Explain core ML concepts
Overview
This question evaluates mastery of foundational machine learning concepts — including linear algebra for PCA (eigenvectors/eigenvalues), impurity measures for decision trees, Bellman equations in reinforcement learning, dropout and other regularization techniques, training stability and optimization landscapes, and attention mechanisms and scaling in transformers — within the Machine Learning domain. It is commonly asked to assess theoretical depth and the ability to connect mathematical formulations to practical model behavior, testing a mix of conceptual understanding and practical application expected of a machine-learning engineer.
ML Theory Check: PCA, Trees, RL, Regularization, Optimization, and Transformers
Context: Provide concise, technically correct explanations suitable for a machine-learning engineer take-home. Use formulas and brief examples where helpful.
Tasks
- PCA: Interpret the eigenvectors (and eigenvalues) of the covariance matrix.
- Decision trees: Define Gini impurity and explain how it is used to choose splits.
- Reinforcement learning: Write the Bellman equation(s) and explain their role.
- Neural networks: Explain dropout as a regularization technique.
- Training stability: Describe gradient clipping, the vanishing-gradient problem, and how ResNets help.
- Optimization landscape: Why are many deep-learning loss surfaces non-convex?
- Transformers: Explain attention mechanisms and what “scaling” means in this context (both the scaled dot product and computational scaling with sequence length).
Solution
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