Over the last few years, neural networks have started penetrating safety
critical systems to take decisions in robots, rockets, autonomous driving car,
etc. A problem is that these critical systems often have limited computing
resources. Often, they use the fixed-point arithmetic for its many advantages
(rapidity, compatibility with small memory devices.) In this article, a new
technique is introduced to tune the formats (precision) of already trained
neural networks using fixed-point arithmetic, which can be implemented using
integer operations only. The new optimized neural network computes the output
with fixed-point numbers without modifying the accuracy up to a threshold fixed
by the user. A fixed-point code is synthesized for the new optimized neural
network ensuring the respect of the threshold for any input vector belonging
the range [xmin, xmax] determined during the analysis. From a technical point
of view, we do a preliminary analysis of our floating neural network to
determine the worst cases, then we generate a system of linear constraints
among integer variables that we can solve by linear programming. The solution
of this system is the new fixed-point format of each neuron. The experimental
results obtained show the efficiency of our method which can ensure that the
new fixed-point neural network has the same behavior as the initial
floating-point neural network.

介绍了一种使用定点算数对已训练的神经网络进行精度调整的新技术，其可仅使用整数操作实施，并用线性规划生成一个新的定点格式，以确保其与浮点格式的行为相同，可用于安全关键系统中。

神经网络固定点代码合成

Fixed-Point Code Synthesis For Neural Networks

Neural Networks are being integrated into safety critical systems, e.g.,
perception systems for autonomous vehicles, which require trained networks to
perform safely in novel scenarios. It is challenging to verify neural networks
because their decisions are not explainable, they cannot be exhaustively
tested, and finite test samples cannot capture the variation across all
operating conditions. Existing work seeks to train models robust to new
scenarios via domain adaptation, style transfer, or few-shot learning. But
these techniques fail to predict how a trained model will perform when the
operating conditions differ from the testing conditions. We propose a metric,
Machine Learning (ML) Dependability, that measures the network's probability of
success in specified operating conditions which need not be the testing
conditions. In addition, we propose the metrics Task Undependability and
Harmful Undependability to distinguish network failures by their consequences.
We evaluate the performance of a Neural Network agent trained using
Reinforcement Learning in a simulated robot manipulation task. Our results
demonstrate that we can accurately predict the ML Dependability, Task
Undependability, and Harmful Undependability for operating conditions that are
significantly different from the testing conditions. Finally, we design a
Safety Function, using harmful failures identified during testing, that reduces
harmful failures, in one example, by a factor of 700 while maintaining a high
probability of success.

本文提出了一种机器学习可靠性指标，可以评估神经网络在不同的操作条件下的成功概率，并通过设计安全功能来减少有害失效，同时在维持高成功概率的前提下，在机器人操纵任务中进行了实际应用测试。

安全关键任务的可靠神经网络

Dependable Neural Networks for Safety Critical Tasks

Safety critical systems involve the tight coupling between potentially
conflicting control objectives and safety constraints. As a means of creating a
formal framework for controlling systems of this form, and with a view toward
automotive applications, this paper develops a methodology that allows safety
conditions -- expressed as control barrier functions -- to be unified with
performance objectives -- expressed as control Lyapunov functions -- in the
context of real-time optimization-based controllers. Safety conditions are
specified in terms of forward invariance of a set, and are verified via two
novel generalizations of barrier functions; in each case, the existence of a
barrier function satisfying Lyapunov-like conditions implies forward invariance
of the set, and the relationship between these two classes of barrier functions
is characterized. In addition, each of these formulations yields a notion of
control barrier function (CBF), providing inequality constraints in the control
input that, when satisfied, again imply forward invariance of the set. Through
these constructions, CBFs can naturally be unified with control Lyapunov
functions (CLFs) in the context of a quadratic program (QP); this allows for
the achievement of control objectives (represented by CLFs) subject to
conditions on the admissible states of the system (represented by CBFs). The
mediation of safety and performance through a QP is demonstrated on adaptive
cruise control and lane keeping, two automotive control problems that present
both safety and performance considerations coupled with actuator bounds.

本文在实时基于优化的控制器的背景下，发展了一种方法论，将以控制层李雅普诺夫函数表达的性能目标与以控制屏障函数表示的安全条件相结合，并在二次规划的框架下演示了自适应巡航控制和车道保持这两个汽车控制问题的安全和性能的调节。