THE DROPOUT INFERENCE MISMATCH

Difficulty: Hard Tags: Deep Learning, Dropout, Training vs Inference

Story

A recommendation model's inference outputs are too small because the serving code applies the training-time dropout mask without inverted scaling. Compute the specified inverted-dropout result for a fixed mask so the behavior is deterministic.

The Math

For activation x_i, keep probability q = 1 - p, and binary mask m_i in {0, 1}, inverted dropout during training returns:

y_i = m_i * x_i / q

During inference, dropout is disabled and y_i = x_i. The mode and mask are given explicitly; if inference mode is selected, the mask is ignored.

Input Format

activations (length n), mask (length n, binary), mode ("train" or "infer"), p (drop probability).

Output Format

n outputs, 6 decimal places.

Constraints

• 1 <= n <= 10^5, 0 <= p < 1, |x_i| <= 10^6.
• Time limit: 1.0 second.

Example

Input

activations = [2, 4, -2, 8], mask = [1, 0, 1, 1], mode = "train", p = 0.5

Output

4.000000 0.000000 -4.000000 16.000000

Explanation: Kept activations are divided by q = 0.5; dropped activations become zero.