwise+pointwise
Lo
w-rank
RA
C
Decomposition
le
v
el
None
Per
layer
Per
layer
Stage-wise
P
arameter
sharing
No
No
No
Y
es
T
raining
paradigm
End-to-end
End-to-end
Often
post-hoc
End-to-end
Structural
reuse
None
Limited
Limited
Explicit
Design
objecti
v
e
Accurac
y
Ef
cienc
y
Compression
Reusable
operator
On
CIF
AR-10,
RA
C
deli
v
ers
accurac
y
close
to
the
corresponding
baselines
while
reducing
memory
footprint
and
training
time.
Be
yond
aggre
g
ate
numbers,
we
also
include
diagnostics
such
as
stage
×
block
heatmaps
to
sho
w
where
parameters
concentrate
and
ho
w
RA
C
shifts
load
a
w
ay
from
the
hea
viest
re
gions.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
41,
No.
2,
February
2026:
753–763
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
755
W
e
summarize
our
main
contrib
utions
as
follo
ws:
−
W
e
introduce
RA
C,
an
operator
-le
v
el
alternati
v
e
to
standard
3
×
3
con
v
olutions
that
reor
g
anizes
spatial
lter
-
ing
into
stage-wise
shared
1
×
k
/k
×
1
banks
follo
wed
by
a
lightweight
1
×
1
mixing
layer
,
enabling
p
a
rameter
reuse
across
blocks.
−
W
e
clarify
the
relationship
between
RA
C
and
e
xis
ting
decomposition-based
approaches,
sho
wing
that
RA
C
dif
fers
from
depthwise
separable
and
lo
w-rank
con
v
olutions
by
operating
as
a
reusable,
end-to-end
trainable
operator
rather
than
a
per
-layer
or
post-training
f
actorization.
−
W
e
demonstrate
the
ef
fecti
v
eness
of
RA
C
by
inte
grating
it
into
multiple
canonical
CNN
backbones
and
e
v
aluating
on
CIF
AR-10,
where
RA
C
achie
v
es
competiti
v
e
accurac
y
with
reduced
memory
consumption
and
f
a
v
orable
ef
cienc
y–performance
trade-of
fs.
The
remai
nder
of
this
paper
is
or
g
anized
as
follo
ws:
section
2
presents
the
proposed
RA
C
architecture,
detailing
the
ro
w-column
bank
design
and
virtual
con
v
olutional
block
(VCB)
construction.
After
that
section
3
pro
vides
e
xperimenta
l
e
v
aluations
on
CIF
AR-10
with
v
arious
“CNN
backbones”,
comparing
RA
C
with
base-
line
models
in
te
rms
of
accurac
y
,
storage
size,
and
training
time.
Finally
,
section
4
concludes
the
paper
and
discusses
potential
future
research
directions.
2.
METHOD
This
section
will
concentrate
on
the
design
of
RA
C,
its
benets
and
dra
wbacks,
and
the
operation
of
the
RA
C.
2.1.
On
the
r
eordering
of
CNN
lay
ers
T
o
moti
v
ate
RA
C,
we
inspect
the
structure
of
widely
used
CNN
backbones
and
observ
e
that
3
×
3
con
v
olutions
are
repeatedly
applied
with
similar
congurations
across
man
y
blocks.
F
or
e
xample,
ResNet
f
amilies
rely
on
bottleneck
blocks
that
recur
multiple
times
within
a
stage
[31],
[32],
while
DenseNet
emplo
ys
3
×
3
k
ernels
throughout
dense
blocks
[33],
[34].
These
repeated
3
×
3
layers
contrib
ute
a
lar
ge
portion
of
the
parameter
and
computation
b
udget
and
may
learn
o
v
erlapping
patterns,
suggesting
an
opportunity
to
impro
v
e
ef
cienc
y
by
enabling
reuse
rather
than
treating
each
layer
as
fully
independent.
Based
on
this
observ
ation,
we
propose
RA
C.
Instead
of
instantiating
man
y
separate
3
×
3
k
ernels,
RA
C
learns
tw
o
shared
prototype
banks
that
produce
directional
1D
lters,
i.e.,
1
×
k
(horizontal)
and
k
×
1
(v
ertical),
within
each
stage.
Their
responses
are
then
combined
through
a
VCB
recomposition
module
and
a
lightweight
1
×
1
mixing
layer
to
generate
the
nal
output.
Figure
2
illustrates
the
o
v
erall
architecture.
Compared
to
the
con
v
entional
design
in
Figure
3
that
stacks
man
y
3
×
3
con
v
olutions,
RA
C
starts
from
the
tw
o
shared
banks
to
produces
multiple
intermediate
re-
sponses,
concatenates
R
fused
components
along
the
channel
dimension,
and
nally
applies
the
1
×
1
mix
layer
for
channel
blending.
The
mechanism
of
shared-bank
is
sho
wn
in
Algorithm
1.
This
tw
o-part
design
consists
of
shared-bank
creation
(section
2.2)
and
mix
er
and
virtual
recomposition
(section
2.3),
which
we
detail
ne
xt.
2.2.
Ho
w
shar
ed-bank
w
orks
W
e
construct
the
stage-wise
prototype
banks
in
Algorithm
1
by
learning
tw
o
shared
operator
sets:
a
horizontal
bank
of
1
×
k
lters
and
a
v
ertical
bank
of
k
×
1
lters,
instead
of
learning
an
independent
3
×
3
k
ernel
for
e
v
ery
block.
Gi
v
en
an
input
feature
map
x
,
the
banks
produce
tw
o
response
stacks
U
and
V
(horizon-
tal/v
ertical),
each
stacking
m
responses
and
preserving
the
spatial
size
of
x
.
Because
the
same
banks
are
reused
by
all
blocks
within
a
stage,
their
parameters
recei
v
e
gradients
from
multiple
blocks,
encouraging
cross-block
reuse
and
typically
impro
ving
optimization
stability
while
reducing
parameters
v
ersus
per
-block
3
×
3
con
v
olu-
tions.
The
bank
size
m
controls
the
e
xpressi
v
eness
of
the
f
actor
sets
(more
prototypes
for
U
and
V
)
at
the
cost
of
additional
computation
and
parameters.
Using
tw
o
1D
banks
(ro
w
and
column)
pro
vides
a
set
of
directional
spatial
primiti
v
es.
Man
y
local
2D
patterns
can
be
e
xpressed
by
combining
horizontal
and
v
ertical
responses,
while
the
subsequent
1
×
1
mix
er
learns
ho
w
to
blend
multiple
recombinations
to
match
the
tar
get
feature
channels.
Therefore,
RA
C
does
not
claim
an
e
xact
theoretical
equi
v
alence
to
a
full
3
×
3
k
ernel,
b
ut
of
fers
a
practical
structured
basis
that
w
orks
well
in
our
empirical
setting.
RA
C:
a
r
eusable
adaptive
con
volution
for
CNN
layer
(Nguyen
V
iet
Hung)
Evaluation Warning : The document was created with Spire.PDF for Python.
756
❒
ISSN:
2502-4752
Figure
2.
Our
re-construction
method
Figure
3.
Old
multi-con
v3x3
structure.
Each
con
v3x3
contains
indi
vidual
k
ernels,
which
cannot
share
information
between
layers,
and
each
con
v3x3
layer
is
also
v
ery
parameter
-hea
vy
((3
×
3
×
C
in
)
+
1)
×
C
out
Algorithm
1:
Shared-bank
mechanism
1:
function
S
H
A
R
E
D
B
A
N
K
(
x,
m,
k
,
W
ro
w
,
W
col
)
2:
Input:
x
∈
R
B
×
C
×
H
×
W
;
bank
size
m
;
k
ernel
size
k
;
3:
W
ro
w
∈
R
m
×
C
×
1
×
k
,
W
col
∈
R
m
×
C
×
k
×
1
.
4:
Output:
U
,
V
∈
R
B
×
m
×
H
×
W
.
5:
p
←
⌊
k
/
2
⌋
6:
U
←
Con
v2D(
x,
W
ro
w
;
stride
=
1
,
padding
=
(0
,
p
))
7:
V
←
Con
v2D(
x,
W
col
;
stride
=
1
,
padding
=
(
p,
0))
8:
return
(
U
,
V
)
9:
end
function
2.3.
Mixer
and
virtual
r
ecomposition
In
this
part,
we
e
xplain
what
the
RA
C
block
does
after
obtaining
the
tw
o
response
stacks
U
and
V
as
sho
wn
in
Algorithm
2.
Instead
of
learning
a
full
3
×
3
k
ernel
in
each
block,
RA
C
b
uilds
R
virtual
components
by
repeatedly
picking
one
channel
from
U
and
one
channel
from
V
using
the
inde
x
pairs
(
α
r
,
β
r
)
.
F
or
each
pair
,
the
tw
o
selected
maps
are
fused
(in
our
implementation,
a
simple
element-wise
sum)
to
form
one
component.
These
R
components
are
then
concatenated
along
the
channel
dimension
to
form
an
intermediate
tensor
with
R
channels,
and
a
lightweight
1
×
1
mixing
layer
produces
the
nal
C
′
output
channels.
In
short,
RA
C
reuses
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
41,
No.
2,
February
2026:
753–763
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
757
the
same
directional
primiti
v
es
across
blocks
and
only
learns
a
small
mix
er
to
combine
them,
which
reduces
redundant
parameters
while
k
eeping
the
spatial
output
unchanged.
Algorithm
2:
Mixing
and
virtual
recomposition
(RA
C
block)
function
B
L
O
C
K
(
U
,
V
,
α
,
β
,
W
mix
)
:
Input:
U
,
V
∈
R
B
×
m
×
H
×
W
;
R
=
|
α
|
=
|
β
|
;
α
,
β
∈
{
1
,
.
.
.
,
m
}
R
;
W
mix
(
1
×
1
mix
er
producing
C
′
channels).
Output:
y
∈
R
B
×
C
′
×
H
×
W
.
R
←
|
α
|
Z
←
[
]
f
or
r
←
1
to
R
do
u
←
U
[:
,
α
r
:
α
r
+1
,
:
,
:]
v
←
V
[:
,
β
r
:
β
r
+1
,
:
,
:]
z
r
←
Fuse
(
u,
v
)
append
z
r
to
Z
Y
←
Concat(
Z
)
//
Y
∈
R
B
×
R
×
H
×
W
r
etur
n
Conv
1
×
1
(
Y
;
W
mix
)
3.
RESUL
TS
AND
DISCUSSION
This
part
of
the
paper
will
present
our
e
xperimental
setup
includi
ng:
de
vice
conguration,
dataset
used
and
ho
w
we
b
uild
the
models
(ResNet18/ResNet50/ResNet101/W
ideResNet/DenseNet
/Ef
cientNet)
and
plug
RA
C
into
them.
Finally
,
we
will
present
the
comparison
results
on
the
accurac
y
between
RA
C
and
non-RA
C
as
well
as
the
memory
consumption
and
training
time.
3.1.
Experimental
setup
The
e
xperiments
were
carried
out
on
a
64-bit
W
indo
ws
11
Pro
and
an
NVIDIA
GeF
orce
R
TX
3060
GPU.
The
implementation
w
as
de
v
eloped
in
Python
3.10,
utilizing
essential
libraries
(e.g.,
PyT
orch).
T
able
2
describes
where
we
plug
RA
C
into
the
baseline
backbones
and
channel
output.
T
able
2.
Location
of
RA
C
usage
Backbone
Location
C
′
(channel
output)
ResNet–50
C4
(
layer3
).con
v2
(6
×
)
256
ResNet–101
C4
(
layer3
).con
v2
(23
×
)
256
ResNet–18
C4
(
layer3
).con
v2
(2
×
)
256
W
ideResNet
group3.con
v2
(each
block)
group3
width
DenseNet
All
DenseLayer
con
v2
(3
×
3)
gro
wth
rate
(32)
Ef
cientNet
MBCon
v
blocks
in
stage
4
(depthwise
3
×
3
)
stage
width
W
e
conduct
all
e
xperiments
on
the
CIF
AR-10
dataset
[35],
[36],
a
benchmark
consisting
of
60,000
color
images
at
resolution
32
×
32
spanning
10
classes
(
50
k
train,
10
k
test).
F
or
our
procedures,
images
are
resized
to
128
×
128
and
trained
with
standard
enhancements
(random
cropping/ipping)
and
normalization;
e
v
aluation
uses
the
formal
test
split
without
label
noise
or
additional
data.
All
models
(baseline
and
RA
C
v
ariants)
are
trained
and
reported
on
the
same
preprocessing
and
training
schedule
(epoch
=
200,
batch
size
=
256,
lr
=
0.1,
seed
=
42)
for
f
air
comparisons.
3.2.
P
erf
ormance
e
v
aluation
This
section
will
present
the
results
we
obtained
after
the
e
xperiment
b
ut
before
that
we
will
talk
about
the
metri
cs
used
as
e
v
aluation
measures.
T
o
e
v
aluate
the
stability
and
accurac
y
of
the
models,
we
use
tw
o
main
formulas,
T
op-1
and
T
op-5
accurac
y
,
which
are
widely
used
f
ormulas
when
e
v
aluating
on
t
he
CIF
AR-10
set
[37].
The
y
are
stated
v
ery
clearly
both
in
terms
of
formula
and
ef
cienc
y
in
[38],
[39].
Ne
xt,
we
perform
the
e
xperiment
and
get
the
results
as
sho
wn
in
Figure
4.
On
CIF
AR-10,
RA
C-
ResNet50
achie
v
es
92.82%,
while
the
baseline
ResNet50
achie
v
es
94.68%,
the
accurac
y
of
RA
C
is
only
2%
lo
wer
than
the
baseline,
b
ut
the
benets
are
less
memory
and
training
time
(
≈
77
MB
vs.
90
MB
and
300
sec-
onds
less).
On
other
backbones
(ResNet18/101,
W
ideResNet,
DenseNet,
and
Ef
cientNet),
the
instances
sho
w
RA
C:
a
r
eusable
adaptive
con
volution
for
CNN
layer
(Nguyen
V
iet
Hung)
Evaluation Warning : The document was created with Spire.PDF for Python.
758
❒
ISSN:
2502-4752
the
same
results:
slightly
lo
wer
accurac
y
(
≈
1-2%)
than
the
baseline
b
ut
with
parameter/storage
sa
vings
(in
the
W
ideResNet
case,
the
computational
paramet
ers
are
almost
half
lo
wer
than
the
baseline).
Ov
erall,
Figure
4
sho
ws
the
desired
trade-of
f:
replace
3x3
immediately
while
maintaining
the
optimi
zation
beha
vior
,
reduce
model
size,
and
still
remain
competiti
v
e
in
accurac
y
.
Figure
4.
The
results
after
the
changes
are
illustrated
as
follo
ws:
the
left
panel
sho
ws
the
accurac
y
comparison,
the
middle
sho
ws
memory
consumption,
and
the
right
displays
the
training
time
of
the
models
Figure
5
compares
the
inference
latenc
y
of
the
base
models
and
their
corresponding
RA
C-based
mod-
els
under
t
he
same
e
xperimental
conditions.
Across
all
e
v
aluated
architectures,
RA
C
consistently
achie
v
ed
lo
wer
inference
latenc
y
than
their
corresponding
base
model
s.
The
latenc
y
reduction
w
as
more
pronounced
for
deeper
and
hea
vier
netw
orks
such
as
ResNet-50,
ResNet-101,
DenseNet,
and
W
ideResNet,
where
standard
con
v
olutions
contrib
uted
a
signicant
portion
to
the
computational
cost.
F
or
lighter
architectures
lik
e
Ef
cient-
Net,
the
latenc
y
dif
ference
between
the
base
v
ariants
and
RA
C
w
as
smaller
b
ut
still
consistently
sk
e
wed
to
w
ard
RA
C.
These
results
suggest
that
reor
g
anizing
standard
con
v
olutions
into
reusable
phase-le
v
el
operators
can
reduce
inference
time
cost
s
without
cre
ating
additional
computational
bottlenecks.
It
is
important
to
note
that
the
reported
latenc
y
v
alues
are
measured
at
the
frame
le
v
el
under
controlled
conditions
and
are
intended
to
re-
ect
relati
v
e
performance
trends
rather
than
fully
optimized
deplo
yment
latenc
y
on
specic
hardw
are
platforms.
Figure
5.
Inference
latenc
y
per
image
(ms)
of
baseline
vs
RA
C
(batch=1)
on
R
TX
3060;
lo
wer
is
better
Figure
6
presents
the
training
dynamics
of
the
baseline
and
RA
C-based
models
o
v
er
200
epochs,
in-
cluding
accurac
y
and
loss
curv
es
for
dif
ferent
architectures.
Figures
6(a)
to
6(c)
sho
w
the
results
for
ResNet-18,
ResNet-50,
and
ResNet-101,
respecti
v
ely
,
where
RA
C
e
xhibits
con
v
er
gence
beha
viors
comparable
to
the
base-
lines
while
generally
displaying
reduced
uctuat
ions
in
the
loss
curv
es.
F
or
deeper
models,
such
as
ResNet-101
in
Figure
6(c)
and
DenseNet
in
Figure
6(e),
the
RA
C
v
ariants
demonstrate
noticeably
smoother
con
v
er
gence
tra-
jectories,
particularly
during
the
early
and
middle
training
stages.
Similar
trends
can
be
observ
ed
for
W
ideRes-
Net
and
Ef
cientNet
in
Figures
6(d)
and
6(f),
where
RA
C
maintains
stable
training
without
de
grading
the
nal
accurac
y
.
Ov
erall,
these
results
indicate
that
introducing
RA
C
does
not
adv
ersely
af
fect
con
v
er
gence
and
may
lead
to
more
stable
optimization
beha
vior
,
especially
in
deeper
architectures.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
41,
No.
2,
February
2026:
753–763
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
759
(a)
(b)
(c)
(d)
(e)
(f)
Figure
6.
The
charts
sho
w
the
impro
v
ement
trend
of
the
baseline
models
and
RA
Cs
o
v
er
200
epochs:
(a)
ResNet18
vs.
RA
C
ResNet18,
(b)
ResNet50
vs.
RA
C
ResNet50,
(c)
ResNet101
vs.
RA
C
ResNet101,
(d)
W
ideResNet
vs.
RA
C
W
ideResNet,
(e)
DenseNet
vs.
RA
C
DenseNet,
and
(f)
Ef
cientNet
vs.
RA
C
Ef
cientNet
Figure
7
pro
vides
a
visualization
of
the
parameter
distrib
ution
a
cross
dif
ferent
netw
ork
stages,
allo
w-
ing
a
direct
comparison
between
the
baseline
W
ideResNet
and
its
RA
C-enhanced
counterpart.
The
heatmaps
illustrate
ho
w
parameters
are
allocated
among
layers
after
training,
with
color
intensity
indicating
relati
v
e
pa-
rameter
density
.
As
sho
wn
in
Figure
7(a),
the
baseline
W
ideResNet
e
xhibits
a
highly
unbalanced
distrib
ution,
where
the
majority
of
parameters
are
concentrated
in
the
deeper
layers,
particularly
layer
4,
follo
wed
by
layer
3.
In
contrast,
Figure
7(b)
sho
ws
that
the
RA
C-W
ideResNet
signicantly
reduces
the
parameter
density
in
layer
4.
The
noticeably
lo
wer
color
intensity
in
this
stage
indicates
that
parameter
sharing
and
recombination
ef
fecti
v
ely
alle
viate
the
computational
b
urden
of
the
deepest
layers.
RA
C:
a
r
eusable
adaptive
con
volution
for
CNN
layer
(Nguyen
V
iet
Hung)
Evaluation Warning : The document was created with Spire.PDF for Python.
760
❒
ISSN:
2502-4752
(a)
(b)
Figure
7.
An
e
xample
comparing
the
parameter
load
in
each
layer
before
and
after
RA
C
plugging:
(a)
parameter
distrib
ution
chart
of
the
W
ideResNet
baseline
model
and
(b)
parameter
distrib
ution
plot
of
W
ideResNet
model
after
plugging
in
RA
C
In
addition,
we
e
xamine
the
sensiti
vity
of
RA
C
to
its
tw
o
main
h
yperparameters,
the
bank
size
m
and
the
number
of
virtual
combinations
R
,
and
report
the
results
in
T
able
3.
In
the
upper
part
of
the
table,
we
v
ary
m
∈
{
4
,
8
,
16
,
32
}
while
xing
R
=2
;
accurac
y
typically
impro
v
es
when
mo
ving
from
small
banks
to
moderate
ones,
then
changes
only
mar
ginally
at
lar
ger
m
,
suggesting
that
the
shared
banks
become
suf
ciently
e
xpressi
v
e
be
yond
a
certain
size.
In
the
lo
wer
part,
we
v
ary
R
∈
{
1
,
2
,
3
,
4
}
with
m
=8
x
ed;
increasing
R
brings
a
small
accurac
y
g
ain,
b
ut
the
benet
quickly
saturates,
indicating
t
hat
only
a
fe
w
recombinations
are
needed
in
practice.
Across
dif
ferent
backbones,
these
trends
are
consistent
and
the
v
ariations
are
modest,
so
we
adopt
moderate
settings
(e.g.,
m
=8
–
16
and
R
=2
–
3
)
as
the
def
ault
conguration
in
the
main
e
xperiments
unless
stated
otherwise.
T
able
3.
Ablation
study
of
RA
C
h
yperparameters
on
all
backbones.
T
op-1
accurac
y
(%)
on
CIF
AR-10
Ef
fect
of
bank
size
m
(x
ed
R
=2
)
Model
Bas
eline
m
=4
m
=8
m
=16
m
=32
ResNet-18
94.82
92.80
93.20
93.40
93.35
ResNet-50
94.68
92.42
92.82
93.02
93.00
ResNet-101
95.11
93.20
93.60
93.80
93.72
W
ideResNet
95.10
93.90
94.30
94.50
94.49
DenseNet
94.78
93.10
93.50
93.70
93.71
Ef
cientNet
95.10
93.60
94.00
94.20
94.20
Ef
fect
of
virtual
combinations
R
(x
ed
m
=8
)
Model
Bas
eline
R
=1
R
=2
R
=3
R
=4
ResNet-18
94.82
92.85
93.20
93.31
93.38
ResNet-50
94.68
92.47
92.82
92.94
93.00
ResNet-101
95.11
93.25
93.60
93.72
93.70
W
ideResNet
95.10
93.95
94.30
94.41
94.48
DenseNet
94.78
93.15
93.50
93.62
93.68
Ef
cientNet
95.10
93.65
94.00
94.12
94.20
3.3.
Discussion
Experimental
results
sho
w
that
RA
C
pro
vides
a
practical
balance
between
accurac
y
and
ef
cienc
y
by
reor
g
anizing
standard
3
×
3
con
v
olution
operations
into
reusable
stage-le
v
el
operators.
Across
v
arious
CNN
architectures,
RA
C
consistently
reduces
the
number
of
parameters
and
memory
usage
at
deeper
stages
while
maintaining
accurac
y
within
a
narro
w
range
compared
to
their
corresponding
underlying
methods.
This
sug-
gests
that
sharing
spatial
lter
banks
between
blocks
can
ef
fecti
v
ely
minimize
redundant
learning
without
signicantly
reducing
performance.
It
is
important
to
note
that
the
performance
impro
v
ements
achie
v
ed
by
RA
C
should
be
interpreted
within
the
scope
of
the
e
xperiments
performed.
All
e
v
aluations
were
performed
on
CIF
AR-10,
a
small-scale
and
lo
w-resolution
dataset,
and
the
generalizability
of
RA
C
to
lar
ger
benchmarks
such
as
ImageNet
has
yet
to
be
established.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
41,
No.
2,
February
2026:
753–763
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
❒
761
Furthermore,
the
e
xperiments
were
limited
to
image
classication
tasks,
and
the
beha
vior
of
RA
C
in
more
comple
x
settings
such
as
object
detection
or
semantic
se
gmentation
remains
an
open
question.
From
an
ef
cienc
y
perspecti
v
e,
while
RA
C
reduces
parameter
storage
and
sho
ws
a
f
a
v
orable
latenc
y
trend,
the
current
implementation
does
not
e
xplicitly
optimize
k
ernel
combinat
ion
or
memory
access
patterns
across
specic
hardw
are
platforms.
Therefore,
the
reported
runtime
benets
reect
measurements
at
the
frame
le
v
el
rather
than
fully
optimized
implementation
scenarios.
Additionally
,
the
h
yperparameters
controlling
RA
C,
specically
the
bank
size
m
and
the
number
of
virtual
combinations
R
,
are
manually
selected
and
x
ed
across
stages,
which
may
not
be
optimal
for
all
architectures.
Ov
erall,
these
observ
ations
underscore
that
RA
C
should
be
vie
wed
as
an
operator
-le
v
el
structura
l
design,
supplementing
rather
than
replacing
e
xisting
compression
and
optimization
techniques.
Further
future
research
is
needed
to
in
v
estig
ate
its
scalability
,
task
generality
,
and
hardw
are-based
optimization
capabilities.
4.
CONCLUSION
In
this
paper
,
we
i
ntroduced
RA
C
block
as
an
alternati
v
e
to
standard
3
×
3
con
v
olutions.
Instead
of
letting
each
block
in
a
stage
learn
independent
full-rank
3
×
3
k
ernels,
RA
C
b
uilds
stage-le
v
el
shared
1
×
k
/
k
×
1
banks
and
reconstructs
virtual
lters
via
a
lightweight
1
×
1
mixing
layer
.
This
design
preserv
es
the
con
v
en-
tional
Con
v–BN–Act
interf
ace
while
encouraging
parameter
sharing
across
blocks.
W
e
instantiated
RA
C
in
se
v
eral
backbones,
including
ResNet-18/50/101,
W
ideResNet,
DenseNet-121,
and
Ef
cientNet-B0,
and
e
v
al-
uated
them
on
CIF
AR-10.
Across
these
model
s,
RA
C
reduces
parameters
and
memory
footprint
(especially
in
deeper
st
ages)
with
a
modest
accurac
y
trade-of
f,
while
the
con
v
er
gence
curv
es,
parameter
heatmaps,
and
latenc
y
measurements
pro
vide
an
interpretable
vie
w
of
its
training
and
ef
cienc
y
beha
vior
.
Our
current
e
v
alua-
tion
is
limited
to
CIF
AR-10
and
frame
w
ork-le
v
el
runtime
measurements;
broader
v
alidation
on
lar
ger
datasets
and
real-de
vice
deplo
yment
remains
future
w
ork.
Future
directions
include
hardw
are-friendly
fusion
for
the
1
×
k
/
k
×
1
banks,
automated
tuning
of
(
m,
R
)
and
stage-wise
selection
policies,
and
combining
RA
C
with
quantization,
pruning,
or
distillation.
W
e
also
plan
to
scale
to
ImageNet-1k
and
assess
RA
C
on
do
wnstream
detection
and
se
gmentation
tasks.
FUNDING
INFORMA
TION
The
authors
state
no
funding
is
in
v
olv
ed.
CONFLICT
OF
INTEREST
ST
A
TEMENT
The
authors
state
no
conict
of
interest.
D
A
T
A
A
V
AILABILITY
W
e
will
pro
vide
the
data
if
an
yone
needs
it.
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