Theorem-to-Experiment Alignment

1 Core Idea

If a paper includes both theory and experiments, the two parts should talk to each other.

The worst pattern is:

theory section proves one thing
experiment section demonstrates something only loosely related
conclusion quietly merges both into a stronger story

2 What Alignment Looks Like

If a theorem claims better dependence on noise, rank, dimension, smoothness, or sample size, the experiments should probe those exact variables where possible.

3 Good Questions To Ask

Which object in the theorem can be varied experimentally?
Which assumption can be stress-tested?
Which failure regime should appear if the theorem’s scope is exceeded?
Does the experiment support the theorem, or only the algorithm narrative?

4 Why This Matters

This page is especially important for math-heavy ML and optimization work, where theory can easily become decorative unless it informs the empirical design.