Represent k-means as an MLP
Company: Sealth
Role: Machine Learning Engineer
Category: Machine Learning
Difficulty: easy
Interview Round: Onsite
Given fixed centroids q_1, ..., q_k and an input vector x, show how the nearest-centroid assignment step of squared-Euclidean k-means can be implemented using a fully connected neural network layer plus an activation function. Use the identity ||x - q_j||^2 = ||x||^2 + ||q_j||^2 - 2 q_j^T x to derive the layer weights and biases, explain how a low-temperature softmax can approximate a one-hot cluster assignment, and describe how to implement the softmax stably when the temperature is very small.
Quick Answer: This question evaluates understanding of how the nearest-centroid step of k-means can be expressed as a fully connected neural network layer with activation, focusing on linear algebra, model equivalence, and numerical behavior of softmax under low temperature.