enables multi-object optimization by considering the conjunction of resource
consumption and performance as the two main objectives. Furthermore, single-
path NAS [SDW+19] extends the multi-path approach of former gradient-based
methods and proposes the integration of ’over-parameterized superkernels’,
which significantly reduces memory consumption.

The focus of NAS is on the optimized combination of humanly predefined CNN
elements with respect to objectives such as resource consumption and
performance. NAS offers automation, however, the realization of the objectives
is strongly limited by the potential of the CNN elements.

##  10 Model Compression

MMSerin Varghese7

Recent developments in CNNs have resulted in neural networks being the state-
of-the-art in computer vision tasks like image classification [KSH12, HZRS15,
MGR+18], object detection [Gir15, RDGF15, HGDG17] and semantic segmentation
[CPSA17, ZSR+19, WSC+19, LBS+19]. This is largely due to the increasing
availability of hardware computational power and an increasing amount of
training data. We also observe a general upwards trend of the complexities of
the neural networks along with their improvement in state-of-the-art
performance. These CNNs are largely trained on back-end servers with
significantly higher computing capabilities. The use of these CNNs in real-
time applications are inhibited due to the restrictions on hardware, model
size, inference time, and energy consumption. This led to an emergence of a
new field in machine learning, commonly termed as model compression. Model
compression basically implies reducing the memory requirements, inference
times and model size of DNNs to eventually enable the use of neural networks
on edge devices. This is tackled by different approaches such as _network
pruning_ (identifying weights or filters that are not critical for network
performance), _weight quantizations_ (reducing the precision of the weights
used in the network), _knowledge distillation_ (a smaller network is trained
with the knowledge gained by a bigger network), and _low-rank factorization_
(decomposing a tensor into multiple smaller tensors). In this section, we
introduce some of these methods for model compression and discuss in brief the
current open challenges and possible research directions with respect to its
use in automated driving applications.

###  10.1 Pruning

MMFalk Kappel13, Serin Varghese7

Pruning has been used as a systematic tool to reduce the complexity of deep
neural networks. The redundancy in DNNs may exist on various levels, such as
the individual weights, filters, and even layers. All the different methods
for pruning try to take advantage of these available redundancies on various
levels. Two of the initial approaches for neural networks proposed weight
pruning in the 1990s as a way of systematically damaging neural networks
[CDS90, Ree93]. As these weight pruning approaches do not aim at changing the
structure of the neural network, these approaches are called _unstructured
pruning_. Although there is reduction in the size of the network when it is
saved in sparse format, the acceleration depends on the availability of
hardware that facilitate sparse multiplications. As pruning filters and
complete layers aim at exploiting the available redundancy in the architecture
or structure of neural networks, these pruning approaches are called
_structured pruning_. Pruning approaches can also be broadly classified into:
data-dependent and data-independent methods. Data-dependent methods [LLS+17,
LWL17, HZS17] make use of the training data to identify filters to prune.
Theis et al.[TKTH18] and Molchanov et al.[MTK+17] propose a greedy pruning
strategy that identifies the importance of feature maps one at a time from the
network and measures the effect of removal of the filters on the training
loss. This means that filters corresponding to those feature maps that have
least effect on training loss are removed from the network. Within data-
independent methods [LKD+17, HKD+18, YLLW18, ZQF+18], the selection of CNN
filters to be pruned are based on the statistics of the filter values. Li et
al.[LKD+17] proposed a straightforward method to calculate the rank of filters
in a CNN. The selection of filters are based on the $\ell_{1}$-norm, where the
filter with the lowest norm is pruned away. He et al.[HZS17] employ a LASSO
regression-based selection of filters to minimize the least squares
reconstruction.

Although the above-mentioned approaches demonstrated that a neural network can
be compressed without affecting the accuracy, the effect on robustness is
largely unstudied. Dhillon et al.[DAL+18] proposed pruning a subset of
activations and scaling up the survivors to show improved adversarial
robustness of a network. Lin et al.[LGH19] quantize the precision of the
weights after controlling the Lipschitz constant of layers. This restricts the
error propagation property of adversarial pertubations within the neural
network. Ye et al.[YLX+19] evaluated the relationship between adversarial
robustness and model compression in detail and show that naive compression has
a negative effect on robustness. Gui et al.[GWY+19] co-optimize robustness and
compression constraints during the training phase and demonstrate improvement
in the robustness along with reduction in the model size. However, these
approaches have mostly been tested on image classification tasks and on
smaller datasets only. Their effectiveness on safety-relevant automated
driving tasks such as object detection and semantic segmentation tasks are not
studied and remains an open research challenge.

###  10.2 Quantization

MMFiras Mualla13

Quantization of a random variable $x$ having a probability density function
$f(x)$ is the process of dividing the range of $x$ into intervals, each is
represented using a single value (also called reconstruction value), such that
the following reconstruction error is minimized:

$\sum_{i=1}^{L}\int_{b_{i}}^{b_{i+1}}(q_{i}-x)^{2}f(x)dx,$ (9)

where $b_{i}$ is the left-side border of the i-th interval, $q_{i}$ is its
reconstruction value, and $L$ is the number of intervals, e.g., $L=8$ for a
3-bit quantization. This definition can be extended to multiple dimensions as
well.

Quantization of neural networks has been around since the 1990s [Guo18],
however, with a focus in the early days on improving the hardware
implementations of these networks. In the deep learning literature, a
remarkable application of quantization combined with unstructured pruning can
be found in the approach of deep compression [HMD16], where 1-dimensional
k-means is utilized to cluster the weights per layer and thus finding the $L$
cluster centers ($q_{i}$ values in (9)) iteratively. This procedure conforms
to an implicit assumption that $f(x)$ has the same spread inside all clusters.
Deep compression can reduce the network size needed for image classification
by a factor of 35 for AlexNet and a factor of 49 for VGG-16 without any loss
in accuracy. However, as pointed out in [JKC+18], these networks from the
early deep learning days are over-parameterized and a less impressing
compression factor is thus expected when the same technique is applied to
lightweight architectures such as MobileNet and SequeezeNet. For instance,
considering SqueezeNet (50 times smaller than AlexNet), the compression factor
of deep compression without accuracy loss drops to about 10.

Compared to scalar quantization used in deep compression, there were attempts
to exploit the structural information by applying variants of vector
quantization of the weights [GLYB14, CEL20, SJG+20]. Remarkably, in the latter
(i.e., [SJG+20]), the reconstruction error of the activations (instead of the
weights) is minimized in order to find an optimal codebook for the weights, as
the ultimate goal of quantization is to approximate the network’s output not
the network itself. This is performed in a layer-by-layer fashion (as to
prevent error accumulation) using activations generated from unlabeled data.

Other techniques [MDSN17, JKC+18] apply variants of so-called “linear”
quantization, i.e., the quantization staircase has a fixed interval size. This
paradigm conforms to an implicit assumption that $f(x)$ in (9) is uniform and
is thus also called uniform quantization. The uniform quantization is widely
applied both in specialized software packages such as the Texas Instruments
Deep Learning Library (automotive boards) [MDS+18] and in general-purpose
libraries such as the Tensorflow Lite. The linearity assumption enables
practical implementations, as the quantization and dequantization can be
implemented using a scaling factor and an intercept, whereas no codebook needs
to be stored. In many situations, the intercept can be omitted by employing a
symmetric quantization mapping. Moreover, for power of 2 ranges, the scaling
ends up being a bitwise shift operator, where quantization and dequantization
differ only in the shift direction. It is also straightforward to apply this
scheme dynamically, i.e., for each tensor separately using a tensor-specific
multiplicative factor. This can be easily applied not only to filters (weight
tensors) but also to activation tensors (see for instance [MDSN17]).

Unless the scale factor in the linear quantization is assumed constant by
construction, it is computed based on the statistics of the relevant tensor
and can be thus sensitive to outliers. This is known to result in a low
precision quantization. In order to mitigate this issue, the original range
can be clipped and thus reduced to the most relevant part of the signal.
Several approaches are proposed in the literature for finding an optimal
clipping threshold: simple percentile analysis of the original range (e.g.,
clipping 2% of the largest magnitude values), minimizing the mean square error
between the quantized and original range in the spirit of (9) [BNS19], or
minimizing the Kullback-Leibler divergence between the original and the
quantized distributions [Mig17]. While the clipping methods trade off large
quantization errors of outliers against small errors of inliers [WJZ+20],
other methods tackle the outliers problem using a different trade-off, see for
instance the outlier channel splitting approach in [ZHD+19].

An essential point to consider when deciding for a quantization approach for a
given problem is the allowed or intended interaction with the training
procedure. The so-called post-training quantization, i.e., quantization of a
pre-trained network, seems to be attractive from a practical point of view: No
access to training data is required and the quantization and training toolsets
can be independent from each other. On the other hand, the training-aware
quantization methods often yield higher inference accuracy and shorter
training times. The latter is a serious issue for large complicated models
which may need weeks to train on modern GPU clusters. The training-aware
quantization can be implemented by inserting fake quantization operators in
the computational graph of the forward-pass during training (simulated
quantization), whereas the backward pass is done as usual in floating-point
resolution [JKC+18]. Other approaches [ZGY+19, ZWN+16] go a step further by
quantizing the gradients as well. This leads to much lower training time, as
the time of the often computationally expensive backward pass is reduced. The
gradient’s quantization, however, is not directly applicable as it requires
the derivative of the quantization function (staircase-like), which is zero
almost everywhere. Luckily, this issue can be handled by employing a straight-
through estimator [BLC13] (approximating the quantization function by an
identity mapping). There are also other techniques proposed recently to
mitigate this problem [UMY+19, LM19].

##  11 Discussion

We have presented an extensive overview of approaches to effectively handle
safety concerns accompanying deep learning: lack of generalization,
robustness, explainability, plausibility, and efficiency. It has been
described which lines of research we deem prevalent, important, and promising
for each of the individual topics and categories into which the presented
methods fall.

The reviewed methods alone will not provide safe ML systems as such – and
neither will their future extensions. This is due to the limitations of
quantifying complex real-world contexts. A complete and plausible _safety
argumentation_ will, thus, require more than advances in methodology and
theoretical understanding of neural network properties and training processes.
Apart from methodological progress, it will be necessary to gain practical
experience in using the presented methods to gather evidence for overall
secure behavior, using this evidence to construct a tight safety argument, and
testing its validity in various situations.

In particular, each autonomously acting robotic system with state-of-the-art
deep-learning-based perception and non-negligible actuation may serve as an
object of study and is, in fact, in need of this kind of systematic reasoning
before being transferred to widespread use or even market entry. We strongly
believe that novel scientific insights, the potential market volume, and
public interest will drive the arrival of reliant and trustworthy AI
technology.

## Acknowledgment

The research leading to these results is funded by the German Federal Ministry
for Economic Affairs and Energy within the project “KI Absicherung – Safe AI
for Automated Driving”. The authors would like to thank the consortium for the
successful cooperation. Furthermore, this research has been funded by the
Federal Ministry of Education and Research of Germany as part of the
competence center for machine learning ML2R (01IS18038B).

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