A saddle is a critical point that's not a local extremum--the Hessian could just... | Hacker News

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banskiachtar on May 25, 2016 | parent | context | favorite | on: Deep Learning Without Poor Local Minima

A saddle is a critical point that's not a local extremum--the Hessian could just be zero, for example, like x^4-y^4 at (0,0).

mjw on May 25, 2016 [–]

Ah yep, true. I'd forgotten you can still get the saddle effect from higher-order derivatives, the Hessian eigenvalues aren't enough to characterise it.

I was thinking of examples like (x-y)^2 at zero, although I guess that's still a local minimum, just not a unique local minimum in any neighbourhood.

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