Near-Lossless Deep Feature Compression for Collaborative Intelligence

Abstract

Collaborative intelligence is a new paradigm for efficient deployment of deep neural networks across the mobile-cloud infrastructure. By dividing the network between the mobile and the cloud, it is possible to distribute the computational workload such that the overall energy and/or latency of the system is minimized. However, this necessitates sending deep feature data from the mobile to the cloud in order to perform inference. In this work, we examine the differences between the deep feature data and natural image data, and propose a simple and effective near-lossless deep feature compressor. The proposed method achieves up to 5% bit rate reduction compared to HEVC-Intra and even more against other popular image codecs. Finally, we suggest an approach for reconstructing the input image from compressed deep features in the cloud, that could serve to supplement the inference performed by the deep model.

Full text

Near-Lossless Deep Feature Compression for
Collaborative Intelligence
Hyomin Choi
School of Engineering Science
Simon Fraser University
Burnaby, BC, Canada
Email: chyomin@sfu.ca
Ivan V. Baji´
c
School of Engineering Science
Simon Fraser University
Burnaby, BC, Canada
Email: ibajic@ensc.sfu.ca
Abstract—Collaborative intelligence is a new paradigm for
efficient deployment of deep neural networks across the mobile-
cloud infrastructure. By dividing the network between the mobile
and the cloud, it is possible to distribute the computational
workload such that the overall energy and/or latency of the
system is minimized. However, this necessitates sending deep
feature data from the mobile to the cloud in order to perform
inference. In this work, we examine the differences between
the deep feature data and natural image data, and propose a
simple and effective near-lossless deep feature compressor. The
proposed method achieves up to 5% bit rate reduction compared
to HEVC-Intra and even more against other popular image
codecs. Finally, we suggest an approach for reconstructing the
input image from compressed deep features in the cloud, that
could serve to supplement the inference performed by the deep
model.
Index Terms—Deep feature compression, collaborative intelli-
gence, deep neural network, input reconstruction
I. INTRODUCTION
Recent advances in deep neural networks (DNNs) are
making various artificial intelligence (AI)-enabled applications
feasible: intelligent surveillance cameras, automated personal
assistants, self-driving cars, unmanned aerial vehicles, and
so on [1]. A common deployment strategy for AI-based
applications on mobile devices is to have the AI model running
in the cloud while the terminus device sends its data to it for
inference, and receives the results back. In certain cases, small
models may run on the terminus device, but the large models
that form the backbone of most AI-enabled systems are too
power hungry to run on a mobile device.
A recent study [2] proposed a new deployment paradigm
called collaborative intelligence, whereby a deep model is
split between the mobile and the cloud. Extensive experiments
under various hardware configurations and wireless connectiv-
ity modes revealed that the optimal operating point in terms
of energy consumption and/or computational latency involves
splitting the model, usually at a point deep in the network.
Today’s common solutions, where the model sits fully in the
cloud or fully at the mobile, were found to be rarely (if
ever) optimal. Another recent study [3] extended the notion
of collaborative intelligence to model training as well. In this
case, data flows both ways: from the cloud to the mobile during
back-propagation in training, and from the mobile to the cloud
during forward passes in training, as well as inference.
In these early studies, the issue of compression for the
purpose of data transfer between the mobile and the cloud
was not studied in detail. In fact, [2] assumed the transfer
of raw 32-bit floating point feature values, which is rather
wasteful. The work in [3] included 8-bit quantization followed
by PNG coding of quantized feature maps. The work in [4]
was the first to study lossy compression of deep feature data
based on HEVC intra coding, in the context of a recent deep
model for object detection [5]. They noted the degradation of
detection performance with increased compression levels and
proposed compression-augmented training to minimize this
loss by producing a model that is more robust to quantization
noise in feature values. However, this is still a sub-optimal
solution, because the codec employed is highly complex [6]
and optimized for natural scene compression rather than deep
feature compression.
A related work [7] presented semantic image compression
by encoding deep features and then reconstructing the input
image from them. The compression was based on uniform
quantization followed by context-based adaptive arithmetic
coding (CABAC) from H.264 [8]. This work was positioned
as an image codec that preserves semantic information for
image classification, rather than a tool for collaborative intel-
ligence, but the similarities are evident. Although the overall
compression efficiency of this approach was somewhat lower
than JPEG and JPEG2000, the authors argued that the benefits
lie in better preservation of semantic information.
With a view towards collaborative intelligence, in this work
we propose a simple and effective near-lossless compression
method tailored to deep feature data. We focus on deep
models for object detection [5] and image classification [9],
but the approach is applicable to other deep models as well. In
Section II we analyze feature data from the two models under
study, and note some of the statistical differences between
deep feature data and input image data. This analysis informs
the design of the proposed compression scheme in Section III.
Furthermore, we demonstrate the capability of reconstructing
the input image from compressed deep features in Section IV
by constructing and training a mirror model of front-end
layers. Experimental results and conclusions are presented in
Sections V and VI, respectively.
arXiv:1804.09963v1 [eess.IV] 26 Apr 2018

Fig. 1. Collaborative intelligence approach with deep feature compression
II. DE EP F EATU RE DATA ANALYS IS
Fig. 1 shows the basic setup for collaborative intelligence,
where the feature data produced by the initial layers of the
deep model are compressed and sent to the cloud for further
processing. The efficiency of this approach lies in the fact
that for many deep models based on convolutional neural
networks (CNNs), the feature data volume (i.e., the total
number of feature values) decreases as we move deeper into
the network [2], [3], [4]. Feature values are typically quantized
using an n-bit uniform quantizer (Q-layer in Fig. 1) prior to
lossless [3] or lossy [4] compression.
e
V=round V−min(V)
max(V)−min(V)·(2n−1)(1)
where V∈RN×M×Cis the feature tensor with Nrows,
Mcolumns, and Cchannels at the point of split, e
Vis
the quantized feature tensor, and min(V)and max(V)are
the minimum and maximum value in V, respectively. In
the studies performed so far [3], [4], [7], this uniform n-bit
quantization was shown to have negligible effect on image
classification and object detection accuracy, for n≥6. For
this reason, when such uniform quantizer is followed up by
a lossless encoder, we refer to the resulting approach as
near-lossless compression. In this work, the Q-layer performs
uniform 8-bit quantization. Note that min(V)and max(V)
need to be transferred to the cloud for the inverse Q process.
The quantized features e
Vare rearranged in a tiled image,
as shown in Fig. 2. With Cchannels, we place
2ceil(1
2log2C)and 2floor(1
2log2C)(2)
feature channels (tiles) width-wise and height-wise, respec-
tively. Here, ceil(·)and floor(·)represent ceiling and flooring
to the nearest integer, respectively.
Fig. 2 shows the tiled quantized features obtained from
YOLOv2 [5] and VGG16 [9] with default weights for the
same input image. For each model, three layers are selected
(max-pooling layers in all cases) where the resulting feature
volume is of comparable size between the two models. We see
that, qualitatively, the features are different between the two
models, which is not surprising considering that they were
trained for different purposes. There are several tiles that still
contain somewhat interpretable structures in Fig. 2(a) and (d),
but the features become more abstract as we move towards
deeper layers (b), (c), (e) and (f). Both sets of features also
differ significantly from natural images.
Fig. 3 shows pixel and feature histograms for two different
input images. As shown in Fig. 3(a) and (d), which present the
luma histograms of input images, pixel intensities in natural
images tend to be distributed over the entire range 0-255.
In these two input images, no pixel value has a probability
above 0.1. Meanwhile, histograms of quantized feature values
in Fig. 3(b), (c), (e), and (f) are much more concentrated, and
they tend to become more concentrated as we move deeper
into the network. Entropy values indicated in figure legends
confirm this quantitatively.
While feature value concentration occurs in both YOLOv2
and VGG16, it is interesting that the concentration points in
these two models are different. VGG16 uses Rectified Linear
Unit (ReLU) activations [10], which are lower-bounded by
zero, and the resulting features values concentrate near zero.
On the other hand, YOLOv2 uses leaky ReLU activations [10],
which admit negative values. Hence, prior to quantization,
feature values concentrate near zero, but negative feature
values exist (i.e., min(V)<0). After quantization (1), zero
gets mapped to a small positive value (usually 15-25), so the
concentration point of quantized features is away from zero.
Next we examine spatial statistics. Specifically, we look at
the similarity between the current pixel and its neighbors:
left (l), top (t), top-left (tl), bottom-left (bl), and top-right
(tr). We also look at the similarity with the 8 most frequent
values in a given histogram: mi, i = 0,1, ...7. To capture the
similarity, we consider indicators ADT
kfor a given threshold
T, where k∈ {m, l, t, tl, bl, tr}. ADT
mis incremented if the
absolute difference between the current pixel/feature value
xand any (one or more) of the mivalues is less than T:
|x−mi|< T for any i. If |x−mi| ≥ Tfor all i, then we
test the similarity with k∈ {l, t, tl, bl, tr}, in that order. If
|x−k|< T , ADT
kis incremented and we move to the next
pixel/feature value. Table I shows ADT
kfor T= 2, expressed
as percentages. The results were obtained on the 2510 images
from the VOC2007 dataset [11]. Compared to the natural
image statistics (second row in the table), we note that feature
values exhibit much more similarity with the most frequent
values (AD2
m), and much less similarity with spatial neighbors
(AD2
k, for k∈ {l, t, tl, bl, tr}). This trend increases as we
move deeper into the network. Hence, one cannot expect that
natural image codecs, which place strong emphasis on spatial
redundancy, would be optimal for encoding deep feature data
– new approaches are needed for this purpose.
TABLE I
SIMILARITY OF PIXEL/FE ATURE VAL UES W IT H SPATIA L NE IGH BO RS AN D
MO ST FR EQU EN T VALUE S
AD2
mAD2
lAD2
tAD2
tl AD2
bl AD2
tr none
Input image 22.06% 26.19% 10.77% 4.83% 4.23% 3.27% 28.65%
YOLOv2
L7 67.59% 9.75% 3.65% 1.27% 1.20% 1.02% 15.52%
L11 73.81% 5.80% 2.34% 0.81% 0.80% 0.71% 15.73%
L17 83.63% 1.12% 0.30% 0.28% 0.28% 0.25% 14.14%
VGG16
L6 64.49% 6.69% 4.30% 1.86% 1.82% 1.56% 19.28%
L10 69.62% 3.75% 2.72% 1.42% 1.41% 1.26% 19.82%
L14 83.68% 1.12% 0.84% 0.45% 0.46% 0.43% 13.02%

(a) (b) (c)
(d) (e) (f)
Fig. 2. Quantized deep features (enhanced for visualization purposes) from YOLOv2 [5] and VGG16 [9] at various points in the network. Top row: (a)
seventh (b) eleventh and (c) seventeenth layer in YOLOv2. Bottom row: (d) sixth (e) tenth and (f) fourteenth layer in VGG16.
(a) (b) (c)
(d) (e) (f)
Fig. 3. (a) and (d) are histograms of pixel values of two input images, (b) and (e) are histograms of the quantized output of the seventh, eleventh and
seventeenth layer of YOLOv2, while (c) and (f) are histograms of the quantized output of the sixth, tenth and fourteenth layer of VGG16. Corresponding
entropies (E, in bits) are indicated in the plots.
III. DEEP FEATURE COMPRESSION
Fig. 4 shows the proposed compression framework for deep
features in collaborative intelligence applications. In the cloud,
deep features are decoded and used for inference. They can
also optionally be used for input reconstruction, as discussed
in Section IV.
Before coding the quantized feature data, the following
parameters are encoded directly using fixed-length coding:
dimensions of the feature tensor, min(V)and max(V)(32-
bit each) and the eight most frequent feature values, mi
for i= 0,1, ...7. The set of {mi}is obtained over the
entire quantized feature tensor. A vector of these values,
p= (p0, p1, ..., p7), is referred to as the palette vector.
Initially, the palette vector is sorted according to the fre-
quency of these values in the first tile, so that p0is the most
frequent of the mi’s in the first tile, p1is the next most
frequent, etc. As we move to other tiles, the palette vector
p= (p0, p1, ..., p7)is re-sorted according to the frequency of
occurrence of mi’s up to the previously coded tile, so that p0
is the most frequent miup to that point, and so on. At the
tile boundary, once pis updated, one element of pis chosen
to minimize the mean absolute difference (MAD) from the
feature values in the to-be-coded tile. Its index is found as
j∗= arg min
0≤j≤7X
i
|xi−pj|(3)

Fig. 4. Proposed deep feature compression for collaborative intelligence
TABLE II
UNARY C ODE F OR T HE PAL ETT E IN DEX
Index j∗Codeword Index j∗Codeword
01411110
110 5111110
2110 61111110
31110 71111111
where igoes over all locations in the tile. Once j∗is found,
it is encoded using the truncated 8-symbol unary code [12]
shown in Table II.
Every 4×4 block of feature values is predicted using one
of five modes: palette (Pal), horizontal (Hor), vertical (Ver),
and two filter modes (Fil). In the Pal mode, all values in
the block are predicted using pj∗. In Hor/Ver modes, the
immediate left/top value is used as a predictor, as indicated in
Fig. 5. If the block is at the left (top) boundary, pj∗is used
as the left (top) value. The two Fil modes are based on 3-
tap filters with coefficients [3,7,22]/32 or [14,0,18]/32 [13],
and use the top-left, top, and left feature values to predict the
current value. Again, at the boundaries, the unavailable values
are replaced by pj∗.
Prediction mode decision is based on the number of bits
required for coding the residual, with the best mode being
the one that requires least bits. In order to minimize the bits
needed to specify the prediction mode, we exploit the most
probable mode (mpm) method [14], where mpm is derived from
the previously-coded left, top-left and top blocks’ prediction
modes. The most frequently used mode among them is con-
sidered the mpm. If the current block’s mode is the same as
mpm, bit 1 is coded by CABAC [15] to indicate it. Otherwise,
bit 0 is coded, followed by two bits to indicate the mode1.
Prediction residuals for each 4×4block are coded by
CABAC. The first bit is the SKIP indicator. If the residual
is all-zero, the SKIP indicator is set to 1 and the encoder
moves to the next block. Otherwise, the SKIP indicator is set
to 0 and residuals are coded using one of three scan orders:
horizontal, vertical, and zig-zag. For the Ver (Hor) prediction
mode, vertical (horizontal) scan order is used. Other modes
use the zig-zag scan order. Locations of non-zero residuals
are first indicated by binarizing the scanned block, with 1’s
1There are five prediction modes in total, so if the mode is not mpm, it
must be one of the other four, which can be indicated by two bits.
Fig. 5. Illustration of Hor (green) and Ver (blue) prediction modes for the
4×4 block (red). Shaded regions are neighbouring feature values.
placed at the locations of non-zero residuals and 0’s placed
elsewhere. This binary vector is coded using CABAC. Finally,
the non-zero residual values are coded in a manner similar to
HEVC [15]: values larger than 1 or 2 are flagged, the flags are
CABAC-coded, and the non-flagged values are binarized using
exponential Golomb-Rice coding, then coded by CABAC.
IV. INPUT RECONSTRUCTION
Although the primary goal of collaborative intelligence is
efficient inference, in some cases it may be desirable to also
have the input image available in the cloud. For example, if
the model detects an object of interest based on the features
that were transmitted to the cloud, it might be useful to have
the whole input image, which can then be stored or further
processed in the cloud. The straightforward way is to simply
send the whole input image from the mobile to the cloud, but
this is not necessary, since a good approximation to the input
image can be reconstructed from the transmitted features.
To demonstrate this, we construct a mirror model, indicated
in the bottom right of Fig. 4, based on the the network in
the mobile. Specifically, given the network in the mobile, the
mirror model consists of the same number of layers, but in
reverse order: convolutional layers from the mobile network
are mapped to the same convolutional layers in the mirror
model, while max-pooling layers from mobile network are
mapped to up-sampling layers.
The goal of the mirror model is to reconstruct the input
image from the deep features transmitted to the cloud. We train
the mirror model using a loss function that combines structural
similarity (SSIM) [16] and mean square error (MSE) between
the input and the reconstructed image, as
L=λ1·(1 −SSIM) + λ2·MSE (4)
We used λ1= 0.6and λ2= 1. The mirror model is trained
from scratch using the Adam optimizer [17] with the initial
learning rate of 10−4. A total of 16,551 images from [11]
and [18] are employed for training the model, with 20%
randomly selected as validation data and the remaining 80%
used for training. The test set consists of another 4,952 images
from [11]. The maximum number of epochs is set to 50 and
batch size to 32. The training stops when the validation loss
starts increasing.
V. EX PE RI ME NT S
The proposed deep feature compression was tested on four
deep models: YOLOv2 [5], Darknet19 448 [19], VGG16 [9]

Fig. 6. Comparison of average bits saving for the three different deep features from each network against conventional compression algorithms
and ResNet [20]. YOLOv2 is a state-of-the-art object detector,
while other models are used for image classification. Table III
shows the size of the feature tensor at the output of three layers
from each of the models, along with the dimensions of the
feature matrix after tiling. For testing compression of YOLOv2
features we used 4,952 images from VOC2007 [11], and for
other models we used 50,000 images from ImageNet [21].
Deep features produced by the various models were com-
pressed using the proposed method, as well as the lossless
versions of HEVC [22], VP9, PNG, JPEG2000 and JPEG. For
HEVC, we followed common test conditions [23] associated
with lossless coding, while changing the largest coding unit
size, also known as CTU, to 32×32 and 16×16.
As usual, evaluation of lossless coding is based on the
number of bits used. Fig. 6 shows the average bit difference
between the proposed method and each of the five competing
methods, on the image datasets described above. Positive
values mean that the competing method uses more bits than the
proposed one. As seen in the figure, HEVC (with both CTU
sizes) needs 0.7-3.0% more bits than the proposed method in
most cases, and up to 5% more for the tenth and fourteenth
layer of VGG16. VP9 also uses more bits than the proposed
method (up to 34% more in the fourtenth layer of VGG16),
except for the seventh layer of the Darkent19 448 where it
uses 0.96% fewer bits. PNG turns out to be a very good
codec for deep feature data. While it uses more bits than the
proposed method in most cases, it needs up to 9% fewer bits
in the fourteenth layer of VGG16. Both JPEG2000 and JPEG
require considerably more bits than other codecs. Compared
to the proposed method, JPEG2000 needs up to 45% more
bits and JPEG needs up to 61% more bits.
Finally, we demonstrate input reconstruction from the fea-
tures generated at the seventh, eleventh and seventeenth layer
of YOLOv2. Hence, three mirror models are trained for
reconstruction, one for each set of features. Table IV shows
the average Peak Signal to Noise Ratio (PSNR, in dB) and
SSIM, along with standard deviations, over the test set. As
seen in the table, the deeper the layer from which features
are extracted, the more difficult is the input reconstruction,
since more information gets lost in max-pooling layers. Visual
results, shown in Fig. 7, look somewhat better than what
is suggested by quantitative results in Table IV. The first
row shows the original input images, while the remaining
rows show reconstructed images from the seventh, eleventh
and seventeenth layer, in that order. Reconstructions from the
seventh layer look reasonably good compared to the original
images. However, reconstructions from deeper layers start to
lose important details.
VI. CONCLUSION
In this study, we examined the characteristics of deep feature
data and proposed a simple and effective method for near-
lossless deep feature compression. The proposed method out-
performs state-of-the-art image codec in this regard. We also
demonstrated input image reconstruction from deep feature
data by constructing and training a mirror model. Future work
will involve the development of lossy compression schemes
for deep feature data.
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DIM ENS IO NS OF F EATU RE TE NS ORS A ND F EATUR E MATR ICE S AT THR EE
DI FFER EN T LAYER S OF E ACH O F THE M ODE LS I N THE S TU DY.
Model Layer Feature tensor Feature matrix
YOLOv2
L7 128×52×52 832×416
L11 256×26×26 416×416
L17 512×13×13 416×208
Darknet19 448
L7 128×56×56 896×448
L11 256×28×28 448×448
L17 512×14×14 448×224
VGG16
L6 128×56×56 896×448
L10 256×28×28 448×448
L14 512×14×14 448×224
ResNet
L43 128×32×32 512×256
L91 256×16×16 256×256
L135 256×16×16 256×256
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TABLE IV
COMPARISON OF PSNR & SSIM INDE X FO R THE R ECO NS TRU CTE D IN PUT
IMAGES COMPARED TO ORIGINAL INPUTS.
PSNR SSIM
Avg. Std. Avg. Std.
L7
Y 23.8633 2.8674 0.7042 0.1107
U 35.8363 3.8942 0.9411 0.0344
V 33.0488 4.1624 0.9160 0.0452
L11
Y 17.5348 1.7231 0.4743 0.1319
U 30.7260 2.6935 0.9106 0.0466
V 27.6556 3.1462 0.8645 0.0613
L17
Y 14.2898 1.7578 0.4044 0.1367
U 28.6288 3.5730 0.9072 0.0505
V 25.8074 3.9733 0.8560 0.0648