java - How can I improve this neural net over MNIST? -

i wrote vanilla neural net project, , trained on famous mnist data set. gets 85% accuracy , wondering why lower 95.3% success rate achieved neural net described on mnist website on paper should similar mine.

more details neural net:

-the input 784 greyscale values (0-255) of each pixel in 28x28 image

-it has layer sizes 784-256-10 plus bias node fixed value of 1 connected hidden , output nodes.

-it uses sigmoid activation function

-the error of output node defined difference between it's value , expected value squared.

-the neural network trained via gradient descent across each of 60,000 training cases once per iteration of training algorithm.

-usually converges after 15 iterations accurate classification percentage across test cases of 84%-88%.

-despite fact literature i've read suggests necessary, neural net performs worse when have bias node versus when comment out (i might doing wrong, lmk).

-test , training cases stored objects hold values , expected output in array of cases.

here main operative code of program:

the initialization of structure

   /**    * method initialize structure of neural net    * adds node every input location needed, adds hidden layer    * connects hidden layer input layer, makes output layer, , connects output layer     * hidden layer     */    public void initializestructure()    {       for(int ii = 0; ii < numinputs; ii++)       {          inputlayer.add(new node());       }          // add node input layer. node has default value of one,        // acts bias every node connected (the bias has magnitude of weight)       // means thing need edit weights(including these ones), not values       node bias = new node();       bias.value = 1.0;       inputlayer.add(bias);          for(int ii = 0; ii < layersize; ii++)       {          node currentnode = new node();          for(node n : inputlayer)          {                                           currentnode.connections.add(new connection(numinputs,n,currentnode,false));          }                   hiddenlayer.add(currentnode);       }         for(int ii = 0; ii < 10; ii++)       {          node output = new node();          for(node n : hiddenlayer)          {             output.connections.add(new connection(numinputs,n,output,true));           }               output.connections.add(new connection(numinputs,bias,output,true));               outputlayer.add(output);       }          } 

the training algorithm

   public void train()    {       for(inputcase current : traincases)       {          int[] expected  = new int[10];          for(int jj = 0; jj < expected.length; jj++)          {             if(jj == current.expectedoutput)                expected[jj] = 1;             else                expected[jj] = 0;          }          for(int jj = 0; jj < current.values.length; jj++)          {          inputlayer.get(jj).value = current.values[jj];          }          run();          double sum = 0;          for(int ii = 0; ii < outputlayer.size(); ii++)          {             node n = outputlayer.get(ii);             for(connection c : n.connections)             {                c.weight -= learningrate * c.origin.value * c.destination.value * (1-c.destination.value) * (c.destination.value - expected[ii]);                sum += c.destination.value * (1-c.destination.value) * (c.destination.value - expected[ii]) * c.weight;             }          }          for(node n : hiddenlayer)          {             for(connection c : n.connections)             {                c.weight -= learningrate * c.origin.value * c.destination.value * (1-c.destination.value) * sum;             }          }       }    } 

if have more questions, or want/need see more code, say!