tanh

简明释义

英[tænˈeɪtʃ;tænʃ;θæn]美[tænʃ]

abbr. 双曲正切（hyperbolic tangent）

英英释义

单词用法

同义词

反义词

例句

1.When Emperor Xuanzong in Tanh dynasty Zhuang-zi is sealed as the Southern China honorable person, therefore is called.

唐玄宗时庄子被封为南华真人，所以<庄子>又称为<南华真经>。

2.Applying the modified extended tanh-function methods, many types of new explicit traveling wave solutions of the (2 + 1) dimensional long wave-short wave resonance interaction equations are obtained.

利用扩展的双曲正切函数法获得了(2 +1)维长波短波共振相互作用方程的多组新显式精确行波解。

3.The nonlinear behavior of the multi-tanh principle used in CMOS IC design is investigated.

研究了CMOS电路中多双曲正切法则的应用对线性度产生的影响。

4.Applying the modified extended tanh-function methods, many types of new explicit traveling wave solutions of the (2 + 1) dimensional long wave-short wave resonance interaction equations are obtained.

利用扩展的双曲正切函数法获得了(2 +1)维长波短波共振相互作用方程的多组新显式精确行波解。

5.The integration uncertain border value is estimated by fuzzy inference and the soft switch control is accomplished by tanh (x) function replacing SGN (x).

根据模糊推理估计集成不确定边界，利用双曲正切函数代替符号函数实现软切换连续控制。

6.The sinh, cosh, and tanh functions also all appear in various calculations in special and general relativity.

双曲正弦、双曲余弦和双曲正切函数也会以常见或特殊形式出现在各种计算中。

7.The range of the tanh 双曲正切 function is between -1 and 1.

tanh 双曲正切函数的范围在-1到1之间。

8.The activation function used in many neural networks is the tanh 双曲正切 function.

许多神经网络中使用的激活函数是tanh 双曲正切函数。

9.To normalize the output data, we can apply the tanh 双曲正切 transformation.

为了规范化输出数据，我们可以应用tanh 双曲正切变换。

10.When training the model, using tanh 双曲正切 can help with convergence.

在训练模型时，使用tanh 双曲正切可以帮助收敛。

11.In some cases, the tanh 双曲正切 function performs better than the sigmoid function.

在某些情况下，tanh 双曲正切函数的表现优于sigmoid函数。

作文

The concept of the hyperbolic tangent function, denoted as tanh, plays a significant role in various fields of mathematics and engineering. It is defined as the ratio of the hyperbolic sine to the hyperbolic cosine. In simpler terms, tanh can be expressed mathematically as tanh(x) = sinh(x) / cosh(x). This function has a range between -1 and 1, making it particularly useful in scenarios where outputs need to be bounded within these limits.One of the most important applications of tanh is in the field of artificial intelligence, specifically in neural networks. In these networks, activation functions are crucial as they determine if a neuron should be activated or not based on the input it receives. The tanh function is favored over other activation functions like the sigmoid because it provides a stronger gradient and helps to mitigate the vanishing gradient problem during training.When we look at the graph of the tanh function, we notice that it is S-shaped, similar to the sigmoid function but with a key difference: tanh is zero-centered. This means that for inputs centered around zero, the output will also be centered around zero, which can lead to faster convergence during optimization. The steepness of the curve near the origin allows for more pronounced changes in output values for small changes in input, which is beneficial for learning complex patterns in data.Moreover, the mathematical properties of tanh make it an interesting function to study. For instance, it is an odd function, meaning that tanh(-x) = -tanh(x). This property indicates that the function is symmetric about the origin, which can simplify calculations and provide insights into its behavior under transformations. Additionally, the derivative of tanh can be expressed elegantly as 1 - tanh²(x), which allows for efficient computation during backpropagation in neural networks.In physics, tanh is also used in various models, such as those describing the behavior of certain materials under stress or the distribution of particles in quantum mechanics. The versatility of the tanh function extends beyond pure mathematics and into practical applications that impact technology and science.To summarize, understanding the function tanh is essential for anyone working in fields that involve mathematical modeling, machine learning, or physics. Its unique properties and applications make it a valuable tool for solving complex problems. As we continue to explore the depths of mathematics and its applications, the importance of functions like tanh will only grow, paving the way for innovations in technology and science that rely on advanced mathematical concepts.

双曲正切函数，记作tanh，在数学和工程的多个领域中扮演着重要角色。它被定义为双曲正弦与双曲余弦的比率。简单来说，tanh可以用数学表达为tanh(x) = sinh(x) / cosh(x)。这个函数的值域在-1到1之间，使其在需要将输出限制在这些范围内的场景中特别有用。tanh最重要的应用之一是在人工智能领域，特别是在神经网络中。在这些网络中，激活函数至关重要，因为它们决定了神经元是否应该根据接收到的输入被激活。tanh函数相较于其他激活函数，如sigmoid，更受青睐，因为它提供了更强的梯度，并有助于在训练过程中缓解梯度消失问题。当我们观察tanh函数的图形时，我们会注意到它呈现S形，类似于sigmoid函数，但有一个关键区别：tanh是以零为中心的。这意味着，对于以零为中心的输入，输出也将以零为中心，这可能导致在优化过程中更快的收敛。曲线在原点附近的陡峭程度允许输入小变化时输出值发生更明显的变化，这对于学习数据中的复杂模式是有益的。此外，tanh的数学性质使其成为一个有趣的研究对象。例如，它是一个奇函数，这意味着tanh(-x) = -tanh(x)。这一特性表明该函数关于原点对称，这可以简化计算并提供关于其在变换下行为的见解。此外，tanh的导数可以优雅地表达为1 - tanh²(x)，这使得在神经网络的反向传播过程中高效计算成为可能。在物理学中，tanh也用于描述某些材料在应力下的行为或量子力学中粒子的分布等各种模型。tanh函数的多样性超越了纯数学，延伸至影响科技和科学的实际应用。总之，理解tanh函数对于任何从事涉及数学建模、机器学习或物理学领域的人来说都是至关重要的。它独特的性质和应用使其成为解决复杂问题的宝贵工具。随着我们继续探索数学及其应用的深度，像tanh这样的函数的重要性只会增加，为依赖于高级数学概念的技术和科学创新铺平道路。