熵、知觉与相对性
Entropy, Perception, and Relativity
摘要：
在本文中，我扩展香农的熵的定义到一个新的形式的熵，允许整合不同的随机事件的信息。香农的熵概念是我的熵的一般定义的一个特例。我使用所谓的性能函数来定义概率，它实际上是一个指数分布。假设我的熵的一般概念反映了概率事件的真实不确定性，我理解我们感知的不确定性是不同的。我认为，我们的感知是两种对立力量的结果，类似于中国哲学中两个著名的对立者：阴和阳。基于这个想法，我表明，我们的感知不确定性匹配的黄金分割率确定的点的真实不确定性。我证明了著名的S形函数，我们通常采用人工神经网络作为一个非线性阈值函数，描述了实际的性能。此外，我提供了爱因斯坦的狭义相对论的时间膨胀的动机，基本上声称，虽然时间膨胀符合我们的感知，它不符合现实。在文章的最后，我展示了如何将这个理论框架应用到实际应用中。我提出了一个模式识别问题的识别率，并提出了一个网络架构，可以利用一般熵来解决复杂的决策问题。
英文摘要：
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy. I define probability using a so-called performance function, which is de facto an exponential distribution. Assuming that my general notion of entropy reflects the true uncertainty about a probabilistic event, I understand that our perceived uncertainty differs. I claim that our perception is the result of two opposing forces similar to the two famous antagonists in Chinese philosophy: Yin and Yang. Based on this idea, I show that our perceived uncertainty matches the true uncertainty in points determined by the golden ratio. I demonstrate that the well-known sigmoid function, which we typically employ in artificial neural networks as a non-linear threshold function, describes the actual performance. Furthermore, I provide a motivation for the time dilation in Einstein's Special Relativity, basically claiming that although time dilation conforms with our perception, it does not correspond to reality. At the end of the paper, I show how to apply this theoretical framework to practical applications. I present recognition rates for a pattern recognition problem, and also propose a network architecture that can take advantage of general entropy to solve complex decision problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
