DEV Community

Super Kai (Kazuya Ito)
Super Kai (Kazuya Ito)

Posted on • Edited on

1

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

Buy Me a Coffee

<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].

Billboard image

Monitor more than uptime.

With Checkly, you can use Playwright tests and Javascript to monitor end-to-end scenarios in your NextJS, Astro, Remix, or other application.

Get started now!

Top comments (0)

A Workflow Copilot. Tailored to You.

Pieces.app image

Our desktop app, with its intelligent copilot, streamlines coding by generating snippets, extracting code from screenshots, and accelerating problem-solving.

Read the docs

👋 Kindness is contagious

Dive into an ocean of knowledge with this thought-provoking post, revered deeply within the supportive DEV Community. Developers of all levels are welcome to join and enhance our collective intelligence.

Saying a simple "thank you" can brighten someone's day. Share your gratitude in the comments below!

On DEV, sharing ideas eases our path and fortifies our community connections. Found this helpful? Sending a quick thanks to the author can be profoundly valued.

Okay