### Contents

- Introduction
- 1. Theoretical Prerequisites for Normalization
- 2. Implementation
- 2.1. Creating a New Class for Our Model
- 2.2. Feed-Forward
- 2.3. Feed-Backward
- 2.4. Changes in the Neural Network Base Classes
- 3. Testing
- Conclusion
- References
- Programs Used in the Article

### Introduction

In the previous article, we started considering methods aimed at increasing the convergence of neural networks and got acquainted with the Dropout method, which is used to reduce the co-adaptation of features. Let us continue this topic and get acquainted with the methods of normalization.

### 1. Theoretical Prerequisites for Normalization

Various approaches to data normalization are used in neural network application practice. However, all of them are aimed at keeping the training sample data and the output of the hidden layers of the neural network within a certain range and with certain statistical characteristics of the sample, such as variance and median. This is important, because network neurons use linear transformations which in the process of training shift the sample towards the antigradient.

Consider a fully connected perceptron with two hidden layers. During a feed-forward pass, each layer generates a certain data set that serves as a training sample for the next layer. The result of the output layer is compared with the reference data. Then, during the feed-backward pass, the error gradient is propagated from the output layer through hidden layers towards the initial data. Having received an error gradient at each neuron, we update the weight coefficients, adjusting the neural network for the training samples of the last feed-forward pass. A conflict arises here: the second hidden layer (H2 in the figure below) is adjusted to the data sample at the output of the first hidden layer (H1 in the figure), while by changing the parameters of the first hidden layer we have already changed the data array. In other words, we adjust the second hidden layer to the data sample which no longer exists. A similar situation occurs with the output layer, which adjusts to the second hidden layer output which has already changed. The error scale will be even greater if we consider the distortion between the first and the second hidden layers. The deeper the neural network, the stronger the effect. This phenomenon is referred to as internal covariate shift.

Classical neural networks partly solve this problem by reducing the learning rate. Minor changes in weights do not entail significant changes in the sample distribution at the output of the neural layer. But this approach does not solve the scaling problem which appears with an increase in the number of neural network layers, and it also reduces the learning speed. Another problem of a small learning rate is that the process can get stuck on local minima, which we have already discussed in article 6.

In February 2015, Sergey Ioffe and Christian Szegedy proposed Batch Normalization as a solution to the problem of internal covariance shift [13]. The idea of the method is to normalize each individual neuron on a certain time interval with a shift in the median of the sample (batch) towards zero and to bring the sample variance to 1.

The normalization algorithm is as follows. First, the average value is calculated for the data batch.

here *m* is the batch size.

Then the variance of the original batch is calculated.

Batch data is normalized to bring the batch to the zero mean and to the variance of 1.

Note that the constant ϵ, a small positive number, is added to the batch variance in the denominator to avoid division by zero.

However, it turned out that such normalization can distort the influence of the original data. Therefore, the method authors have added one more step: scaling and shift. They have introduced two variables, γ andβ, which are trained together with the neural network by gradient descent method.

The application of this method makes enables the obtaining of a data batch with the same distribution at each step of training, which makes neural network training more stable and allows an increase in the learning rate. In general, this method assists in improving the quality of training while reducing the time spent on neural network training.

However, this increases the cost of storing additional rates. Also, historical data of each neuron for the entire batch size should be stored for the calculation of the average value and dispersion. Here we can check the application of the exponential average. The figure below shows the graphs of the moving average and moving variance for 100 elements in comparison with the exponential moving average and exponential moving variance for the same 100 elements. The chart is built for 1000 random elements in the range between -1.0 and 1.0.

In this chart, the moving average and the exponential moving average approach each other after 120-130 iterations and then the deviation is minimal (so that it can be neglected). In addition, the exponential moving average graph is smoother. EMA can be calculated by knowing the previous value of the function and the current element of the sequence. Let us view the formula for the exponential moving average.

,

where

*m*is the batch size,*i*is an iteration.

It took a little more iterations (310-320) to bring the moving variance and the exponential moving variance graphs closer together, but the overall picture is similar. In the case of variance, the use of the exponential algorithm not only saves memory, but it also significantly reduces the number of calculations, since for the moving variance the deviation from the average would be calculated for the entire batch.

The experiments carried out by the method authors show that the use of the Batch Normalization method also serves as a regularizer. This reduces the need for other regularization methods, including the previously considered Dropout. Furthermore, later research show that the combined use of Dropout and Batch Normalization has a negative effect on the neural network learning results.

The proposed normalization algorithm can be found in various variations in modern neural network architectures. The authors suggest using Batch Normalization immediately before the nonlinearity (activation formula). The Layer Normalization method presented in July 2016 can be considered as one of the variations of this algorithm. We have already considered this method when studying the attention mechanism (article 9).

### 2. Implementation

#### 2.1 Creating a New Class for Our Model

Now that we have considered the theoretical aspects, let us implement it in our library. Let us create a new classCNeuronBatchNormOCL to implement the algorithm.

class CNeuronBatchNormOCL:public CNeuronBaseOCL{protected: CNeuronBaseOCL*PrevLayer; uintiBatchSize; CBufferDouble *BatchOptions; virtual boolfeedForward(CNeuronBaseOCL *NeuronOCL); virtual boolupdateInputWeights(CNeuronBaseOCL *NeuronOCL);public: CNeuronBatchNormOCL(void); ~CNeuronBatchNormOCL(void); virtual boolInit(uint numOutputs, uint myIndex, COpenCLMy *open_cl, uint numNeurons, uint batchSize, ENUM_OPTIMIZATION optimization_type); virtual int getOutputIndex(void){return (iBatchSize>1 ? Output.GetIndex() : PrevLayer.getOutputIndex()); } virtual int getGradientIndex(void){return (iBatchSize>1 ? Gradient.GetIndex() : PrevLayer.getGradientIndex());} virtual int getOutputVal(double &values[]) {return (iBatchSize>1 ? Output.GetData(values) : PrevLayer.getOutputVal(values)); } virtual int getOutputVal(CArrayDouble *values) {return (iBatchSize>1 ? Output.GetData(values) : PrevLayer.getOutputVal(values)); } virtual int getGradient(double &values[]){return (iBatchSize>1 ? Gradient.GetData(values) : PrevLayer.getGradient(values));} virtual CBufferDouble *getOutput(void) {return (iBatchSize>1 ? Output : PrevLayer.getOutput());} virtual CBufferDouble *getGradient(void) {return (iBatchSize>1 ? Gradient : PrevLayer.getGradient());} virtual boolcalcInputGradients(CNeuronBaseOCL *NeuronOCL); virtual boolSave(int const file_handle); virtual boolLoad(int const file_handle); virtual int Type(void)const{return defNeuronBatchNormOCL;}};

The new class will inherit from the CNeuronBaseOCL base class. By analogy with the CNeuronDropoutOCL class, let us add the PrevLayer variable. The data buffer replacement method demonstrated in the previous article will be applied when specifying the batch size less than "2", which will be saved to theiBatchSize variable.

The Batch Normalization algorithm requires saving of some parameters which are individual for each neuron of the normalized layer. In order not to generate many separate buffers for each individual parameter, we will create a single BatchOptions buffer of parameters with the following structure.

It can be seen from the presented structure that the size of the parameter buffer will depend on the applied parameter optimization method and, therefore, will be created in the class initialization method.

The set of class methods is already standard. Let us have a look at them. In the class constructor, let us reset the pointers to objects and set the batch size to one, which practically excludes the layer from the network operation until it is initialized.

CNeuronBatchNormOCL::CNeuronBatchNormOCL(void):iBatchSize(1){ PrevLayer=NULL; BatchOptions=NULL;}

In the class destructor, delete the object of the parameter buffer and set the pointer to the previous layer to zero. Please note that we are not deleting the object of the previous layer, but only zeroing the pointer. The object will be deleted where it was created.

CNeuronBatchNormOCL::~CNeuronBatchNormOCL(void){ if(CheckPointer(PrevLayer)!=POINTER_INVALID)PrevLayer=NULL; if(CheckPointer(BatchOptions)!=POINTER_INVALID)delete BatchOptions;}

Now, consider the class initialization method CNeuronBatchNormOCL::Init. In the parameters, pass to the class the number of neurons of the next layer, an index for identifying the neuron, a pointer to the OpenCL object, the number of neurons in the normalization layer, the batch size and the parameter optimization method.

At the beginning of the method, call the relevant method of the parent class, in which the basic variables and data buffers will be initialized. Then save the batch size and set the layer activation function to ** None**.

Please pay attention to the activation function. The use of this functionality depends on the architecture of the neural network. If the neural network architecture requires the inclusion of normalization before the activation function, as recommended by the authors of the method, then the activation function must be disabled on the previous layer and the required function must be specified in the normalization layer. Technically, the activation function is specified by calling the *SetActivationFunction* method of the parent class, after initializing a class instance. If normalization should be used after the activation function in accordance with the network architecture, the activation method should be specified in the previous layer and there will be no activation function in the normalization layer.

bool CNeuronBatchNormOCL::Init(uint numOutputs,uint myIndex,COpenCLMy *open_cl,uint numNeurons,uint batchSize,ENUM_OPTIMIZATION optimization_type){ if(!CNeuronBaseOCL::Init(numOutputs,myIndex,open_cl,numNeurons,optimization_type))return false; activation=None; iBatchSize=batchSize; if(CheckPointer(BatchOptions)!=POINTER_INVALID)delete BatchOptions; int count=(int)numNeurons*(optimization_type==SGD ? 7 : 9); BatchOptions=new CBufferDouble(); if(CheckPointer(BatchOptions)==POINTER_INVALID || !BatchOptions.BufferInit(count,0))return false; return true;}

At the end of the method, we create a buffer of parameters. As mentioned above, the buffer size depends on the number of neurons in the layer and the parameter optimization method. When using SGD, we reserve 7 elements for each neuron; when optimizing by the Adam method, we need 9 buffer elements for each neuron. After successful creation of all buffers, exit the method with *true*.

The full code of all classes and their methods is available in the attachment.

#### 2.2. Feed-Forward

As the next step, let us consider the feed-forward pass. Let us start by considering the direct pass *BatchFeedForward*. The kernel algorithm will be launched for each separate neuron.

The kernel receives in parameters pointers to 3 buffers: initial data, buffer of parameters and a buffer for writing the results. Additionally, pass in parameters the batch size, the optimization method and the neuron activation algorithm.

At the kernel beginning, check the specified size of the normalization window. If normalization is performed for one neuron, exit the method without performing further operations.

After successful verification, we get the stream identifier, which will indicate the position of the normalized value in the input data tensor. Based on the identifier, we can determine the shift for the first parameter in the tensor of normalization parameters. At this step, the optimization method will suggest the structure of the parameter buffer.

Next, calculate the exponential mean and variance at this step. Based on this data, calculate the normalized value for our element.

The next step of the algorithm of Batch Normalization is shifting and scaling. Earlier, during initialization, we filled the parameter buffer with zeros, so if we perform this operation "in its pure form" at the first step, we will receive "0". To avoid this, check the current value of the γ parameter and, if it is equal to "0", change its value to "1". Leave the shift at zero. Perform shifting and scaling in this form.

__kernel void BatchFeedForward(__global double *inputs, __global double *options, __global double *output, int batch int optimization, int activation){ if(batch<=1)return; int n=get_global_id(0); int shift=n*(optimization==0 ? 7 : 9); for(int i=0;i<(optimization==0 ? 7 : 9);i++)if(isnan(options[shift+i])) options[shift+i]=0; double mean=(options[shift]*((double)batch-1)+inputs[n])/((double)batch); double delt=inputs[n]-mean; double variance=options[shift+1]*((double)batch-1.0)+pow(delt,2); if(options[shift+1]>0)variance/=(double)batch; double nx=delt/sqrt(variance+1e-6); if(options[shift+3]==0)options[shift+3]=1; double res=options[shift+3]*nx+options[shift+4]; switch(activation) {case 0:res=tanh(clamp(res,-20.0,20.0));break;case 1:res=1/(1+exp(-clamp(res,-20.0,20.0)));break;case 2:if(res<0) res*=0.01;break;default:break; } options[shift]=mean; options[shift+1]=variance; options[shift+2]=nx; output[n]=res;}

After obtaining the normalized value, let us check if we need to execute the activation function on this layer and perform the necessary actions.

Now, simply save the new values to the data buffers and exit the kernel.

The *BatchFeedForward* kernel building algorithm is rather straightforward and thus we can move on to creating a method for calling the kernel from the main program. This functionality will be implemented by the*CNeuronBatchNormOCL::feedForward* method.The method algorithm is similar to the relevant methods of other classes. The method receives in parameters a pointer to the previous neural network layer.

At the beginning of the method, check the validity of the received pointer and the pointer to the OpenCL object (as you might remember this is a replica of a standard library class for working with the OpenCL program).

At the next step, save the pointer to the previous layer of the neural network and check the batch size. If the size of the normalization window does not exceed "1", copy the type of the activation function of the previous layer and exit the method with the *true* result. This way we provide data for replacing buffers and exclude unnecessary iterations of the algorithm.

bool CNeuronBatchNormOCL::feedForward(CNeuronBaseOCL *NeuronOCL){ if(CheckPointer(OpenCL)==POINTER_INVALID || CheckPointer(NeuronOCL)==POINTER_INVALID)return false; PrevLayer=NeuronOCL; if(iBatchSize<=1) {activation=(ENUM_ACTIVATION)NeuronOCL.Activation();return true; } if(CheckPointer(BatchOptions)==POINTER_INVALID) {int count=Neurons()*(optimization==SGD ? 7 : 9);BatchOptions=new CBufferDouble();if(!BatchOptions.BufferInit(count,0)) return false; } if(!BatchOptions.BufferCreate(OpenCL))return false; uint global_work_offset[1]= {0}; uint global_work_size[1]; global_work_size[0]=Neurons(); if(!OpenCL.SetArgumentBuffer(def_k_BatchFeedForward,def_k_bff_inputs,NeuronOCL.getOutputIndex()))return false; if(!OpenCL.SetArgumentBuffer(def_k_BatchFeedForward,def_k_bff_options,BatchOptions.GetIndex()))return false; if(!OpenCL.SetArgumentBuffer(def_k_BatchFeedForward,def_k_bff_output,Output.GetIndex()))return false; if(!OpenCL.SetArgument(def_k_BatchFeedForward,def_k_bff_batch,iBatchSize))return false; if(!OpenCL.SetArgument(def_k_BatchFeedForward,def_k_bff_optimization,(int)optimization))return false; if(!OpenCL.SetArgument(def_k_BatchFeedForward,def_k_bff_activation,(int)activation))return false; ResetLastError(); if(!OpenCL.Execute(def_k_BatchFeedForward,1,global_work_offset,global_work_size)) {printf("Error of execution kernel Batch Feed Forward: %d",GetLastError());return false; } if(!Output.BufferRead() || !BatchOptions.BufferRead())return false; BatchOptions.BufferFree(); return true;}

If, after all the checks, we have reached the launch of the direct pass kernel, we need to prepare the initial data for launching it. First, check the validity of the pointer to the parameter buffer of the normalization algorithm. Create and initialize a new buffer if necessary. Next, create a buffer in the video card memory and load the buffer contents.

Set the number of launched threads equal to the number of neurons in the layer and pass the pointers to the data buffers, along with the required parameters, to the kernel.

After the preparatory work, send the kernel for execution and read back the updated buffer data from the video card memory. Please note that data from two buffers are received from the video card: information from the algorithm output and a parameter buffer, in which we saved the updated mean, variance and normalized value. This data will be used in further iterations.

After the completion of the algorithm, delete the parameter buffer from the video card memory in order to free up memory for buffers of further layers of the neural network. Then, exit the method with *true*.

The full code of all classes and their methods from the library is available in the attachment.

#### 2.3. Feed-Backward

The feed-backward pass again consists of two stages: error back propagation and updating of weights. Instead of usual weights, we will train parametersγ andβ of the scaling and shifting function.

Let us start with the gradient descent functionality. Create the kernel*CalcHiddenGradientBatch* to implement its functionality. The kernel receives in parameters pointers to tensors of normalization parameters received from the next layer of gradients, previous layer output data (obtained during the last feed-forward pass) and tensors of previous layer gradients, to which the algorithm results will be written. The kernel will also receive in parameters the batch size, the type of the activation function, and the method for optimizing parameters.

As with the direct pass, at the kernel beginning check the batch size; if it is less than or equal to 1, then exit the kernel without performing other iterations.

The next step is to get the serial number of the thread and to determine the shift in the parameters tensor. These actions are similar to those described earlier in the feed-forward pass.

__kernel void CalcHiddenGradientBatch(__global double *options, __global double *matrix_g, __global double *matrix_i, __global double *matrix_ig, uint activation, int batch, int optimization ){ if(batch<=1)return; int n=get_global_id(0); int shift=n*(optimization==0 ? 7 : 9); double inp=matrix_i[n]; double gnx=matrix_g[n]*options[shift+3]; double temp=1/sqrt(options[shift+1]+1e-6); double gmu=(-temp)*gnx; double gvar=(options[shift]*inp)/(2*pow(options[shift+1]+1.0e-6,3/2))*gnx; double gx=temp*gnx+gmu/batch+gvar*2*inp/batch*pow((double)(batch-1)/batch,2.0); if(isnan(gx))gx=0; switch(activation) {case 0:gx=clamp(gx+inp,-1.0,1.0)-inp;gx=gx*(1-pow(inp==1 || inp==-1 ? 0.99999999 : inp,2));break;case 1:gx=clamp(gx+inp,0.0,1.0)-inp;gx=gx*(inp==0 || inp==1 ? 0.00000001 : (inp*(1-inp)));break;case 2:if(inp<0) gx*=0.01;break;default:break; } matrix_ig[n]=clamp(gx,-MAX_GRADIENT,MAX_GRADIENT);}

Next, sequentially calculate the gradients for all functions of the algorithm.

And finally, propagate the gradient through the activation function of the previous layer. Save the resulting value to the gradient tensor of the previous layer.

Following the *CalcHiddenGradientBatсh* kernel, let us consider the *CNeuronBatchNormOCL::calcInputGradients* method which will start kernel execution from the main program. Similar to the relevant methods of other classes, the method receives in parameters a pointer to the object of the previous neural network layer.

At the beginning of the method, check the validity of the received pointer and of the pointer to the OpenCL object. After that, check the batch size. If it is less than or equal to 1, then exit the method. The result returned from the method will depend on the validity of the pointer to the previous layer, which was saved during the feed-forward pass.

If we move further along the algorithm, check the validity of the parameter buffer. If an error occurs, exit the method with the result *false*.

Please note that the propagated gradient belongs to the last feed-forward pass. That is why, at the last two points of control, we checked the objects participating in the feed-forward.

bool CNeuronBatchNormOCL::calcInputGradients(CNeuronBaseOCL *NeuronOCL){ if(CheckPointer(OpenCL)==POINTER_INVALID || CheckPointer(NeuronOCL)==POINTER_INVALID)return false; if(iBatchSize<=1)return (CheckPointer(PrevLayer)!=POINTER_INVALID); if(CheckPointer(BatchOptions)==POINTER_INVALID || !BatchOptions.BufferCreate(OpenCL))return false; uint global_work_offset[1]= {0}; uint global_work_size[1]; global_work_size[0]=Neurons(); if(!OpenCL.SetArgumentBuffer(def_k_CalcHiddenGradientBatch,def_k_bchg_matrix_i,NeuronOCL.getOutputIndex()))return false; if(!OpenCL.SetArgumentBuffer(def_k_CalcHiddenGradientBatch,def_k_bchg_options,BatchOptions.GetIndex()))return false; if(!OpenCL.SetArgumentBuffer(def_k_CalcHiddenGradientBatch,def_k_bchg_matrix_g,Gradient.GetIndex()))return false; if(!OpenCL.SetArgumentBuffer(def_k_CalcHiddenGradientBatch,def_k_bchg_matrix_ig,NeuronOCL.getGradientIndex()))return false; if(!OpenCL.SetArgument(def_k_CalcHiddenGradientBatch,def_k_bchg_activation,NeuronOCL.Activation()))return false; if(!OpenCL.SetArgument(def_k_CalcHiddenGradientBatch,def_k_bchg_batch,iBatchSize))return false; if(!OpenCL.SetArgument(def_k_CalcHiddenGradientBatch,def_k_bchg_optimization,(int)optimization))return false; ResetLastError(); if(!OpenCL.Execute(def_k_CalcHiddenGradientBatch,1,global_work_offset,global_work_size)) {printf("Error of execution kernel Batch CalcHiddenGradient: %d",GetLastError());return false; } if(!NeuronOCL.getGradient().BufferRead())return false; BatchOptions.BufferFree(); return true;}

As with the feed-forward pass, the number of kernel threads launched will be equal to the number of neurons in the layer. Send the contents of normalization parameter buffer to the video card memory and pass required tensor and parameter pointers to the kernel.

After performing all the above operations, run the kernel execution and calculate the resulting gradients from the video card memory into the corresponding buffer.

At the end of the method, remove the tensor of normalization parameters from the video card memory and exit the method with the result *true*.

After propagating the gradient, it is time to update the shift and scale parameters. To implement these iterations, create 2 kernels, according to the number of the previously described optimization methods, *UpdateBatchOptionsMomentum* and *UpdateBatchOptionsAdam*.

Let us start with the *UpdateBatchOptionsMomentum* method. The method receives in parameters pointers to two tensors: of normalization parameters and or gradients. Also, pass optimization method constants in the method parameters: the learning rate and the momentum.

At the beginning of the kernel, obtain the thread number and determine the shift in the tensor of the normalization parameters.

Using the source data, let us calculate delta for γ and β. For this operation, I used vector calculations with the 2-element double vector. This method allows the parallelizing of computations.

Adjust parameters γ, β and save the results in the appropriate elements of the normalization parameters tensor.

__kernel void UpdateBatchOptionsMomentum(__global double *options, __global double *matrix_g, double learning_rates, double momentum ){ const int n=get_global_id(0); const int shift=n*7; double grad=matrix_g[n]; double2 delta=learning_rates*grad*(double2)(options[shift+2],1) + momentum*(double2)(options[shift+5],options[shift+6]); if(!isnan(delta.s0) && !isnan(delta.s1)) {options[shift+5]=delta.s0;options[shift+3]=clamp(options[shift+3]+delta.s0,-MAX_WEIGHT,MAX_WEIGHT);options[shift+6]=delta.s1;options[shift+4]=clamp(options[shift+4]+delta.s1,-MAX_WEIGHT,MAX_WEIGHT); }};

The *UpdateBatchOptionsAdam* kernel is built according to a similar scheme, but there are differences in the optimization method algorithm. The kernel receives in parameters pointers to the same parameter and gradient tensors. It also receives optimization method parameters.

At the beginning of the kernel, define the thread number and determine the shift in the parameter tensor.

Based on the data obtained, calculate the first and second moments. The vector calculations used here allow the calculation of moments for two parameters at the same time.

Based on the obtained moments, calculate the deltas and new parameter values. Calculation results will be saved into the corresponding elements of the tensor of normalization parameters.

__kernel void UpdateBatchOptionsAdam(__global double *options, __global double *matrix_g, const double l,const double b1,const double b2){ const int n=get_global_id(0); const int shift=n*9; double grad=matrix_g[n]; double2 mt=b1*(double2)(options[shift+5],options[shift+6])+(1-b1)*(double2)(grad*options[shift+2],grad); double2 vt=b2*(double2)(options[shift+5],options[shift+6])+(1-b2)*pow((double2)(grad*options[shift+2],grad),2); double2 delta=l*mt/sqrt(vt+1.0e-8); if(isnan(delta.s0) || isnan(delta.s1))return; double2 weight=clamp((double2)(options[shift+3],options[shift+4])+delta,-MAX_WEIGHT,MAX_WEIGHT); if(!isnan(weight.s0) && !isnan(weight.s1)) {options[shift+3]=weight.s0;options[shift+4]=weight.s1;options[shift+5]=mt.s0;options[shift+6]=mt.s1;options[shift+7]=vt.s0;options[shift+8]=vt.s1; }};

To launch kernels from the main program, let us create the *CNeuronBatchNormOCL::updateInputWeights* method. The method receives in parameters a pointer to the previous neural network layer. Actually, this pointer will not be used in the method algorithm, but it is left for the inheritance of methods from the parent class.

At the beginning of the method, check the validity of the received pointer and of the pointer to the OpenCL object. Like for the previously considered*CNeuronBatchNormOCL::calcInputGradients* method, check the batch size and the validity of the parameter buffer. Load the contents of the parameter buffer into the video card memory. Set the number of threads equal to the number of neurons in the layer.

Further, the algorithm can follow two options, depending on the specified optimization method. Pass the initial parameters for the required kernel and restart its execution.

Regardless of the parameter optimization method, calculate the updated contents of the normalization parameters buffer and remove the buffer from the video card memory.

bool CNeuronBatchNormOCL::updateInputWeights(CNeuronBaseOCL *NeuronOCL){ if(CheckPointer(OpenCL)==POINTER_INVALID || CheckPointer(NeuronOCL)==POINTER_INVALID)return false; if(iBatchSize<=1)return (CheckPointer(PrevLayer)!=POINTER_INVALID); if(CheckPointer(BatchOptions)==POINTER_INVALID || !BatchOptions.BufferCreate(OpenCL))return false; uint global_work_offset[1]= {0}; uint global_work_size[1]; global_work_size[0]=Neurons(); if(optimization==SGD) {if(!OpenCL.SetArgumentBuffer(def_k_UpdateBatchOptionsMomentum,def_k_buom_options,BatchOptions.GetIndex())) return false;if(!OpenCL.SetArgumentBuffer(def_k_UpdateBatchOptionsMomentum,def_k_buom_matrix_g,Gradient.GetIndex())) return false;if(!OpenCL.SetArgument(def_k_UpdateBatchOptionsMomentum,def_k_buom_learning_rates,eta)) return false;if(!OpenCL.SetArgument(def_k_UpdateBatchOptionsMomentum,def_k_buom_momentum,alpha)) return false;ResetLastError();if(!OpenCL.Execute(def_k_UpdateBatchOptionsMomentum,1,global_work_offset,global_work_size)){ printf("Error of execution kernel UpdateBatchOptionsMomentum %d",GetLastError()); return false;} } else {if(!OpenCL.SetArgumentBuffer(def_k_UpdateBatchOptionsAdam,def_k_buoa_options,BatchOptions.GetIndex())) return false;if(!OpenCL.SetArgumentBuffer(def_k_UpdateBatchOptionsAdam,def_k_buoa_matrix_g,Gradient.GetIndex())) return false;if(!OpenCL.SetArgument(def_k_UpdateBatchOptionsAdam,def_k_buoa_l,lr)) return false;if(!OpenCL.SetArgument(def_k_UpdateBatchOptionsAdam,def_k_buoa_b1,b1)) return false;if(!OpenCL.SetArgument(def_k_UpdateBatchOptionsAdam,def_k_buoa_b2,b2)) return false;ResetLastError();if(!OpenCL.Execute(def_k_UpdateBatchOptionsAdam,1,global_work_offset,global_work_size)){ printf("Error of execution kernel UpdateBatchOptionsAdam %d",GetLastError()); return false;} } if(!BatchOptions.BufferRead())return false; BatchOptions.BufferFree(); return true;}

After successful completion of the operations, exit the method with the result *true*.

Methods for buffer replacement were described in detail in the previous article and so I think they should not cause any difficulties. This also concerns operations with files (saving and loading a trained neural network).

The full code of all classes and their methods is available in the attachment.

#### 2.4. Changes in the Neural Network Base Classes

Again, after creating a new class, let us integrate it into the general structure of the neural network. First, let us create an identifier for the new class.

#define defNeuronBatchNormOCL 0x7891

Next, define constant macro substitutions for working with new kernels.

#define def_k_BatchFeedForward 24 #define def_k_bff_inputs 0#define def_k_bff_options1#define def_k_bff_output 2#define def_k_bff_batch3#define def_k_bff_optimization 4#define def_k_bff_activation 5#define def_k_CalcHiddenGradientBatch 25 #define def_k_bchg_options 0#define def_k_bchg_matrix_g1#define def_k_bchg_matrix_i2#define def_k_bchg_matrix_ig 3#define def_k_bchg_activation4#define def_k_bchg_batch 5#define def_k_bchg_optimization6#define def_k_UpdateBatchOptionsMomentum26 #define def_k_buom_options0#define def_k_buom_matrix_g 1#define def_k_buom_learning_rates 2#define def_k_buom_momentum 3#define def_k_UpdateBatchOptionsAdam27 #define def_k_buoa_options0#define def_k_buoa_matrix_g 1#define def_k_buoa_l2#define def_k_buoa_b1 3#define def_k_buoa_b2 4

In the neural network constructor CNet::CNet, let us add blocks which create new class objects and initialize new kernels (changes are highlighted in the code).

CNet::CNet(CArrayObj *Description){ if(CheckPointer(Description)==POINTER_INVALID)return;................................................ for(int i=0; i<total; i++) {prev=desc;desc=Description.At(i);if((i+1)<total){ next=Description.At(i+1); if(CheckPointer(next)==POINTER_INVALID)return;}else next=NULL;int outputs=(next==NULL || (next.type!=defNeuron && next.type!=defNeuronBaseOCL) ? 0 : next.count);temp=new CLayer(outputs);int neurons=(desc.count+(desc.type==defNeuron || desc.type==defNeuronBaseOCL ? 1 : 0));if(CheckPointer(opencl)!=POINTER_INVALID){................................................CNeuronBatchNormOCL *batch=NULL; switch(desc.type) {................................................................case defNeuronBatchNormOCL: batch=new CNeuronBatchNormOCL(); if(CheckPointer(batch)==POINTER_INVALID) {delete temp;return; } if(!batch.Init(outputs,0,opencl,desc.count,desc.window,desc.optimization)) {delete batch;delete temp;return; } batch.SetActivationFunction(desc.activation); if(!temp.Add(batch)) {delete batch;delete temp;return; } batch=NULL; break;default: return; break; }}................................................................ if(CheckPointer(opencl)==POINTER_INVALID)return; opencl.SetKernelsCount(28);................................................................ opencl.KernelCreate(def_k_BatchFeedForward,"BatchFeedForward"); opencl.KernelCreate(def_k_CalcHiddenGradientBath,"CalcHiddenGradientBath"); opencl.KernelCreate(def_k_UpdateBatchOptionsMomentum,"UpdateBatchOptionsMomentum"); opencl.KernelCreate(def_k_UpdateBatchOptionsAdam,"UpdateBatchOptionsAdam"); return;}

Similarly, initiate new kernels when loading a pre-trained neural network.

bool CNet::Load(string file_name,double &error,double &undefine,double &forecast,datetime &time,bool common=true){ if(MQLInfoInteger(MQL_OPTIMIZATION) || MQLInfoInteger(MQL_TESTER) || MQLInfoInteger(MQL_FORWARD) || MQLInfoInteger(MQL_OPTIMIZATION))return false;................................................ if(CheckPointer(opencl)==POINTER_INVALID) {opencl=new COpenCLMy();if(CheckPointer(opencl)!=POINTER_INVALID && !opencl.Initialize(cl_program,true)) delete opencl;else{ opencl.SetKernelsCount(28);................................................ opencl.KernelCreate(def_k_BatchFeedForward,"BatchFeedForward"); opencl.KernelCreate(def_k_CalcHiddenGradientBath,"CalcHiddenGradientBath"); opencl.KernelCreate(def_k_UpdateBatchOptionsMomentum,"UpdateBatchOptionsMomentum"); opencl.KernelCreate(def_k_UpdateBatchOptionsAdam,"UpdateBatchOptionsAdam");} }................................................................................}

Add a new type of neurons into the method that loads the pre-trained neural network.

bool CLayer::Load(const int file_handle){ iFileHandle=file_handle; if(!CArrayObj::Load(file_handle))return false; if(CheckPointer(m_data[0])==POINTER_INVALID)return false; CNeuronBaseOCL *ocl=NULL; CNeuronBase*cpu=NULL; switch(m_data[0].Type()) {case defNeuronBaseOCL:case defNeuronConvOCL:case defNeuronAttentionOCL:case defNeuronMHAttentionOCL:case defNeuronMLMHAttentionOCL:case defNeuronDropoutOCL:case defNeuronBatchNormOCL:ocl=m_data[0];iOutputs=ocl.getConnections();break;default:cpu=m_data[0];iOutputs=cpu.getConnections().Total();break; } return true;}

Similarly, let us add a new type of neurons into dispatcher methods of the *CNeuronBaseOCL* base class.

bool CNeuronBaseOCL::FeedForward(CObject *SourceObject){ if(CheckPointer(SourceObject)==POINTER_INVALID)return false; CNeuronBaseOCL *temp=NULL; switch(SourceObject.Type()) {case defNeuronBaseOCL:case defNeuronConvOCL:case defNeuronAttentionOCL:case defNeuronMHAttentionOCL:case defNeuronMLMHAttentionOCL:case defNeuronDropoutOCL:case defNeuronBatchNormOCL: temp=SourceObject; return feedForward(temp); break; } return false;}bool CNeuronBaseOCL::calcHiddenGradients(CObject *TargetObject){ if(CheckPointer(TargetObject)==POINTER_INVALID)return false;................................................ CNeuronBatchNormOCL *batch=NULL; switch(TargetObject.Type()) {................................................case defNeuronBatchNormOCL: batch=TargetObject; temp=GetPointer(this); return batch.calcInputGradients(temp); break; } return false;}bool CNeuronBaseOCL::UpdateInputWeights(CObject *SourceObject){ if(CheckPointer(SourceObject)==POINTER_INVALID)return false; CNeuronBaseOCL *temp=NULL; switch(SourceObject.Type()) {case defNeuronBaseOCL:case defNeuronConvOCL:case defNeuronAttentionOCL:case defNeuronMHAttentionOCL:case defNeuronMLMHAttentionOCL:case defNeuronDropoutOCL:case defNeuronBatchNormOCL: temp=SourceObject; return updateInputWeights(temp); break; } return false;}

The full code of all classes and their methods is available in the attachment.

### 3. Testing

We continue to test new classes in the previously created Expert Advisors, which produces comparable data for the evaluation of the performance of individual elements. Let us test the normalization method base on the Expert Advisor from the article 12, replacing Dropout with Batch Normalization. The neural network structure of the new Expert Advisor is presented below. Here, the learning rate was increased from 0.000001 to 0.001.

CLayerDescription *desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=(int)HistoryBars*12;desc.type=defNeuronBaseOCL;desc.optimization=ADAM;desc.activation=None;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=(int)HistoryBars*12;desc.type=defNeuronBatchNormOCL;desc.window=100;desc.optimization=ADAM;desc.activation=TANH;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=(int)HistoryBars;desc.type=defNeuronConvOCL;desc.window=12;desc.step=12;desc.window_out=24;desc.optimization=ADAM;desc.activation=None;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=(int)HistoryBars*24;desc.type=defNeuronBatchNormOCL;desc.window=100;desc.optimization=ADAM;desc.activation=SIGMOID;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=(int)HistoryBars;desc.type=defNeuronMLMHAttentionOCL;desc.window=24;desc.window_out=4;desc.step=8;desc.layers=5;desc.optimization=ADAM;desc.activation=SIGMOID;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=200;desc.type=defNeuron;desc.activation=None;desc.optimization=ADAM;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=200;desc.type=defNeuronBatchNormOCL;desc.window=100;desc.optimization=ADAM;desc.activation=TANH;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=200;desc.type=defNeuron;desc.activation=TANH;desc.optimization=ADAM;if(!Topology.Add(desc)) return INIT_FAILED;desc=new CLayerDescription();if(CheckPointer(desc)==POINTER_INVALID) return INIT_FAILED;desc.count=3;desc.type=defNeuron;desc.activation=SIGMOID;desc.optimization=ADAM;

The Expert Advisor was tested on EURUSD, H1 timeframe. Data of 20 latest candlestick were input into the neural network, similarly to previous tests.

The neural network prediction error graph shows that the EA with batch normalization has a less smoothed graph, which can be caused by a sharp increase in the learning rate. However, the prediction error is lower than that of the previous tests almost throughout the test.

Prediction hit graphs of all three Expert Advisors are quite close and thus we cannot conclude that any of them is definitely better.

### Conclusion

In this article, we continued considering methods aimed at increasing the convergence of neural networks and have added a Batch Normalization class to our library. Testing has shown that the use of this method can reduce the neural network error and increase the learning rate.

### References

- Neural networks made easy
- Neural networks made easy (Part 2): Network training and testing
- Neural networks made easy (Part 3): Convolutional networks
- Neural networks made easy (Part 4): Recurrent networks
- Neural networks made easy (Part 5): Multithreaded calculations in OpenCL
- Neural networks made easy (Part 6): Experimenting with the neural network learning rate
- Neural networks made easy (Part 7): Adaptive optimization methods
- Neural networks made easy (Part 8): Attention mechanisms
- Neural networks made easy (Part 9): Documenting the work
- Neural networks made easy (Part 10): Multi-Head Attention
- Neural networks made easy (Part 11): A take on GPT
- Neural networks made easy (Part 12): Dropout
- Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
- Layer Normalization

### Programs Used in the Article

# | Issued to | Type | Description |
---|---|---|---|

1 | Fractal_OCL_AttentionMLMH_b.mq5 | Expert Advisor | An Expert Advisor with the classification neural network (3 neurons in the output layer) using the GTP architecture, with 5 attention layers + BatchNorm |

2 | NeuroNet.mqh | Class library | A library of classes for creating a neural network |

3 | NeuroNet.cl | Code Base | OpenCL program code library |

4 | NN.chm | HTML Help | A compiled Library Help CHM file. |

## FAQs

### What is batch normalization in neural networks? ›

Batch normalization is **a technique for training very deep neural networks that normalizes the contributions to a layer for every mini-batch**. This has the impact of settling the learning process and drastically decreasing the number of training epochs required to train deep neural networks.

**What is batch normalization formula? ›**

Batch Normalization (BN) is **a normalization method/layer for neural networks**. Usually inputs to neural networks are normalized to either the range of [0, 1] or [-1, 1] or to mean=0 and variance=1. The latter is called Whitening. BN essentially performs Whitening to the intermediate layers of the networks.

**When should I use batch normalization? ›**

When to use Batch Normalization? We can use Batch Normalization in **Convolution Neural Networks, Recurrent Neural Networks, and Artificial Neural Networks**. In practical coding, we add Batch Normalization after the activation function of the output layer or before the activation function of the input layer.

**Is batch normalization a hidden layer? ›**

**Batch Norm is just another network layer that gets inserted between a hidden layer and the next hidden layer**. Its job is to take the outputs from the first hidden layer and normalize them before passing them on as the input of the next hidden layer. Just like the parameters (eg.

**What is the benefit of batch normalization? ›**

Using batch normalization **allows us to use much higher learning rates, which further increases the speed at which networks train**. Makes weights easier to initialize — Weight initialization can be difficult, and it's even more difficult when creating deeper networks.

**Why is batch normalization used in CNN? ›**

There is no clear consensus on which of these approaches is better. Batch normalization turned out to **improve the efficiency of CNN training significantly**. It helps avoid vanishing or exploding gradient by keeping the activations more stable during training, which in turn allows to use larger learning rates.

**Does batch normalization prevent overfitting? ›**

**Reduces overfitting**. Batch normalisation has a regularising effect since it adds noise to the inputs of every layer. This discourages overfitting since the model no longer produces deterministic values for a given training example alone.

**Does batch normalization improve accuracy? ›**

Batch normalization (BN) is a technique to normalize activations in intermediate layers of deep neural networks. **Its tendency to improve accuracy** and speed up training have established BN as a favorite technique in deep learning.

**Is batch normalization applied at every layer? ›**

Your first sentence is correct, **batch normalization is applied at each layer**. The only difference between train and test time is that at test time, the running estimates of the mean and variance are not updated.

**What is the difference between layer normalization and batch normalization? ›**

Batch Normalization vs Layer Normalization

**Batch normalization normalizes each feature independently across the mini-batch.** Layer normalization normalizes each of the inputs in the batch independently across all features. As batch normalization is dependent on batch size, it's not effective for small batch sizes.

### Why do we need normalization in deep learning? ›

Normalization can help training of our neural networks as the different features are on a similar scale, which helps to stabilize the gradient descent step, allowing us to use larger learning rates or help models converge faster for a given learning rate.

**Why is normalization important? ›**

Normalization is necessary **to ensure that the table only contains data directly related to the primary key, each data field contains only one data element, and to remove redundant (duplicated and unnecessary) data**.

**How many parameters does a batch normalization layer? ›**

Consequently, batch normalization adds two trainable parameters to each layer, so the normalized output is multiplied by a “standard deviation” parameter (gamma) and add a “mean” parameter (beta).

**What is the advantages of layer normalization over batch normalization? ›**

Batch normalization works better with fully connected layers and convolutional neural network (CNN) but it shows poor results with recurrent neural network (RNN). On the other hand, the main advantage of Layer normalization is that **it works really well with RNN**.

**Why batch normalization helps in faster convergence? ›**

BatchNorm impacts network training in a fundamental way: **it makes the landscape of the corresponding optimization problem be significantly more smooth**. This ensures, in particular, that the gradients are more predictive and thus allow for use of larger range of learning rates and faster network convergence.

**Is batch normalization layer trainable? ›**

**training=False** : The layer will normalize its inputs using the mean and variance of its moving statistics, learned during training.

**What is normalization in deep learning? ›**

Normalization is **a data pre-processing tool used to bring the numerical data to a common scale without distorting its shape**. Generally, when we input the data to a machine or deep learning algorithm we tend to change the values to a balanced scale.

**Does batch normalization prevent vanishing gradient? ›**

Batch Normalization (BN) **does not prevent the vanishing or exploding gradient problem** in a sense that these are impossible. Rather it reduces the probability for these to occur.

**Why is CNN dropping out? ›**

Dropout layers are important in training CNNs because **they prevent overfitting on the training data**. If they aren't present, the first batch of training samples influences the learning in a disproportionately high manner.

**What is batch normalization in keras? ›**

Batch normalization is **a technique for training very deep neural networks that standardizes the inputs to a layer for each mini-batch**. This has the effect of stabilizing the learning process and dramatically reducing the number of training epochs required to train deep networks.

### Where should I put batch normalization? ›

This normalization step is applied right before (or right after) the nonlinear function. All the current deep learning frameworks have already implemented methods which apply batch normalization. It is usually used as a module which could be inserted as a standard layer in a DNN.

**When was batch normalization invented? ›**

Batch normalization (also known as batch norm) is a method used to make training of artificial neural networks faster and more stable through normalization of the layers' inputs by re-centering and re-scaling. It was proposed by Sergey Ioffe and Christian Szegedy in **2015**.

**How do I stop overfitting? ›**

**How to Prevent Overfitting in Machine Learning**

- Cross-validation. Cross-validation is a powerful preventative measure against overfitting. ...
- Train with more data. It won't work every time, but training with more data can help algorithms detect the signal better. ...
- Remove features. ...
- Early stopping. ...
- Regularization. ...
- Ensembling.

**What is disadvantages of batch normalization? ›**

**Not good for Recurrent Neural Networks**

Batch normalization can be applied in between stacks of RNN, where normalization is applied “vertically” i.e. the output of each RNN. But it cannot be applied “horizontally” i.e. between timesteps, as it hurts training because of exploding gradients due to repeated rescaling.

**Should I use batch normalization with Lstm? ›**

**No, you cannot use Batch Normalization on a recurrent neural network**, as the statistics are computed per batch, this does not consider the recurrent part of the network. Weights are shared in an RNN, and the activation response for each "recurrent loop" might have completely different statistical properties.

**How do I reduce Underfitting? ›**

Techniques to reduce underfitting:

**Increase model complexity**. Increase the number of features, performing feature engineering. Remove noise from the data. Increase the number of epochs or increase the duration of training to get better results.

**Which of the following is true for batch normalization? ›**

(ii) True. We are normalizing the input to each layer with batch normalization, so it certainly **helps with lessening the coupling between layers and makes the learning process more independent**.

**What is momentum in batch normalization? ›**

Momentum **helps in reducing the noise in gradient update term and thus helps to converge faster to the optimal (or near optimal) value**. Batch normalization reduces the coupling (sensitivity) of prior layers parameters to the later stage parameters thus stabilizing the inputs feed to a layer.

**Why do we normalize layers? ›**

Layer normalization (LayerNorm) is a technique to normalize the distributions of intermediate layers. It **enables smoother gradients, faster training, and better generalization accuracy**.

**What is Axis in batch normalization? ›**

axis: **Integer, the axis that should be normalized (typically the features axis)**. For instance, after a Conv2D layer with data_format="channels_first", set axis=1 in BatchNormalization. momentum: Momentum for the moving average. epsilon: Small float added to variance to avoid dividing by zero.

### What is difference between standardization and normalization? ›

...

Difference between Normalization and Standardization.

S.NO. | Normalization | Standardization |
---|---|---|

8. | It is a often called as Scaling Normalization | It is a often called as Z-Score Normalization. |

**What is normalization explain with example? ›**

Normalization is **the process of organizing data in a database**. This includes creating tables and establishing relationships between those tables according to rules designed both to protect the data and to make the database more flexible by eliminating redundancy and inconsistent dependency.

**Which normalization method is best? ›**

The best normalization technique is **one that empirically works well**, so try new ideas if you think they'll work well on your feature distribution. When the feature is more-or-less uniformly distributed across a fixed range. When the feature contains some extreme outliers. When the feature conforms to the power law.

**Is normalization necessary for neural networks? ›**

**Yes, normalisation/scaling is typically recommended and sometimes very important**. Especially for neural networks, normalisation can be very crucial because when you input unnormalised inputs to activation functions, you can get stuck in a very flat region in the domain and may not learn at all.

**Where is normalization used? ›**

Normalization is used **to minimize the redundancy from a relation or set of relations**. It is also used to eliminate undesirable characteristics like Insertion, Update, and Deletion Anomalies.

**How do you normalize data? ›**

**Here are the steps to use the normalization formula on a data set:**

- Calculate the range of the data set. ...
- Subtract the minimum x value from the value of this data point. ...
- Insert these values into the formula and divide. ...
- Repeat with additional data points.

**What are the stages of normalization? ›**

**Normalization rules are divided into the following normal forms:**

- First Normal Form.
- Second Normal Form.
- Third Normal Form.
- BCNF.
- Fourth Normal Form.

**What is dropout and batch normalization? ›**

BN normalizes values of the units for each batch with its own mean and standard deviation. Dropout, on the other hand, randomly drops a predefined ratio of units in a neural network to prevent overfitting.

**What is affine in batch normalization? ›**

affine = False is equivalent to simply computing: **y = (x - mu) / sqrt(var + eps)** **where, mu is the running (propagated) mean and var is the running (propagated) variance**. Equivalently, this can be interpreted as fixing gamma=1 and beta=0 (These will then be non-trainable.

**Why do we normalize image data? ›**

the point from normalization comes behind calibrating the different pixels intensities into a normal distribution which makes the image looks better for the visualizer. Main purpose of normalization is **to make computation efficient by reducing values between 0 to 1**.

### What is beta and gamma in batch normalization? ›

gamma and beta are learn-able parameters, hence they can during training they can learn any other distribution, only if they are equal to sigma_sq and mu respectively they undo the (2) step, this is important because if there was no need for normalization the batch normalization layer would simply learn this during ...

**What is batch size in deep learning? ›**

The batch size is **a number of samples processed before the model is updated**. The number of epochs is the number of complete passes through the training dataset. The size of a batch must be more than or equal to one and less than or equal to the number of samples in the training dataset.

**What is normalization techniques in machine learning? ›**

Normalization is a technique often applied as part of data preparation for machine learning. The goal of normalization is **to change the values of numeric columns in the dataset to use a common scale, without distorting differences in the ranges of values or losing information**.

**Where is batch normalization on CNN? ›**

It can be used **at several points in between the layers of the model**. It is often placed just after defining the sequential model and after the convolution and pooling layers.

**What is the difference between layer normalization and batch normalization? ›**

Batch Normalization vs Layer Normalization

**Batch normalization normalizes each feature independently across the mini-batch.** Layer normalization normalizes each of the inputs in the batch independently across all features. As batch normalization is dependent on batch size, it's not effective for small batch sizes.

**What is dropout and batch normalization? ›**

BN normalizes values of the units for each batch with its own mean and standard deviation. Dropout, on the other hand, randomly drops a predefined ratio of units in a neural network to prevent overfitting.

**Does batch normalization prevent overfitting? ›**

We can use higher learning rates because batch normalization makes sure that there's no activation that's gone really high or really low. And by that, things that previously couldn't get to train, it will start to train. It reduces overfitting because it has a slight regularization effects.

**Why do we normalize data in neural network? ›**

Normalization can help training of our neural networks as the different features are on a similar scale, which **helps to stabilize the gradient descent step, allowing us to use larger learning rates or help models converge faster for a given learning rate**.

**What is batch normalization in keras? ›**

Batch normalization is **a technique for training very deep neural networks that standardizes the inputs to a layer for each mini-batch**. This has the effect of stabilizing the learning process and dramatically reducing the number of training epochs required to train deep networks.

**What is Normalisation in deep learning? ›**

Normalization is **a data pre-processing tool used to bring the numerical data to a common scale without distorting its shape**. Generally, when we input the data to a machine or deep learning algorithm we tend to change the values to a balanced scale.

### Why batch normalization helps in faster convergence? ›

BatchNorm impacts network training in a fundamental way: **it makes the landscape of the corresponding optimization problem be significantly more smooth**. This ensures, in particular, that the gradients are more predictive and thus allow for use of larger range of learning rates and faster network convergence.

**What is Axis in batch normalization? ›**

axis: **Integer, the axis that should be normalized (typically the features axis)**. For instance, after a Conv2D layer with data_format="channels_first", set axis=1 in BatchNormalization. momentum: Momentum for the moving average. epsilon: Small float added to variance to avoid dividing by zero.

**Why is CNN dropping out? ›**

Dropout layers are important in training CNNs because **they prevent overfitting on the training data**. If they aren't present, the first batch of training samples influences the learning in a disproportionately high manner.

**What is Softmax layer in CNN? ›**

The softmax function is used as **the activation function in the output layer of neural network models that predict a multinomial probability distribution**. That is, softmax is used as the activation function for multi-class classification problems where class membership is required on more than two class labels.

**Should batch norm before or after ReLU? ›**

So the Batch Normalization Layer is actually inserted right after a Conv Layer/Fully Connected Layer, but **before feeding into ReLu** (or any other kinds of) activation.

**Where should I put batch normalization? ›**

This normalization step is applied right before (or right after) the nonlinear function. All the current deep learning frameworks have already implemented methods which apply batch normalization. It is usually used as a module which could be inserted as a standard layer in a DNN.

**Is batch normalization layer trainable? ›**

**training=False** : The layer will normalize its inputs using the mean and variance of its moving statistics, learned during training.

**Does batch normalization prevent vanishing gradient? ›**

Batch Normalization (BN) **does not prevent the vanishing or exploding gradient problem** in a sense that these are impossible. Rather it reduces the probability for these to occur.