Top-K Accuracy Computation

hardPROImage ClassificationMetricsCV: Recognition

Implement top-k accuracy metric used for evaluating classification models.

Top-k accuracy checks if the correct class is among the k highest-probability predictions:

$\text{Top-k Acc} = \frac{1}{N} \sum_{i=1}^{N} \mathbf{1}[y_i \in \text{top}_k(\hat{y}_i)]$

For ImageNet, top-5 accuracy is standard (correct class in top 5 predictions).

Implementation:

For each sample, get indices of k largest logits (argsort descending)
Check if true label is in these k indices
Average across all samples

Example

Input

logits = [[0.1, 0.2, 0.7], [0.8, 0.1, 0.1]]  # 2 samples, 3 classes
labels = [2, 0]  # True classes
k = 2

Output

1.0

Reasoning

Inputs: logits is a $2 \times 3$ grid of raw scores (rows = samples, columns = classes); labels gives each sample's true class index ( $y_1 = 2$ , $y_2 = 0$ ); k $= 2$ means a sample is a hit if its true class has one of its 2 highest scores.
Sample 1: scores $(0.1, 0.2, 0.7)$ . Ranked by score: $2$ ( $0.7$ ), then $1$ ( $0.2$ ), so $\text{top}_2 = \{2, 1\}$ . The true class $2$ is in the set, so the indicator is $1$ .
Sample 2: scores $(0.8, 0.1, 0.1)$ . Class $0$ leads with $0.8$ ; the second slot goes to one of the tied classes $1$ or $2$ . Either way $\text{top}_2$ contains $0$ , so the indicator is $1$ .
Average: $\frac{1}{2}(1 + 1) = 1.0$ , the output 1.0 (a fraction between 0 and 1).
Notice that only the ranking of scores matters, and a tie at the cut-off matters only if the true class is one of the tied ones. With $k = 3$ (every class), any label would be a hit and the accuracy would always be $1.0$ .

Constraints

logits: Tensor (batch_size, num_classes) - raw model outputs
labels: Tensor (batch_size,) - ground truth class indices
k: Number of top predictions to consider
Return: Top-k accuracy as float (0-1)

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Concept primerPREVIEW

Top-K Accuracy Computation: Background & Strategy

Background Knowledge

Top-k accuracy is a relaxed evaluation metric for multi-class classification that measures whether the correct class appears among the model's k highest-confidence predictions. Unlike top-1 accuracy (which requires the highest-probability prediction to be correct), top-k accuracy allows the model k attempts to identify the true class. This metric is particularly valuable in scenarios with class ambiguity or large label spaces—ImageNet's 1,000 classes make top-5 accuracy a standard benchmark because distinguishing between similar object categories is inherently difficult.

The mathematical formulation uses an indicator function: for each sample i, you check if the true label $y_i$ belongs to the set of k classes with the highest predicted probabilities. The metric then averages these binary correctness indicators across all N samples. This approach naturally handles the trade-off between model confidence and practical utility: a model might not confidently predict the exact correct class, but placing it in the top-k predictions is often sufficient for downstream applications.

Key insight: Top-k accuracy is fundamentally about ranking. Rather than comparing absolute probability values, you're checking whether the correct class ranks within the top k positions when all classes are sorted by their predicted scores (logits or probabilities). This ranking perspective is crucial for efficient implementation.

Algorithm/Approach

The solution follows a straightforward three-step pattern:

Rank the predictions: For each sample, identify which k classes have the highest predicted scores
Check membership: Determine if the true label appears in this top-k set
Aggregate: Compute the proportion of samples where the check succeeded

The key algorithmic operation is partial sorting or argsort: you need the indices of the k largest values, not necessarily all values sorted. This distinction matters for efficiency when k is small relative to the total number of classes.

Step-by-Step Strategy

Step 1: Understand the input shapes

Predictions: shape $[N, C]$ where N is batch size and C is number of classes (logits or probabilities)
True labels: shape $[N]$ containing class indices (0 to C-1)
k: integer specifying how many top predictions to consider

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solution.py

Python 3.13

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