Assuming you want to understand a bit more about saddle points: http://graemebell.net/pubs/taros05-bl-embedded-preprint.pdf http://graemebell.net/pubs/taros05-

Assuming you want to understand a bit more about saddle points: http://graemebell.net/pubs/taros05-bl-embedded-preprint.pdf http://graemebell.net/pubs/taros05-bl-embedded-preprint.pdf Section 3 has some low dimensional examples with simulated robots and donkeys. Take a look at Figure 3 with the donkey. Burridan's Ass is a classic philosophical example where a saddle point prevents success. Basically, place a donkey between two piles of food in front of it that are equally attractive. The donkey moves in whatever direction will take it towards food. So at first, it can move forward (reducing its distance to both piles of food) up to a point, but then it gets stuck because both piles are equally attractive. It can't move forward or back either because that moves it away from both piles of food. There is nothing to 'push' the donkey to the left or the right. ('push'/hunger being analogous to 'following the gradient' for neural net training or robot navigation here) If you add a bit of a random wobble, it's enough to free the donkey from its indecision and make one of the piles slightly closer. But things are more complex than that especially as you move into higher-dimensions of space beyond 2D and 3D [as you see when training neural nets, for example]. And a random wobble is not enough to guarantee success. It may have consequences for physical devices (your robot shakes around and falls over), it may have consequences for realism and immersion in games/simulations (the AI monster stops and does a mad shake for a minute to creep its way around a rock to get you, rather than moving smoothly/normally around the rock)