Saddle Point

A Saddle Point is a surface point that ...

• See: Contour Line, Surface (Mathematics), Graph of a Function, Function (Mathematics), Orthogonal Function, Stationary Point, Local Extremum, Minimum, Maxima And Minima, Saddle, Mountain Pass.

---

---

References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/saddle_point Retrieved:2017-6-8.
  • In mathematics, a saddle point or minimax point is a point on the surface of the graph a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes. The saddle point will always occur at a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis.

    The name derives from the fact that the prototypical example in two dimensions is a surface that curves up in one direction, and curves down in a different direction, resembling a riding saddle or a mountain pass between two peaks forming a landform saddle. In terms of contour lines, a saddle point in two dimensions gives rise to a contour graph or trace that appears to intersect itself—such conceptually might form a 'figure eight' around both peaks; assuming the contour graph is at the very 'specific altitude' of the saddle point in three dimensions.

2014

• (Dauphin et al., 2014) ⇒ Yann N. Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, and Yoshua Bengio. (2014). “Identifying and Attacking the Saddle Point Problem in High-dimensional Non-convex Optimization.” In: Proceedings of the 27th International Conference on Neural Information Processing Systems.

---