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We want computations to be fast, and we want them to be understandable. As we show, the need for computations to be fast naturally leads to neural networks, with 1-layer networks being the fastest, and the need to be understandable naturally leads to fuzzy logic and to the corresponding “and”and “or”-operations. Since we want our computations to be both fast and understandable, a natural question is: which “and”and “or”-operations of fuzzy logic can be represented by the fastest (i.e., 1-layer) neural network? And a related question is: which activation functions allow such a representation? In this paper, we provide an answer to both questions: the only “and”and “or”-operations that can be thus represented are max(0,a+ b− 1) and min(a+ b,1), and the only activations functions allowing such a representation are equivalent to the rectified linear function – the one used in deep learning. This result provides an additional explanation of why rectified linear neurons are so successful. With also show that with full 2-layer networks, we can compute practically any “and”and “or”-operation.

acta polytechnica hungarica

Towards Fast and Understandable Computations: Which “And”- and “Or”-Operations Can Be Represented by the Fastest (i.e., 1-Layer) Neural Networks? Which Activations Functions Allow Such Representations?