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Backpropagation
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==Limitations== [[File:Extrema example.svg|thumb|250px|Gradient descent may find a local minimum instead of the global minimum.]] * Gradient descent with backpropagation is not guaranteed to find the [[Maxima and minima|global minimum]] of the error function, but only a local minimum; also, it has trouble crossing [[Plateau (mathematics)|plateaus]] in the error function landscape. This issue, caused by the [[Convex optimization|non-convexity]] of error functions in neural networks, was long thought to be a major drawback, but [[Yann LeCun]] ''et al.'' argue that in many practical problems, it is not.<ref>{{cite journal |first1=Yann |last1=LeCun|author-link1=Yann LeCun |first2=Yoshua |last2=Bengio |first3=Geoffrey |last3=Hinton |title=Deep learning |journal=Nature |volume=521 |issue=7553 |year=2015 |pages=436β444 |doi=10.1038/nature14539 |pmid=26017442|bibcode=2015Natur.521..436L |s2cid=3074096 |url=https://hal.science/hal-04206682/file/Lecun2015.pdf }}</ref> * Backpropagation learning does not require normalization of input vectors; however, normalization could improve performance.<ref>{{Cite book|title=AI Techniques for Game Programming|last1=Buckland|first1=Matt|last2=Collins|first2=Mark |location=Boston |publisher=Premier Press |year=2002 |isbn=1-931841-08-X }}</ref> * Backpropagation requires the derivatives of activation functions to be known at network design time.
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