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.

翻译：在过去几年里,神经网络开始渗透安全临界系统,以便在机器人、火箭、自主驾驶汽车等方面作出决定。 问题在于这些关键系统往往具有有限的计算资源。 它们往往使用固定点算法来计算其许多优点(快速、与小型内存装置兼容)。 在本篇文章中,采用了一种新技术来调整已经受过训练的神经网络的格式(精度),使用固定点算术只能使用整数操作。新的优化神经网络用固定点数计算输出,而没有将精确度修改到用户确定的临界值。固定点代码是针对新的优化神经网络合成的,以确保尊重在分析中确定的范围[xmin,xmax]的任何输入矢的临界值。从技术角度出发,我们对我们浮动神经网络进行初步分析,以确定最坏的情况,然后我们用直线编程程序对整数变量产生线性限制系统。这个系统的解决方案是每个神经神经网络的新的固定点格式,确保每个神经神经神经网络的新的固定度格式。实验结果显示我们作为新固定网络的初始状态的效率。