Error Analysis and Ablations

"A failed example is not an embarrassment; it is a coordinate system for improvement."

Overview

Error analysis turns aggregate scores into failure structure; ablations test which component actually caused an improvement.

The chapter treats evaluation as a mathematical object: a controlled protocol that maps model behavior into evidence with uncertainty. A result is not just a number; it is an estimate produced by a task distribution, a scoring rule, and an aggregation rule.

This section is written in LaTeX Markdown. Inline mathematics uses $...$, and display equations use `

`. The emphasis is practical but rigorous: every metric should be linked to the statistical assumptions that make it meaningful.

Prerequisites

• Descriptive Statistics
• Hypothesis Testing
• Regression Analysis
• Capability Benchmarks
• Robustness and Distribution Shift

Companion Notebooks

Learning Objectives

After completing this section, you will be able to:

• Define the core objects used in error analysis and ablations
• Write empirical estimators for model scores and risks
• Attach uncertainty statements to finite evaluation results
• Separate protocol design from metric computation
• Identify common leakage, sampling, and aggregation failures
• Use synthetic experiments to test statistical intuitions
• Connect offline metrics to downstream AI decisions
• Explain where this section ends and where adjacent chapters begin
• Design exercises and notebooks that make the math executable
• Read modern LLM evaluation papers with sharper statistical judgment

Study Flow

1. Read the pages in order and pause after each page to restate the main definition or theorem.
2. Run theory.ipynb when you want to check the formulas numerically.
3. Use exercises.ipynb after the reading path, not before it.
4. Return to this overview page when you need the chapter-level navigation.

Runnable Companions

• Theory notebook
• Exercises notebook