Optimize Nearest-Center Assignment Without Materializing NxKxD Distances
Company: Mistral AI
Role: Machine Learning Engineer
Category: Machine Learning
Difficulty: medium
Interview Round: Onsite
Given points `X` with shape `N x D` and cluster centers `C` with shape `K x D`, return an assignment for each point to its nearest center by L2 distance. The straightforward implementation materializes an `N x K x D` tensor. Explain the memory problem and design a more memory-efficient implementation.
### Constraints & Assumptions
- Use squared L2 distance; square roots are unnecessary.
- Return one center index per point.
- Inputs are dense numeric arrays.
- You may discuss vectorized and blocked implementations.
### Clarifying Questions to Ask
- What are the expected ranges for N, K, and D?
- Is GPU memory or CPU memory the bottleneck?
- Do we need exact nearest centers?
- Can we process points or centers in batches?
### What a Strong Answer Covers
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### Follow-up Questions
- How would this change for cosine distance?
- How would you support streaming points?
- How would you accelerate this on GPU?
- How would approximate nearest neighbors change the trade-off?
Quick Answer: This Mistral AI machine learning question tests vectorized reasoning for nearest-center assignment without materializing an expensive intermediate tensor. It is useful preparation for interviews that probe memory-aware numerical computing, broadcasting trade-offs, and efficient ML implementation.