Inverted dropout · Ingénierie IA

Dropout sets a random part of the activations to 0 during training. Inverted dropout also divides the kept activations by 1 - p, so the expected value of each activation does not change. At inference time the layer then does nothing. You write the forward pass for both modes and the backward pass.

Task

Write two functions.

dropout_forward(x, p, rng, training=True) returns (out, mask).
dropout_backward(grad_output, mask, p) returns the gradient of the loss with respect to x.

In training mode, build the mask with exactly one call:

\text{mask} = (\texttt{rng.random(x.shape)} \geq p)

True in the mask means kept. Each entry is dropped with probability p. The output is

\text{out} = x \cdot \text{mask} / (1 - p)

In inference mode (training=False), return a copy of x and a mask that is True everywhere. Do not draw from rng in inference mode.

The backward pass uses the mask from the forward pass: \partial L / \partial x = \text{grad\_output} \cdot \text{mask} / (1 - p).

Input and output

Name	Type	Shape	Meaning
`x`	float array	any shape	the activations
`p`	float		the probability to drop an entry, `0 <= p < 1`
`rng`	`np.random.Generator`		the random generator for the mask
`training`	bool		`True` for training mode, `False` for inference mode
`grad_output`	float array	same as `x`	the gradient of the loss with respect to `out`
`mask`	bool array	same as `x`	the mask from `dropout_forward`

dropout_forward returns a tuple (out, mask). out is a float array and mask is a bool array. Both have the shape of x.
dropout_backward returns a float array with the shape of x.

Constraints

x has 1 to 4 axes and at most 40000 entries.
0 <= p < 1.
Do not change the input arrays.
Use numpy only.

Examples

python

x = np.array([[1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0]])
out, mask = dropout_forward(x, 0.5, np.random.default_rng(0))
grad = dropout_backward(np.ones((2, 4)), mask, 0.5)

text

out
[[ 2.  0.  0.  0.]
 [10. 12. 14. 16.]]
mask
[[ True False False False]
 [ True  True  True  True]]
grad
[[2. 0. 0. 0.]
 [2. 2. 2. 2.]]

python

out, mask = dropout_forward(x, 0.5, np.random.default_rng(0), training=False)

text

out
[[1. 2. 3. 4.]
 [5. 6. 7. 8.]]
mask
[[ True  True  True  True]
 [ True  True  True  True]]