12 August 2011

Neural Network (Part 3): The Layer


The Layer

The purpose of a layer is mainly to group and manage neurons that are functionally similar, and provide a means to effectively control the flow of information through the network (forwards and backwards). The forward pass is when you convert input values into output values, the backwards pass is only done during network training.

In my neural network, the Layer is an essential building block of the neural network. They can work individually or as a team. Let us just focus on one layer for now

This is what a layer with two neurons looks like in my neural network:



As you can see from the picture above, I tend to treat each neuron as an individual.
Both neurons have the same connEntry values (cEn11 = cEn21) and (cEn12 = cEn22), which stem from the layerINPUTs. Other than that, the rest is different.  Which means that Neuron1 could produce an output value close to 1, and at the same time Neuron2 could produce an output close to 0, even though they have the same connEntry values at the start.


The following section will describe how the layerINPUTs get converted to actualOUTPUTs.

Step1: Populate the layerINPUTs:
layerINPUTs are just a placeholder for values that have been fed into the neural network, or come from a previous layer within the same neural network. If this is the first layer in the network, then the layerINPUTs would be the Neural Network's input values (eg Sensor data). If this is the 2nd layer in the network, then the layerINPUTs would equal the actualOUTPUTs of Layer One



Step2: Send each layerINPUT to the neuron's connection in the layer.
You will notice that every neuron in the same layer will have the same number of connections. This is because each neuron will connect only once to each of the layerINPUTs. The relationship between layerINPUTs and the connEntry values of a neuron are as follows.

          layerINPUTs1:                                                                                 
          cEn11 = layerINPUTs1                  Neuron1.Connection1.connEntry
          cEn21 = layerINPUTs1                  Neuron2.Connection1.connEntry


          layerINPUTs2:                                                                                  
          cEn12 = layerINPUTs2                  Neuron1.Connection2.connEntry
          cEn22 = layerINPUTs2                  Neuron2.Connection2.connEntry

Therefore, the connEntry of the first connection of every neuron in this layer will equal the first layerINPUT value in this layer.




Step3: Calculate the connExit values of each connection (including bias)

           Neuron 1:                       
           cEx11 = cEn11  x  cW11
           cEx12 = cEn12  x  cW12
             bEx1 =    1      x    bW1

           Neuron 2:                       
           cEx21 = cEn21  x  cW21
           cEx22 = cEn22  x  cW22
             bEx2 =    1      x    bW2




Step4: Calculate the NeuronInputValue for each neuron

          Neuron1:                                                                       
          Neuron1.NeuronInputValue = cEx11  +  cEx12  +  bEx1


          Neuron2:                                                                       
          Neuron2.NeuronInputValue = cEx21  +  cEx22  +  bEx2




Step5: Send the NeuronInputValues through an Activation function to produce a NeuronOutputValue

          Neuron1:                                                                                                        
          Neuron1.NeuronOutputValue= 1/(1+EXP(-1 x Neuron1.NeuronInputValue))


          Neuron2:                                                                                                 
          Neuron2.NeuronOutputValue= 1/(1+EXP(-1 x Neuron2.NeuronInputValue))


          Please note that the NeuronInputValues for each neuron are different !





Step6: Send the NeuronOutputValues to the layer's actualOUTPUTs
  • actualOUTPUT1 = Neuron1.NeuronOutputValue
  • actualOUTPUT2 = Neuron2.NeuronOutputValue



The NeuronOutputValues become the actualOUTPUTs of this layer, which then become the layerINPUTs of the next layer. And the process is repeated over and over until you reach the final layer, where the actualOUTPUTs become the outputs of the entire neural network.


Here is the code for the Layer class:


processing code Layer Class

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class Layer{
  Neuron[] neurons = {};
  float[] layerINPUTs={};
  float[] actualOUTPUTs={};
  float[] expectedOUTPUTs={};
  float layerError;
  float learningRate;
  
  
  /* This is the default constructor for the Layer */
  Layer(int numberConnections, int numberNeurons){
    /* Add all the neurons and actualOUTPUTs to the layer */
    for(int i=0; i<numberNeurons; i++){
      Neuron tempNeuron = new Neuron(numberConnections);
      addNeuron(tempNeuron);
      addActualOUTPUT();
    }
  }
    
  
  /* Function to add an input or output Neuron to this Layer */
  void addNeuron(Neuron xNeuron){
        neurons = (Neuron[]) append(neurons, xNeuron);
  }
  
  
  /* Function to get the number of neurons in this layer */
  int getNeuronCount(){
    return neurons.length;
  }
  
  
  /* Function to increment the size of the actualOUTPUTs array by one. */
  void addActualOUTPUT(){
      actualOUTPUTs = (float[]) expand(actualOUTPUTs,(actualOUTPUTs.length+1));
  }
  
  
  /* Function to set the ENTIRE expectedOUTPUTs array in one go. */
  void setExpectedOUTPUTs(float[] tempExpectedOUTPUTs){
    expectedOUTPUTs=tempExpectedOUTPUTs;
  }
  
  
  /* Function to clear ALL values from the expectedOUTPUTs array */
  void clearExpectedOUTPUT(){
       expectedOUTPUTs = (float[]) expand(expectedOUTPUTs, 0);
  }
  
  
  /* Function to set the learning rate of the layer */
  void setLearningRate(float tempLearningRate){
    learningRate=tempLearningRate;
  }
  
  
  /* Function to set the inputs of this layer */
  void setInputs(float[] tempInputs){
    layerINPUTs=tempInputs;
  }
  
  
  
  /* Function to convert ALL the Neuron input values into Neuron output values in this layer, 
     through a special activation function. */
  void processInputsToOutputs(){
    
    /* neuronCount is used a couple of times in this function. */
    int neuronCount = getNeuronCount();
    
    /* Check to make sure that there are neurons in this layer to process the inputs */
    if(neuronCount>0) {
      /* Check to make sure that the number of inputs matches the number of Neuron Connections. */
      if(layerINPUTs.length!=neurons[0].getConnectionCount()){
        println("Error in Layer: processInputsToOutputs: The number of inputs do NOT match the number of Neuron connections in this layer");
        exit();
      } else {
        /* The number of inputs are fine : continue
           Calculate the actualOUTPUT of each neuron in this layer, 
           based on their layerINPUTs (which were previously calculated).
           Add the value to the layer's actualOUTPUTs array. */
        for(int i=0; i<neuronCount;i++){
          actualOUTPUTs[i]=neurons[i].getNeuronOutput(layerINPUTs);
        }
      }
    }else{
      println("Error in Layer: processInputsToOutputs: There are no Neurons in this layer");
      exit();
    }
  }
  
  
  /* Function to get the error of this layer */
  float getLayerError(){
    return layerError;
  }
  
  
  /* Function to set the error of this layer */
  void setLayerError(float tempLayerError){
    layerError=tempLayerError;
  }
  
  
  /* Function to increase the layerError by a certain amount */
  void increaseLayerErrorBy(float tempLayerError){
    layerError+=tempLayerError;
  }
  
  
  /* Function to calculate and set the deltaError of each neuron in the layer */
  void setDeltaError(float[] expectedOutputData){
    setExpectedOUTPUTs(expectedOutputData);
    int neuronCount = getNeuronCount();
    /* Reset the layer error to 0 before cycling through each neuron */
    setLayerError(0);
     for(int i=0; i<neuronCount;i++){
       neurons[i].deltaError = actualOUTPUTs[i]*(1-actualOUTPUTs[i])*(expectedOUTPUTs[i]-actualOUTPUTs[i]);
       
       /* Increase the layer Error by the absolute difference between the calculated value (actualOUTPUT) and the expected value (expectedOUTPUT). */
       increaseLayerErrorBy(abs(expectedOUTPUTs[i]-actualOUTPUTs[i]));
     }
  }
  
  
  /* Function to train the layer : which uses a training set to adjust the connection weights and biases of the neurons in this layer */
  void trainLayer(float tempLearningRate){
    setLearningRate(tempLearningRate);
    
    int neuronCount = getNeuronCount();
    
    for(int i=0; i<neuronCount;i++){
      /* update the bias for neuron[i] */
      neurons[i].bias += (learningRate * 1 * neurons[i].deltaError);
      
      /* update the weight of each connection for this neuron[i] */
      for(int j=0; j<neurons[i].getConnectionCount(); j++){
          neurons[i].connections[j].weight += (learningRate * neurons[i].connections[j].connEntry * neurons[i].deltaError);
      }   
    }
  }
}

Within each layer, you have neuron(s) and their associated connection(s). Therefore it makes sense to have a constructor that automatically sets these up.


If you create a new Layer(2,3), this would automatically
  • add 3 neurons to the layer
  • create 2 connections for each neuron in this layer (to connect to the previous layer neurons).
  • randomise each neuron bias and connection weights.
  • add 3 actualOUTPUT slots to hold the neuron output values.


                                                                                                                                         
Here are the functions of the Layer class:
  • addNeuron() : adds a neuron to the layer
  • getNeuronCount() : returns the number of neurons in this layer
  • addActualOUTPUT() : adds an actualOUTPUT slot to the layer.
  • setExpectedOUTPUTs() : sets the entire expectedOUTPUTs array in one go.
  • clearExpectedOUTPUT() : clear all values within the expectedOUTPUTs array.
  • setLearningRate() : sets the learning rate of the layer.
  • setInputs() : sets the inputs of the layer.
  • processInputsToOutputs() : convert all layer input values into output values
  • getLayerError() : returns the error of this layer
  • setLayerError() : sets the error of this layer
  • increaseLayerErrorBy() : increases the layer error by a specified amount.
  • setDeltaError() : calculate and set the deltaError for each neuron in this layer
  • trainLayer() : uses a training set to adjust the connection weights and biases of the neurons in this layer
There are a few functions mentioned above, which I have not yet discussed, and are used for neural network training (back-propagation). Don't worry, we'll go through them in the "back-propagation" section of the tutorial.


Next up:  Neural Network (Part 4) : The Neural Network class



To go back to the table of contents click here


2 comments:

  1. Thank you very much for your great articles and effort and the way you describe in details .... I really appreciate your great effort ...
    Many Thanks again

    ReplyDelete

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