Find the cause of an improvement.

This is the same reference used in Technical mode. Expand it whenever you need the exact numbers, assumptions or further explanation.

Start with the question

Adding a curved feature helps alone; adding shrinkage helps alone. Must both together give the sum of those gains?

Mechanism and worked comparison

A factorial comparison evaluates baseline, A only, B only and both. Here A enables a quadratic feature and B adds weight shrinkage. Every cell starts from its declared deterministic initialization and uses the same training and development memberships. The baseline remains a serious model; on the line task a quadratic coefficient can be unnecessary.

For an error metric E, interaction is E(A+B) − E(A) − E(B) + E(base). With errors 10, 7, 8 and 6, the interaction is 1. Separate improvements would predict error 5, but the combined system has error 6: its improvement is smaller than the additive prediction. Negative interaction means a larger combined error reduction. Always state whether the outcome is an error or a reward before interpreting signs.

Equal updates control one resource but not every cost. The quadratic model computes another feature and coefficient gradient; shrinkage adds arithmetic. Training-example visits exclude validation, data construction and browser work. A fair study states which resource is matched and which is measured separately. Do not remove failed runs or select the best seed. A factorial pattern identifies behavior in this experiment; it does not prove a universal causal mechanism across datasets.

Try and explain

Inspect baseline, A, B and A+B on the same task and seed. Change the budget for every cell together and explain the signed interaction.

Open the reproducible study project or use the implementation studio.