Neural Networks Learning Differential Data
Ryusuke Masuoka · 2000
Introduction In many of machiD learni= problems,i i essentie to use not only thetrai1=+ data, but also apri+W knowledge about how the worldi constraiD40 In many cases, such knowledgei gi en i the forms of constrai ts ondi++G0 ti+ data or more speci1W1=D parti1 dirti tit equati=D (PDEs). Examples of such cases are gi en i [8] and [3]. Si].D et al. [8]descri ed how thei vari2O= of patternrecogniOj1 wic respect to such as translatis -D rotati+W+ scalii+ etc. can be i terpreted as constrai ts on first orderdierD+ tie data. The output of the neural network as a patternrecogni=G should stay same for such transformatiDi of theieD=F That constrai ti si nterpreted as that diD=++WOD4 deri ati es of the outputwiu respect to the di=+0OFD4 of transformatisf have to be zeros. Horni et al. [3] i]D tiD+ several areas ofappliG= tipl requiG= approxiroD+O to an unknownmappi0 and id deri ati es, such as robotlearni+D determi4+O1G chaos, economiD4 sensiiD4 y analyses, etc. Inthi i troductiFG wedes