Subject: [xsl] Performance results of an XML-based neural network versus a map-based neural network From: "Dr. Roger L Costello costello@xxxxxxxxx" <xsl-list-service@xxxxxxxxxxxxxxxxxxxxxx> Date: Wed, 22 Jul 2020 11:24:41 -0000 |
Hi Folks, I implemented a neural network. My first implementation was XML-based. Running the neural network revolves around processing this XML document: <?xml version="1.0" encoding="UTF-8"?> <neuralNetwork> <!-- Set number of nodes in each input, hidden, output layer --> <inodes>784</inodes> <hnodes>100</hnodes> <onodes>10</onodes> <!-- Matrix containing the weights for the input to hidden layer (wih) --> <Matrix id="wih"> <row> <col>-0.015882097402764903</col> <col>0.04906187053472448</col> <col>-0.025639452565869168</col> ... </row> ... </Matrix> <!-- Matrix containing the weights for the hidden to output layer (who) --> <Matrix id="who"> <row> <col>-0.029846534548482826</col> <col>0.09713823372280408</col> <col>-0.07405568240941922</col> ... </row> ... </Matrix> <!-- Learning rate --> <lr>0.3</lr> </neuralNetwork> There are lots of matrix operations involved in running a neural network -- lots of matrix addition, transpose, dot product, etc., operations. The operations update the <Matrix> elements in <neuralNetwork>. I used the SAXON profile tool to see the performance of my implementation. The performance of the matrix operations was very slow. Here's the performance of two of the matrix operations: matrix:addition average time (net/ms) = 273.170 total time (net/ms) = 27,043.813 matrix:dot-product average time (net/ms) = 257.718 total time (net/ms) = 25,514.069 [Michael Kay: what does "net/ms" mean?] In my second implementation I converted the first implementation to be map-based. I replaced the above XML with this map: <xsl:map> <!-- Set number of nodes in each input, hidden, output layer --> <xsl:map-entry key="'inodes'" select="784"/> <xsl:map-entry key="'hnodes'" select="100"/> <xsl:map-entry key="'onodes'" select="10"/> <!-- Learning rate --> <xsl:map-entry key="'lr'" select="0.3"/> <!-- weights between the input layer and the hidden layer (wih) --> <xsl:map-entry key="'wih'" select="(-0.015882097402764903, 0.04906187053472448, -0.025639452565869168, ...)"/> <!-- weights between the hidden layer and the output layer (who) --> <xsl:map-entry key="'who'" select="(-0.029846534548482826, 0.09713823372280408, -0.07405568240941922, ...) "/> </xsl:map> I again used the SAXON profile tool to see the performance. The performance of the matrix operations for this implementation was astoundingly fast. Here's the performance of two of the matrix operations: matrix:addition average time (net/ms) = 0.003 total time (net/ms) = 0.254 matrix:dot-product average time (net/ms) = 0.001 total time (net/ms) = 0.131 For all the matrix operations the map-based version was millions of times faster than the XML-based version. Surprisingly, however, the overall time to train the XML-based neural network was faster than the time to train the map-based neural network: neural-network:train XML-based: average time (net/ms) = 1711.572 total time (net/ms) = 169,445.644 map-based: average time (net/ms) = 3633.811 total time (net/ms) = 359,747.295 I don't understand how this could possibly happen. In the map-based version of the train function, I have these statements to update the weights of the input layer to hidden layer (wih) and the weights of the hidden layer to output layer (who): <xsl:variable name="neural-network-with-new-wih" select="map:put($neural-network, 'wih', $updated-wih)" /> <xsl:variable name="neural-network-with-new-wih-and-new-who" select="map:put($neural-network-with-new-wih, 'who', $updated-who)" /> <xsl:sequence select="$neural-network-with-new-wih-and-new-who" /> Notice that those statements create two new maps. Every time I call the train function, two new maps are created. The train function is called many times. Could that be the cause of why my map-based implementation is running slower than the XML-based implementation? Is there a way to _replace_ a value in a map, rather than _creating_ a whole new map? /Roger
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