Mechanistic Interpretability Take-Home — Sample-Aspect Double Descent

Mechanistic-interpretability team take-home: design and run an experiment that reproduces sample-aspect double descent on a small model, explain why double descent occurs using theory, and propose a fix. Deliverable is a slide deck or notebook plus a live discussion. Requirements 4-hour at-home assignment. Build the experiment yourself — pick the model class, the data-scaling axis, and the metric. Show the double-descent curve clearly. Reported successful approach: linear regression with varying training-set size and Random Matrix Theory analysis. Explain the phenomenon. Why does test error spike near the interpolation threshold and decrease again? Propose a remediation. Regularization (ridge) is the textbook fix and was reported as the candidate's chosen answer. Wrap up in a slide deck for the live review. Notes Mechanistic-interpretability hiring runs separately from the standard loop; the take-home replaces what would otherwise be a coding round. Only one detailed report is available publicly. Use this as the structural template; expect the specific phenomenon under study to drift over time. Preparation Internalize the classical double-descent setup: model capacity (or sample size) on x-axis, test error on y-axis, peak at n_params ≈ n_samples. Read at least one Random Matrix Theory primer on the over-parameterized linear-regression regime. Run the experiment yourself before the interview — generate the U-shape on synthetic data, fit a ridge baseline that smooths it.