Non-Euclidean Vector Product for Neural Networks
Non-Euclidean Vector Product for Neural Networks
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DOI：
10.1109/icassp.2018.8461709
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发表时间：
2018-04
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通讯作者：
Arman Afrasiyabi;Diaa Badawi;Baris Nasir;Ozan Yildiz;F. Yarman-Vural;A. Çetin
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作者：
Arman Afrasiyabi;Diaa Badawi;Baris Nasir;Ozan Yildiz;F. Yarman-Vural;A. Çetin
提出了人工神经网络的非欧几里得向量积。向量乘积运算符不需要任何乘法，同时提供两个向量之间的相关信息。普通神经元需要两个向量的内积。基于所提出的非欧几里得向量积，我们提出了一类在Lebesgue可积函数空间上具有普遍逼近性质的神经网络。在这个新的网络中，两个实数的“乘积”被定义为它们绝对值的和，其符号由两个数的乘积的符号决定。这个“乘积”用于构造RN中的向量乘积。向量积导出l1范数。加性神经网络成功地解决了异或问题。在MNIST和CIFAR数据集上的实验表明，所提出的加性神经网络的分类性能与相应的多层感知器和卷积神经网络相当。
We present a non-Euclidean vector product for artificial neural networks. The vector product operator does not require any multiplications while providing correlation information between two vectors. Ordinary neurons require inner product of two vectors. We propose a class of neural networks with the universal approximation property over the space of Lebesgue integrable functions based on the proposed non-Euclidean vector product. In this new network, the “product” of two real numbers is defined as the sum of their absolute values, with the sign determined by the sign of the product of the numbers. This “product” is used to construct a vector product in RN. The vector product induces the l1 norm. The additive neural network successfully solves the XOR problem. Experiments on MNIST and CIFAR datasets show that the classification performance of the proposed additive neural network is comparable to the corresponding multi-layer perceptron and convolutional neural networks.