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相关概念视频

Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

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Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
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Algebraic Expressions01:26

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Algebraic expressions are essential in mathematics. They represent relationships through variables, constants, and operations. These expressions help describe patterns and solve problems in various mathematical fields. Understanding their components, classifications, and operations allows for efficient simplification and manipulation.Each algebraic expression consists of individual parts, including numbers and symbols, that work together to form meaningful mathematical statements. The numerical...
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Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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Solving Equations Graphically01:27

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Graphical methods provide an intuitive and visual means of solving equations by representing functions on the coordinate plane. These methods are especially helpful for estimating solutions, analyzing complex expressions, or understanding the behavior of functions.To solve an equation graphically, it must first be expressed in the form y = f(x). The solution to the original equation corresponds to the x-values where the graph intersects the x-axis, meaning where f(x) = 0.For example, the linear...
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Graphs of Functions01:30

Graphs of Functions

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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
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Graphical Representation of Inequalities

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The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
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相关实验视频

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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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使用图形表示和生成图形神经网络的数学表达式探索.

Jingyi Liu1, Weijun Li1, Lina Yu1

  • 1AnnLab, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China; School of Integrated Circuits & Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, 100049, Beijing, China.

Neural networks : the official journal of the International Neural Network Society
|March 27, 2025
PubMed
概括
此摘要是机器生成的。

本研究介绍了基于图形的深度符号回归 (GraphDSR),这是一种使用定向环形图 (DAG) 和图形神经网络进行数学表达式发现的新方法. 与传统的基于树的方法相比,GraphDSR提供了一种更有效和更直观的方法.

关键词:
定向非循环图是指向非循环图.图表神经网络的神经网络强化学习是一种强化学习.象征性回归是一种象征性回归.

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科学领域:

  • 人工智能的人工智能
  • 机器学习 机器学习
  • 计算数学 计算数学 计算数学

背景情况:

  • 符号回归 (SR) 传统上使用树表示,这可能是多余的.
  • 深度学习已经推进了以树为中心的SR,但对SR的基于图形的深度学习尚未得到充分探索.
  • 计算图提供了比树更简洁的数学表达式的表示.

研究的目的:

  • 引入一种新的深度学习方法,用于使用指向环形图 (DAG) 进行符号回归.
  • 利用生成图形神经网络来实现高效和直观的数学表达式发现.
  • 为了解决基于树的SR方法中冗余子结构的局限性.

主要方法:

  • 建议使用DAG表示的基于图形的深度符号回归 (GraphDSR).
  • 使用生成图形神经网络逐步构建DAG.
  • 利用矢量化节点类型和邻近矩阵用于图形表示.
  • 集成的有效性检查和域异性约束来指导搜索过程.
  • 使用SGD和BFGS优化常数,并通过强化学习完善神经网络.

主要成果:

  • 在110个不同的基准标准中证明了GraphDSR的有效性.
  • 取得了强有力的结果,突出了DAG在斯里兰卡代表的优势.
  • 展示了图形神经网络在生成连贯的数学表达式方面的能力.

结论:

  • 图形DSR为传统的基于树的SR方法提供了强大而高效的替代方案.
  • 与生成图形神经网络相结合的DAG表示显著提高了SR性能.
  • 这种方法为象征回归和自动化科学发现中的深度学习应用开辟了新的途径.