Openai·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Interviewed for an ML Engineer role at OpenAI and got a coding question that looked deceptively simple on the surface. K-means with k=1 sounds like a toy problem until you realize they want you to both derive the math and verify it through iteration.

Questions Asked (1)

Implement a K-means clustering routine using Euclidean distance, but constrained to a single cluster (k=1). Given an array of d-dimensional points, return the centroid. You should also verify your result through iterative updates, not just the closed-form solution.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was to just return the coordinate-wise mean and call it done, which is technically correct for L2 with k=1.

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AI HintsAI Generated

Suggested Approach

First, clarify that for k=1, the optimal centroid is the mean of all points, which minimizes the sum of squared Euclidean distances. Then, implement the iterative K-means update: initialize the centroid (e.g., randomly or as the mean), assign all points to the single cluster, and recompute the centroid as the mean of assigned points until convergence. Finally, compare the iterative result with the closed-form mean to verify correctness.

Pro tip: Emphasize that the iterative approach, while unnecessary for k=1, demonstrates the general K-means algorithm and highlights the convergence property. Mention that in practice, for k=1, the closed-form solution is always preferred for efficiency.

1. Clarify the problem and assumptions

Confirm that k=1 means all points belong to a single cluster, and the goal is to find the centroid that minimizes the sum of squared Euclidean distances. State that the closed-form solution is the arithmetic mean.

2. Implement the closed-form solution

Compute the centroid as the element-wise mean of all points across each dimension. This provides a baseline for verification.

3. Implement iterative K-means updates

Initialize the centroid (e.g., randomly or as the mean). Then repeatedly assign all points to the single cluster and update the centroid to the mean of assigned points until the centroid change is below a tolerance or a maximum number of iterations is reached.

4. Verify convergence and compare results

Check that the iterative centroid converges to the closed-form mean. Discuss why convergence is guaranteed for k=1 and note any numerical precision considerations.

5. Analyze complexity and trade-offs

Compare the time complexity: closed-form is O(n*d) while iterative is O(t*n*d) where t is the number of iterations. Highlight that for k=1, the closed-form is always preferred, but the iterative approach illustrates the general algorithm.

Key Points to Mention

The objective function for K-means is minimizing the sum of squared Euclidean distances.
For k=1, the optimal centroid is the arithmetic mean of all points.
The iterative update rule: assign points to nearest centroid (only one cluster) and recompute centroid as mean of assigned points.
Convergence is guaranteed because the objective function decreases monotonically and the centroid stabilizes.
Numerical stability: consider using float64 and handling potential overflow for large datasets.
Trade-offs: closed-form is more efficient, but iterative demonstrates the general K-means algorithm and can be extended to k>1.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.