IEEE Computational Intelligence Magazine - August 2021 - 19

10
2
4
6
8
0.7
100
125
r/τ = 5
r/τ = 1
r/τ = 0.2
0.75
0.8
Accuracy
MobileNet
0.85
0.9
25
50
75
0.75
0.8
0.85
Accuracy
VGG-16
0.9
0.95
10
r/τ = 5
r/τ = 1
r/τ = 0.2
2
4
6
8
0.8
0.85
0.9
Accuracy
LeNet-5
FIGURE 7 The aggregation scores on CIFAR-10 (MobileNet and VGG-16) and MNIST (LeNet-5) under three different reward over penalty ratios.
The scores are individually normalized by the aggregation score obtained by the uncompressed models.
different parameter coding schemes. Each point stands for one
compressed model in the solution set obtained by EMOMC.
The results demonstrate that in terms of diversity the solution
sets show similar patterns with the bi-objective optimization of
accuracy and energy consumption.
Furthermore, it can be observed that although COO and
CSR are developed to store a sparse matrix, sometimes they
do not save the memory space for the compressed models,
compared with the normal coding scheme. For example, if
pursuing high model accuracy, the normal coding scheme is
the best one among the three coding schemes
for
MoblieNet. The reason is that although the COO and CSR
coding schemes only store non-zero elements, they still need
several extra bits to record the position of each non-zero element.
If attempting to keep the model accuracy at a high
level, the compression rate cannot be high, making the
memory space saved from the sparsity of the filter less than
the overhead of those extra bits. In this case, the normal coding
scheme is a better choice. However, if allowing a certain
level of accuracy loss, then CSR is the best among the three
coding schemes.
D. Aggregation of Accuracy and Energy Efficiency
Theoretically, higher accuracy comes with higher energy consumption.
Most previous model compression approaches only
allow a negligible loss of accuracy. For applications on edge
devices, it will be acceptable to sacrifice a little bit of accuracy
to achieve substantial improvement in energy efficiency. For
VGG-16, as shown in Figure 5, if 2% of accuracy loss is
acceptable, the energy consumption can be reduced by around
80%. In the solution sets displayed in Figure 5, there are some
knee points if considering the balance of both the model accuracy
and the energy consumption. To help users select the
model for deployment on edge devices, a new metric called
aggregation score is defined as:
AScore fr ff111 2
$$x
=+ - (( ))/,
(8)
22
21
1
2-1
2-2
0.70
0.75
0.80
0.85
Accuracy
FIGURE 8 The energy consumption of VGG-16 over the energy consumption
of MobileNet under different accuracy scores on CIFAR-10.
0.90
0.95
where f1
is the accuracy of the model, and f2
is the corresponding
energy consumption. When classifying an image, if
the result is correct, a reward r can be obtained; otherwise, a penalty
x is performed. By giving a fixed amount of energy budget,
the number of images that can be classified is inversely proportional
to the energy consumed per image
f .2
From Equation (8),
it can be seen that one of the key parameters in this aggregation
score system is the ratio between the reward and the penalty /r x,
which indicates the significance of accuracy. The selection of the
optimal solution highly depends on the ratio /r x.
r/τ = 5
r/τ = 1
r/τ = 0.2
0.95
1
X:Y
FX:FY
CI:CO
X:FX
COO CSR-Relative
Normal
23
22
21
1
2-1
2-3
2-2
0.70
0.75
0.80
0.85
Accuracy
FIGURE 9 The model size of VGG-16 over the model size of MobileNet
under different accuracy scores on CIFAR-10.
0.90
0.95
AUGUST 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 19
Normalized Score
Normalized Score
Ratio of Model Size
Ratio of Energy Cons.
Normalized Score

IEEE Computational Intelligence Magazine - August 2021

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