Global or Local Minima and Maxima and Saddle Points in Deep Learning

<Global and Local Minima>

A global minimum is the globally minimal point whose gradient is zero but not a local minimum.
A local minimum is the locally minimal point whose gradient is zero but not a global minimum.

*Memos:

I use…


This content originally appeared on DEV Community and was authored by Super Kai (Kazuya Ito)

<Global and Local Minima>

  • A global minimum is the globally minimal point whose gradient is zero but not a local minimum.

  • A local minimum is the locally minimal point whose gradient is zero but not a global minimum.

Image description

*Memos:

  • I used math3d.
  • The left formula is 10x/e^(x^2+y^2)(-x)^e. *x∈ is [-3, 3] and y∈ is [-3, 3].
  • The right formula is -4x/e^(x^2+y^2)(x)^e. *x∈ is [-3, 3] and y∈ is [-3, 3].

<Global and Local Maxima>

  • A global maximum is the globally maximal point whose gradient is zero but not a local maximum.

  • A local maximum is the locally maximal point whose gradient is zero but not a global maximum.

Image description

*Memos:

  • I used math3d.
  • The left formula is -10x/e^(x^2+y^2)(-x)^e. *x∈ is [-3, 3] and y∈ is [-3, 3].
  • The right formula is 4x/e^(x^2+y^2)(x)^e. *x∈ is [-3, 3] and y∈ is [-3, 3].

<Saddle Points>

A saddle point is the combination point of a local minimum and maximum.

Image description

Image description

*Memos:

  • I used math3d.
  • The formula is x^2-y^2. *x∈ is [-4, 4] and y∈ is [-4, 4].


This content originally appeared on DEV Community and was authored by Super Kai (Kazuya Ito)


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Super Kai (Kazuya Ito) | Sciencx (2024-06-19T17:13:18+00:00) Global or Local Minima and Maxima and Saddle Points in Deep Learning. Retrieved from https://www.scien.cx/2024/06/19/global-or-local-minima-and-maxima-and-saddle-points-in-deep-learning/

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