Problems

Mode Collapse

Easy

Implement a specified diversity heuristic for detecting possible mode collapse. Compute the population standard deviation of every feature across the generated batch, then average those deviations.

s_j = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_{ij}-\mu_j)^2}

s = \frac{1}{D}\sum_{j=1}^{D}s_j

Here, $N$ is the number of generated samples, $D$ is the number of features, $x_{ij}$ is feature $j$ of sample $i$ , $\mu_j$ is that feature's batch mean, $s_j$ is its population standard deviation, and $s$ is the diversity score. Mark the batch as collapsed only when $s$ is strictly less than threshold. Return a dictionary containing diversity_score as a Python float and is_collapsed as a boolean.

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Examples

Input: generated_samples = [[1,2,3],[1,2,3],[1,2,3]], threshold = 0.1

Output: {"diversity_score":0,"is_collapsed":true}

Explanation: Identical rows have zero deviation in every feature, so their diversity score falls below the threshold.

Input: generated_samples = [[1,0],[-1,2],[0.5,-1.5],[2,1],[-0.5,0.5]], threshold = 0.1

Output: {"diversity_score":1.112646,"is_collapsed":false}

Input: generated_samples = [[1,2],[1.01,2.02],[0.99,1.98],[1,2.01]], threshold = 0.1

Output: {"diversity_score":0.010931,"is_collapsed":true}

Hint 1

Reduce the standard deviation over axis zero.

Hint 2

Average the resulting per-feature values before comparing with the threshold.

Requirements

Use NumPy.
Compute population standard deviations across the batch axis.
Average the per-feature deviations.
Use a strict comparison with the supplied threshold.
Return exactly the documented dictionary.

Constraints

generated_samples has shape $(N, D)$ .
$2 \le N \le 9$ and $1 \le D \le 6$ .
threshold is a positive finite float.
All sample values are finite real numbers.

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