Batch Size impact on Batch Normalisation Layer

[MKR]

Hello,

I want/have to train a network with a Batch Size of 1. Should I set the "use_global_stats" in my Batch Normalization Layers to true or false during training and testing?

If yes, do I have to add parameters like "lr","moving_average_fraction" or "eps"... ?

My guess is:
- Training: True
- Testing: True

But first experiments showed that:
- Training: False
- Testing: False
was much better.

Thanks for your help!

[MKR]

This is my Network:

name: "ResNet-50"
layer {
  name: "data"
  type: "Input"
  top: "data"
  input_param {
    shape {
      dim: 1
      dim: 3
      dim: 224
      dim: 224
    }
  }
  include {
    phase: TRAIN
  }
}

layer {
  name: "label"
  type: "Input"
  top: "label"
  input_param {
    shape {
      dim: 1
      dim: 1
      dim: 1
      dim: 1
    }
  }
  include {
      phase: TRAIN
  }
}

layer {
  name: "res_conv1"
  type: "Convolution"
  bottom: "data"
  top: "res_conv1"
  param { lr_mult: 0 decay_mult: 0 }
  param { lr_mult: 0 decay_mult: 0 }
  convolution_param {
    num_output: 1
    pad: 0
    kernel_size: 224
    stride: 1 
    weight_filler {
      type: "constant"    
      value: 1
    }
    bias_filler {
      type: "constant" 
      value: 0
    }
  }
}

layer {
  name: "bn_conv1"
  type: "BatchNorm"
  bottom: "res_conv1"
  top: "res_conv1"
  include {
    phase: TRAIN
  }
  batch_norm_param {
    use_global_stats: false
  }
}

layer {
  name: "bn_conv1"
  type: "BatchNorm"
  bottom: "res_conv1"
  top: "res_conv1"
  include {
    phase: TEST
  }
  batch_norm_param {
    use_global_stats: false
  }
}

layer {
  name: "scale_conv1"
  type: "Scale"
  bottom: "res_conv1"
  top: "res_conv1"
  scale_param {
    filler {
      value: 1 
    }
    bias_term: true
    bias_filler {
      value: 0
    }
  }
  param { lr_mult: 0 decay_mult: 0 }
  param { lr_mult: 0 decay_mult: 0 }
}

layer {
  name: "fc1000"
  type: "InnerProduct"
  bottom: "res_conv1"
  top: "fc1000"
  inner_product_param {
    num_output: 2
    weight_filler {
      type: "gaussian"
      std: 0.01
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}

layer {
  name: "prob"
  type: "Softmax"
  bottom: "fc1000"
  top: "prob"
  include: {
    phase: TEST
  }
}

layer {
  name:"argmax"
  type: "ArgMax"
  bottom: "prob"
  top: "argmax"
  include: {
    phase: TEST
  }
}

layer {
  type: 'SoftmaxWithLoss'
  name: 'loss'
  top: 'loss'
  bottom: 'fc1000'
  bottom: 'label'
  include: {
    phase: TRAIN
  }
}

Input are ones with shape (224,224,3). I set the weights and bias to these values to analyze the problem.
ee what is happening (attached file). I cannot explain it ...