Xavier and He Weight Initialization

Weights that start too big or too small make deep networks hard to train. Two standard schemes pick the scale from the layer size, where fan_in is the number of inputs and fan_out the number of outputs:

method	returns
`"xavier_uniform"`	limit √(6 / (fan_in + fan_out)), weights drawn from [-limit, limit]
`"xavier_normal"`	standard deviation √(2 / (fan_in + fan_out))
`"he_uniform"`	limit √(6 / fan_in)
`"he_normal"`	standard deviation √(2 / fan_in)

Xavier (Glorot) suits sigmoid and tanh layers; He suits ReLU layers.

Implement init_bound(method, fan_in, fan_out).

Input

method: One of "xavier_uniform", "xavier_normal", "he_uniform" or "he_normal".

fan_in, fan_out: The layer's number of inputs and outputs.

Output

Return the limit or standard deviation as a decimal number.

Constraints

1 ≤ fan_in, fan_out ≤ 100,000

Examples

Example 1

Input:
method = "xavier_uniform"
fan_in = 3
fan_out = 3

Expected output:
1.0

Explanation

√(6 / (3 + 3)) = √1 = 1, so weights are drawn from [-1, 1].

Example 2

Input:
method = "he_normal"
fan_in = 50
fan_out = 10

Expected output:
0.2

Explanation

He only uses fan_in: √(2 / 50) = √0.04 = 0.2.

References

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

method = "xavier_uniform"
fan_in = 3
fan_out = 3

Expected output:

1.0

Your output

Example 2 Not run
Input:
```
method = "he_normal"
fan_in = 50
fan_out = 10
```
Expected output:
```
0.2
```
Your output

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