[Kaggle Extra Study] 13. Weight Initialization

Weight Initialization?

• When training a neural network, one of the things we should care about is where we should start on the loss function to reach the optimal solution more easily and quickly.
• When training a neural network, the method of determining the starting position on the loss function is called Model Initialization.
• In particular, weights account for the largest portion of the model's parameters.
• The learning performance varies greatly depending on the weight initialization method.
• Also prevents Vanishing / Exploding gradients problem.

1. Zero Initialization(Constant Initialization)

• Sets all weights to 0.
• Problem:
  • All neurons output the same values, preventing effective learning.
• Same problem occurs when we intialize with other constants.
• If all parameter values are the same, even after updating through back propagation, they will all change to the same value.
• If all parameters of neural network nodes are identical, having multiple nodes in the neural network becomes meaningless. 
  • This is because it effectively becomes equivalent to having just one node per layer.
  • Initializing all weights to the same constant creates symmetry in the neural network, causing all neurons in the same layer to operate identically.
  • Therefore, initial values must be set randomly.

2. Random Initialization

• Initializes with small random values.
• The easiest way to assign random(different) values to parameters is to use a probability distribution.
  • Typically drawn from uniform or normal distribution between -0.01 and 0.01.
• Simple but may cause gradient vanishing/exploding problems in deep networks.
• Details:
  • For example, we can set all weights differently by assigning values that follow a normal distribution.
  • When activation values are close to 0 and 1, the derivative of the logistic function(sigmoid func) is nearly zero.
  • This leads to the gradient vanishing phenomenon where learning does not occur.
  • So, we can reduce the standard deviation to prevent values from being skewed towards these extremes.
  • By this way, we can get rid of the gradient vanishing effect. 
  • However, most output values are located around 0.5. 
  • As mentioned in the constant initialization, when all nodes' activation function outputs are similar, having multiple nodes loses its meaning.

3. Xavier/Glorot Initialization

• Xavier initialization is an initialization method designed to solve the problems mentioned above.
• Xavier initialization doesn't use a fixed standard deviation.
  • Instead, it adjusts based on the number of nodes in the previous hidden layer.
  • When there are n nodes in the previous hidden layer and m nodes in the current hidden layer, weights are initialized using a normal distribution with a standard deviation of 2 / √(n + m).
  • Formula: W = random_normal(0, sqrt(2/(fan_in + fan_out)))
    • fan_in: number of input nodes(number of neurons in previous layer)
    • fan_out: number of output nodes(number of neurons in current layer)
• As a result, activation values will be spread much more evenly than in the previous 2 methods.
  • Because weights are initialized according to the number of nodes in each layer, it's much more robust than using a fixed standard deviation, even when setting different numbers of nodes per layer.
• Suitable for tanh or sigmoid activation functions.
• But not suitable for ReLU.

4. He Initialization

• Suitable for ReLU family activation functions.
  • Very effective for ReLU and widely used in deep learning.
• Uses twice the variance of Xavier.
• Even as the layers get deeper, all activation values maintain an even distribution.
• Formula: W = random_normal(0, sqrt(2/fan_in))

5. LeCun Initialization

• Suitable for SELU activation function.
  • SELU activation function: 
    • It was designed to have self-normalizing characteristics in deep learning networks.
      • Automatically normalizes input values' mean and variance.
      • Maintains consistent mean and variance of activations during training.
    • Solves gradient vanishing/explosion problem.
    • Enables stable training of deeper networks.
    • Fast learning speed.
    • Model becomes simpler as normalization layers are not needed.
• Uses normal distribution with mean 0 and variance 1/fan_in.
• Formula: W = random_normal(0, sqrt(1/fan_in))

6. Orthogonal Initialization(직교 행렬 초기화)

• In RNN(Recurrent Neural Network)s, orthogonal initialization is used.
• Orthogonal initialization ensures that weights for hidden states in recurrent cells don't become too large or too small when multiplied repeatedly.

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Reference

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가중치 초기화 (Weight Initialization) · Data Science

 

 

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