基于模板的位置乘法在神经网络训练和推理中的应用
Template-Based Posit Multiplication for Training and Inferring in Neural Networks
摘要：
数字系统可以说是当今算术中最有前途和讨论的话题。最近的突破所声称的格式提出的约翰L。古斯塔夫森把假设放在聚光灯下。在这项工作中，我们首先描述了一个算法乘以两个整数，即使指数位的数量为零。这种配置在文献中很少涉及，特别有趣，因为它允许部署快速S形函数。然后将所提出的乘法算法作为模板集成到众所周知的FloPoCo框架中。综合结果显示，比较与浮点乘法提供的FloPoCo以及。其次，研究了假设在神经网络的训练和推理阶段的性能。据我们所知，这是第一次使用训练格式进行训练，即使使用减少的训练格式配置，也能为二进制分类问题取得令人满意的结果。在推理阶段，处理MNIST数据集时，8位定位与浮点一样好，但在CIFAR-10中失去了一些准确性。
英文摘要：
The posit number system is arguably the most promising and discussed topic in Arithmetic nowadays. The recent breakthroughs claimed by the format proposed by John L. Gustafson have put posits in the spotlight. In this work, we first describe an algorithm for multiplying two posit numbers, even when the number of exponent bits is zero. This configuration, scarcely tackled in literature, is particularly interesting because it allows the deployment of a fast sigmoid function. The proposed multiplication algorithm is then integrated as a template into the well-known FloPoCo framework. Synthesis results are shown to compare with the floating point multiplication offered by FloPoCo as well. Second, the performance of posits is studied in the scenario of Neural Networks in both training and inference stages. To the best of our knowledge, this is the first time that training is done with posit format, achieving promising results for a binary classification problem even with reduced posit configurations. In the inference stage, 8-bit posits are as good as floating point when dealing with the MNIST dataset, but lose some accuracy with CIFAR-10.
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