IEEE Computational Intelligence Magazine - August 2021 - 20

TABLE II Energy consumption comparison of the compressed models obtained by EMOMC
and the peer methods for VGG-16 on CIFAR-10.
METHOD
EMOMC
(OURS)
PRUNING
FILTERS [26]
PLAY AND
PRUNE [50]
ACCURACY
LOSS
0.3%
0.2%
0.1%
XY :
1.7
ENERGY CONSUMPTION (MJ)
CC:IO
1.7
FF:XY
2.3
18.5
9.5
19.6
12.6
18.5
9.5
XF: X
2.6
19.3
11.2
XY:
14.0
1.2
2.4
EFFICIENCY IMPROVEMENT (×)
CC:IO
12.2
FF:XY
10.4
1.1
1.7
1.3
2.5
1.2
2.0
AGGREGATION SCORE
XF: X
8.9
r/5.0x = /1.0
125.6
1.2
2.2
1.2
2.2
r x = /0.2
97.0
r x =
30.0
1.4
2.5
TABLE III Model size comparison of the compressed models obtained by MOMC
and the peer methods for VGG-16 on CIFAR-10.
METHOD
EMOMC (OURS)
PRUNING
FILTERS [26]
PLAY AND
PRUNE [50]
ACCURACY
LOSS
0.3%
0.2%
0.1%
NORMAL
9.8
34.7
15.1
MODEL SIZE (MB)
CSR
8.0
37.9
16.5
COMPRESSION RATE (×)
COO NORMAL CSR
6.1
1.7
24.5
57.3
24.6
3.9
7.4
1.6
3.6
COO
2.4
1.0
2.4
occupies around 50% less memory
space than the MobileNet when the
accuracy is below 88%. This observation
shows that although MobileNet is
designed for computation efficiency,
one should select a compressed model
from a more complex neural network
such as VGG-16. It is more efficient
than the compressed model from simpler
neural networks, in terms of energy efficiency
and model size. The reason is that
the number of the parameters or the
Figure 7 displays the aggregation scores of different solutions
under three different values of /r x . Each curve is
plotted based on the results from one execution of the
multi-objective optimization. As the multi-objective solver
generates discrete points (i.e., solutions), they are plotted in a
line using a smooth function called cspline, which connects
consecutive points by natural cubic splines after rendering
the data monotonic. The scores are individually normalized
by the aggregation score obtained by original uncompressed
models. From the results, it can be observed that most accuracy-energy
curves have one peak point. For the complex
neural networks such as VGG-16, the highest scores will be
125 # higher than the uncompressed model due to its high
compression rate. For the simpler networks such as
MobileNet and LeNet, the highest aggregation score is
around 9 # more than the original model.
E. On Selection of Neural Networks
On the same dataset, the selection of an optimal neural network
depends on how one compresses the model. For instance,
MobileNet is specially designed for computation efficiency;
although its accuracy is slightly lower than VGG-16, it uses
much fewer hardware resources than VGG-16, in terms of
energy efficiency and model size. However, this statement is
true only for the original uncompressed MobileNet and VGG16.
After model compression, VGG-16 may be more efficient
than MobileNet. Figures 8 and 9 show the ratios of energy
consumption and model size between VGG-16 and MobileNet,
in four dataflow designs and three coding schemes. The results
show that apart from dataflow design :CC
IO and the normal
coding scheme, VGG-16 consumes around 50% less energy and
20 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
precision of the parameters in VGG-16 can be lower than those
of MobileNet after the mode compression.
F. Comparison to the State-of-the-Art
Tables II and III report the results of different model compression
methods, in terms of the energy consumption and
the aggregation scores, and model size, respectively. Table II
shows that under negligible accuracy loss (typically, less than
0.5% accuracy loss), EMOMC improves the energy efficiency
and model compression rate by a factor of .411 # and
53 . #,
on average. There are two reasons for such improvements.
Firstly, the evolutionary multi-objective solver optimizes the
problem generation by generation. By allowing a certain
range of accuracy loss, it can generate many intermediate
results, and these results contribute to the improvements in
energy efficiency or compression rate. Compared with previous
methods which take accuracy loss as a hard constraint,
EMOMC is more likely to find better results. Secondly, the
exploration space of the model compression process is significantly
reduced by adopting both pruning and quantization
techniques. Without the proposed two-stage pruning and
quantization co-optimization strategy, previous approaches
suffer from too high computation cost to explore and exploit
such a huge search space. In addition to energy efficiency and
compression rate, the proposed method also shows an average
84 .2 # improvement on aggregation scores.
In practice, one needs to select an optimal solution
(from the solution set obtained by an EMO algorithm) for
the machine learning task on a specific device. For instance,
after solving the bi-objective optimization problem of accuracy
and energy efficiency, a set of solutions can be obtained
IEEE Computational Intelligence Magazine - August 2021

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - August 2021
